.5MHINIVERS/A 
 
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 v, .. ^ ; .v A" -- ^>5 
 
 A TREATISE 
 
 PRINCIPLES OF CHEMISTRY.
 
 SonHon: C. J. CLAY AND SONS, 
 
 CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, 
 
 AVE MARIA LANE. 
 
 : DEIGHTON, BELL, AND CO. 
 
 ILnpjtcj : F. A. BROCKHAUS.
 
 A TREATISE 
 
 ON THE 
 
 PRINCIPLES OF CHEMISTRY 
 
 M. M. PATTISON MUIR, M.A., F.R.S.E. 
 
 FELLOW, AND PIUELECTOk I:T CHEMISTRY, OF GONVILLE AND CAIUS COLLEGE, 
 CAMBRIDGE. 
 
 SECOND EDITION. 
 
 "In nature everything is distinct, yet nothing defined into absolute 
 independent singleness." WORDSWORTH. 
 
 CAMBRIDGE: 
 
 AT THE UNIVERSITY PRESS. 
 1889 
 
 [All Rights reserved. ]
 
 Cambridge : 
 
 PRINTED BY C. J. CLAY, M.A. AND SONS, 
 AT THE UNIVERSITY P^Go.
 
 4S-3 
 
 
 If in this book I have shewn any just 
 appreciation of the scientific study of nature, 
 I owe it to the teaching of 
 
 PROFESSOR SIR WILLIAM THOMSON. 
 To him, therefore, I dedicate my work.
 
 PREFACE. 
 
 THIS book is intended to give a fairly complete account 
 of the present state of knowledge regarding the principles 
 and general laws of chemistry. 
 
 It is addressed to students of this science who have 
 already a considerable acquaintance with descriptive che- 
 mistry, but it is hoped that by such students the book will 
 be found complete in itself; so that while it certainly deals 
 with chemical principles and theories on the supposition that 
 its readers have some knowledge of chemical facts, yet the 
 book may fairly claim to rank as a systematic treatise on 
 chemical philosophy. 
 
 While I have tried to supply full information regarding 
 those points which appear to me of most importance, I have 
 also sought to avoid great detail, and to present a sketch of 
 the principles of chemistry the parts of which shall hang 
 together as being mutually dependent. 
 
 To know what to omit has been one of the most difficult 
 parts of my undertaking. The chemical student is too often 
 subjected to a shower-bath of facts; he is made to feel that
 
 viii PREFACE. 
 
 'to sit as a passive bucket and be pumped into... can in the 
 long-run be exhilarating to no creature.' 
 
 An attempt is made in this book to treat the principal 
 theories of modern chemistry to some extent from an his- 
 torical point of view, and to trace the connexions between 
 the older theories and those which now prevail in the science. 
 It is hoped that the student may thus gain a firmer grasp of 
 those theories than he is able to do when they are put before 
 him as entirely creations of recent times. 
 
 I have tried to deal with chemical facts and generalisa- 
 tions so as to shew their reality. This can best be done, 
 I believe, by following in the very foot-prints of the great 
 discoverers, by watching them as they make their footing 
 sure, and as they feel their way up the heights. That the 
 student may be able to verify the accounts I have given of 
 the more important investigations, and more especially that 
 he may fill in the details which I have necessarily omitted, 
 I have given copious references to original memoirs and 
 papers; these references will, I believe, be found correct, at 
 least I have spared no pains to make them so. I have also 
 endeavoured to make the index full and complete. 
 
 So far as I am aware, no sufficiently comprehensive guide 
 to the study of the principles of chemistry exists, in an 
 English form, although we have many excellent works dealing 
 with descriptive chemistry, with the materials, that is to say, 
 from which chemical science is being constructed. Professor 
 Lothar Meyer's Die modernen Theorien der C/iemie, to a 
 considerable extent meets the wants of the German student. 
 I have made free use of that book in preparing my own ; but 
 I venture to think I have incorporated in my general plan 
 many important facts and principles which do not find a
 
 PREFACE. IX 
 
 place in that admirable treatise. I have also regarded the 
 whole subject from a stand-point somewhat different from 
 that occupied by the German Professor 1 . 
 
 To name all the books and journals from which I have 
 derived assistance would be tedious and absurd; they are 
 sufficiently indicated in the notes and references 2 . 
 
 I have tried to rest every important statement on first- 
 hand authority. When chemistry is regarded from the point 
 of view of the great workers therein, it wears an aspect 
 very different from that with which it confronts the mere 
 text-book-taster. 
 
 The book is divided into two parts. The first part is 
 occupied with the statement and discussion of the atomic and 
 molecular theory, and the applications thereof to such sub- 
 jects as allotropy, isomerism, and the classification of elements 
 and compounds. Somewhat full accounts are also given, in 
 this part, of thermal, optical, and other departments of physi- 
 cal, chemistry, in so far as the results and methods of these 
 branches of the science are applicable to the questions re- 
 garding the composition of chemical systems which are 
 connoted by the term Chemical Statics. 
 
 The second part of the book is devoted to the subjects 
 of dissociation, chemical change and equilibrium, chemical 
 affinity, and the relations between chemical action and the 
 distribution of the energy of the changing system. These, 
 and cognate questions, I have ventured to summarise in the 
 expression Chemical Kinetics. 
 
 1 An English edition of Modern Theories is now published. 
 
 2 The full titles of the various journals referred to are given on pp. xxii, x>
 
 X PREFACE. 
 
 I have been much aided in my task by my friends 
 Mr C. Slater 1 , B.A., of St John's College, and Mr R. Threlfall 2 , 
 B.A., Scholar of Gonville and Caius College. The former 
 has read considerable portions of the proofs and has made 
 many valuable suggestions ; the latter has read all, except 
 the first chapter of Book I, and by his criticisms and remarks 
 has helped me to make many important points much clearer 
 and more accurate than they would otherwise have been. 
 
 M. M. PATTISON MUIR. 
 
 CAMBRIDGE, October 1884. 
 
 1 Now Lecturer in Bacteriology at St George's Hospital. - 
 
 2 Now Professor of Physics in the University of Sydney.
 
 PREFACE TO THE SECOND EDITION. 
 
 THE aim and scope of the book have not been changed. 
 The whole has been thoroughly revised, and Book II has 
 been entirely rewritten. The revision will, I hope, make 
 clearer than before the mutual dependence of the parts. 
 
 Since the first edition was published, much important 
 work has been done on subjects treated in Book I ; the 
 results of this work have been noticed in the present edition ; 
 at the same time some chapters have been shortened, especially 
 that dealing with valency and isomerism ; the arrangement 
 of these, and some other, chapters has been altered. The 
 chapters on physical methods have been rewritten. 
 
 When the first edition was published, the study of chemical 
 affinity was entering on a new phase ; since 1884 progress has 
 been very rapid, and to-day we are much nearer the goal than 
 we were five years ago. The great importance of recent work 
 on affinity has compelled me entirely to rewrite Book II. In 
 doing this I have largely followed Ostwald's Lehrbuch der 
 allgemeinen CJtemie ; without that admirable treatise, the 
 part of my book dealing with affinity could not have been 
 written. I am anxious to express, as strongly and warmly
 
 xii PREFACE TO THE SECOND EDITION. 
 
 as I can, my indebtedness to Prof. Ostwald. I also thank 
 my friend Mr Douglas Carnegie, M.A. for help given in 
 revising the proofs of Book II. 
 
 ' As this edition has been some time passing through the 
 press, and as the progress of chemistry has been very rapid 
 during that time, the lists of errata and addenda are fuller 
 than is usual in a book of this character. The student is 
 requested to pay attention to these lists, and to incorporate 
 the corrections and additions in the text. 
 
 M. M. P. M. 
 
 April 1889.
 
 TABLE OF CONTENTS. 
 
 BOOK I. CHEMICAL STATICS. 
 CHAPTER I. ATOMS AND MOLECULES. 
 
 Paragraph Page 
 
 If TRODUCTORY I 
 
 Beginnings of atomic theory i 7 
 
 Daltonian conception of atoms 2, 3 8 
 
 Volumetric combination of elementary gases ) 
 
 Law of Gay-Lussac \ 4 I2 
 
 Dalton's criticism of this law 5 12 
 
 Avogadro's generalisation ........ 6 13 
 
 Wollaston's equivalents 7 14 
 
 Berzelius' work on atomic synthesis 8 16 
 
 The Berzelian double atom 9 19 
 
 Dumas' attempts to determine molecular and atomic weights . 10 20 
 
 Notation, and system, of Laurent and Gerhardt .... 1 1 22 
 
 The atom, the molecule, and the equivalent differentiated . 12 24 
 
 The molecular theory of the constitution of matter ... 13 25 
 Application of Avogadro's law to determine relative weights of 
 
 elementary molecules ........ 14 29 
 
 Table of molecular weights of elements 15 32 
 
 Precautions to be observed in determining molecular weights . 16 34 
 
 Correction of values obtained ....... 17 35 
 
 Deduction, from application of Avogadro's law, of definition of 
 
 atomic weight 18 37 
 
 Table of data for finding maximum atomic weights of elements . 19 38 
 
 Atomicity of elementary molecules 20 45 
 
 Formulae of liquid and solid compounds 21 46 
 
 Table of maximum atomic weights of elements .... 22 48 
 
 Law of Dulong and Petit 23 48 
 
 Application of this law, in modified form, to compounds . . 24 50 
 
 Data concerning atomic heats of elements 25 51 
 
 Indirect determination of atomic heats 26 54 
 
 Discussion of law of Dulong and Petit 27 59 
 
 M. C. b
 
 xiv TABLE OF CONTENTS. 
 
 Paragraph Page 
 
 Specific heat of beryllium 28 61 
 
 boron, silicon, and carbon 29 63 
 
 Limitations to application of law of Dulong and Petit ... 30 66 
 Comparison of law of Avogadro with that of Dulong and Petit as 
 
 aids in finding values of atomic weights .... 31 67 
 
 Mitscherlich's law of isomorphism 32 69 
 
 Groups of isomorphous elements 33 72 
 
 Application of this law to determine values of atomic weights . 34 74 
 
 Raoult's method of determining molecular weights ... 35 76 
 
 Chemical methods for finding molecular and atomic weights . 36 78 
 Comparison of chemical with physical methods for determining 
 
 these constants 37-85 
 
 Table of atomic weights, with summary of data (and references to 
 
 original memoirs) 38 85 
 
 CHAPTER II. ATOMIC AND MOLECULAR SYSTEMS. 
 SECTION I. NASCENT ACTIONS. 
 
 Examples of actions called nascent 39 96 
 
 Explanation of these actions in terms of the molecular theory . 40 97 
 
 Nascent state of compounds 41 99 
 
 Special cases: action of acids on metals 42 100 
 
 Experimental evidence of difference between actions of atsms and 
 
 molecules 43 106 
 
 All reacting bodies in a chemical change influence that change . 44 107 
 Should the expression 'nascent action' be retained in chemical 
 
 nomenclature? 45 109 
 
 SECTION II. THE DUALISTIC AND UNITARY HYPOTHESES. 
 
 Electro-chemical investigations of Davy 46 1 1 1 
 
 ,, ,, Berzelius 47 113 
 
 The Berzelian dualistic hypothesis 48 115 
 
 Dualistic conception of acid and salt 49 116 
 
 Faraday's electrolytic laws . . . . . . . 50 117 
 
 Reaction against dualism led by Dumas, Laurent, and Gerhardt . 51 117 
 
 Conception of compound radicle retained by the new school . 52 119 
 
 Classification by use of typical substances 53 120 
 
 SECTION III. EQUIVALENCY OF ATOMS. 
 
 Conception of definite substituting value applied to atoms . . 54 122 
 Fundamental data for determining precise meaning of terms 
 
 monovalent, divalent, &c 55 124 
 
 Application of these terms to classification of atoms of elements . 56 125
 
 TABLE OF CONTENTS. XV 
 
 Paragraph Page 
 
 Further explanation of expression valency of an atom . . 57 59 129 132 
 Consideration of possible meanings of expressions 'bonds' or 'units 
 
 of affinity ' as applied to atoms 60 62 132 137 
 
 General considerations regarding valencies of atoms, especially as 
 these are supposed to be deduced from study of non-gasifiable 
 compounds .......... 63 137 
 
 SECTION IV. ALLOTROPY AND ISOMERISM. 
 
 The molecule considered as a structure 64 138 
 
 Differences of atomic arrangements are connected with differences 
 
 in energies of molecules 65 139 
 
 Two kinds of variations in atomic arrangement possible . . 66 139 
 
 Allotropy 67 141 
 
 Polymerism 68 142 
 
 Isomeric and metameric molecules 69 1 43 
 
 Formula for finding maximum number of monovalent atoms in a 
 
 molecule ; saturated and unsaturated molecules ... 70 144 
 Possible isomerides of same empirical formula . . . . 71 145 
 Formulae of molecules which cannot exhibit isomerism . . 72 146 
 Illustrations of determinations of structural formulae . . . 73 146 
 Atomic groups characteristic of classes of carbon compounds . 74 151 
 Recapitulation of paragraphs concerning applications of hypo- 
 thesis of valency 75 154 
 
 Generalisations used as guides in finding structural formulae . 76 156 
 
 Illustrations of use of these generalisations 77 156 
 
 Further application of hypothesis of valency to conception of the 
 
 molecule as a structure 78 162 
 
 Functions of parts of a molecule are dependent on nature and struc- 
 ture of the whole molecule ....... 79 162 
 
 Illustrations of dependence of functions of parts of a molecule on 
 the nature and arrangement, relatively to given parts, of other 
 
 atoms in the molecule 80 163 
 
 Illustrations of influence exerted on the function of one atom, or 
 group of atoms, by the arrangement of all the atoms in the 
 
 molecule 81 165 
 
 Chemical stability of a molecule is the result of balance between 
 
 functions of various parts of the molecule . . . . 82 171 
 Many physical properties of compounds are also correlated with 
 
 such molecular balance 83, 84 172 
 
 Thermal data connected with isomerism .... 85 89 174 179 
 General considerations regarding relations illustrated in pars. 85 
 
 to 89 . . 90 179 
 
 Application of these considerations to prevalent views on valency 91 180 
 
 Limitations usually placed on atomic explanation of isomerism . 92 181 
 
 Geometrical isomerism 93 182 
 
 b2
 
 xvi TABLE OF CONTENTS. 
 
 Paragraph Page 
 
 Examples of use of hypothesis of geometrical isomerism . . 94,95 185 
 
 Summary of section iv 96 191 
 
 Appendix to section IV 
 
 Lossen's criticism of the various meanings assigned to term 
 
 valency .......... 193 
 
 ' Are the carbon bonds of 'equal value?' 198 
 
 SECTION V. MOLECULAR COMPOUNDS. 
 
 Hypothesis of valency not strictly applicable to phenomena sug- 
 gested by terms molecular compounds and atomic compounds 97 199 
 Definition of molecular compounds impossible .... 98 200 
 Illustrations of phenomena exhibited by bodies classed as mo- 
 lecular compounds 99 201 
 
 Probable existence of particles more complex and less stable than 
 
 the molecule 100 207 
 
 Work of Lehmann and others on physical isomerism . . . 101 208 
 
 No fixed boundary between molecular and atomic compounds . 102 218 
 
 The physical and the chemical conception of the molecule . . 103 219 
 
 CHAPTER III. THE PERIODIC LAW. 
 
 Earlier investigations into connexions between atomic weights 
 
 and properties of elements 104 222 
 
 Statement of the periodic law ....... 105 223 
 
 Illustrations of periodic connexion between atomic weights and 
 
 properties of elements . . . . . . . . 106 224 
 
 Relations between atomic weights and atomic volumes . . 107 224 
 
 ,, and fusibilities of elements . 108 228 
 
 ,, ,, ,, and various physical constants 
 
 of elements .......... 109 229 
 
 Illustrations of applications of periodic law : 
 
 (1) to predict properties of unknown elements . . . no 230 
 
 (2) to guide the study of properties of similar elements . in 232 
 ' Odd series' , 'even series', ' long periods' 1 , and ' typical elemeitts' . 112 235 
 Connexions between general formulae of classes of compounds and 
 
 atomic weights of elements in these compounds . . . 113 239 
 Valency considered as a periodic function of atomic weights of the 
 
 elements . 114 241 
 
 General remarks on the periodic law applied to classification . 115 243
 
 TABLE OF CONTENTS. 
 
 CHAPTER IV. APPLICATIONS OF PHYSICAL METHODS 
 TO QUESTIONS OF CHEMICAL STATICS. 
 
 Paragraph Page 
 
 Introductory 116 246 
 
 SECTION I. THERMAL METHODS. 
 
 Introductory 117 247 
 
 Notation used in thermal chemistry 118 248 
 
 Endothermic and exothermic reactions . . . . . 119 252 
 
 Calculation of thermal values of chemical changes . . . 120 254 
 Illustrations of connexion between chemical changes and changes 
 
 of energy 121 259 
 
 A chemical change consists of at least two parts . . . . 122 262 
 
 Attempts to determine thermal values of molecular decompositions 123 263 
 Thermal results applied : 
 
 (1) to reactions between metals and acids . . . . 124 264 
 
 (2) to allotropy . . . .".... . . . 125 266 
 
 (3) to classification of elements 126 266 
 
 (4) to classification of compounds 127 267 
 
 (5) to neutralisation of acids by bases, and of bases by acids . 128 269 
 Connexions between thermal and material changes occurring in 
 
 same chemical system 129 274 
 
 Influence of temperature on thermal value of a chemical change . 130 275 
 Influence of masses of reacting bodies on thermal value of a chemi- 
 cal change 131 276 
 
 Thermal value of a chemical reaction is the sum of several partial 
 
 values 132 277 
 
 The law of maximum work . . . . . . . . 133 278 
 
 Illustrations of application of thermal methods to determine struc- 
 tural formulae 134 282 
 
 Connexions between boiling points and composition of hydro- 
 carbons 135 286 
 
 Concluding remarks to this section 136 289 
 
 SECTION II. OPTICAL METHODS. 
 
 Statement of methods to be considered in this section . . . 137 289 
 
 Formulae for calculating the refraction-equivalent of a carbon 
 
 compound . . . . . . . . . . 138 289 
 
 Is the value to be assigned to the refraction-equivalent of an ele- 
 ment constant in all liquid compounds of that element? . 139 291 
 
 Method of calculating atomic refraction from determinations of 
 
 molecular refractions of compounds 140 291
 
 xviii TABLE OF CONTENTS. 
 
 Paragraph Page 
 
 Connexions between molecular refraction and isomerism . . 141 292 
 Applications of connexions examined in preceding paragraph 142, 143 295 
 
 Specific rotatory powers of substances 144 299 
 
 Rotatory power depends on atomic composition of molecules, but 
 is also modified by reactions between optically active and in- 
 active molecules 145 303 
 
 van't HofFs hypothesis regarding connexions between molecular 
 
 structure and specific rotatory power 146 304 
 
 Illustrations of modifying influence exerted by optically inactive 
 
 substances on rotatory power of optically active compounds . 147 309 
 Magnetic rotatory powers of liquid compounds . . . . 148 311 
 Connexions between absorption-spectra and structure of molecules 
 
 of carbon compounds 149 314 
 
 SECTION III. METHODS BASED ON DETERMINATIONS OF THE 
 MOLECULAR VOLUMES OF COMPOUNDS. 
 
 Explanation of constant considered in this section . . . 1 50 317 
 Data to illustrate connexions between molecular volumes and 
 
 composition of compounds 151 319 
 
 Data to illustrate connexions between molecular volumes and 
 
 actual valencies of atoms in given molecules . . . . 152 320 
 Data to illustrate connexions between molecular volumes and 
 
 distribution of interatomic actions . ..... 153 4 321 
 
 Molecular volumes of solid compounds 155 325 
 
 Discussion of meaning of molecular volume . . . . 156 32 J 
 
 SECTION IV. METHOD BASED ON 'ETHERIFICATION-VALUES'. 
 
 Statement of method, and illustrations of application of this 
 
 method 157 331 
 
 SECTION V. MISCELLANEOUS METHODS. 
 
 Capillarity-constants 158 335 
 
 Transpiration-rates 159 336 
 
 Electrolysis 1 60 336 
 
 Concluding Remark* to Book 1 161 338
 
 BOOK II. CHEMICAL KINETICS. 
 
 CHAPTER I. THE LAW OF MASS-ACTION. 
 
 Paragraph Page 
 
 Introductory remarks on subject of this Book .... 162 339 
 
 Early history of term affinity ....... 163 340 
 
 Bergmann's tables of affinity 164 340 
 
 Berthollet's Essai de Statique Chimique 165 341 
 
 Bergmann's and Berthollet's views on affinity contrasted . . 166 345 
 
 Experiments on influence of mass 167 346 
 
 Guldberg and Waage's law of mass-action 168 347 
 
 Equation of equilibrium arrived at without using notion of chemical 
 
 force 169 3^p 
 
 Experimental verifications of equation of equilibrium . . . 170,171 351 
 
 CHAPTER II. CHEMICAL DYNAMICS. 
 
 Methods of measuring chemical forces 172 355 
 
 SECTION I. VELOCITY OF CHEMICAL CHANGE. 
 
 Equation for representing reaction-velocity 173, 174 356 
 
 Amount of change proportional to mass of changing body . . 175 357 
 
 Cases where several bodies undergo change simultaneously . . 176 359 
 
 Principle of coexistence of reactions 177 361 
 
 Case of a solid reacting with a liquid 1 78 362 
 
 SECTION II. CHEMICAL EQUILIBRIUM. 
 
 General sketch of methods 179 363 
 
 System of two changing bodies 180 363 
 
 System of four changing bodies 181,182 367 
 
 Thomsen's experiments on partition of a base between two acids . 183 368 
 
 Ostwald's experiments on the same subject 184 372 
 
 Etherification of alcohols 185 374
 
 XX TABLE OF CONTENTS. 
 
 Paragraph Page 
 
 Equilibrium of physically heterogeneous systems . . . . 186 374 
 Summary of law of mass-action and principle of coexistence of 
 
 reactions 187 378 
 
 SECTION III. THERMODYNAMICAL METHODS APPLIED TO CHEMICAL 
 EQUILIBRIUM. 
 
 Horstmann's condition of equilibrium 188 379 
 
 Gibbs' ...... 189 380 
 
 von Helmholtz's_/9-w and bound energy ..... 190 382 
 
 Berthelot's law of maximum work 191 383 
 
 SECTION IV. MOLECULAR METHODS APPLIED TO CHEMICAL 
 EQUILIBRIUM. 
 
 Williamson's hypothesis 192 385 
 
 Guldberg and Waage's treatment of the subject .... 193 386 
 
 Application of vortex-atom theory by J. J. Thomson . . . 194 387 
 
 SECTION V. DISSOCIATION. 
 
 Instances of dissociation 195 389 
 
 So called abnormal vapour-densities 196 391 
 
 Equilibrium-pressure in dissociation-processes .... 197 392 
 Dissociation of ammonium chloride compared with that of 
 
 hydrogen iodide 198 392 
 
 Dissociation of a solid into a solid and a gas . . . . 199 394 
 
 Dissociation when several compounds may exist together . . 200, 201 394 
 Absorption of gases by solids contrasted with combination of 
 
 gases with solids 202 398 
 
 Application to dissociation of equations of equilibrium . . 203 398 
 
 Thermodynamical aspects of dissociation 204 401 
 
 Molecular ,, ,, 205, 206 402 
 
 Dissociation may be due to molecular collisions or to action of 
 
 external agencies 207 405 
 
 Summary of Chapters I. and II. of this Book .... 208 405 
 
 CHAPTER III. CHEMICAL AFFINITY. 
 
 Retrospect 209 407 
 
 Coefficients of affinity arrived at by using Guldberg and Waage's 
 
 equation of equilibrium 210 408 
 
 SECTION I. SPECIFIC AFFINITY-COEFFICIENTS OF ACIDS AND BASES. 
 
 Statement of equation of equilibrium in suitable form . . . 211 409 
 
 Thomsen's method of finding affinities of acids .... 212 410
 
 TABLE OF CONTENTS. xxi 
 
 Paragraph Page 
 Ostwald's examination of the constancy of the affinity of an acid 
 
 or base . . . . . . . . . . 213 412 
 
 The same subject continued 214-220415-422 
 
 There is a definite connexion between electrical conductivities of 
 
 acids in solution and the velocity-constants of the changes 
 
 brought about by these acids . . . . . .221 422 
 
 Molecular conductivity of an acid defined 222 424 
 
 Law of dilution for monobasic acids 223 424 
 
 Affinities of monobasic acids connected with relative conductivities 
 
 stated in terms of maximum conductivities .... 224 427 
 
 The law of Kohlrausch 225 428 
 
 Method for finding maximum conductivity of a monobasic acid . 226 431 
 
 Conductivities of polybasic acids 227 432 
 
 Conductivities of bases 228 435 
 
 Determination of affinity of a monobasic acid from measurements 
 
 of conductivity of its aqueous solution 229 436 
 
 SECTION II. CONNEXIONS BETWEEN THE AFFINITY-COEFFICIENTS 
 AND THE CONSTITUTION OF ACIDS. 
 
 Statement of method for finding affinity-coefficients . . . 230 439 
 
 Examples . . . - 231 440 
 
 Dibasic acids .......... 232 443 
 
 General remarks on results obtained ...... 233 446 
 
 SECTION III. CHEMICAL CHANGE. 
 
 Recapitulation of former paragraphs bearing on this subject . . 234 450 
 
 van't Hoff's law of osmotic pressure 235 450 
 
 Planck's work in the same direction 236 454 
 
 Arrhenius' development of the law of van't Hoff .... 237 454 
 
 Additive and cumulative properties 238 456 
 
 Ostwald's examination of the hypothesis of electrolytic dissociation 239 457 
 
 Summary of preceding paragraphs ...... 240 460 
 
 Hypothesis of chemical change occurring between electrolytes . 241 460 
 
 Limitations applied to this hypothesis 242 464 
 
 Action of the solvent on the dissolved electrolyte .... 243 465 
 
 Instances of chemical changes which occur only in presence of 
 
 water ........... 244 466 
 
 Constitutive properties ........ 245 468 
 
 Affinity and valency 246 469 
 
 Affinity and energy-changes . ....... 247 471 
 
 Energy-changes and electromotive force 248 473 
 
 Concluding remarks 249 475
 
 TITLES OF JOURNALS CONTAINING MEMOIRS TO 
 WHICH REFERENCES ARE MADE. 
 
 ABBREVIATED TITLES. 
 
 Phil. Trans. 
 Proc. R. S. 
 Proc. R. S. E. 
 C. S. Journal. 
 
 C. S. Proc. 
 
 Phil. Mag. 
 
 Chem. News. 
 
 Nature. 
 
 Brit. Ass. Reports. 
 
 Proc. R. I. 
 
 Amer. Chem. Journal. 
 
 I Amer. Journ. of Set. a 
 or 1 Arts 
 
 Amer. Journal. 
 
 lAmet 
 J Af 
 
 (Sill. 
 
 Proc. Amer. Acad. of Arts 
 
 andSci. 
 Gilberfs Ann. 
 
 Pogg. Ann. 
 Wied. Ann. 
 
 Pogg. Beibldtter. 
 
 FULL TITLES. 
 
 Philosophical Transactions. 
 
 Proceedings of the Royal Society. 
 
 Proceedings of the Royal Society of Edinburgh. 
 
 Journal of the Chemical Society. 
 
 [Memoirs and Proceedings, 3 vols. (1841-1847). 
 Journal, series 1, 15 vols. (1848-1862). 
 ,, series 2, 15 vols. (1863-1877). 
 ,, Transactions and Abstracts paged 
 separately, from 1878 to present time. The 
 volumes of this Journal are sometimes referred 
 to by numbers beginning with volume i of series 
 i, and running on consecutively to the present 
 time.] 
 
 Proceedings of the Chemical Society. [Beginning 
 1884.] 
 
 Philosophical Afagazine. [Series 1 to 5.] 
 
 The Chemical News. [Beginning from 1860.] 
 
 Nature. [1879, an( ^ onwards.] 
 
 Reports of the British Association for the Advance- 
 ment of Science. [1831, and onwards.] 
 
 Proceedings of the Royal Institution of Great 
 Britain. [1851, and onwards.] 
 
 American Chemical Journal. [1879, and onwards.] 
 
 American Journal of Science and Arts; since 1880 
 the title is American Journal of Science. [Con- 
 ducted by Sillimann, and subsequently by Silli- 
 mann and Dana. Series 1 to 3.] 
 
 Proceedings of the American Academy of Arts ana 
 Sciences. [Series 1 and 2.] 
 
 Gilbert's Annalen der Physik und Chemie. [i 799- 
 1824.] 
 
 Poggendorjfs Annalen der Physik und Chemie. 
 [1824-1876.] 
 
 Wiedemann's Annalen der Physik und Chemie. 
 [Continuation of Pogg. Ann. from 1877; fre- 
 quently quoted in memoirs, &c., as Ann. Phys. 
 Chem. Series 2.] 
 
 Beibldtter zu den Annalen der Physik und Chemie. 
 [1877, onwards.]
 
 TITLES OF JOURNALS OF REFERENCE. 
 
 XXlll 
 
 ABBREVIATED TITLES. 
 Annalen. 
 
 J.fiir prakt. Chemie. 
 Ber. 
 
 (Fresenius's Zeitschr. \ 
 \Zeitschr. anal. Chemie} 
 Zeitschr. fiir Chemie. 
 
 Zeitschr. fiir physikal. Chemie. 
 
 Zeitschr. fiir Krystallog. 
 Schweigger 's Journal. 
 Sitzber. der K. Akad. zu Wien. 
 
 Sitzber. der Wiss. Akad. zu 
 
 Berlin. 
 Jahresberichte. 
 
 Compt. rend. 
 Mem. de FAcad. 
 
 Ann. -Chim. Phys. 
 Bull. Soc. Chim. 
 
 Mem. de la Soc. d^Arcueil. 
 
 Mem. couronn. de fAcad. 
 Brux. 
 
 Ann. Min. 
 Gas. 
 
 FULL TITLES. 
 
 Liebig's Annalen der Chemie und Pharmacie. 
 [Continued since Liebig's death under same title.] 
 
 Journal fiir praktische Chemie. [Series 1 and 2.] 
 
 Berichte der Deutschen Chemischen Gesellschaft. 
 [Abstracts of papers published elsewhere are 
 paged consecutively with the transactions until 
 1883; from 1884 and onwards the abstracts, 
 Referate, are paged separately.] 
 
 Zeitschrift fiir analytische Chemie, herausgegeben 
 von Dr C. R. Fresenius. [1862, onwards.] 
 
 Zeitschrift fiir Chemie. [Conducted by Beilstein 
 and Fittig. Series 1 and 2. 1858 to 1871. 
 Publication discontinued.] 
 
 Zeitschrift fiir Physikalische Chemie, Stochiometrie 
 und Verwandtschaftslehre ; herausgegeben von 
 W. Ostwald und J. H. van't Hoff. [1887, on- 
 wards.] 
 
 Zeitschrift fiir Krystallographie und Mineralogic. 
 [1877, onwards.] 
 
 Journal fiir Chemie und Physik. [Conducted by 
 J. S. C. Schweigger. 1811-1833.] 
 
 Sitzungsberichte der Matfiematisch-naturwisscn- 
 schaftliche Classe der Kaiserliche Akademie der 
 Wissenschaften (Wien). [Each volume contains 
 i or 3 parts (Abtheilungen) ; each part is bound 
 and paged as a separate volume ; the arrange- 
 ment is perplexing.] 
 
 Sitztingsberichte der Akademie der Wissenschaften 
 zu Berlin. [1854, and onwards.] 
 
 Jahresberichte iiber die Fortschritte der Chemie, &c. 
 [Staedel edited a very useful Jahresber. iiber die 
 Fortschritte auf dem Gebiete der Reinen Chemie 
 1873-1881.] 
 
 Comptes rendus hebdomadaires des Stances de 
 P Academic des Sciences. [1835, onwards.] 
 
 Memoir es de FAcademie Roy ale des Sciences de 
 Flnstitut de France. [ 1 8 1 6, onwards. ] 
 
 Annales de Chimie et de Physique. [Series 1 to 6.] 
 
 Bulletin de la Societe Chimique de Paris. [1864, 
 onwards.] 
 
 Memoires de Physique et de Chimie de la Societe 
 cTArcueil. [3 vols. 1807-1817.] 
 
 Memoires couronnts par FAcademie royale des 
 Sciences et Belles- Lettres de Bruxelles. [1827, 
 onwards.] 
 
 Annales des Mines. [Series 1 to 8.] 
 
 Gazetla chimica italiana.
 
 ERRATA. 
 
 The Student is advised to insert the following corrections in their proper places 
 in the text. 
 
 28. Note i; for 'Chap. III.' read 'Chap. II. sections 4 and 5'. 
 
 33. Dele nos. 1 1 and 1 2 in table. 
 
 Note i; for '1888' read '14. 410'. 
 
 34. Note i; for '1888' read '14. 410'. 
 
 ,, Notes n and 12; dele, and substitute 'Biltz (Zeitschr. fur physikal. Ckemie, 
 2. 920) shews that the molecular weight of sulphur gas is represented 
 only by the formula S 2 '. 
 
 38. Fourth line from top ; for 'the weight of of hydrogen' read 'twice 
 
 the specific gravity of a gas referred to hydrogen as unity'. 
 
 42. Fourth line from bottom; for '257*0' (in fourth column) read '254-84', 
 
 and/or '193' (in fifth column) read '191'. 
 
 43. Line 5 from bottom; in place of data for ferric chloride insert '5' 15 | 
 
 i48'68 | i62'oi | 55'9 iron+io6'ii chlorine'. 
 
 44. Note 5; for '1887' read '14. 410'. 
 
 Note 6; dele and insert 'Biltz and Meyer, Zeitschr. fur physikal. Chemie, 
 
 2. 184'. 
 Note 12; dele and insert 'Griinewald and V. Meyer, Ber. 21. 687'. 
 
 45. Table; dele last column. 
 
 48. Table; for '[Iron ni'8]' read 'Iron 55'9', and for '[Gallium 138]' read 
 
 'Gallium 69-9'. 
 
 ,, Table; for 'Osmium i93(?)' read 'Osmium 191'. 
 ,, Note i; dele. 
 
 Note i;for 'elements' read 'element'. 
 53. Bottom line ; for 'in' read 'on'. 
 
 60. Second line from top ; for ' omitting the three elements which are placed 
 in brackets in the former table, of the 43 elements' read 'omitting the 
 element which is placed in brackets in the former table, of the 45 
 elements'. 
 
 ,, Fourteenth line from top; for 'there are three elements viz. iron, 
 
 copper, and gallium' read 'there is one element viz. copper'; 
 
 and make the necessary corrections in other parts of this page. 
 71. Sixth line from bottom ; for 'form' read 'forms'. 
 88. Third line from top of table, second column ; for ' Fe 2 Cl 6 ' 
 
 read 'FeCl 3 '. \ See Addenda. 
 
 ,, fifth column; dele '[see p. 60]'.
 
 ERRATA. XXV 
 
 PAGE 
 
 91. Second line from bottom of table; for '193' read 'igi';for '48-25' read 
 '4775'; a f ier 'Osmium tetroxide' add 'Potassium-osmium chloride'; 
 dele note in column VIH. referring to osmium; transpose data regarding 
 osmium so as to come above data for iridium. See Addenda. 
 99. Note carried on from p. 98 ; dele last two lines of this note. 
 in. Note; dele this note. 
 
 126. Note; dele 'determinations of the spec, gravity this question' and 
 
 insert 'According to Thorpe and Hambly (C. S. Journal, B5. 163) there 
 is no evidence for the separate existence of a definite gaseous molecule 
 of hydrogen fluoride other than HF'. 
 128. Line 12 from bottom ; for '37' read '39' l 
 Line it from bottom ; for 'six' read 'nine' j k 
 
 130. Line 1 8 from bottom; for 'six' read 'nine', and for '37' read '39'. 
 
 131. Line 12 from bottom; for '37' read '39'. 
 
 141. Line 13 from top; for 'six' read 'five', and dele 'sulphur'. 
 ,, Line 18 from top; dele from 'the molecule of sulphur' to '2 atoms'. 
 ,, Line 6 from bottom; dele from 'of the hexatomic' to 'of sulphur'. 
 143. Line 13 from bottom; dele from 'another instance' to 'SnCl 2 '. 
 1 86. Line 2 from bottom; for 'carbonation' read 'carbon atom'. 
 210. Line 10 from bottom ; for '195' read '195'. 
 225. Table, Group fn ; for 'Ga = 69' read 'Ga = 7o'. 
 
 ,, ,, vni ; for ( Os=i93(?)' read '05=191', and transpose Os and 
 Ir, putting Os before Ir. 
 
 229. Line 15 from top; for '585' read '585'. 
 
 230. Line 1 4 from bottom ; for '69' read '70'. 
 
 231. Line 2 from top ; for '69' read '69'9'. 
 
 236. Table, Group ill; for 'Ga=69' read 'Ga=7o'. 
 
 ,, ,, vni ; for '05=193' read ' 05=191', and place Os before Ir. 
 292. Line 8 from bottom; paragraphing wrong, for '41' raz</'141'. 
 309. Note 3; for ' Journal'' read 'ZeitscAr'. 
 
 k' k' 
 
 352. In the equation ;for l (p- *) = j (/ + *)' read '(/> x)= j (P' + x)'. 
 
 355. Line 8 from bottom ; for 'constant' read 'coefficient'. 
 
 359. Line 3 from top; for 'cases where more than one body undergoes' read 
 
 'cases where limited quantities of more than one body undergo'. 
 361. Line 5 from top; for 'if A = FeSO 4 and B = KC1O 3 ' read 'if A = the 
 
 quantity of potassium chlorate and B = the quantity of ferrous sulphate'. 
 
 364. Line 1 1 from top ; for ' obtained ' read ' attained '. 
 
 ,, Line 14 from bottom; dele 'and as these masses are independent of the 
 original values of/ and/". 
 
 365. Line 1 6 from bottom; dele 'constancy of the'. 
 
 367. Line 13 from top; after 'and therefore' insert 'by the same reasoning'. 
 
 371. Line 5 from top; dele 'and '. 
 
 372. Lines 9 and 10 from bottom; for 'increase' read 'decrease'. 
 
 373. Line 17 from bottom ; for 'greater' read 'smaller'. 
 
 ,, Line 15 from bottom ; for 'increase' read 'decrease'. 
 
 376. Line 15 from top; for 'a constant temperature' read 'constant temper- 
 atures'.
 
 ADDENDA. 
 
 The Student is advised to insert the following additions in their proper places 
 in the text. 
 
 PAGE 
 
 34. Line 3 from top; add 'Biltz and Meyer (Ber. 22. 725) have vaporised 
 arsenic, antimony, bismuth, phosphorus, and thallium, at about 1700; 
 the vapour densities point to the molecular formulae As,, Sb,, Bi, ?P 2 , 
 T1 2 . These results are not regarded as final by Biltz and Meyer'. 
 39 43. Insert in table ; 
 
 ' 3b Tellurium diethide 6-47 i86'8 182*88 125 tellurium + 47-88 carbon 
 
 + 10 hydrogen'. 
 <3c Bismuth triethide 9*1 262-2 252-91 208 bismuth +35-91 carbon 
 
 + 9 hydrogen '. 
 
 1 12 F err ous chloride 4-31 124-43 127-64 55-9 iron +71-74 chlorine'. 
 44. Note i ; add 'See also Thorpe and Hambly C. S. Journal, 55. 163'. 
 Insert Note; '3 b and 3. Marquardt, Ber. 21. 2035'. 
 
 Note ii ; in loth line of note insert 'see also Roux and Louise, Compt. rend. 
 106. 73; also Quincke, Zeit. fiir physikal. Chemie, 3. 164. For a col- 
 lection of data bearing on vapour densities of the chlorides of Al and 
 allied metals, see Young, Nature, 39. 198'. 
 
 Insert note; ' 12". Nilson and Pettersson, C. S. Journal, 53. 827'. 
 Note 13; at end of note add 'See also Nilson and Pettersson, C. S. Journal, 
 
 53. 822'. 
 
 76. Note; add ' For practical methods of applying Raoult's law see (among 
 others) Hentschel Zeitschr. fur physikal. Chemie, 2. 306; Beckmann, 
 ibid. 2. 638, Eykman, ibid. 2. 964 '. 
 
 83. Note ; add ' The example given in the text is not a good one, as the existence 
 of any definite gaseous molecules of ferric and ferrous chloride except 
 FeCl 3 and FeCl 2 is very doubtful; see p. 44'. 
 88. First line of table, second column; <M&/'?CrQ 2 '. 
 
 Eighth line of table, second column; add 'GaCI 3 , GaCl 2 '. 
 90. Sixth line of table, second column ; add ' InCU, ? InCl . 
 95. Reference to Os; #</</' Seubert, Ber. 21. 1839'. 
 
 Reference to Pt ; add ' (See also Seubert, Ber. 21. 2179) '
 
 ADDENDA. XXV11 
 
 PAGE 
 
 127. To list of monovalent atoms ; add ' ? In '. 
 
 To list of divalent atoms ; add ' In, Ga, Fe, ? Cr '. 
 To list of trivalent atoms ; add ' Fe, Ga '. 
 
 To list of data on lower part of page; add 'PInCI, InCl 2 , FeClj, FeCl 3 , 
 GaCl 2 , GaCl 3 ,?CrCl 2 '. 
 
 128. Line 7 from- bottom; insert ' the atoms of gallium, iron, and indium, and 
 
 probably also the atom of chromium, are divalent and trivalent'. 
 
 229. Note 5; add to this note, ' But de Boisbaudran has calculated the atomic 
 weights of gallium and germanium from considerations based on the 
 relations between the atomic weights, and the wave-lengths of the chief 
 lines in the spectra, of similar elements. (See articles Gallium and 
 Germanium in the new edition of Watts' Dictionary of Chemistry, 
 vol. ii.)'. 
 
 267. Note; add to this note 'The following data for solid mercury compounds 
 are given by Nernst (Zeitschr. filr physikal. Chemie, 2. 23). 
 [Hg, 0*1 = 53,200 [Hg, ^ = 40,5000 [Hg, I 2 ] = 24,300 ) . 
 
 298. Note 6; add ' See also Conrady, Zeitschr. fur physikal. Chemie, 3. 210'. 
 
 299. Note; add 'Weegman (Zeitschr. filr physikal. Chemie, 2. 218,258) has 
 
 conducted a series of very careful measurements of R for chloro- and 
 bromo-derivatives of hydrocarbons; his results on the whole confirm 
 those of Briihl ; they also emphasise the need of further researches'. 
 
 311. Notey, <*/</'1888. 561'. 
 
 317. Note 2; to list of memoirs add 'An historical sketch, by Kopp, of the 
 position of our knowledge of the molecular volumes of liquid compounds 
 is to be found in Anna If n, 250. i [1889]'.
 
 " L'action chimique est reciproque : son effet est le resultat d'une tendance 
 mutuelle a la combinaison ; on ne peut pas, a la rigeur, dire plutot qu'un liquide 
 agit sur un solide, qu'on ne peut dire que le solide agit sur le liquide : la 
 commodite de 1 'expression fait transporter sans inconvenient toute 1'action dans 
 1'une des deux substances, quand on veut examiner 1'effet de cette action plutot 
 que 1'action elle-meme." BERTHOLLET.
 
 I 
 
 LOS ANQELJLS, -:- CAL. 
 
 INTRODUCTORY. 
 
 CHEMISTRY is preeminently the science which concerns 
 itself with the changes presented in material phenomena; it 
 is the science which attempts to classify the mutations that 
 matter undergoes. 
 
 In the chemical examination of any kind of matter two 
 questions have always pressed for answers: What can this 
 substance do? Of what is this substance composed? While 
 attempting to answer these questions separately, and while 
 thus more or less adopting two schemes of classification, 
 chemists have for the most part recognised that no complete 
 answer could be given to either question considered wholly 
 apart from the other; hence the two methods of chemical 
 investigation, and the two lines of chemical advance, have 
 generally been closely interwoven. 
 
 In older times a substance was said to be capable of 
 doing this or that because it contained certain elements or 
 essences ; substances were classed together because of simi- 
 larity of actions, but the points of resemblance on which 
 classification was based were uncertain and undefined: the 
 conception of element was paramount. The substances in 
 a class shewed many or a few points of resemblance because 
 each member of the class contained the same element, and 
 v hence was a more or less perfect means for exhibiting the 
 properties of that element- The ideas of composition and 
 properties, as we now use these expressions, were both im- 
 plied in the older conception of element. 
 
 M, C. I
 
 2 INTRODUCTORY. 
 
 If it be granted that the various forms of matter are 
 vehicles for displaying the properties of a few elements, it 
 follows that the addition or withdrawal of this or that ele- 
 ment will probably suffice to change one into another form 
 of matter. Hence arose the art of alchemy and the pursuit 
 of the philosopher's stone. This pursuit resulted in the ac- 
 cumulation of many facts most of which could for some time 
 be explained by aid of the one underlying general concep- 
 tion of element. But as facts accumulated the foundation 
 was found to be too narrow to bear the structure raised upon 
 it; a need was felt for minor explanations and for partial 
 hypotheses. Observers began to contrast sour, acid, sub- 
 stances, with mild, tasteless, non-corrosive, substances; hence 
 arose the division of a large class of bodies into two minor 
 classes, acids and alkalis. This classification when carried 
 to completion produced the school of tatro-chemists, in 
 whose hands chemical science became a branch of the art 
 of medicine. But once again facts were observed which 
 could not be explained by the theories of the medical 
 chemists: the experimental method was recognised as alone 
 leading to definite and trustworthy results in the examination 
 of natural phenomena; but the experimental method, it was 
 found, to be of value must be accurate, and to be accurate 
 must be quantitative. Advance became rapid. The con- 
 ception of element remained, but in modified form ; the dis- 
 tinction between alkali and acid remained, but proved to 
 mean at once less and more than its originators supposed. 
 Bodies were compared as to their actions and as to their 
 composition ; the comparison led on the one hand to the 
 recognition of force exerted by one body on another, called 
 affinity, and on the other hand to the recognition of ultimate 
 forms of matter, called elements, of which all bodies are com- 
 posed. 
 
 From this point the two broad paths of advance become 
 more easily distinguished ; advance is made by seeking answers 
 to questions such as these : What is the nature of the ele- 
 ments ? What is the composition of compounds ? Can the 
 facts regarding elementary combinations be generalised ?
 
 INTRODUCTORY. 3 
 
 Advance is also made .by pursuing inquiries indicated by 
 such questions as these : What connexion, if any, exists 
 between the properties of elements and of compounds of these 
 elements ? What actions are these compounds capable of 
 performing? And advance is also made by combining both 
 methods of inquiry in seeking answers to such a question as 
 this: Why are the properties of these compounds such as 
 they are observed to be? 
 
 At one time those chemists for whom the composition of 
 compounds was all-important have been supreme; at another 
 time the place of authority has been occupied by those who 
 regarded function, or power of doing, as the essential subject 
 of study. The greatest outcome of the work of the former 
 school is the atomic hypothesis, now merged in the wider 
 molecular and atomic theory; the most important result of 
 the studies of the latter school is the conception of chemical 
 affinity ; both have taken part in the development of the 
 modern views regarding molecular structure and rational 
 formulas. 
 
 While assigning the credit of special advances to one of 
 the two great schools of chemistry, we cannot but recog- 
 nise that these advances have been made by the help of 
 suggestions borrowed from the other: recent developments 
 of the atomic theory cannot be separated from the rise of the 
 unitary system ; the latest hypotheses regarding the structure of 
 molecules are connected with the subject of chemical affinity. 
 
 Eighty years ago Berthollet attempted to arrange the 
 facts of chemical action under a general conception which 
 should serve to connect chemical with physical changes; but 
 the attempt was only partially successful because of the scanty 
 supply of purely chemical data. General views of chemical 
 action were soon abandoned for a study of the properties of 
 the products of this action ; but of late years many chemists 
 have resumed the investigation of the general conditions of 
 chemical action, and have obtained results which give good 
 grounds for hoping that this study will throw light on the 
 masses of facts already accumulated concerning compounds, 
 and groups of compounds, and, taken along with that method 
 
 I 2
 
 4 INTRODUCTORY. 
 
 of investigation which is based on a study of the composition 
 of compounds, will lead to the establishment of chemistry as 
 a branch of the science of physical dynamics. 
 
 The study of the motions of material bodies considered as 
 accompanying mutual actions between these bodies belongs 
 to the general science of dynamics. Phenomena presented 
 by mutually acting bodies wherein the properties of these 
 bodies are not permanently modified belong to the domain of 
 physical science. Chemistry deals with those reactions 
 between elements and compounds wherein permanent modifi- 
 cations in the properties of the bodies occur. Or, we may 
 say that whereas physical science is concerned with the pro- 
 perties of this or that kind of matter considered for the most 
 part apart from the action on it of other kinds of matter, 
 chemistry is concerned with the mutual actions which occur 
 between matter of different but definite kinds whereby per- 
 sistent changes in the properties of the reacting kinds of 
 matter occur. 
 
 Chemistry furnishes problems for the solution of which 
 physical and dynamical methods are applicable. Chemical 
 science is ever tending toward abstract truths, i.e. truths 
 involved in many phenomena although actually seen in none: 
 but before she gains abstract truths chemistry amasses many 
 general truths, i.e. 'truths which sum up many facts.' 1 
 
 The chemist is set to solve the problem : Why are the 
 properties of elements and compounds permanently modified 
 under certain conditions? In attempting to find a solution, 
 he must divide the phenomena which he observes into their 
 factors, and study each of these as far as possible indepen- 
 dently of the others. 
 
 The chemist need not regard the methods pursued by 
 those sciences which are more concrete than his own, 
 although he may furnish them with subject-matter for in- 
 vestigation ; inasmuch however as the science of matter and 
 
 1 The abstract and the general truths of chemistry are scarcely yet so 
 differentiated as to allow of each class being considered separately. I do not 
 purpose attempting more than a very rough separation in this book.
 
 INTRODUCTORY. 5 
 
 motion is a more abstract science than that of chemistry, he 
 must seek help for his work in the methods of that science, 
 always remembering that this help is given to solve chemical 
 problems, and that with purely physical problems, he, as a 
 chemist, is not concerned 1 . 
 
 Pursuing then an almost purely analytical method the 
 chemist finds that his subject branches off into two main 
 divisions. The properties of bodies are modified; he studies 
 the relations between the new substances and those by the 
 mutual action of which the new bodies were produced : but 
 changes in the properties of bodies involve a consideration of 
 the relative positions of the changing body and of other 
 bodies, in other words involve the action of force ; he en- 
 deavours to elucidate the laws of action of this force. 
 
 The hypothesis that bodies consist of small parts called 
 molecules in motion, is one of the lines along which dyna- 
 mical science pursues its advance into the sphere of chemistry. 
 The study of chemical phenomena is also brought within the 
 pale of dynamical methods by the application to these pheno- 
 mena of the general principles of the conservation and de- 
 gradation of energy 2 . The latter (thermo-dynamic) method 
 is more applicable to the study of the laws of chemical forces 
 than of the properties of the substances depending on the 
 actions of these forces, which properties have been chiefly 
 elucidated by the help of the molecular theory. 
 
 We may indeed study relations between forces accom- 
 panying changes in the distribution of certain material magni- 
 tudes, which we may call molecules, without reference to what 
 is generally known as the molecular theory of matter. 
 
 But it seems certain that no chemical phenomenon and it 
 is well for the student to bear in mind that the chemical part 
 is always but one aspect of any natural occurrence can be 
 fully explained unless both methods of investigation are 
 applied ; unless the relations between the reacting bodies and 
 the products of the reaction, and the relations between the 
 
 1 Chemistry, being more concrete, is less exact than physics ; mathematical 
 'methods can scarcely as yet be applied to purely chemical data. 
 
 2 See Clerk Maxwell : Science Conferences at South Kensington, 1876.
 
 6 INTRODUCTORY. 
 
 forces exhibited in the phenomenon in question, are con- 
 sidered. 
 
 In the following pages an attempt is made to gather 
 together the more important data on which the leading 
 generalisations of chemistry are based, and in the light of 
 this material to discuss these generalisations. 
 
 By the use of the terms Chemical Statics and Chemical 
 Kinetics I would indicate, roughly, that the phenomena in- 
 cluded under the first of these headings are on the whole 
 those exhibited by chemical bodies or systems of bodies in 
 equilibrium, while the phenomena classed together as chemical 
 kinetics relate more to bodies or systems of bodies when 
 chemically active. 
 
 It may seem pedantic to make use of terms having definite 
 and precise significations when from the very nature of the 
 facts they can be employed only in the broadest and roughest 
 way. I only wish to indicate that the subject-matter of 
 chemical science is considered in this book as divisible into 
 two large parts, of which one comprises the facts and prin- 
 ciples concerned, on the whole, with chemical composition, 
 and the other those which, broadly speaking, relate to chemical 
 action. 
 
 It will of course be found that chemical occurrences pre- 
 sent, I think one may say always present, both statical and 
 kinetical problems ; the two sides of any chemical problem 
 can scarcely be regarded apart, in the present state of know- 
 ledge at any rate, without danger; it may therefore be that 
 phenomena ranked by one chemist as statical would by 
 another be classed as kinetical. 
 
 I begin by considering the facts and principles roughly 
 classed as statical, because although the study of kinetics 
 seems naturally to precede that of statics, yet in chemistry 
 our knowledge of composition is much in advance of our 
 knowledge of action : I then consider the data and generalisa- 
 tions of so-called chemical kinetics; and lastly I endeavour 
 to review some of those phenomena, explanations of which, 
 generally only very partial explanations, can be gained, or 
 hoped for, only by the help of both methods.
 
 BOOK I. l] 
 
 BOOK I. 
 CHEMICAL STATICS. 
 
 CHAPTER I. 
 
 ATOMS AND MOLECULES. 
 
 1 THE experimental foundations of the modern chemical 
 atomic theory were laid in the later years of last century 
 by the German chemist Richter 1 . The work of Bergmann*, 
 although of earlier date than that of Richter, cannot be re- 
 garded of equal importance as concerns the history of the 
 atomic theory. 
 
 Richter studied the neutralisation of acids by bases, and 
 of bases by acids, and shewed that a definite amount of acid 
 (or base) always combines with a definite amount of base 
 (or acid) when neutralisation is accomplished. By determining 
 the masses of various bases neutralised by one and the same 
 mass of each acid, and the masses of various acids neutralised 
 by one and the same mass of each base, Richter was able to 
 arrange many acids and bases in order of neutralisation. 
 Fischer 3 , in 1803, published the first table of chemical equi- 
 valents. Richter had given a series of numbers for each base 
 expressing the quantities thereof which would neutralise 1000 
 parts by weight of sulphuric acid, or 1000 parts of hydro- 
 chloric acid, or 1000 parts of nitric acid &c. : Fischer saw 
 that it was sufficient to attach a single number to each base 
 and a single number to each acid ; 1000 parts by weight of 
 
 1 Ueber die nnuren Gegenstande der Chemie, 1791 1802: and Anfangsgrundc 
 der Stochio metric oiler Messkunst chemischer Element 'f, 1822. 
 - Chemische Werke, 2. 25 et seq, 
 3 In a note to Berthollet's Essai de Statiqite Chimiqtte (1803).
 
 8 ATOMS AND MOLECULES. [BOOK I. 
 
 sulphuric acid being adopted as the unit of neutralisation. 
 Fischer's numbers expressed the masses of bases, or acids, 
 which were of equal value so far as power to neutralise a 
 constant mass of a certain acid or base was concerned 1 . 
 
 Foreshadowings of the atomic theory are to be found in 
 a work by W. Higgins entitled A comparative view of the 
 Phlogistic and Antiphlogistic Theories, -with Inductions (1791) 
 [see Henry's Life of Dalton p. 75 et seql\\ but to Dalton is 
 undoubtedly due the signal honour of introducing a clear and 
 self-consistent theory regarding the composition and structure 
 of chemical substances, a theory which in its essential points 
 has stood the test of rigorous experimental verification, and 
 has adapted itself to the wants of each successive school of 
 chemical thought. 
 
 2 Dalton 2 , and others, found that elements were united in 
 many compounds in fixed proportions by weight, and more- 
 over that in certain compounds of one element with others 
 the amount by weight of this element could be expressed by 
 whole multiples of one fundamental number. The facts re- 
 garding the quantitative combinations of the elements are 
 expressed in the three laws of chemical combination : 
 
 I. The masses of the constituents of any compound 
 
 stand in an unalterable proportion to each other 
 and to the mass of the compound. 
 
 II. When two elements combine to form more than one 
 
 compound the masses of one of the elements 
 which combine with a constant mass of the other 
 element bear a simple relation to each other. 
 
 III. The masses of different elements which severally 
 
 combine with one and the same mass of another 
 element are also the masses of those different 
 
 1 For more details regarding the work of Richter and Fischer, see Wurtz, The 
 Atomic Theory, pp. 12 22. 
 
 2 It is important to note that Dalton's atomic theory was conceived by him in 
 1802 from considering the results of physical experiments: he distinctly states in 
 a paper on the absorption of gases in liquids read to the Manchester Philosophical 
 Society in that year that he had lately been prosecuting 'with remarkable 
 success,' 'an inquiry into the relative weights of the ultimate particles of bodies.'
 
 CHAP. i. 2] DALTON'S ATOMIC WEIGHTS. 9 
 
 elements which combine with each other, or they 
 bear a simple relation to these masses. 
 
 To account for the facts' of chemical combination Dalton 
 recalled the atomic theory of the Greek philosophers ; but he 
 transformed an interesting speculation about the possible 
 causes of vaguely observed occurrences into a scientific theory 
 of quantitatively established facts. 
 
 Every chemical substance, simple or compound, is made 
 up of atoms, or small undivided parts 1 ; the properties of 
 each substance are dependent on the properties, and to some 
 extent the arrangement, of these atoms: the old hypothesis 
 had gone as far as this. Dalton added, the atom of every 
 chemical substance has a definite mass, and although this 
 mass cannot be determined, we nevertheless can determine 
 the relative masses of the atoms of all bodies. It is only 
 necessary to choose some substance as a standard, then the 
 mass of the smallest quantity of any other substance which 
 combines with the unit mass of the standard substance repre- 
 sents the mass of the atom of the combining substance in 
 terms of the unit chosen. 
 
 As this point is of supreme importance it may be well 
 that we should have Dalton's own words before us. In the 
 New System of Chemical Philosophy (1808) after discussing 
 the constitution of mixed gases, Dalton proceeds : 
 
 " When any body exists in the elastic state its ultimate particles are 
 separated from each other to a much greater distance than in any other 
 state ; each particle occupies the centre of a comparatively large sphere, 
 and supports its dignity by keeping all the rest, which by their gravity or 
 otherwise are disposed to encroach upon it, at a respectful distance. 
 When we attempt to conceive the number of particles in an atmosphere, 
 it is somewhat like attempting to conceive the number of stars in the 
 universe ; we are confounded by the thought. But if we limit the subject, 
 by taking a given volume of any gas, we seem persuaded that, let the 
 divisions be ever so minute, the number of particles must be finite; just 
 as in a given space of the universe the number of stars and planets cannot 
 be infinite. 
 
 Chemical analysis and synthesis go no further than to the separation 
 
 1 Dalton's application of the term atom to the small chemically indivisible 
 parts of compounds, seems to shew that he did not regard his atoms as absolutely 
 indivisible : see Life by Henry, p. 88.
 
 IO ATOMS AND MOLECULES. [BOOK I. 
 
 of particles one from another, and to their reunion. No new creation or 
 destruction of matter is within the reach of chemical agency. We might 
 as well attempt to introduce a new planet into the solar system, or to 
 annihilate one already in existence, as to create or destroy a particle of 
 hydrogen. All the changes we can produce consist in separating particles 
 that are in a state of cohesion or combination, and joining those that 
 were previously at a distance. 
 
 In all chemical investigations it has justly been considered an im- 
 portant object to ascertain the relative weights of the simples which 
 constitute a compound. But unfortunately the inquiry has terminated 
 here ; whereas from the relative weights in the mass, the relative weights 
 of the ultimate particles or atoms of the bodies might have been inferred, 
 from which their number and weight in various other compounds would 
 appear, in order to assist and to guide future investigations, and to correct 
 their results. Now it is one great object of this work, to shew the im- 
 portance and advantage of ascertaining the relative weights of the ultimate 
 particles both of simple and compound bodies, the number of simple 
 elementary particles which constitute one compound particle, and the 
 number of less compound particles which enter into the formation of one 
 more compound particle. 
 
 If there are two bodies, A and B, which are disposed to combine, the 
 following is the order in which combination may take place, beginning 
 with the most simple : namely 
 
 I atom of A + i atom of B = 
 
 1 A + 2 atoms B= 
 
 2 atoms A + i atom B= 
 i atom A +3 atoms B= 
 
 3 atoms A + i atom B= 
 
 atom of C, binary, 
 D, ternary, 
 , ternary, 
 f, quaternary, 
 G, quaternary.' 1 
 
 &c., &c. 
 
 Dalton then states the following rules respecting chemical 
 synthesis, which he employed in determining the relative 
 weights of the smallest chemically indivisible parts of com- 
 pound bodies 1 . 
 
 " ist. When only one combination of two bodies can be obtained, it 
 must be presumed to be a binary one, unless some cause appears to the 
 contrary. 
 
 2nd. When two combinations are observed they must be presumed 
 to be a binary and a ternary. 
 
 3rd. When three combinations are obtained, we may expect one to 
 be a binary, and the other two ternary. 
 
 1 By the 'smallest chemically indivisible part' of a substance is meant an 
 amount such that, if divided, substances (or a substance) are produced different in 
 properties from the original substance.
 
 CHAP. I. 2, 3] THE DALTONIAN THEORY. 1 1 
 
 4th. When four combinations are observed, we should expect one 
 binary, two ternary, and one quaternary." &c. &c. 
 
 " From the application of these rules," Dalton says, " to the chemical 
 facts already well ascertained, we deduce the following conclusions : 
 ist. That water is a binary compound of hydrogen and oxygen, and 
 the relative weights of the two elementary atoms are as i : 7 nearly. 
 2nd. That ammonia is a binary compound of hydrogen and azote, and 
 the relative weights of the two atoms are as i : 5 nearly. ...In all these 
 cases the weights are expressed in atoms of hydrogen each of which is 
 denoted by unity." 
 
 As an example of Dalton's applications of these rules, 
 let us take the two oxides of carbon. These two oxides 
 are composed, according to Dalton, of 5-4 parts by weight of 
 carbon combined respectively with 7 and with 14 parts by 
 weight of oxygen : the first of these bodies, in accordance 
 with Dalton's second rule, was considered to be a binary, 
 and the second a ternary, compound; the formulae given were 
 CO and CO, respectively. [C = 5-4, O = 7.] 
 
 But Dalton's CO 2 might have been regarded as a com- 
 pound of 27 parts by weight of carbon with 7 parts by 
 weight of oxygen, in which case its formula would have 
 been written CO [C = 27] ; Dalton's CO would then have 
 become C 2 O [C 2 = 5'4J. The atomic weight of carbon would 
 be determined as 2*7 or 5*4 according as carbon monoxide 
 or carbon dioxide was decided to be a binary compound. 
 
 At a later time it was said by some chemists that a binary 
 compound is always more stable than a ternary; if this rule 
 were applied to the case of the oxides of carbon, Dalton's 
 number for the atomic weight of carbon would be confirmed 1 . 
 3 These examples illustrate the great shortcoming of the 
 Daltonian theory: the atomic weights of Dalton are either 
 multiples or submultiples of a certain number, but we can- 
 not tell what multiple or what submultiple. Hydrogen 
 being taken as unity, let the relative masses of two elements 
 which form a compound B, be Q and Q lt and let the atomic 
 weights of these elements be A and A^ respectively; then 
 Q'.Q^'.-.nA : n v A^ where and n^ are whole numbers. But 
 inasmuch as the values of n, ,, A, and A l are unknown, it is 
 
 1 See especially Daubeny's Atomic Theory (ind edition i8;o\ pp. 119 120.
 
 12 ATOMS AND MOLECULES. [BOOK I. 
 
 evident that analysis alone, aided by the Daltonian theory, 
 cannot determine the atomic weights of the elements which 
 compose the substance B. 
 
 This shortcoming in the theory could not be supplied 
 without further data: Dalton distinctly states that in order to 
 determine the number of elementary atoms in the atom of a 
 compound a knowledge of the composition of many com- 
 pounds of the given elements is required. 
 
 4 A few months after the announcement of Dalton's law 
 of multiple proportions and atomic theory, Gay Lussac and 
 Humboldt 1 began their volumetric investigations which cul- 
 minated three years later in the beautiful discovery of the 
 former naturalist 2 , that gaseous substances unite in fixed 
 volumetric proportions which may be simply expressed. 
 
 There is a constant simple relation, said Gay Lussac, 
 between the volume of a gaseous compound and the volumes 
 of its constituent elements. Let one volume be defined as 
 the volume occupied by unit mass of hydrogen; then the 
 combining volume of any gaseous element is always expressed 
 by a whole number; e.g. one volume of nitrogen combines 
 with one volume of oxygen to form two volumes of nitric 
 oxide, two volumes of hydrogen and one volume of oxygen 
 combine to form two volumes of water-gas, one volume of 
 nitrogen and three volumes of hydrogen form two volumes of 
 ammonia, &c. &c. Condensation sometimes occurs, some- 
 times the volume of the compound is equal to the sum of the 
 volumes of the combining elements. 
 
 This discovery appeared to add fresh arguments to the 
 theory of Dalton. The ratios of the masses of these com- 
 bining volumes of the elements, hydrogen being taken as 
 unity, represent, it was said, the relative masses of the atoms 
 of these elements; and the conclusion was drawn, 'equal 
 volumes of gaseous substances, measured at the same tem- 
 perature and pressure, contain equal numbers of atoms.' 
 
 5 Dalton however refused to accept Gay Lussac's gene- 
 ralisation, and regarded his experimental methods as un- 
 trustworthy. We cannot, I think, fail to be struck with 
 
 1 Journal de Physique, 60. 129. * Mhu, de la Soc. d'Arciieil, 2. 207.
 
 CII. I. 4-6] AVOGADRO'S ATOMS AND MOLECULES. 13 
 
 the justness of Dalton's objection to the statement 'equal 
 volumes contain equal numbers of atoms:' he argued some- 
 what as follows : one volume of nitrogen and one volume 
 of oxygen form two volumes of nitric oxide ; but one atom 
 of nitrogen and one atom of oxygen form one atom of nitric 
 oxide ; therefore, had the above statement been correct, the 
 volume of nitric oxide would have been equal to, not twice 
 as great as, the volume of oxygen or of nitrogen. So again, 
 one atom of hydrogen and one atom of oxygen form one 
 atom of water, according to Dalton's rules : but Gay Lussac 
 shewed that two volumes of hydrogen combine with one volume 
 of oxygen to produce two volumes of water-gas ; hence the 
 atom of hydrogen occupies twice the volume occupied by the 
 atom of oxygen, and therefore the statement of Gay Lussac 
 is incorrect. If Dalton's definition of atom and his rules 
 regarding atomic synthesis are adopted, Gay Lussac's state- 
 ment that ' equal volumes contain equal numbers of atoms ' 
 must be abandoned. 
 
 6 The difficulty was removed by Avogadro 1 , who (in 1811) 
 introduced the conception of two kinds of small particles : 
 "molecules int/grantes," or as we should now say molecules; 
 and " molecules e'le'mentaires" or as we should now say atoms. 
 
 The molecules of elements are decomposed in chemical 
 processes, said Avogadro, and the atoms unite to form new 
 compounds. "Equal volumes of gases contain equal numbers 
 of molecules." The reaction between nitrogen and oxygen 
 inexplicable by Gay Lussac's law now becomes clear ; each 
 molecule of nitrogen and each molecule of oxygen divides 
 into two parts, and these parts unite to form the new mole- 
 cules of nitric oxide ; hence there are twice as many mole- 
 cules of nitric oxide produced as there were molecules of 
 nitrogen or oxygen originally present. 
 
 By thus recognising a higher order of atoms, as it were, 
 Avogadro reconciled Dalton's theory with Gay Lussac's 
 results. 
 
 1 Journal de Physique, 73. 58 : also Essai d'tine mantere de determiner les 
 lasses relatives des molecules element air es des corps, &c.
 
 14 ATOMS AND MOLECULES. [BOOK I. 
 
 Ampere 1 in 1814 drew prominent attention to the hypo- 
 thesis of Avogadro, and attempted by its help to explain the 
 structure of crystals. But the hypothesis had come before 
 the times were fully ripe. 
 
 7 Wollaston 2 accepted Dalton's theory but proposed to 
 use the word equivalent* in place of atom. In his paper 
 published in 1814 (loc. cit.) Wollaston drew up a table of 
 equivalents which he thought would be serviceable to the 
 practical chemist in determining the amount of an acid which 
 would combine with a given weight of base, or the weight of 
 precipitate obtainable in a given reaction, &c. He arranged 
 his numbers on a scale with a slider attached, and adopted a 
 mechanical contrivance for aiding the analyst in using the table. 
 Although Wollaston employed the word equivalent in place 
 of atom, his scale and table must be regarded as helping to 
 extend the use of the atomic theory*. For the practical purpose 
 which he had in view Wollaston did not deem it necessary to 
 adopt any theory; at the same time he regarded the atomic 
 weights of Dalton, especially the atomic weights of compounds, 
 as too hypothetical, and he thought that equivalents were to 
 be preferred for most purposes. 
 
 Wollaston referred his equivalent numbers to oxygen as 
 10: the amount by weight of any element which combined 
 with 10 parts by weight of oxygen was regarded by him 
 as the equivalent of that element. But the system of 
 equivalents was liable to the same objection as had been 
 urged against the system of atomic weights : it was too 
 vague. 
 
 (1) Thus 7'5 parts by weight of carbon unite with 20 
 parts by weight of oxygen, said Wollaston, therefore the 
 formula of the compound produced is CO 2 . 
 
 (2) Again 7*5 parts by weight of carbon unite with 10 
 parts by weight of oxygen, therefore the formula of the com- 
 pound produced is CO. 
 
 1 Ann. Chim. Phys. 90. 43. 
 - Phil. Trans, for 1814, r et seq. 
 
 3 Wollaston appears to have first used this term in 1808 (Phil. 7'rans.). 
 
 4 See Cannizzaro, C. S. Journal [i], 10. 945.
 
 CHAP. I. 7] EQUIVALENTS. 15 
 
 But he might also have said 
 
 (0 375 parts by weight of carbon unite with 10 parts 
 by weight of oxygen, and the formula of the product is 
 CO ; and 
 
 (2) 7-5 of carbon unite with 10 of oxygen, therefore the 
 formula of the compound is C 2 O. 
 
 It seemed impossible to determine the equivalent weight 
 of carbon, just as in Dalton's system it was impossible to 
 determine the atomic weight of carbon 1 . 
 
 If the unit of equivalency is 8 parts by weight of oxygen, 
 what is the equivalent of copper ? An electric current is 
 passed through a voltameter and also through molten cuprous 
 chloride ; for every 8 parts by weight of oxygen set free 
 in the voltameter 63 '5 parts by weight of copper appear in 
 the second vessel : cupric chloride is substituted for cuprous 
 chloride, and now 3175 parts of copper are eliminated for 
 every 8 parts of oxygen. So in the compounds of copper 
 and oxygen, we have in one case 63-5 of copper combined 
 with 8 of oxygen, in the other 3175 of copper with 8 of 
 oxygen. 
 
 So long as the term equivalent was applied to acids and 
 bases, or to oxides, it had a definite meaning. The mass of 
 oxide which neutralised unit mass of standard acid was the 
 equivalent of that oxide, because it was equal, so far as 
 neutralising power went, to some other mass of another oxide. 
 
 " When we speak of the equivalent of a body," said Gerhardt, " we 
 should always indicate to what other body, to what functions, to what 
 properties, that equivalent corresponds." 2 
 
 Richter shewed that there is a constant relation between 
 the amount of oxygen in an oxide and the amount in the acid 
 which neutralises this oxide : e.g., in sulphuric acid, he said, 
 the oxygen is three times, and in nitric acid five times, that 
 in the oxide neutralised. This rule was made general. Now 
 
 1 Thus for iron we have the equivalents 28 and 18*6: for carbon, the 
 equivalents 3, 4, 8, and 12: for nitrogen, 4-6 and 2'^: for oxygen, 8 and 16 : 
 for silicon, 7 and 3-5, &c. c. Williamson, C. S. Journal, 22. 328. 
 
 1 Quoted by J. J. Griffin in The Radical Theory in Chemistry, p. 32.
 
 1 6 ATOMS AND MOLECULES. [BOOK I. 
 
 the equivalent of aluminium 1 was said to be 1375: the 
 formula of sodium sulphate, in accordance with Richter's rule, 
 was written NaO . SO g ; hence the formula of aluminium sul- 
 phate should have been written AUO . SO 3 (1375x1 = amount 
 of aluminium uniting with 8 parts by weight of oxygen) ; but 
 the formula was almost invariably written A1 2 O 3 . 3SO 3 , which 
 is a departure from a strictly equivalent notation. 
 
 Mohr (Meckanische Theorie der Chemischen Affinitaf), who 
 strongly upheld an -equivalent notation, admits (loc. cit. 
 pp. 143 144) that no equivalency exists between the oxides 
 RO and R 2 O 3 ; he also despairs of determining the equivalent 
 of phosphoric acid. Those quantities of two substances are 
 equivalent, according to Mohr, which by interaction with 
 other bodies produce similar compounds ; but he fails to 
 define 'similar compounds,' or rather he admits the im- 
 possibility of finding a definition. 
 
 That the masses of elements which mutually combine 
 do not always represent equivalent quantities of these ele- 
 ments was gradually discovered ; but the so-called equivalent 
 notation assumed that these masses do represent equivalent 
 quantities of the combining elements. 
 
 8 The systems of chemical notation founded respectively 
 on the atomic weights of Dalton and on the equivalents of 
 Wollaston continued to hold divided sway over the minds of 
 chemists 2 . A man of preeminent powers of classification was 
 required. 
 
 1 The reasons for adopting the number 1375 were somewhat as follows: 
 28 parts by weight of iron combine with 8 of oxygen, therefore the equivalent of 
 iron is 28; but in ferric chloride 28x2 parts by weight of iron are combined 
 with 35-5 x 3 parts by weight of chlorine (the equivalent of chlorine is 35-5, be- 
 cause this is the mass of that element which combines with unit mass of hydrogen). 
 Now aluminium chloride is very similar in properties to ferric chloride, therefore, 
 reasoning from analogy, this compound contains two equivalents of aluminium ; 
 but aluminium chloride is composed of the elements aluminium and chlorine com- 
 bined in the ratio 27-5 : (3 x 35-5), therefore tlie equivalent of aluminium is 
 
 a The student who wishes to pursue this subject -in greater detail may consult 
 any of the older text-books, on the laivs of combination and atomic weights, e.g. 
 Turner's Chemistry, pp. -212 235 ; he will thus become persuaded how impossible
 
 ( HAP. I. 8.] BEKZELIUS' ATOMIC WEIGHTS. "17 
 
 The system of chemical classification and notation elabo- 
 rated by Jacob Berzelius (1779 1848) was essentially electri- 
 cal. The dualism of the Berzelian school was the logical 
 development of the views of Lavoisier concerning salts, and of 
 the hypothesis of Davy regarding the relations between 
 electrical and chemical actions 1 . At present, however, this 
 part of the work of the great Swedish chemist does not 
 specially concern us. 
 
 Berzelius recognised the necessity of extending the general- 
 isations already made concerning the combinations of atoms. 
 To say that when two elements by combining together form 
 only one compound, that compound is composed of one 
 atom of each element, was, according to Berzelius, not fully 
 warranted by facts. 
 
 To discover the laws of atomic combinations was the task 
 that Berzelius proposed to himself. He argued that inasmuch 
 as the number of compounds formed by the mutual actions of 
 any two or three elements is evidently very limited, there 
 must be certain laws expressing the conditions under which 
 alone atoms combine. 
 
 Berzelius regarded Gay Lussac's law of gaseous combi- 
 nation 'equal volumes contain equal numbers of atoms' 
 as the most important of the generalisations made concerning 
 atomic combinations, but he restricted the application of this 
 law to elementary gases. He admitted that a compound gas 
 might be composed of half, or even less than half, as many 
 atoms as composed an equal volume of an elementary gas ; 
 he did not compare the atomic composition of elementary 
 and compound gases: he thus evaded the objections urged by 
 Dalton against the law of Gay Lussac, and at the same time 
 he declined to accept the statement of Avogadro, 'equal 
 volumes contain equal numbers of molecules.' 
 
 The ratios of the weights of the combining volumes of 
 
 it was to determine the values of atomic weights with certainty. Some interesting 
 points especially regarding the proposal to give two equivalents, or atomic 
 weights, to some of the elements will be found in Griffin's Radical Theory, 
 PP- 3043- 
 
 1 For a brief notice of the system of Berzelius regarding the constitution of 
 compounds see Chap. n. pp. 113116. 
 
 .M. C. 2
 
 1 8 ATOMS AND MOLECULES. [ROOK I. 
 
 elementary gases were regarded by Berzelius as representing 
 the ratios of the weights of the atoms of those elements ; 
 therefore to water, nitric oxide, and ammonia he gave the 
 formulae, H 2 O, NO, and NH 3 ; because two volumes of hydro- 
 gen unite with one volume of oxygen to form water, one 
 volume of nitrogen unites with one volume of oxygen to 
 form nitric oxide, and ammonia is produced by the union of 
 one volume of nitrogen with three volumes of hydrogen. 
 
 But the volumetric method was of limited application to 
 the problems of chemical synthesis. Berzelius attempted to 
 state general rules with regard to the combinations of atoms. 
 These rules referred chiefly to the compounds of oxygen, 
 compounds which played so important a part in the mineral 
 chemistry wherewith Berzelius largely concerned himself. The 
 most important of the Berzelian rules were three. 
 
 I. If an element forms two oxides with twice as much 
 
 oxygen by weight in one as in the other, that with 
 the smaller mass of oxygen is to be represented 
 as a compound of one atom of element united with 
 one atom of oxygen, and that with the larger 
 mass of oxygen as a compound of one atom of 
 element with two atoms of oxygen. 
 
 II. If an element forms two oxides, one of which con- 
 
 tains one and a half times as much oxygen by 
 weight as the other, that with the less oxygen is 
 to be represented as composed of one atom of 
 element and one atom of oxygen, and the other 
 compound as formed by the union of two atoms 
 of element with three atoms of oxygen. 
 
 III. The mass of oxygen in an acid is a simple multiple 
 
 of the mass of oxygen in any base with which the 
 acid combines 1 , and this multiple generally also 
 expresses the number of atoms of oxygen in the 
 acid : thus in the case of sulphuric acid and 
 potash, an amount of acid containing 24 parts 
 by weight of oxygen neutralises that amount of 
 
 1 This had been stated by Richter many years before Berzelius: see ante p. 15.
 
 CHAP. I. 8-9] BERZELIUS' ATOMIC WEIGHTS. 19 
 
 potash which contains 8 parts by weight of oxygen, 
 therefore, by the Berzelian rule, there are three 
 atoms of oxygen in one atom of sulphuric acid. 
 When nitric acid neutralises potash there are 40 
 parts by weight of oxygen in the acid for every 8 
 parts in the base ; therefore an atom of nitric acid 
 contains five atoms of oxygen. 
 
 By the use of these rules Berzelius determined the for- 
 mulae of many metallic oxides and salts. While he was thus 
 engaged, Dulong and Petit 1 announced their ' law of atomic 
 heats' ; and shortly afterwards Mitscherlich 2 made known his 
 ' law of isomorphism.' 
 
 Berzelius adopted both laws, and by their help 3 , along 
 with his own rules, he drew up a table of atomic weights 
 which in very many cases were almost identical with those 
 now in general use. 
 
 TABLE OF ATOMIC WEIGHTS. (Berzelius*.') 
 
 Arsenic 75'33 Manganese S7' 2 Silver 2i6 - 6i 
 
 Calcium 41-03 Sodium 46-62 Silicon 44'47 
 
 Chlorine 35'47 Phosphorus 31 '43 Nitrogen 14-18 
 
 Iron 54'36 Mercury 202*86 
 
 Iodine 123*2 Oxygen i6'oo Hydrogen = I. 
 
 Carbon 12*25 Sulphur 32*24 
 
 Berzelius himself admits that the atomic weights deter- 
 mined by his rules are in many cases open to doubt (Lehrbuch, 
 1st edition, vol. ill. part i. pp. 87 102). Berzelius had a 
 remarkable amount of tact ; his rules were empirical, but he 
 balanced probabilities so well that he generally got the best 
 possible result. 
 
 9 The separation which Berzelius made between the for- 
 mulae of elementary and compound bodies, and his refusal 
 
 > See p. 49 . 
 
 8 See pp. 6976. 
 
 s Berzelius formulated the law of isomorphism in its bearing on the problem of 
 determining atomic weights thus ; (Lehrbuch, 3rd ed., vol. I. p. 98) when one body 
 is isomorphous with another the number of atoms in which is known, then the 
 number of atoms in the other is known also, because isomorphism is a mechanical 
 consequence of identity of atomic structure. 
 
 4 Jahresberichte, 1828. 73. 
 
 2 2
 
 -:20 ATOMS AND MOLECULES. [BOOK I 
 
 to accept Avogadro's hypothesis while admitting Gay Lussac's 
 "generalisation, led him to a very curious result. 
 
 Two volumes of hydrogen, weighing 2, combine with one 
 volume of oxygen, weighing 16, to form two volumes of 
 water-gas. Therefore, said Berzelius, two atoms of hydrogen 
 combine with one atom of oxygen to form one atom of water- 
 gas. But water contains less oxygen, relatively to hydrogen, 
 than any other known oxide of hydrogen, therefore it is 
 better to regard it as a compound of one atom of oxygen 
 with one double atom, or with one atom itself composed of two 
 equivalents, of hydrogen. Again, in the formation of the 
 lowest oxide of nitrogen two volumes of nitrogen combine 
 with one of oxygen ; but it is better to regard the nitrogen 
 as composed of double atoms each occupying twice the 
 volume of the atom of oxygen. Once more; hydrogen and 
 chlorine combine in equal volumes, and the volume of the 
 product hydrochloric acid is equal to the sum of the 
 volumes of its constituents ; but as the hydrogen atom was 
 regarded by Berzelius as double, he wrote the atomic syn- 
 thesis of hydrochloric acid as 
 
 H 2 + C1 2 = H 2 CI 2 . 
 2 vols. 2 vols. 4 vols. 
 
 These results are evidently to be traced to the failure of 
 Berzelius clearly to distinguish atom from equivalent, and to 
 his refusal fully to accept the distinction between atom and 
 molecule enunciated by Avogadro 1 . 
 
 To the great French chemists, Dumas, Gerhardt and 
 Laurent, is chiefly due the introduction into general use of 
 a system of notation and classification founded on Avogadro's 
 distinction between atoms and molecules. 
 10 Dumas early accepted Avogadro's hypothesis ; from the 
 specific gravities of gases he deduced the relative weights of 
 the molecules of these gases : in order to gain more informa- 
 tion regarding molecular weights he introduced a new method 
 for finding the specific gravities of gases. By this method he 
 
 1 For a more detailed account of the work of Berzelius on atomic weights see 
 Ladenburg's Entwickelnngsgeschiihtc d?r Chetnic, pp. 89 100.
 
 CIIAI'. I. 10] WORK OF GERHARDT AND LAURENT. 21 
 
 determined the molecular weight of sulphur to be 96, and 
 that of phosphorus to be 1 24 ; but from the analogy of 
 sulphur compounds with those of oxygen, from various 
 chemical considerations regarding phosphorus compounds, 
 and, I think we must add, from not keeping Avogadro's 
 statement quite distinct from that of Gay Lussac, Dumas 
 convinced himself that these results were incorrect. The 
 molecular weight of mercury also seemed to be abnormal. 
 Dumas knew of exceptions to the law of Dulong and Petit. 
 Mitscherlich's law of isomorphism remained ; but Mitscherlich 
 had himself shewn that the same compound might assume 
 more than one crystalline form ; how then could trustworthy 
 conclusions regarding atomic structure be deduced from so 
 vague a law ? Dumas, and indeed chemists generally, began 
 to despair of the whole theory of atoms ; they tried to find 
 relief in equivalents, so called, and in spite of the many 
 difficulties they gradually tended towards an equivalent 
 notation, a notation which nevertheless they could not make 
 thoroughly self-consistent, but which seemed to involve fewer 
 hypotheses than that founded on the theory of atoms 1 . 
 
 L. Gmelin even regarded the law of fixity of composition 
 as only true under special conditions. When the affinity 
 between two bodies is small, they may be united, said Gmelin, 
 in almost any proportions, when the affinity is large they 
 tend to combine in fixed proportions. A number may be 
 given to each element representing the relative amount of 
 that element which combines with other elements to form 
 stable and well-marked compounds; this 'combining weight' 
 may be called ' atomic weight,' but it is only a number. 
 Gmelin adopted 8 as the combining weight of oxygen, 6 as 
 that of carbon &c.: the formula of water on his system again 
 became HO. 
 
 The notation used by Gmelin was at best a compromise, 
 and unsatisfactory, but it was very generally adopted for many 
 years. 
 
 Inorganic chemistry had failed to introduce an accurate 
 
 1 For a general account of Dumas' influence on chemical theories see his 
 Lt'.'0>is stir la Philosophic Chiiniqiie, republished in 1878.
 
 22 ATOMS AND MOLECULES. [BOOK I. 
 
 and satisfactory theory of chemical structure; it was now the 
 turn of organic chemistry to attempt the task. 
 11 Among the most ardent followers of the new chemistry 
 introduced by Dumas, were two men whose names are ever to 
 be associated as those of a brilliant pair of students of nature 
 who died all too early for the work which seemed given them 
 to do. Gerhardt and Laurent occupy a prominent place 
 among the modern reformers of chemistry; they introduced 
 order into chemical notation, and system, where system had 
 been conspicuous by its absence 1 . 
 
 In criticising the system of so-called equivalent weights 
 Gerhardt adopted the only true method; he studied actually 
 occurring chemical reactions. 
 
 In a number of reactions between compounds of carbon 
 in which carbon dioxide, water, and ammonia were produced, 
 Gerhardt 2 found that when so-called equivalent weights of 
 the reacting bodies were employed, the smallest quantities of 
 these three compounds produced were always those repre- 
 sented by the formulae C 2 O 4 , H 2 O 2 , and NH 3 , respectively 
 (C = 6, N = 14, O = 8). He therefore concluded that these 
 formulae, rather than the commonly accepted formulae, CO 2 , 
 HO (and NH 8 ), must represent equivalent weights of the 
 compounds in question. Similarly he concluded that the 
 equivalent formulae of sulphur dioxide and carbon monoxide 
 must be S 2 O 4 and C 2 O 2 respectively (S=i6, O = 8, C = 6): 
 and arguing from these conclusions he thought himself 
 justified in saying that the true equivalents of carbon, sulphur, 
 and oxygen, are 12, 32, and 16, and not 6, 16, and 8, as 
 generally adopted. Gerhardt likewise applied his acute 
 reasoning powers to an examination of the arguments which 
 determined Berzelius and others to adopt formulae represent- 
 ing weights of four volumes of many carbon compounds ; 
 these arguments he proved to be fallacious. 
 
 Laurent examined the groundwork on which the systems 
 
 1 Laurent's Chemical Method (Cavendish Society Publications) gives a general 
 account of the more important work of these chemists. 
 
 2 J- fur prakt. Chemie, 27. 439; and Ann. Chim. Phys. [3] 7. 129: and 8.
 
 CHAP. i. 1 1] LAURENT'S NOTATION. 23 
 
 of equivalent and atomic notation were based. His methods 
 of reasoning were founded on experimentally determined 
 facts, hence their irresistible force. If formulae are to re- 
 present equivalent masses of substances, then said Laurent, 
 a standard must be adopted. But it had been frequently 
 shewn that the quantities represented by so-called combin- 
 ing weights were not always mutually equivalent. Power of 
 neutralising unit mass of standard substance might be adopted 
 as the reaction on which to base the system, but this method 
 could be applied only to a limited number of substances. 
 
 The idea of equivalency is associated with function. What 
 is a given substance capable of doing?: this question must 
 be answered before the equivalent of the substance can be 
 determined. But in one action certain weights of two bodies 
 may be equivalent, while altogether different weights of the 
 same bodies are equivalent in another reaction. 
 
 Laurent affirmed that it was possible to found a systematic 
 notation on equivalent weights assigned to the elements. 
 Thus, in ferrous oxide 28 parts by weight of iron are combined 
 with 8 parts by weight of oxygen; let Fe = 28, then ferrous 
 sulphate is represented by the formula Fe 2 SO 4 : but in ferric 
 oxide there are 2.^ (i.e. i8'6) parts by weight of iron for 
 every 8 parts by weight of oxygen ; let fe = 1 8'6, then the 
 formula for ferric sulphate is fe 2 SO 4 . The formulae Fe 2 SO 4 
 and fe 2 SO 4 represent strictly equivalent quantities of the two 
 sulphates of iron. So also if the composition of potassium- 
 hydrogen sulphate is expressed by the formula KHSO 4 , then, 
 in a system of notation founded on equivalent weights, the 
 composition of the double sulphate of potassium and alu- 
 minium is represented by the formula K^A1|SO 4 (Al = 27'3). 
 But such a notation is inconvenient, and it frequently conceals 
 most important facts: e.g. in a strictly equivalent notation 
 the differences between monobasic and polybasic acids dis- 
 appear ; thus, the compositions of the masses of monobasic 
 hydrochloric acid, dibasic sulphuric acid, and tribasic phos- 
 phoric acid, which severally neutralise equal masses of potash, 
 are expressed by the formulae HC1, HS^O,, and HP^^. re- 
 spectively (Cl = 35-5, S = 32, O = 16, P = 31).
 
 24. ATOMS AND MOLECULES. [BOOK I. 
 
 Laurent returned to the generalisation of Avogadro and 
 made that the basis of his system; he clearly distinguished 
 between molecules and atoms, and he applied the law of equal 
 volumes and equal numbers to molecules only. He admitted 
 that apparent exceptions to the Avogadrean law existed, 
 e.g. the molecules of sulphuric acid and salammoniac vapour 
 appeared to occupy twice the volume occupied by the mole- 
 cule of hydrogen; but he said that this hypothesis gene- 
 ralised the facts better than any other which had been pro- 
 posed. 
 
 Laurent founded his system on an atomic basis, and a 
 fundamental point was the distinction between atom and 
 molecule. He adopted formulae representing two volumes: 
 the facts of 'nascent' action he sought to explain by the con- 
 ception of atoms as distinct from molecules. A molecule he 
 defined to be "the amount of a gaseous substance which 
 occupies twice the volume occupied by an atom of hydro- 
 gen," or, "the smallest amount of a substance capable of 
 taking part in a chemical reaction." An atom he defined as 
 "the smallest amount of an element which enters into the 
 composition of a compound." Here we have the application 
 of the term molecule to elements and compounds alike, while 
 atom is used of elements only. 
 
 Equivalents are the amounts of bodies which are of equal 
 value in performing a stated action. 
 
 Gerhardt and Laurent adopted the laws of atomic heat 
 and isomorphism as aids in determinations of atomic weights. 
 12 Chemical evidence in favour of the division of elementary 
 molecules during chemical changes was accumulated by 
 Brodie, Wurtz, Williamson and others; but the work of these 
 chemists will be referred to in more detail when we come to 
 speak of the chemical methods for determining molecular 
 weights (see pp. 7985). 
 
 Thus, at last, we have arrived at a clear separation between 
 the meanings of the terms atom, molecule, equivalent. 
 
 The system now adopted in chemistry is essentially that 
 of Gerhardt and Laurent; it is founded on the conception of 
 atoms and molecules. Dalton's fundamental idea has been
 
 CHAP. I. 12-13] MOLECULAR THEORY OF MATTER. 2$ 
 
 amply confirmed by modern research. We have maintained 
 the idea of equivalency, but we no longer speak, as Wollaston 
 did, of the equivalent of an element ; we compare the 
 elementary atoms among themselves and arrange them in 
 groups, all the members of each of which are equivalent in 
 respect of a certain definite action they are capable of per- 
 forming. 
 
 A true and fundamental conception once gained in science 
 is never lost; it may be largely modified, it may even appear 
 at times to be abandoned, but it develops slowly and bears 
 much fruit at last. 
 
 The vicissitudes in the fortunes of a truly scientific idea are 
 aptly illustrated by the history of the atomic theory. After a 
 period of dormancy of more than 2000 years, the atomic 
 theory was revived and rendered definite by Dalton; was 
 firmly established on an experimental basis by Berzelius; was 
 almost abandoned by the school founded by the same 
 chemist; was rehabilitated and again nearly despaired of by 
 Dumas; was largely advanced by Avogadro; was subdivided 
 and its parts clearly distinguished by Gerhardt and Laurent, 
 and is now the foundation-stone of a great and ever-increasing 
 edifice. 
 
 13 Thus far I have dealt with the development of the atomic 
 and molecular theory regarded almost entirely from the 
 chemical point of view. So great however is the importance 
 of clearly perceiving the position which this theory occupies 
 in modern chemistry, and of realising the nature of the 
 physical evidence on which, in its more recent development, 
 the theory so largely rests, that I must endeavour very briefly 
 to give a sketch of that evidence, remembering always that 
 it is as chemists, not as physicists, that we are interested in 
 this subject. 
 
 There are two general theories of the structure of material 
 substances: one assumes that apparently homogeneous bodies 
 are really homogeneous throughout ; a theory which is in- 
 capable of explaining the observed properties of matter ; 
 and the other asserts that apparently homogeneous bodies 
 are possessed of a grained structure.
 
 26 ATOMS AND MOLECULES. [BOOK I. 
 
 Viewed from a distance, a brick wall, or a body of soldiers, 
 appears to be one reddish-coloured homogeneous mass, but a 
 nearer observer sees that the wall is made up of distinct parts, 
 that the company is composed of individual men. 
 
 The molecular theory supposes that were our senses 
 sufficiently acute, we should see the grains or particles of 
 which an apparently homogeneous mass of matter is com- 
 posed. 
 
 The theory begins by assuming that any material body 
 "is made up of parts (each of which is capable of motion), 
 and that these parts act on each other in a manner consistent 
 with the principle of the conservation of energy." 1 These 
 parts are called molecules. 
 
 The dynamical conception of a gaseous molecule is " That 
 minute portion of a substance which moves about as a whole, so 
 that its parts, if it has any, do not part company during the 
 motion of agitation of the gas?* 
 
 This conception is entirely independent of chemical facts. 
 
 All the molecules of one element are of the same mass, 
 else differences would be observed in the properties of different 
 parts of an elementary gas, e.g. hydrogen ;' such differences 
 arising from the separation of the gas into portions each more 
 or less unlike the others. 
 
 The relations between the motions and the space occupied 
 by these little parts, assuming their existence and mutual 
 independence, may be dynamically deduced by the aid of a 
 theorem of Clausius, and, with a justifiable assumption as to the 
 dynamical meaning of temperature, the equation thus arrived 
 at expresses with considerable accuracy the relations actually 
 existing between temperature and pressure, and volume, in the 
 case of rarefied gases ; the equation, that is to say, expresses 
 the laws of Charles and Boyle. When the gas is more 
 condensed the equation ceases to express the relations 
 existing between temperature and pressure, and volume : 
 hence the theory asserts the existence in such a gas of mutual 
 attractions or repulsions between the little parts, or mole- 
 
 1 Clerk Maxwell, Article 'Atom' In Encycl, firilannica. (Qth Ed.) 
 IbiJ.
 
 CHAP. I. 13] MOLECULAR THEORY OF MATTER. 2/ 
 
 cules ; it asserts that these parts are no longer mutually 
 independent. 
 
 "The hypothesis that a gas consists of molecules in motion, which 
 act on each other only when they come together during an encounter, 
 but which during the intervals between their encounters which con- 
 stitute the greater part of their existence are describing free paths, and 
 ;ire not acted on by any molecular forces," 1 
 
 having been justified by dynamical reasoning, the next step 
 is made by investigating mathematically the properties of 
 such a system of molecules. And one deduction thus made 
 is " If equal volumes of two gases are at equal temperatures and 
 pressures, tlie number of molecules in each is the same, and 
 therefore the masses of the two kinds of molecules are in the 
 same ratio as the densities of the gases to wJiich they belong."* 
 
 This statement is of paramount importance to the chemist, 
 inasmuch as on it is based his system of molecular weights. 
 It is very necessary to bear in mind that this proposition is 
 deduced by dynamical reasoning from a simple hypothesis as 
 to the structure of matter, itself justified by many facts. 
 
 By analogous reasoning, various deductions are made 
 from the theory, which express generalisations of experi- 
 mentally determined facts concerning gaseous phenomena 3 . 
 
 Passing to more complex occurrences, the molecular theory 
 gives a simple explanation of the diffusion of matter, diffusion 
 of motion, and diffusion of heat in gases ; these phenomena 
 being regarded by the theory as dependent on the frequency 
 of the molecular encounters, and on the nature of the actions 
 between the encountering molecules. 
 
 The molecular theory has also been successfully applied 
 to explain, broadly, many of the phenomena of evaporation, 
 condensation, electrolysis, and spectroscopy. 
 
 To explain spectroscopic phenomena it is apparently 
 necessary to assume molecules to be elastic substances, but 
 elasticity is just the property of matter to explain which the 
 
 1 Clerk Maxwell, Article 'Atom' in Encycl. Brit. 
 
 - Ibid. Strictly speaking this statement applies only to perfett gases, i.e. gases 
 the molecules of which are without action on each other. 
 
 3 For some of the most important of these see Clerk Maxwell's Theory of 
 Heat, pp. 307 322 (6th edition).
 
 28 ATOMS AND MOLECULES. [BOOK I. 
 
 molecular hypothesis was first assumed. The theory of 
 ' vortex atoms/ developed by Sir William Thomson from the 
 original conception of Helmholtz, explains spectroscopic 
 facts and generally those facts which must be explained by 
 a successful molecular theory better than any other which 
 has yet been suggested. A short account of this theory will 
 be found in the article 'Atom' in the last edition of the 
 Encyclopedia Britannica, where we read 
 
 " The success of this theory in explaining phenomena does not depend 
 on the ingenuity with which its contrivers 'save appearances' by intro- 
 ducing first one hypothetical force and then another. When the vortex 
 atom is once set in motion all its properties are absolutely fixed, and 
 determined by the laws of motion of the primitive fluid which are fully 
 expressed in the fundamental equation." 1 
 
 Attempts have been made to determine the absolute size 
 of molecules 2 , and although the results must be regarded as 
 but rough estimates, nevertheless they shew that to measure 
 molecules is a legitimate object of scientific investigation. 
 The smallest portion of matter visible by the help of a good 
 microscope may be taken to be a cube each side of which 
 measures 4^-^th of a millimetre in length ; such a cube will 
 contain, according to the rough measurements hitherto 
 made, from 60 to 100 millions of molecules 3 . 
 
 The foundations of a truly mathematical theory of the 
 structure of matter have been laid by Helmholtz and Thom- 
 son in their theory of vortex atoms ; but, apart from this, the 
 fact that the proposition commonly known as Avogadro's 
 law may be deduced by dynamical reasoning from a simple 
 hypothesis which admits, although as yet only to a limited 
 extent, of the application of mathematical methods, and 
 which is justified by a large number of physical facts, suffices 
 to make that law of extreme importance. 
 
 Attempts have recently been made to apply to certain- 
 chemical phenomena a more strictly dynamical method of 
 
 1 For a few more details regarding the application of this theory to chemical 
 occurrences see Book II. Chap. in. 
 
 2 See especially Sir W. Thomson, Nature 1. p. 551, and also 28. pp. 203, 
 1 so, 274. 
 
 3 Clerk Maxwell, Ice. cit.
 
 CUAP.I. 13-14] PARTS OF MOLECULES. 29 
 
 reasoning than is employed in the molecular theory, the 
 methods of which are essentially statistical ; these will be 
 referred to under the second main division of this book. 
 
 An atomic theory has been elaborated by the chemist ; a 
 molecular theory of matter has been propounded by the 
 physicist, and has been advanced so far as to allow of wide 
 conclusions being deduced therefrom by dynamical reasoning ; 
 no theory asserting the continuity of matter has been found 
 capable of explaining the observed phenomena of matter ; 
 hence to accept the molecular theory, as, at present, the only 
 feasible working hypothesis, is simply to obey the dictates of 
 the scientific method. 
 
 14 Let us then turn to the applications of this theory to che- 
 mical facts. It is well to repeat the terms in which Clerk 
 Maxwell has expressed the physical conception of the mole- 
 cule : " A gaseous molecule is that minute portion of a sub- 
 stance which moves about as a w]iole, so that its parts, if it has 
 any, do not part company during the motion of agitation of the 
 gas." One of the deductions from this conception is that 
 equal volumes, of so-called perfect gases, measured at the same 
 temperature and pressure, contain equal numbers of molecules. 
 
 This statement must now be applied to chemical interac- 
 tions between gases. 
 
 Consider, for instance, the combination of hydrogen with 
 chlorine and that of nitrogen with hydrogen. 
 
 Hydrogen combines with chlorine to form hydrochloric acid. 
 2 vols. combine with 2 vols. 4 vols. 
 
 But since equal volumes of gases contain equal numbers 
 of molecules, and since each molecule of hydrochloric acid is 
 composed of both hydrogen and chlorine, it is evident that 
 each molecule of hydrogen by combination with one molecule 
 of chlorine produces not one but two molecules of hydrochloric 
 acid. 
 
 So again, 
 
 Nitrogen combines with hydrogen to form ammonia. 
 2 vols. combine with 6 vols. 4 vols. 
 
 Here again each nitrogen molecule has given rise to two
 
 30 ATOMS AND MOLECULES. [BOOK I. 
 
 molecules of ammonia. Hence it is evident that although the 
 parts of a molecule of hydrogen, nitrogen, or chlorine " do not 
 part company during the motion of agitation of the gas " to 
 which the molecule belongs, these parts nevertheless do part 
 company in those chemical reactions which are stated above. 
 When various reactions between gaseous substances are 
 studied this conclusion is found to hold good throughout 
 a large range of chemical phenomena. Hence the chemist 
 is obliged to recognise a portion of matter smaller than 
 the molecule ; this smaller portion of matter, this part of 
 a molecule, is the atom 1 . 
 
 In the above and in other reactions it is shewn that the 
 molecules of hydrogen, nitrogen, and chlorine split into at least 
 two parts when these molecules act chemically on each other 
 or on other molecules ; hence, if the symbols H, Cl, and N, are 
 used to denote an atom of hydrogen, chlorine, and nitrogen, 
 respectively, the molecules of these three elements may be 
 represented by the symbols H 2 , C1 2 , and N 2 . These symbols 
 represent the masses of equal volumes of the three elements ; if 
 one of these masses be taken as the unit, the others are 
 evidently the masses of the molecules of the gases in question 
 referred to this unit ; because equal volumes contain equal 
 numbers of molecules, and therefore ' the masses of the two 
 kinds of molecules are in the same ratio as the densities of the 
 gases to which they belong.' 
 
 Hydrogen is the universally adopted standard of reference 
 for molecular and atomic weights : the atomic weight of 
 hydrogen is taken as unity, and therefore, according to the 
 reasoning sketched above, the molecular weight of this element 
 is not less than two. 
 
 But it might be urged that when molecules of hydrogen 
 and chlorine interact, each molecule separates into more than 
 two parts, into 3, 4, 5, &c. parts. Granting ' Avogadro's law,' 
 the data given on p. 29 shew that the number of molecules of 
 
 1 It is well to note that the molecular theory of matter as applied to chemical 
 phenomena does not assert or deny the finite divisibility of matter. In C. S. 
 Journal [2], 13. 501, there is a most interesting paper by Clerk Maxwell on ' The 
 dynamical evidence of the molecular constitution of bodies.'
 
 CHAP. I. 14] PARTS OF MOLECULES. 31 
 
 hydrochloric acid produced is twice the number of molecules 
 of hydrogen or chlorine which have interacted to produce 
 them ; therefore, if each molecule of hydrogen and each of 
 chlorine has separated into, say, four parts, each molecule of 
 hydrochloric acid must be composed of two of those parts of 
 hydrogen and two of chlorine. But if this is so, it ought to 
 be possible to remove the hydrogen, or the chlorine, from a 
 molecule of hydrochloric acid in two separate portions ; in 
 other words, interactions ought to occur between hydrochloric 
 acid and other bodies, not themselves compounds of hydrogen 
 or chlorine, resulting in the evolution of hydrogen, or chlorine, 
 and the production of a new compound, or new compounds, of 
 chlorine, hydrogen, and the interacting body or constituents 
 of this body. But no such interactions occur ; therefore hydro- 
 gen, or chlorine, cannot be removed in parts from a molecule 
 of hydrochloric acid ; if the molecule is decomposed and 
 hydrogen, or chlorine, is removed, the whole of the hydrogen, 
 or chlorine, is removed. Therefore it is extremely improbable 
 that a molecule of hydrochloric acid is built up of more than 
 one small chemically indivisible part, or atom, of each of the 
 elements which compose it ; and therefore it is extremely im- 
 probable that when molecules of hydrogen and chlorine 
 interact to produce molecules of hydrochloric acid, each mole- 
 cule of hydrogen, or chlorine, separates into more than two 
 parts or atoms. Therefore, as we have agreed to regard the 
 weight of an atom of hydrogen as unity, we say that the 
 molecular weight of hydrogen is two. 
 
 The modern molecular theory of matter is not identical 
 with the atomic theory of Dalton ; it is based on evidence of 
 a different kind ; it is essentially a physical and dynamical 
 theory, although strengthened by chemical arguments. The 
 atomic theory of modern chemistry may be regarded as grow- 
 ing out of the application of reasoning founded on chemical 
 facts to the molecular theory of matter. 
 
 Assuming 'Avogadro's law,' and remembering that the 
 molecule of hydrogen, which is the standard body in terms of 
 which all other molecular weights are stated, divides into at 
 least two, and probably into only two, parts in many chemical
 
 32 ATOMS AND MOLECULES. [BOOK I. 
 
 changes, we arrive at the practical definition of molecular 
 weight. 
 
 The molecular weight of a gas is the weight of that volume 
 thereof which is equal to the volume occupied at the same tem- 
 perature and pressure by two parts by weight of hydrogen^. 
 
 In determining the specific gravity of a gas it is easier, 
 and less liable to error, to find the weight of the vessel filled 
 with air than with hydrogen ; the result is therefore stated as 
 specific gravity referred to air as unity. Now the specific 
 gravity of hydrogen is -06926 [air= i]; the molecular weight 
 required is equal to twice the specific gravity of the gas 
 referred to hydrogen ; hence if M= molecular weight, and 
 
 d specific gravity referred to air as unity, M=^ ^=28*87 d. 
 
 Hence the practical rule for determining the molecular weight 
 of a gas : 
 
 Find tJie specific gravity, i.e. the ratio between the weights 
 of equal volumes of the gas and air under the same conditions 
 of temperature and pressure, and multiply this by 28-87. 
 15 The following table presents the results hitherto obtained 
 regarding the molecular weights of elementary gases. 
 
 1 The volume occupied by two parts by weight of hydrogen, or twice the 
 volume occupied by unit mass of hydrogen, is often called two volumes.
 
 CHAP. I. 15] MOLECULAR WEIGHTS OF ELEMENTS. 
 
 33 
 
 [The numbers in column v are not always exactly equal to the products 
 
 obtained in column IV ; for an explanation see par. 17.] 
 
 Molecular weights of elementary Gases. 
 
 I 
 
 Name of element 
 
 II 
 
 Spec, gravity 
 (air=i) 
 
 III 
 
 Temp, of 
 observation 
 
 IV 
 
 Sp. gr. 
 
 X28-8; 
 
 V 
 
 Molecular 
 weight 
 
 1 Hydrogen 
 
 06926 
 
 
 
 ,, 
 
 2 
 
 2 Sodium 
 
 8 7 
 
 1200 1500 
 
 25-5 
 
 23 
 
 3 Nitrogen 
 
 0-9713 
 
 
 
 28-04 
 
 28-02 
 
 4 Oxygen 
 
 rio6 
 1-10563 
 
 about 1400 
 
 
 
 31-94 \ 
 31-92 J 
 
 31-92 
 
 _ (ozone) 
 
 1-658 
 
 
 
 47-86 
 
 . 47-88 
 
 7 Potassium 
 
 i'3 
 
 1200 1500 
 
 377 
 
 39^4 
 
 8 Sulphur 
 
 2-23 
 
 860 
 
 64-4 ) 
 
 
 J) 
 
 2-24 
 
 1040 
 
 64-6 
 
 63-96 
 
 10 
 
 2-17 
 
 about 1400 
 
 62-6 ) 
 
 
 11 
 
 2-93 
 
 665 
 
 84-6 
 
 p 
 
 12 
 
 6-62 
 
 524 
 
 191-1 
 
 191-88 
 
 13 Zinc 
 
 2-38 
 
 about 1400 
 
 68-7 
 
 64-9 
 
 14 Chlorine 
 
 2-45 
 
 200 
 
 7073 ) 
 
 
 15 
 
 2'6l 
 
 about 1000 
 
 75*35 
 
 7074 
 
 10 
 
 2-44 
 
 about 1200 
 
 7072 j 
 
 
 17 Cadmium 
 
 3-94 
 
 about 1000 
 
 113-7 
 
 112*1 
 
 18 Phosphorus 
 
 1!) 
 
 4-35 
 4-50 
 
 about 1000 
 
 125-6 ) 
 129-9 J 
 
 I23-84 
 
 20 
 
 3-03 
 
 1430 
 
 87-5 
 
 p 6 1*92] 
 
 21 Arsenic 
 
 22 
 
 IO"2 
 IO-65 
 
 860 
 644-- 668 
 
 294-5 \ 
 307-4 } 
 
 299-6 
 
 23 
 
 6-53 1430 
 
 188-5 
 
 [? 149-8] 
 
 24 Bromine 
 
 5'54 
 
 100 
 
 1 59-9 / 
 
 
 25 
 
 
 100 
 
 I55'3 i 
 
 r 59"5 
 
 26 
 
 4'43 
 
 about 1500 
 
 117-9 
 
 ? 
 
 27 Selenion 
 
 5-68 
 
 about 1400 
 
 161*1 
 
 157-6 
 
 28 
 
 6-37 
 
 about 1000 
 
 183-9 
 
 p 
 
 29 
 
 7-67 
 
 860 
 
 221-4 
 
 236-4 
 
 30 Mercury 
 
 6-96 
 
 about 1000 
 
 200-93 j 
 
 
 31 
 
 32 I 
 
 6-98 
 7-03 
 
 446" 
 424 
 
 201-5 I 
 203-0 [ 
 
 199-8 
 
 33 
 
 67 
 
 882 
 
 I93-4 J 
 
 
 34 Iodine 
 
 8-8 
 
 250 450 
 
 254-0 S 
 
 
 35 
 
 872 
 
 185 
 
 2517 
 
 
 37 
 
 8-70 
 8-72 
 
 447 
 about 1000 
 
 251-2 
 251-7 
 
 253-07 
 
 38 
 39 
 
 5) 
 
 8-84 
 8-55 
 
 250 
 665 
 
 255-2 
 246-8 j 
 
 
 40 
 
 5-87 
 
 about 1 1 00 
 
 169-4 
 
 ? 
 
 41 
 
 42 Tellurium 
 
 476 
 9-08 
 
 about 1500 
 about 1400 
 
 262*1 
 
 [? 126-53] 
 255 
 
 1 REGNAULT, Compt. rend. 20. 975. 2 SCOTT, Proc. R. S. E. 1888. 
 
 3 REGNAULT, loc. cit. 4 V. MEYER, Ber. 12. 1426. 5 REGNAULT, loc. cit. 
 
 M. C. 3
 
 34 ATOMS AND MOLECULES. [P.OOK I. 
 
 Mensching and Meyer (Annalen, 240. 317) have obtained values for 
 the specific gravity of antimony gas which shew that at 1400 1500 
 the molecular weight of this element is less than Sb 4 . 
 
 16 So many determinations of molecular weights of com- 
 pound gases have been made that an enumeration of all the 
 results would be perplexing, and of no special value. The 
 method is applicable to elements and compounds alike. The 
 following numbers are given here as they illustrate a point of 
 general importance. 
 
 Specific gravities of certain compound gases. 
 
 fSp. gr. 5-08 4'QQ 4'3 3'6o 3-66 
 Phosphorus pcntachlonde...-L F 
 
 \Temp. 180 190 230 290 335 
 
 fSp. err. 2'8 2-4 2-03 1-83 i - 5 
 N,,rogen,e,rox,dc ............ 
 
 Nitric oxide ..................... &. gr. ,'039 ,-039 
 
 [Temp. -70 1 6 
 
 fSp. gr. 13-8 1378 
 
 Arsemous oxide ............... I-.-- 
 
 [Temp. 570 1400 
 
 From these numbers, and from those of the previous table, 
 it is apparent that the specific gravities of certain elementary 
 and compound gases decrease as the temperature increases, 
 
 6 SORET, Compt. rend. 61. 941 ; and 64. 904. 7 SCOTT, Proc. R. S. E. 1888. 
 
 s and 9 DEVILLE and TROOST, Compt. rend. 56. 891. 10 V. MEYER, Ber. 12. 
 
 r 1 12. n TROOST, Compt. rend. 95. 30. 12 DUMAS, Ann. Chim. 
 
 Phys. (2) 50. 170. 13 MENSCHING and MEYER, Ber. 19. 3295. 14 LUD- 
 
 WIG, Ber. 1. 232. 15 V. MEYER, Ber. 13. 400. 16 Id. do. 15. 2773 
 
 (mean of 5 experiments). 17 DEVILLE and TROOST, Compt. rend. 49. 239. 
 
 is nd w /,/_ fa 56> 891. 20 MENSCHING and MEYER, Annalen, 240. 317. 
 
 21 D. and T. loc. cit. ** MITSCHERLICH, Annalen, 12. 159. 23 MEN- 
 
 SCHING and MEYER, Annalen, 240. 317. 24 MITSCHERLICH, loc. cit. 
 
 25 V. MEYER, Ber. 13. 406. 26 CRAFTS, Compt. rend. 90. 183. - 1 - " 8and w DE- 
 VILLE and TROOST, loc. cit. 30 V. MEYER, Ber. 13. 1107 and mo (mean 
 
 of 6 experiments). 31 DUMAS, Ann. Chim. Phys. (2) 33. 337. 32 MIT- 
 
 SCHERLICH, loc. cit. 33 BINEAU, Compt. rend. 49. 799. 34 V. MEYER, 
 
 and MEIER and CRAFTS, Ber. 13. 868 (mean of 7 experiments). 35 DUMAS, 
 
 loc. cit. 36nd37 DEVILLE and TROOST, loc. cit. 38 V. MEYER, Ber. 
 
 13. 396. 39 TROOST, Compt. rend. 95. 30. 40 V. MEYER, Ber. 13. 1115. 
 
 41 Id. do. 13. to 10. 42 DEVILLE and TROOST, loc. cit. 
 
 Note to preceding table. The expression ' specific gravity of a gas ' will be 
 employed to denote the specific gravity referred to air as unity : the expression 
 ' vapour density of a body ' to denote the specific gravity of a body in the gaseous 
 state referred to hydrogen as unity.
 
 CHAP. I. l6-I7] SPECIFIC GRAVITIES OF VAPOURS. 35 
 
 while in the case of other gases the density is practically 
 independent of the temperature ; a limiting value is however 
 generally found for the specific gravity of a gas. 
 
 It would therefore appear that a chemical substance may 
 have more than one molecular weight; but if the molecule is the 
 smallest part of a substance which exhibits the characteristic 
 properties of that substance, this is equivalent to saying that 
 certain substances when heated may pass through a succession 
 of changes, each phase being marked by the existence of a 
 distinct kind of matter. More accurate experiment has shewn 
 that the vapours of phosphorus pentachloride and nitrogen 
 tetroxide, at high temperatures, are mixtures of phosphorus 
 pentachloride and trichloride, and chlorine, and of nitrogen 
 tetroxide and nitrogen dioxide (N 2 O 4 and NOJ, respectively, 
 so that at these temperatures we have to deal not with 
 homogeneous vapours, but with mixtures of different gases 
 varying in composition at different moments. The con- 
 nexion existing between temperature and the densities of 
 gaseous elements and compounds will be examined in more 
 detail in a future chapter 1 (see Book II.). 
 
 The practical outcome of these considerations is that in 
 determining a molecular weight the gas must be proved to 
 be really a homogeneous substance, and not a mixture pro- 
 duced by the decomposing action of heat on the original sub- 
 stance ; and, further, that the value obtained for the specific 
 gravity must be constant throughout a considerable range of 
 temperature. 
 
 [7 In determining the specific gravity of a gas, especially 
 if at a somewhat high temperature, many sources of error 
 are present ; the result cannot therefore be more than mode- 
 rately accurate 2 . But experimental errors are more easily 
 
 1 Avogadro's law may he deduced from the molecular theory of matter, but 
 inasmuch as this theory is based upon more or less inexact hypotheses, and is as 
 yet but in an early stage of development, inasmuch also as the deductions made 
 from it concerning gaseous laws are strictly applicable only to ' perfect gases," it 
 follows that Avogadro's law cannot be regarded, at present, as absolutely true. 
 The laws of Boyle and of Charles, which are also deducible from the molecular 
 theory, do not give a complete account of the relations of gases to temperature and 
 pressure. 
 
 - Dumas' method for determining vapour densities is described in Ann. Chim. 
 
 32
 
 36 ATOMS AND MOLECULES. [BOOK I. 
 
 avoided in the determination of the mass of an element which 
 combines with one part by weight of hydrogen, 7-98 parts by 
 weight of oxygen, or 3 5 '37 parts by weight of chlorine. Now, 
 if this mass is called the combining iveight of an element, 
 it is evident that the molecular weight of an element must 
 be equal to, or a multiple of, its combining weight, and the 
 molecular weight of a compound must be equal to the sum, 
 or to a multiple of the sum, of the combining weights of its 
 constituent elements. Hence if the combining weight, and 
 the specific gravity in the gaseous state, of an element are 
 carefully determined, we have the necessary data for an 
 accurate determination of the molecular weight of that element; 
 the combining weight being an accurately determined num- 
 ber, and the specific gravity deciding what multiple of that 
 number represents the molecular weight. So also the data 
 required for an accurate determination of the molecular 
 weight of a compound are; the combining weights of the 
 constituent elements, and the specific gravity of the com- 
 pound in the state of gas. Thus Regnault found for the 
 
 Phys. [2] 33. 337; Gay Lussac's in Biot's Traitt de Phys. 1. 291; Hofmann's in 
 Ber. 1. 198; and Victor Meyer's in Ber. 11. 1868 and 2253. For criticisms on, 
 and modifications of, Meyer's method see Ber. 12. 609 and 1112: 13. 401, 851, 991, 
 1079, 1185, and 2019: 14. 1727: and 15. 137, 1161 and 2775: (in the last paper by 
 V. Meyer [Ber. 15. 2775] will be found an interesting and valuable criticism of the 
 various methods for finding the Sp. Grs. of gases). See also Ber. 16. 1051; 19. 
 1 86 1 ; also C. S. Journal Trans, for 1880. 491. Modifications of Dumas' method 
 are described by Bunsen, see Gasometrische Methoden, 2nd ed. (1877), p. 172: also 
 by Petterson and Ekstrand, Ber. 13. 1191 : and especially by Pawlewski, Ber. 16. 
 1293. Thorpe [C. S. Jotirnal Trans, for 1880. 147150] has described a very 
 complete method based on Hofmann's process. V. Meyer [Ber. 9. 1260: and 10. 
 2068] has described a method based on the displacement of mercury. In Wied. ' 
 Ann. 22. 465 and 493, von Klobukow describes two processes for determining 
 vapour densities with great accuracy ; one is adapted for bodies with low boiling 
 points, the other for bodies which boil at high temperatures. La Coste (Ber. 18. 
 2122) describes a modification of V. Meyer's apparatus whereby the vapour 
 densities of easily decomposable compounds may be determined at low tempera- 
 tures and under very small pressures. A modification of V. Meyer's apparatus, 
 by which a vapour density and the exact temperature of observation can be simul- 
 taneously determined, is described by Nilson and Pettersson in J. fiir prakt. 
 Chem. [2] 33. r. See also Schall, Ber. 20. 1433. Malfatti and Schoop (Zeitschr. 
 f. physikal. Chemie, 1. 159) describe an apparatus for determining vapour densities 
 under small pressures.
 
 CHAP. I. I7-I8] ATOMIC WEIGHTS. 37 
 
 specific gravity of chlorine the number 2*44 ; this multiplied 
 into 28*87 gives 70*44. The combining weight of chlorine as 
 most carefully determined by Stas is 35'37: now 35'37 x 2 
 = 7074, which is very nearly equal to the molecular weight 
 calculated from Regnault's numbers ; hence 7074 is taken to 
 be the molecular weight of chlorine. Again, Thomson found 
 the specific gravity of marsh gas to be O'557, which multiplied 
 into 28*87 gives 16*1 as approximately the molecular weight 
 of this compound : the combining weight of carbon is 2*99 
 (H = i), and in marsh gas carbon and hydrogen are united in 
 the proportion of 2*99 to I ; hence the molecular weight of 
 this gas is 3*99 or a multiple thereof. But 3*99 x 4= 15*96 ; 
 therefore the molecular weight of marsh gas is taken to be 
 15-96. 
 
 The numbers in column V of the table on p. 33 represent 
 the molecular weights of the various elements found by the 
 method of specific gravity aided by determinations of the 
 combining weights of the elements in question. 
 L8 Facts have already been mentioned which on the as- 
 sumption of the truth of Avogadro's law oblige us to 
 conclude that in certain chemical reactions the molecules of 
 the reacting elementary bodies undergo subdivision ; indeed 
 we are forced to the conclusion that the greater number of 
 the molecules of those elements which have been gasified 
 are not homogeneous but are built up of smaller parts 1 . 
 These parts of molecules, or atoms, are the ultimate portions 
 of matter with which we have at present to deal in chemistry. 
 Now it is evident that the molecule of an element must be 
 composed of at least two atoms, unless indeed the atom and 
 molecule should be identical; and that the molecule of a 
 compound must be composed of at least one atom of each 
 of its constituent elements. Therefore if we determine the 
 smallest mass of an element in the molecule of any compound 
 thereof, we shall have determined the maximum atomic weight 
 of the element in question. 
 
 Hence we arrive at the following definition. 
 
 1 Reactions are known in which it is not necessary to assume that subdivision 
 of elementary molecules occurs, e.g. 
 
 Hg + Cl s = HgCl,, 
 Volumes 2 2 form 2.
 
 38 ATOMS AND MOLECULES. [BOOK I. 
 
 The maximum atomic weight of an element is the 
 smallest mass, in terms of hydrogen as unity, of that element 
 which combines with other elements to form a gaseous molecule. 
 
 Molecular weight has been already defined as the weight of 
 two volumes of any gas referred to the weight of two volumes 
 of hydrogen ; hence the data which must be obtained before 
 the maximum atomic weight of an element can be determined 
 are, (i) the specific gravities of several gaseous compounds of 
 the element in question, and (2) careful analyses of these 
 compounds. 
 
 Suppose it is required to determine the maximum atomic 
 weight of oxygen, such data as are indicated in the following 
 table are obtained. 
 
 Data for determining maximum atomic weiglit of oxygen. 
 
 
 Weight of 
 
 
 
 2 volumes, as 
 
 
 Name of compound 
 
 gas, referred to 
 
 Analysis of these 2 volumes 
 
 
 hydrogen, i. e. 
 
 
 
 molecular weight 
 
 
 Water 
 
 17-99 
 
 1 5 '96 oxygen + 2 hydrogen 
 
 Carbonous oxide 
 
 27-96 
 
 !5'9 6 ,, + ii '97 carbon 
 
 Carbonic dioxide 
 
 44' 1 5 
 
 31-92 + 11-97 
 
 Nitrous oxide 
 
 43'9 
 
 J 5'96 n + 28*02 nitrogen 
 
 Methylic alcohol 
 
 32'3 
 
 (15-96 + 1 1-97 carbon 
 | + 4 hydrogen 
 
 Methyl nitrate 
 Nitric oxide 
 
 76-2 
 30-0 
 
 } 47'88 +11 -97 carbon 
 ' +3hydrogen+ 14-01 nitrogen 
 15-96 oxygen + 14-01 
 
 Sulphurous oxide 
 
 64-9 
 
 31-92 + 31-98 sulphur 
 
 Sulphuric oxide 
 
 86-9 
 
 47-88 + 31-98 
 
 Phosphorus oxychloride 
 
 155*9 
 
 '5 '96 + 30-96 phosphorus 
 
 
 
 + 106-11 chlorine 
 
 Osmium tetroxide 
 
 257 
 
 63-84 +198*6 osmium 
 
 If the smallest mass of hydrogen found in a molecule of any 
 compound of that element is called one part by weight, then 
 in no molecule of any of the compounds in this table is there 
 less than 15 '96 parts by weight of oxygen; this number is 
 therefore adopted as the maximum atomic weight of oxygen. 
 19 The following table (taken for the most part from Lothar 
 Meyer's Die modernen Theorien der Chemic) contains the 
 most important data hitherto accumulated for determining the 
 maximum atomic weights of the elements by the application 
 of Avogadro's law.
 
 CHAP. I. 19] MOLECULAR AND ATOMIC WEIGHTS. 
 
 39
 
 40 
 
 ATOMS AND MOLECULES. 
 
 [BOOK i. 
 
 bjo 6Jo 
 
 8 S 
 
 T3T3 > 
 >> >, 
 ^ ,G 
 
 vO SO 
 
 > 
 
 * 
 
 5>-fl 
 
 ill 
 
 ' + 
 
 
 
 bsvb ^b 
 
 K 
 
 .5 g .9 o 5 fe -g S 
 
 . ~ co S ~ J? N * 
 
 M IL< 
 
 |S-c 
 
 ON ON fO ON ^ O yo p O tv. ON O fO N OO tv. u-i ri OO *- ro, O C< ON ON JH 
 
 B *i 
 
 ^j- *- >-o\o to r^.oo o co co tx.\ 
 
 M unvO 
 
 ) O^ O t^ ON >-O -< 
 
 cnVoo "- b ~ 
 
 
 o Jz 
 2 a S 
 
 o .T: .i; . .~ 
 
 i 
 
 i s 
 
 Si 
 
 u c i o " "* ' A SJL< a -'i3 c c c "J _ 
 
 l.|l|lll||||||Il| 
 
 II 
 
 oj aJ
 
 CHAP. I. Ip] MOLECULAR AND ATOMIC WKHHITS. 
 c c 
 
 4' 
 
 .53 c 
 
 22- |: 
 
 ^=3 2 
 
 Is! 
 
 oS"2 
 
 + O 0> 
 
 I 
 
 
 T^- vO (SVO^ 
 
 vb ' O\ ON ON 
 
 "MD 
 
 8 
 
 w + 
 
 OJ C C 
 
 s -i'g^ 
 ,198 
 
 I--Q ^-\O 
 
 ' o r^ r^ 
 
 rp>R8^ 
 
 + + + 
 
 O\ O\ pN ON pv ON O\ p^ ON p^ C> p^ p^ ON p\'5i 
 
 I - 
 
 II j 'iil 
 
 ,8-1 8 51 P-- 
 
 * r^ tv-^o .ti .S co co oo co 
 
 " (^ r>. ro c^ PO 
 
 p> O 
 
 ro unco O ^ <^^O Pio'^-'^'^OPl-^-:^ 1 ^- rOThu^r 
 r^ PI co PI N jo pv tn "I >p p^ - j^ M2 ij-> p\ vp cp c 
 
 PI p> ^J- p 
 
 -S w 
 
 oj'C <u^3 
 
 ^^ ,__^^ re _...._ -JW 
 
 Iff I | Illlll lltf 8 8888 Illll 1 11 11 
 u u u u u u ffi u u"5S S coco co co co <2 rt rt UU co P Ktoco coco
 
 42 
 
 ATOMS AND MOLECULES. [BOOK I. 
 
 Molecula 
 weight 
 
 S 6 
 
 Up 
 
 
 
 OCOOOOOOOOOOOrj 
 
 O Vh ON f*">OO Vj- 
 
 ^oo oo 1- r^- o 
 
 tnO M 
 
 O O 
 
 i O f> T^OO ^O O p O O O ON O O 
 
 M <*"> -* ON "1OO O t^ \O t^ r>. vr 
 
 r* O\ 50 ^t 7*- ."> .* N ^p w ON P< \p <N >p N j^ N ON poo _ r) ON*p ro to ON 
 OO ON O K O fO M OO ON b\ C) \b '-^- ro ^- ON 'd-cio O^OO ONN\boO ^uiloin 
 
 i! 
 
 i 
 
 . 
 
 Ill^Siiiili 
 
 
 1 1 llllll.a s llll 1 
 
 - 1 CJ
 
 CHAP. I. 19] MOLECULAR AND ATOMIC WEIGHTS. 
 
 43 
 
 _L a i <u L <u 
 
 
 N - CO 
 
 el 
 
 3 J3 
 VJS' 
 
 g 
 
 .1 s 
 
 PT3 E 3 
 
 s 
 
 .a a 
 
 f P .0 
 UOOOOOCO Tt-^- 
 
 OOO 
 
 OO'* ^ 
 P P 
 
 <> N O i^> ' N fO O ^O 
 t^^O O -* ON r>. t^ 
 n P) m ro ro c< ri 
 
 ci O O O O O O O O O 
 ' ' 
 
 LT> O O oo vp 
 rh t^ b '- ^ 
 r< r^oo O -* 
 
 |. 
 
 lfll3&S-fr8g,8-fil iiios
 
 44 ATOMS AND MOLECULES. [BOOK I. 
 
 Notes to the preceding Table. 
 
 I The density of hydrofluoric acid was determined indirectly by Gore (Phil. 
 Trans, for 1869. 173) at 100. Mallet (Amer. Chem. Journal 3. 189) by directly 
 weighing i litre of the gas at 30 found the specific gravity to be 1-42, which 
 gives a molecular weight of 41-02. The molecular weight of this gas therefore 
 decreases as temperature increases. 
 
 2nd3 indirectly determined by Bineau (Ann. Chim. Phys. [2] 68. 424); two 
 volumes of each hydride when decomposed by metal yielded 2 vols. of hydrogen, 
 78 parts by weight of selenion in one case, and 128 parts by weight of tellurium 
 in the other case, being produced. 
 
 34 Michaelis, Ber. 20. 1780, and 2488. Temp. abt. 450. 
 
 4 Potassium iodide was vaporised at about 1300 by means of a new apparatus 
 described by Mensching and Meyer (s. Zeitschr.f. physikal. Chemie, 1. 157). 
 
 5 Determined at 1200 1500 by Scott; Proc. R. S. E. 1887. 
 
 6 At a temperature slightly above its boiling point the specific gravity of 
 gaseous stannous chloride points to the molecular weight 377; but at 200 higher 
 the specific gravity is as given in the table ; this gas therefore, like hydrofluoric 
 acid, has two molecular weights: see Meyer and Ziiblin (Ber. 13. 811). 
 
 7 GeCl 4 , GeI 4 , and GeS have been gasified by Nilson and Pettersson (Zeit.f. 
 physikal. Chemie, 1. 27). 
 
 8 Kriiss and Nilson, Ber. 20. 1671. Temp. abt. 1200. 
 
 9 See Nilson and Pettersson, Ber. 17. 987; also J.fiir prakt. Chem. [2] 33. i; 
 and Humpidge, Proc. R. S. 38. 188. 
 
 10 There is some doubt whether the vapour of mercurous chloride does or does 
 not contain mercury and mercuric chloride: the number in the table is from a 
 paper by Fileti, who states that by vaporising a mixture of the two chlorides of 
 mercury, the protochloride remains undissociated (see abstract of Fileti's paper in 
 C. S. Journal Abstracts for 1882. 466). 
 
 II Nilson and Pettersson (Zeitschr.f. physikal. Chemie, 1. 459) have found that 
 the sp. gr. of gaseous aluminium chloride at 800 1200 agrees with the formula 
 A1C1 3 ; at 400 or so it agrees with the formula A1 2 C1 6 . Odling (Phil. Mag. [4] 
 29. 316) gave the specific gravity of aluminium trimethide at temperatures above 
 200 as 2 '5, and at 1 30 as 5 'o ; but it is undecided whether the gas at 200 was 
 homogeneous or a mixture of the products of decomposition by heat of molecules 
 existing at lower temperatures (see Wanklyn loc. cit. 313, and Williamson do. 395). 
 If the gas at 200 was really homogeneous, we should have 2-5 x 28-87 = 72-5 as 
 the molecular weight of aluminium trimethide ; and this quantity of the gas con- 
 tains 27-02 aluminium + 35-91 carbon + 9 hydrogen (=71-93). Chromium hexa- 
 
 Jluoride (CrF 6 ) is frequently mentioned in text-books as a gaseous compound of 
 chromium ; the evidence in favour of the existence of a definite fluoride of 
 chromium is meagre ; and no determinations of its density (if it exists) have been 
 made: see Unverdorben (Pogg. Ann. 1. 311). According to Oliveri (Gaz. 16, 218) 
 the supposed hexafluoride is really an oxyfluoride, of chromium, and has the com- 
 position CrO 2 F 2 . 
 
 12 V. Meyer (Ber. 17. 1335) has obtained results which seem to shew that 
 gaseous ferrous chloride at moderate temperatures consists chiefly of molecules having 
 the composition Fe 2 Cl 4 , and at higher temperatures chiefly of molecules of FeCl 2 . 
 
 13 At 450 the sp. gr. of the vapour of gallic chloride is 7-8, and at the same
 
 CHAP. I. 2O] MOLECULAR AND ATOMIC WEIGHTS. 
 
 45 
 
 temperature in presence of an indifferent gas acting as diluent, it is 6*6 : the gas 
 dissociates under these conditions. (See Lecoq de Boisbaudran, Comft. rend. 93. 
 294, 329 and 815.) 
 
 The maximum atomic weights deduced from these data 
 may in many cases be regarded with a large degree of proba- 
 bility as the true atomic weights of the elements. The 
 greater the number of gaseous compounds of an element 
 analysed, the greater is the probability that the number which 
 represents the smallest mass of that element in two volumes, 
 i.e. in a gaseous molecule, of any of these compounds is the 
 true atomic weight of the element. 
 
 20 When the atomic and molecular weights of an element 
 are known, the atomicity of the molecule, i.e. the number of 
 atoms in the molecule, is known. 
 
 In the following table the molecules of the elements, so 
 far as the relative weights of these have been determined by 
 the method founded on Avogadro's law, are classified in 
 accordance with their atomicity. 
 
 Atomicity of Elementary Molecules 1 . 
 
 Monatomic 
 
 Diatomic 
 
 Triatomic 
 
 Tetratomic 
 
 Hexatomic 
 
 Sodium 
 Potassium 
 
 Hydrogen 
 Chlorine 
 
 Oxygen (ozone) 
 Selenion 
 
 Phosphorus 
 Arsenic 
 
 Sulphur 
 (450 to 
 
 Zinc Bromine 
 Cadmium Iodine 
 
 (700 to 800) 
 
 (to near a 
 white heat) 
 
 about 550, 
 
 Mercury ' (200 to about 
 
 
 
 
 Iodine 1000) 
 
 
 
 
 (at about 1 500) Oxygen 
 (? Bromine at ' Sulphur 
 
 
 
 
 about 1800) (at 800 and 
 
 
 
 
 upwards) 
 
 
 
 
 Selenion 
 
 
 
 
 
 (at 1200 and 
 
 
 
 
 
 upwards) 
 
 
 
 
 
 Tellurium 
 
 
 
 
 
 Nitrogen 
 
 
 
 
 
 Phos- ) (at 
 
 
 
 
 
 phorus>white 
 
 
 
 
 
 Arsenic) heat) 
 
 
 
 
 1 This table shews that many elementary gases have complex structures ; 
 hence arise difficulties in forming accurate physical conceptions of actions and 
 reactions among the parts of these structures. This will be again referred to when 
 dealing with atomic heats (see p. 67).
 
 46 ATOMS AND MOLECULES. [BOOK I. 
 
 The molecules of several elements in this table are 
 diatomic, but inasmuch as the molecular and atomic weights 
 of only 1 6 elements have been determined it is impossible 
 to say whether a majority of all the elementary molecules 
 are composed each of two atoms. Six, of the sixteen, 
 elements in the table have more than one molecular weight; 
 of the remaining ten, five are monatomic and five are 
 diatomic. 
 
 The table contains five well-defined metals, sodium, potas- 
 sium, zinc, cadmium, and mercury ; the molecules of these 
 elements are monatomic, and hence are of a simpler structure 
 than the molecules of the distinctly nonmetallic elements. 
 21 Chemical formulae for the most part profess to repre- 
 sent not only the elementary composition, but also the rela- 
 tive weights of the molecules, of the bodies formulated : but 
 unless some method for determining molecular weights other 
 than that founded on Avogadro's law is adopted, it is evident 
 from the data in the table on pp. 39 43 that the majority of 
 the formulae employed in mineral chemistry cannot certainly 
 be regarded as molecular formulae. Thus analysis shews that 
 17-96 parts by weight of water are composed of 15 '96 parts 
 of oxygen and 2. parts of hydrogen ; analysis also shews that 
 58*37 parts by weight of sodium chloride are composed of 
 23 parts of sodium and 35'3/ parts of chlorine. The specific 
 gravity of water vapour shews that the molecular weight of 
 this compound is about 18, hence assuming the atomic 
 weight of oxygen to be 1 5^96 the molecular formula is written 
 H 2 O ( 1 7-96). But no determination of the specific gravity of 
 sodium chloride vapour has yet been made ; hence the mole- 
 cular weight may be about 59, or it may be a multiple of this 
 number (assuming the atomic weights of sodium and chlorine 
 to be known), and hence the formula NaCl (58'37) is not 
 necessarily molecular, and is therefore not strictly comparable 
 with the formula H 2 O. 
 
 Even if a formula does express the relative weight of the 
 molecule of the body formulated it is well to remember that 
 it is the weight of the gaseous molecule which is thus ex- 
 pressed ; the formula does not necessarily also represent the
 
 CHAP. I. 2l] FORMULA OF GASES AND SOLIDS. 47 
 
 relative weight of the molecule of the same body when 
 solid : indeed the definition of molecule (p. 26) is applicable 
 to gases only. 
 
 As a general rule, the melting and boiling points of bodies 
 with large molecular weights are high : thus in any homologous 
 series of hydrocarbons the boiling and melting points increase 
 with increase of molecular weight 1 ; the same connexion 
 between these constants is noticed in many series of oxides, 
 e.g. the oxides of nitrogen 2 . It would therefore appear pro- 
 bable that the molecular weight of a solid, using the term 
 molecular weight in a wide sense, is greater than that of the 
 same substance when in the state of gas. So also, as a rule, 
 the action of heat is to produce molecules of less, from those 
 of greater, weight : thus N a O 4 exists at low temperatures, but 
 becomes NO a when heated (see numbers on p. 34); so S 6 
 exists at 500, but S 2 at 1000 ; at temperatures above 300 
 the molecule O 3 decomposes into O 2 . Reactions are known 
 in which heat appears to favour the production of particles of 
 greater weight and complexity than those previously existing; 
 but these more complex particles generally mark intermediate 
 stages towards the formation of less complex and compara- 
 tively lighter particles. Thus the action of heat on sodium- 
 hydrogen sulphate is generally formulated in two stages, (i) 
 2NaHS0 4 =Na 2 S 2 7 +H 2 0; (2) Na 2 S 2 O 7 = Na 8 SO 4 + SO 3 : so 
 also when mercuric cyanide is decomposed by heat, molecules 
 of cyanogen are produced having the formula wCN where 
 11 > 2, but at 800 900 these are separated into the lighter 
 molecules C 2 N 2 : again, lead monoxide, wPbO, when heated 
 forms the heavier oxide Pb 3 O 4 : &c. In many of these cases 
 however we are not certain that the formulae employed 
 represent the relative weights of true molecules. 
 
 The physical phenomena presented by liquids and solids 
 cannot be expressed by such comparatively simple generali- 
 sations as those which express the properties of gases; the 
 
 1 Thus, C 4 H 10 , C 5 H 12 , C 6 H 14 , C 7 H, 6 , C 8 H 18 , C 9 H W , C^H^ &c. 
 B. P.= i 38 70 99 124 148 167 &c. 
 
 2 Thus, NO N 2 O N 2 O 3 N. 2 O 4 N 2 O 5 
 gaseous at - 110, B.P. = -88, about -20, 42. M.P. = 3O.
 
 4 8 
 
 ATOMS AND MOLECULES. 
 
 [BOOK i. 
 
 molecular phenomena of the former classes of bodies are 
 evidently more complex than those of the latter class. Great 
 caution must therefore be used in applying deductions made 
 from the study of the molecular phenomena of gases to 
 solid or liquid bodies 1 . 
 
 22 The following table gathers together the results of obser- 
 vations recorded in the table on pp. 39 43, so far as regards 
 the maximum atomic weights of elements determined by the 
 application of Avogadro's law. 
 
 Maximum atomic weights of elements. (AVOGADRO'S law.) 
 
 Name 
 
 Maximum 
 atomic 
 weight 
 
 Name 
 
 Maximum 
 atomic 
 weight 
 
 Name 
 
 Maximum 
 atomic 
 weight 
 
 Hydrogen 
 
 I 
 
 Manganese 
 
 55 
 
 Antimony 120 
 
 Beryllium 
 
 9'I 
 
 Zinc 
 
 64-9 
 
 Tellurium 
 
 125 
 
 Boron 
 
 IQ'95 
 
 Germanium 
 
 72'3 
 
 Iodine I26'53 
 
 Carbon 
 
 II'97 
 
 Arsenic 
 
 74'9 
 
 [Copper I26-8] 2 
 
 Nitrogen 
 
 I4-OI 
 
 Selenion 
 
 78-8 
 
 Caesium 132-7 
 
 Oxygen 
 
 15-96 
 
 Bromine 
 
 7975 
 
 [Gallium 138]* 
 
 Fluorine 
 
 I9-I 
 
 Rubidium 
 
 85-2 
 
 Tantalum 182 
 
 Aluminium 
 
 27-02 
 
 Zirconium 
 
 90 
 
 Tungsten j 183-6 
 
 Silicon 
 
 28 
 
 Niobium 
 
 94 
 
 Osmium 
 
 193 (?) 
 
 Phosphorus 
 Sulphur 
 
 30-96 
 31-98 
 
 Molybdenum 
 Silver 
 
 95-8 
 107-66 
 
 Mercury !99'8 
 Thallium 203-6 
 
 Chlorine 
 
 35'37 
 
 [Iron 
 
 in-8] 2 
 
 Lead 206-4 
 
 Potassium 39'O4 
 
 Cadmium 
 
 112 
 
 Bismuth 208 
 
 Titanium 48 
 
 Indium 
 
 II3-4 
 
 Thorium 
 
 231-87 
 
 Vanadium 
 
 51-2 
 
 Tin 
 
 II7-8 
 
 Uranium 
 
 240 
 
 Chromium 
 
 52-4 
 
 
 
 
 
 About two-thirds of the known elements are found in this 
 table. 
 
 Some method other than that based on the determination 
 
 of the specific gravities of gaseous compounds must if possible 
 
 be discovered for finding the atomic weights of the elements. 
 
 23 In his New System of Chemical Philosophy* (pp. 70 75), 
 
 Dalton discusses hypotheses regarding the quantities of 
 
 1 The comparison of the molecular phenomena of gases with those of solids 
 and liquids will be considered more fully in a future chapter. See Book ii. 
 Chap. iv. 
 
 2 Especial reference will be made to the elements in brackets in a later 
 paragraph : see p. 60. 
 
 3 Published in 1 808.
 
 CHAP. I. 22-23] ATOMIC HEATS. 49 
 
 heat contained In various elastic fluids, and decides in favour 
 of that which asserts that, 
 
 " The quantity of heat belonging to the ultimate particles of all elastic 
 fluids must be the same under the same pressure and temperature." 
 
 From this Dalton deduced the corollary, 
 
 "The specific heats of equal weights of any two elastic fluids are 
 inversely as the weights of their atoms or molecules." 
 
 The values of very few specific heats had been determined 
 when Dalton wrote, and therefore he did not possess data 
 sufficient to test the justness of his general principle. Dalton 
 calculated the theoretical specific heats of various gases by 
 the aid of the above corollary, employing atomic weights de- 
 termined by himself. Regarding the table of numbers thus 
 obtained he remarks, 
 
 " Upon the whole there is not any established fact in regard to the 
 specific heat of bodies, whether elastic or fluid, that is repugnant to the 
 above table so far as I know ; and it is to be hoped that some principle 
 analogous to the one here adopted may soon be extended to solid and 
 liquid bodies in general." 
 
 In 1819 a paper by Petit and Dulong appeared in the 
 Annales de Chimie et de Physique [10. 395], containing the re- 
 sults of determinations of the specific heats of thirteen solid 
 elements; viz. copper, gold, iron, lead, nickel, platinum, 
 sulphur, tin, zinc, bismuth, cobalt, silver, and tellurium. A 
 nearly constant product was obtained by multiplying the 
 specific heats of the nine elements from copper to zinc, in this 
 list, by the then generally accepted atomic weights of these 
 elements, and the specific heat of bismuth, cobalt, silver, and 
 tellurium, by a sub-multiple of the accepted atomic weight 
 of each of these elements. Generalising from these results 
 the French physicists -concluded that "the atoms of all the 
 simple bodies have exactly the same capacity for heat" 
 
 The introduction of more accurate methods for determin- 
 ing specific heats has necessitated considerable alterations in 
 many of the numbers to be found in the original paper of 
 Petit and Dulong, nevertheless their general conclusion re- 
 mains, although it cannot now be stated in terms quite so 
 absolute as those used by its promulgators. 
 
 M. C. 4
 
 50 ATOMS AND MOLECULES. [BOOK I. 
 
 24 In 1831 F. Neumann 1 published determinations of the 
 specific heats of various solid compounds, chiefly of natur- 
 ally occurring minerals, and deduced the general statement: 
 " The amounts of cJtemically similar compounds expressed by 
 their formulce possess equal specific heats." 
 
 A few years later (1833 4) Avogadro 2 detailed measure- 
 ments of the specific heat of carbon, and of various com- 
 pound substances, and drew certain general conclusions there- 
 from ; he spoke of those atomic weights which were deduced 
 from measurements of specific heats as the weights of thermal 
 atoms (atomes thermiques]. 
 
 R. Hermann 3 made a number of determinations of specific 
 heats, and from these deduced the combining weights of 
 several elements. The weights thus obtained were in some 
 cases different from the Berzelian weights then in general use. 
 Hermann supposed that the specific heat of certain elements, 
 e.g. sulphur and oxygen, varies according as the element is 
 in the free state or in combination with other elements. 
 
 Regnault 4 , in a series of classical memoirs, added much to 
 our knowledge of specific heats, and gave a general confirma- 
 tion to the laws of Dulong and Petit, and Neumann. He 
 arranged a table of so-called thermo-atomic weights, as follows : 
 Regnaulfs Thermo-atomic weights. [See KOPP 5 .] 
 
 Al =137 
 
 Sb = 61 
 
 As =37-5 
 
 Ba =68-5 
 
 Bi =105 
 
 B =10-9 
 
 Br =40 
 
 Cd=s6 
 
 Ca=2o 
 
 C = 12 
 
 Cl =1775 
 
 1 PSS- Ann. 23. i. Neumann measured the specific heats of 8 carbonates, 
 4 sulphates, 4 sulphides, 5 oxides of the type MO, and 3 of the type M 2 O 3 . 
 
 2 Published in condensed form in Ann. Chim. Phys. [2] 55. 80: and 57. 113. 
 
 3 Noweaux Mt 'moires de la Socittt Imptriale des Naturalistes de Moscou (1834). 
 3. 137. 
 
 4 Ann. Chim. Phys. [2] 63. 5. [3] 1. 129: 9. 322: 26. 261 and 268: 38. 129: 
 46. 257: 63. 5. 5 Annakn, Supplbd. 3. i and 289. 
 
 Cr =26-1 
 
 Mn = 27'5 
 
 Se =397 
 
 Co =29-4 
 
 Hg = ioo 
 
 Ag=54 
 
 Cu =317 
 
 Mo = 48 
 
 Na = ii'5 
 
 F =9'5 
 
 Ni =29-4 
 
 Sr =43-8 
 
 Au =98-5 
 
 N =7 
 
 S =16 
 
 I =63-5 
 
 Os =99-6 
 
 Te=64 
 
 Ir =99 
 
 Pd= 53 -3 
 
 Tl =102 
 
 Fe =28 
 
 P =15-5 
 
 Sn= S9 
 
 Li =3-5 
 
 Pt =987 
 
 Ti =25 
 
 Pb= 103-5 
 
 K =19-5 
 
 W =92 
 
 Mg=I2 
 
 Rh=52-2 
 
 Zn =32-6
 
 CH. I. 24-25] GARNIER-CANNIZZARO GENERALISATION. 5 I 
 
 Gamier 6 (in 1852) further generalised the relations between 
 the formulae and the specific heats of solid compounds ; and 
 Cannizzaro 7 somewhat advanced the generalisation of Gamier. 
 
 The Garnier-Cannizzaro generalisation may be stated 
 thus : 
 
 A C 
 
 = constant (about 6-4) ; 
 
 where A = the formula-weight of a compound, C = the specific 
 heat of the same compound, and n = the number of elementary 
 atoms in the formula of the compound. 
 
 15 Kopp 8 has gathered together most of the trustworthy 
 results of specific heat determinations, and added many of 
 his own, besides discussing the whole subject in detail. 
 
 Table of Specific Heats of the Elements 9 . 
 
 Name 
 
 s & 
 
 Temp. 
 
 Atomic 
 weight 
 
 Sp. ht. 
 X at wt. 
 
 Observer 
 
 Lithium 
 
 0-941 
 
 
 7-01 
 
 6-6 
 
 Rg. 
 
 1 Beryllium 
 2 Boron 
 
 0-62 
 ?o- 5 
 
 450 to 500 
 about iooo? 
 
 I0'9 
 
 5-6 
 5'5 
 
 He. 
 Wb. 
 
 3 Carbon 
 
 0-463 
 
 980 
 
 11-97 
 
 5'5 
 
 Wb. 
 
 Sodium 
 
 0-293 
 
 -34 to +7 
 
 23 
 
 6-7 
 
 Rg- 
 
 Magnesium 
 
 0-245 
 
 
 24 
 
 5'9 
 
 Kp. 
 
 M 
 
 0-25 
 
 
 
 
 6-0 
 
 Rg. 
 
 Aluminium 
 
 0-202 
 
 
 27-02 
 
 5-5 
 
 Kp. 
 
 99 
 
 0-214 
 
 
 >9 
 
 I' 8 
 
 Rg. 
 
 >? 
 
 0-225 
 
 
 H 
 
 6-r 
 
 Mt. 
 
 4 Silicon 
 
 0-203 
 
 232 
 
 28-3 
 
 5-8 
 
 Wb. 
 
 Phosphorus (cryst.) 
 
 0-174 
 
 -78 to + 10 
 
 30-96 
 
 5'4 
 
 Rg. 
 
 " 
 
 0-189 
 O'2O2 
 
 
 9) 
 
 99 
 
 
 
 Rg- 
 Kp. 
 
 " (red) 
 
 0-I70 
 
 
 
 5 '3 
 
 Rg. 
 
 Sulphur 
 
 0-188 
 
 
 31*98 
 
 6'o 
 
 D.P. 
 
 rhombic 
 
 0-163 
 
 
 M 
 
 5-2 
 
 Kp. 
 
 n >9 
 
 O-I7I 
 
 
 n 
 
 5 "5 
 
 Bn. 
 
 J9 99 
 
 0-178 
 
 
 
 57 
 
 Rg- 
 
 6 Potassium 
 
 0-166 
 
 -78 to +10 
 
 39 ! 4 
 
 6'5 
 
 Rg. 
 
 Calcium 
 
 0-I70 
 
 
 39'9 
 
 6-8 
 
 Bn. 
 
 Titanium 
 
 0-1485 
 
 o to 300 
 
 48 
 
 7'i 
 
 N.P. 
 
 6 CompL rend, 35. 278: 37. 130. 
 
 7 // Nuovo Cimento 7. 321 ; Abstract in Bull. Soc. Chitn. for 1863. 171. 
 
 8 Annalen, Supplbd. 3. i and 289. 
 
 9 When no temperature is given the determinations were made somewhere 
 between the limits o and 100: the numbers may in these cases be regarded as 
 approximately the mean specific heats for the temperature-interval 40 60. 
 
 42
 
 ATOMS AND MOLECULES. 
 
 [BOOK i. 
 
 Name 
 
 Spec, 
 heat 
 
 Temp. 
 
 Atomic 
 weight 
 
 Sp. ht. 
 x at. wt. 
 
 Observer 
 
 6 Chromium 
 
 O'lO 
 
 
 52-4 
 
 5*2 
 
 Kp. 
 
 7 Manganese 
 
 O*I22 
 
 
 55 
 
 67 
 
 
 Iron 
 
 0*112 
 
 
 55 '9 
 
 6*3 
 
 Kp. 
 
 J} 
 
 0*114 
 
 
 j? 
 
 6-4 
 
 Rg. 
 
 5j 
 
 O'HO 
 
 
 
 
 6-1 
 
 DP. 
 
 Nickel 
 
 0-108 
 
 
 58*6 
 
 6-3 
 
 Rg. 
 
 Cobalt 
 
 0-107 
 
 
 59 
 
 6'3 
 
 Rg. 
 
 Copper 
 
 0-093 
 
 
 63-4 
 
 6-0 
 
 Kp. 
 
 
 
 0-095 
 
 
 
 
 6-1 
 
 Rg. 
 
 55 
 
 0-095 
 
 
 
 6-1 
 
 D.P. 
 
 Zinc 
 
 0-0932 
 
 
 64-9 
 
 6-1 
 
 Kp. 
 
 M 
 
 0-0935 
 
 
 
 
 6-1 
 
 Bn. 
 
 
 0-0955 
 
 
 
 
 6*2 
 
 Rg. 
 
 5) 
 
 0-093 
 
 
 ?> 
 
 6-0 
 
 D.P. 
 
 8 Gallium 
 
 0-079 
 
 12 tO 23 
 
 69 
 
 5 '4 
 
 Bt. 
 
 Germanium 
 
 0-077 
 
 tO 200 
 
 
 5-64 
 
 N.P. 
 
 Arsenic amorphous 
 
 0-076$ 
 
 
 74'9 
 
 
 B.W. 
 
 crystalline 
 
 0-083*): 
 
 
 
 6"2 
 
 B.W. 
 
 J5 55 
 
 0-0814 
 
 
 w 
 
 7*1 
 
 Rg. 
 
 55 55 
 
 0-0822 
 
 
 jj 
 
 6*2 
 
 N. 
 
 9 Selenion amorphous 
 
 0-0746 
 
 -27 to +8 
 
 78*8 
 
 5'9 
 
 Rg. 
 
 crystalline 
 
 0-0745 
 
 -18 to + 7 
 
 B 
 
 5'9 
 
 Rg. 
 
 55 5 
 
 0-0762 
 
 
 9 
 
 6*0 
 
 Rg. 
 
 55 55 
 
 0-086 1 
 
 
 B 
 
 6*8 
 
 N: 
 
 55 55 
 
 0-084$ 
 
 
 }) 
 
 6-7 
 
 B.W. 
 
 Bromine solid 
 10 Zirconium 
 
 0-0843 
 0-0666 
 
 -78* tO -20 
 
 7975 
 90*0 
 
 67 
 6-0 
 
 Rg- 
 
 M.D. 
 
 11 Molybdenum 
 
 0-0722 
 
 
 95-8 
 
 6-9 
 
 Rg. 
 
 Rhodium 
 
 0-058 
 
 
 104 
 
 6*0 
 
 Rg. 
 
 Ruthenium 
 
 0-06 1 1 
 
 
 104-5 
 
 6-4 
 
 Bn. 
 
 Palladium 
 
 0-0593 
 
 
 IO6'2 
 
 6-3 
 
 Rg. 
 
 Silver 
 
 0-056 
 
 
 107-66 
 
 6-0 
 
 Kp. 
 
 
 
 0-0559 
 
 
 55 
 
 6-0 
 
 Bn. 
 
 95 
 
 0-057 
 
 
 
 6-1 
 
 Rg. 
 
 Cadmium 
 
 0-0542 
 
 
 112 
 
 6-0 
 
 4. 
 
 
 
 0-0548 
 
 
 55 
 
 6-1 
 
 Bn. 
 
 Indium 
 
 0-0567 
 
 0-057 
 
 
 55 
 
 6*5 
 
 Rg. 
 
 Bn. 
 
 Tin 
 
 0-0548 
 
 
 II7-8 
 
 6-5 
 
 Kp. 
 
 55 
 
 0-0559 
 
 
 55 
 
 6*6 
 
 Bn. 
 
 >5 
 
 0-0562 
 
 
 
 6-6 
 
 Rg. 
 
 )5 
 
 0-0514 
 
 
 
 6-0 
 
 D.P. 
 
 Antimony 
 
 0-0523 
 
 
 I20'0 
 
 6-2 
 
 Kp. 
 
 
 
 0-0495 
 
 
 
 5 '9 
 
 Bn. 
 
 55 
 
 0-0508 
 
 
 
 6-0 
 
 Rg. 
 
 55 
 
 0-0507 
 
 
 
 6-0 
 
 D.P. 
 
 Tellurium 
 
 0-0475 
 
 
 125 
 
 5'94 
 
 Kp. 
 
 Iodine 
 Lanthanum 
 
 0-0474 
 0-0541 
 0-0449 
 
 
 126*53 
 138*5 
 
 5'94 
 6-8 
 6-2 
 
 Rg. 
 Rg. 
 
 Hd. 
 
 Cerium 
 
 0-0448 
 
 
 141 
 
 6*3 
 
 Hd,
 
 CHAP. I. 25] SPECIFIC HEATS OF ELEMENTS. 
 
 53 
 
 Name 
 
 Spec, 
 heat 
 
 Temp. 
 
 Atomic 
 weight 
 
 Sp. ht. 
 
 X at. WL 
 
 Observer 
 
 Didymium 
 
 0-0456 
 
 
 144 
 
 6-5 
 
 Hd. 
 
 Tungsten 
 
 0-0334 
 
 
 183-6 
 
 6-0 
 
 Rg. 
 
 Osmium 
 
 0-03II 
 
 
 193 
 
 6-0 
 
 Rg- 
 
 Iridium 
 
 0-0326 
 
 
 194 
 
 6-2 
 
 Rg- 
 
 Platinum 
 
 0-0325 
 
 
 195 
 
 6-4 
 
 Kp. 
 
 
 
 0-0324 
 
 
 
 6'3 
 
 Rg. 
 
 
 0-0314 
 
 
 
 
 6'3 
 
 D.P. 
 
 12 Gold 
 
 0-0324 
 
 
 197 
 
 6-3 
 
 Rg. 
 
 13 Mercury solid 
 
 0-0319 
 
 - 78 to - 40 
 
 199-8 
 
 6-4 
 
 Rg. 
 
 14 Thallium 
 
 0-0335 
 
 
 203-6 
 
 6-8 
 
 Rg. 
 
 Lead 
 
 0-0307 
 
 
 206'4 
 
 6-3 
 
 Rg. 
 
 ' yj 
 
 0-0315 
 
 
 
 
 6-5 
 
 Kp. 
 
 
 0-0314 
 
 
 
 
 6-5 
 
 Rg. 
 
 Bismuth 
 
 0-0305 
 
 
 208 
 
 6-3 
 
 Kp. 
 
 )) 
 
 0*0308 
 
 
 
 
 6'3 
 
 Rg. 
 
 Thorium 
 
 0-0276 
 
 
 232-4 
 
 6-4 
 
 Nn 
 
 Uranium 
 
 0-028 
 
 
 240 
 
 6-6 
 
 Zn. 
 
 Notes to preceding Table. 
 
 I The number for beryllium is that calculated by Humpidge from a series 
 of determinations at temperatures varying from 100 to 450 made with a specimen 
 of beryllium containing 99*2 per cent, of the metal: for fuller discussion of specific 
 heat of beryllium see par. 28, pp. 62, 63. 
 
 2 - 3 - 4 Spec, heats of boron, carbon, and silicon are discussed on pp. 63 65, 
 par. 29. 
 
 5 The higher temperature (+ 10) is not given in Regnault's paper, but judging 
 from the context it appears to be approximately correct. 
 
 6 This number for chromium is probably too low ; see Kopp, Annalen, Supplbd. 
 3. 77 (note). 
 
 7 The specimen of manganese employed contained a little silicon. 
 
 8 Spec, heat of molten gallium between 109 and 119= "0802. (Berthelot, 
 Bull. Soc. Ckim. 31. 229.) 
 
 9 Spec, heat of amorphous selenion determined at high temperatures is ab- 
 normal, because of the large quantity of heat absorbed before fusion. 
 
 10 Spec, heat of zirconium calculated by Mixter and Dana from determinations 
 made with a sample containing known quantities of aluminium. 
 
 II The specimen of molybdenum employed contained carbon. 
 
 12 Spec, heat of gold is nearly constant from o to 600 ; at 900 sp. ht. = '0345 ; 
 and at 1000= "0352. [Violle, Compt. rend. 89. 702.] 
 
 13 Spec, heat of liquid mercury at 55= '033 (Regnault). 
 
 14 The specimen of thallium employed contained a little oxide. 
 
 The numbers marked with J are probably too large; see Weber's papers 
 referred to in next page.
 
 54 ATOMS AND MOLECULES. [BOOK I. 
 
 The names of the various observers are abbreviated in the table : 
 
 {Ann. Chitn. Phys. [2] 73. 5 : 
 [3] 1. 129: 9. 322: 26. 
 261 : 38. 129: 46. 257: 
 63. 5 : and 67. 427. 
 
 KP. ,, ,, KOPP, ,, Annalen 126. 362 : and 
 
 Supplbd. 3. i and 289. 
 
 N. NEUMANN, ,, Fogg. Ann. 126. 123. 
 
 BN. ,, ,, BUNSEN, ,, ,, Pogg- Ann. 141. i. 
 
 WB. WEBER, Pogg. Ann. 154. 367 [trans- 
 
 lation in Phil. Mag. (4) 
 49. 161 and 276.] 
 
 D. P. Du LONG and PETIT, Ann. Chitn. Phys. 10. 395. 
 
 BT. ,, ,, BERTHELOT, ,, Compt. rend. 86. 786. 
 
 HD. ,, ,, HILLEBRAND, ,, Pogg. Ann. 163. 71 [trans- 
 
 lation in Phil. Mag. (5) 
 3. 109]. 
 
 B. W. BETTENDORF and WULLNER Pogg. Ann. 133. 293. 
 
 M. D. MIXTER and DANA, Annalen, 169. 388. 
 
 NN. ,, NILSON, ,, Ber. 15. 2519. 
 
 HE. HUMPIDGE Proc. R. S. 35. 137: 38. 1 88: 
 
 39. i. 
 
 MT. ,, MALLET, ,, ,, ,, ,, Chem. News, 46. 178. 
 
 ZN. ZIMMERMANN Ber. 15. 849. 
 
 N. P. NILSON and PETTERSSON Zeit. f. Physlkal. Chetnie. 1. 
 
 27. 
 26 The preceding table contains the names of 5 1 elements, 
 
 the specific heats of which have been directly determined. 
 For eleven of the remaining elements values have been 
 
 obtained which are regarded by some chemists as representing 
 
 the specific heats of these elements : the method employed is 
 
 based on the assumption that the molecular heat 1 of a solid 
 
 compound is equal to the sum of the atomic heats of its 
 
 constituent elements. (See Kopp, Annalen, Supplh. 3. 
 
 321 339.) Thus Kopp found the mean molecular heat 1 of 
 
 metallic sulphides of the form RS to be equal to 12: the 
 
 atomic heat of sulphur is 57; but 12-57 = 6-3; therefore 
 
 6'3 is regarded as the value of the atomic heat of any one of 
 
 the metals R. The mean value of the atomic heats of these 
 
 metals found by direct experiment is 6'4. 
 
 1 By molecular heat is to be understood the product obtained by multiplying 
 the specific heat of a compound into the mass expressed by the generally accepted 
 formula of that compound; the expressions formula-weight and reacting weight 
 will be employed to signify this mass of any compound.
 
 CHAP. I. 26] ATOMIC HEATS INDIRECTLY DETERMINED. 55 
 
 Kopp has applied this indirect method to calculate the 
 atomic heats of various elements with which direct experi- 
 ments could not be made 1 . 
 Chlorine: 
 Molecular heats of metallic haloid salts : 
 
 RC1 =12-8 RBr=i3'9 RI=i3'4 
 RCl 2 =i8'5 ..................... RI 2 =i9'4. 
 
 Now as (i) the atomic heat of each of the metals R is 
 about 6-4 ; (2) the atomic heat of solid bromine and that of 
 iodine is about 6'6; (3) the chlorides, bromides, and iodides 
 examined are chemically analogous; and (4) the molecular 
 heats of the analogous salts are nearly the same ; Kopp con- 
 cludes that the atomic heat of solid chlorine is about 6-4. 
 
 RC1 (i2-8)-R (6-4) = 6-4 : RC1 2 (i8'5)-R (6-4) = 12-1, and ^ = 6-05. 
 
 A further argument in favour of this conclusion is afforded 
 by these data: 
 
 Molecular heat of KC1O 3 = 24'8 
 
 hence the atomic heats of arsenic and chlorine are probably 
 nearly the same ; but the atomic heat of arsenic is 6'i ; there- 
 fore the atomic heat of solid chlorine is probably about 6'i. 
 Fhwrine : 
 
 Molecular heat of CaF 2 = 16*4 
 atomic heat of Ca= 6'8, 
 
 16-4-6-8 
 hence atomic heat of fluorine = - =4'o. 
 
 Nitrogen : 
 Molecular heats of various more or less analogous compounds: 
 
 RAsO 3 =25'3 RSiO 3 =2o'5 
 
 RPO 3 =22'i RNO 3 = 23'o. 
 
 Hence, it is argued, the atomic heat of solid nitrogen is 
 probably rather less than that of chlorine or arsenic (about 6), 
 somewhat greater than that of carbon or silicon (about 5'2), 
 and nearly equal to that of phosphorus (about 5 '8); therefore 
 the value of the atomic heat of solid nitrogen probably lies 
 between 5-5 and 5 '8. 
 
 1 For detailed data see Kopp, Annalen, Supplb. 3. 329.
 
 56 ATOMS AND MOLECULES. [BOOK I. 
 
 Oxygen : the molecular heats of metallic oxides are, as a 
 rule, rather less than those of corresponding haloid salts ; 
 therefore, it is said, the atomic heat of solid oxygen is pro- 
 bably less than 6 ; thus, 
 
 RO =iri RC1 =i2'8 RBr=i3'9 RI =I3'4, 
 
 RO 2 =i37 RCl 2 =i8'6 RI 2 =i9'4. 
 
 Further data for finding the value sought for are these : 
 
 Molecular heats R 2 O 3 = 2/-2 ; KAsO 3 =25'3 : KC1O 4 = 26'3; 
 
 KMnO 4 =28'3. 
 
 The values deduced for the atomic heat of solid oxygen 
 are as follows : 
 
 from RO ...4*6, from KAsO 3 ...4'2 
 
 RO 2 ...37, KC1O 4 ...3'5 [assuming Cl = 6] 
 R 2 3 ...4'8, KMn0 4 ...3'8, 
 
 hence the mean value is 4-1. 
 
 Hydrogen : the principal data are these : 
 (i) Molecular heat of ice (H 2 O) = 9 : molecular heat of Cu 2 O = 15*6. 
 Hence, it is argued, the atomic heat of solid hydrogen is 
 
 probably less than that of copper by the amount = 3'3 : 
 
 but atomic heat of copper = 6*4 ; therefore the atomic heat of 
 solid hydrogen = 3-1. 
 
 fbut atomic heat 1 of N is about 5'6) 
 
 (n) Molecular heat of NH 4 C1 = 20: \ , . , . . _. ? \, 
 
 [and atomic heat 1 of Cl 6'4j ' 
 
 o 
 
 Now 20 12 = 8, and - = 2 ; therefore the atomic heat of 
 
 4 
 hydrogen is about 2. 
 
 (iii) Molecular heat of NH 4 NO 3 = 3 
 
 oxides R 2 O 3 = 27-2 
 
 Hence 36*4 - 27*2 = 9-2, and = 2*3. 
 
 4 
 
 The mean of these three results is 2-4, a number which 
 may perhaps be provisionally accepted as the atomic heat of 
 solid hydrogen : the method of calculation however involves 
 many assumptions and the use of numbers themselves ob- 
 tained by indirect means. From experiments with palladium 
 
 1 Indirectly determined, see p. 55.
 
 CHAP. I. 26] ATOMIC HEATS INDIRECTLY DETERMINED. 57 
 
 charged with hydrogen, Beketoff deduced the number 5 '9 as 
 representing the atomic heat of solid hydrogen '. 
 
 The molecular heats of the oxides, chlorides, carbonates, 
 nitrates, and sulphates, of calcium, barium, and strontium are 
 nearly the same as the molecular heats of the corresponding 
 salts of metals the atomic heats of which have been directly 
 determined and found to be represented by the mean number 
 6*4 ; hence the atomic heats of calcium, barium, and strontium 
 are probably represented by a number approximately equal 
 to 6-4. 
 
 The agreement noticed between the values of the molecular 
 heats of the chloride and carbonate of rubidium, of the oxides 
 and chlorides of chromium and titanium, and of the oxides of 
 vanadium and zirconium, and the molecular heats of corre- 
 sponding salts of other metals which themselves exhibit the 
 mean atomic heat 6*4, shews that the atomic heat of rubidium, 
 that of titanium, of zirconium, of chromium, and of vanadium, 
 is probably 2 about 6-4. (See notes 6 and 10 to table of speci- 
 fic heats of elements, p. 53.) 
 
 The following numbers representing the molecular heats 
 of salts of some of the rarer elements are given by Nilson; 
 (Ber. 13. 1459 et se 4-}- 
 
 '{feat C Temperature. "! 
 
 Scandium salts (80 = 44-03) Sc 2 O 3 'I53 o 100 2O'8i 
 
 Sc. 2 3SO 4 0-1639 62-42 
 
 Erbium salts (E,r=\66) Er 2 O 3 0-065 2 47 
 
 Er 2 3SO 4 0-104 64-5 
 
 Yttrium salts ( = 89-5) Y 2 O 3 0-1026 23-3 
 
 Y 23 S0 4 0-1319 6r6 
 
 Ytterbium sails (Yb=i73) Yb 2 O 3 0-0646 25-5 
 
 Yb 23 S0 4 0-104 ' 65-8 
 
 Gallium oxide Ga^j 0-1062 19-5 
 
 Indium oxide In 2 O 3 0-0807 22*2 
 
 If we assume that the atomic heat of oxygen is 4-1 (see 
 p. 56), and regard only the oxides in the above table, then 
 
 1 See abstract of BeketofFs paper (original is in Russian) in Ber. 12. 687. 
 
 s For a full collection of specific heat data see F. W. Clarke's Constants of 
 Nature, part n: or, Landolt and Bernstein's Physikalisch-chemische Tabcllen. In 
 connexion with this subject of molecular heats see also Kopp, Ber. 19. Si i.
 
 58 ATOMS AND MOLECULES. [BOOK I. 
 
 the following values are found for the atomic heats of the 
 metals in these oxides : 
 
 Sc=4'2 Er = 6-i Y=5'5 Yb = 6'6 : Ga=3'6 In = 5'o. 
 If a similar process is applied to the sulphates (atomic heat 
 of S = 6), then the atomic heats of the metals are all repre- 
 sented by negative numbers; hence either (i) the value of 
 the atomic heat of oxygen in compounds is not constant, or 
 (2) that of sulphur varies, or (3) that of the metals Sc, Er, Y, 
 Yb, Ga, In, is negative in their sulphates, and, for some of 
 these metals, is abnormal in their oxides. 
 
 The last hypothesis can scarcely be adopted. Indeed if 
 the atomic heats of gallium and indium as determined by 
 direct experiment are placed beside the numbers obtained by 
 calculation from the molecular heats of the oxides (assuming 
 O = 4'i) we have this result : 
 
 Directly Calculated from 
 
 determined. oxides. 
 
 Atomic heat of Gallium 5*4 3 '6 
 
 Indium 6*5 5'o 
 
 We can scarcely hesitate which numbers to prefer. 
 
 It seems then that the value to be assigned to the atomic 
 heat of oxygen in oxides 1 (and probably also the value of the 
 atomic heat of sulphur in sulphates) is not a constant number, 
 but varies according to the metal with which the oxygen is 
 combined 2 : but if this is so, much doubt must necessarily be 
 thrown on the accuracy of the conclusions regarding the 
 atomic heats of chlorine, nitrogen, and other elements, deduced 
 from the molecular heats of compounds of these elements. 
 It appears then that the Garnier-Cannizzaro generalisation 
 (see ante, p. 51) cannot always be applied 3 . 
 
 1 Such phrases as 'atomic heat of oxygen in oxides,' 'atomic heat of sulphur 
 in sulphates' are perhaps rather misleading; they seem to assume that an 
 elementary atom has different capacities for heat according to the nature (and 
 number) of other atoms with which it is combined, and that measurements of 
 these various capacities are obtainable; this assumption is not, I think, fully 
 justified by facts. 
 
 8 See Kopp, Ber. 19. 813; also post, chapter in. par. in. 
 
 3 Measurements of the ratio of specific heat at constant volume to that at 
 constant pressure for various gases composed of diatomic molecules have shewn 
 that the value of this ratio is considerably smaller in some cases than in others ;
 
 CHAP. I. 26] ATOMIC HEATS INDIRECTLY DETERMINED. 59 
 
 Although a knowledge of the molecular heats (so-called) 
 of solid compounds may give considerable help towards fixing 
 the formulae of these compounds, and so, indirectly, deciding 
 what multiple of the combining number of an element is 
 to be adopted as the atomic weight of that element, yet, it 
 appears to me, that so far as concerns the direct determination 
 of atomic weights, only those values for specific heats which 
 have been obtained by experiments on the solid elements 
 themselves are of much value. 
 
 It is certain that in some cases erroneous conclusions 
 regarding the value of an atomic weight may be deduced 
 from measurements of the specific heats of solid compounds. 
 Thus it was for some time doubtful whether the value 120 
 or 240 should be assigned to the atomic weight of uranium. 
 In 1878 Donath found the specific heat of uranoso-uranic 
 oxide to be -0798 (Ber. 12. 742); assuming the specific heat 
 
 of solid oxygen to be 0*25 (i.e. ^J , the specific heat of 
 
 uranium was calculated to be -0497; now '0497 x 120=5*96; 
 therefore it was concluded by Donath that the atomic weight 
 of uranium is 120. But in 1880 I pure uranium was pre- 
 pared by Zimmermann (for details see Ber. 14. 440 and 779 : 
 15. 849), and the specific heat of this metal was found by him 
 to be -028; but -028 x 120 = 3-3: hence, to bring the atomic 
 heat of uranium into agreement with that of the majority of 
 the elements it is necessary to assign to the atomic weight 
 of this metal the value 240. 
 27 If the table of maximum atomic weights (p. 48) is com- 
 
 hence a complete theory of specific heat, even when applied to gases, must 
 take account not only of the number but also of the nature of the atoms in a 
 molecule (compare Ostwald, Lehrbuch der allgemeinen Chetnie, 1. 230). When 
 the 'molecular heat' of a compound is smaller than the calculated value it may 
 be that the molecule of the compound is built up of groups of atoms each of 
 which group counts as a single atom. If the atoms forming a molecule are 
 symmetrically arranged (i.e. if the distance between one pair of atoms is much 
 the same as that between any other pair) then the total kinetic energy of the 
 molecules is very probably proportional to the number of atoms ; but if some of 
 the atoms are arranged in groups or systems, the total kinetic energy will be 
 proportional to the number of systems, and not to the number of atoms (see 
 'Aggregation, States of in the new Ed. of Watts's Dictionary of Chemistry).
 
 60 ATOMS AND MOLECULES. [BOOK I. 
 
 pared with that which gives the specific heats of elements 
 (pp. 51 53), it will be found that omitting the three ele- 
 ments which are placed in brackets in the former table of 
 the 43 elements (omitting those in brackets) whose atomic 
 weights have been determined by the application of Avoga- 
 dro's law, 34 have also had values assigned to their specific 
 heats by direct experiments. Comparing the products ob- 
 tained by multiplying the atomic weight into the specific heat 
 in each of these 34 cases, it is found that 5 of these products 
 fall below 5 '8 (varying from 57 to 5'2), and that 29 vary from 
 6'8 to 6, giving a mean value of 6*4, round which number most 
 of the values are grouped. The conclusion to be drawn is 
 that the atomic heat of the 29 elements in question is repre- 
 sented by the number 6'4. There are three elements in 
 brackets in the table on p. 48, viz. iron, copper, and gallium : 
 if the maximum atomic weight of each, as deduced by Avo- 
 gadro's law, is multiplied into the specific heat of the element 
 the product is found to be about 12, but if the true atomic 
 weights are assumed to be half as large as the numbers in the 
 table, then the atomic heat of each of these elements is repre- 
 sented by the mean number 6'4- Now there are no valid 
 reasons against adopting half the maximum values obtained 
 by Avogadro's law as the true values of the atomic weights 
 of the three elements in question, indeed there are strong 
 chemical reasons in favour of this course. 
 
 Hence we have a very considerable mass of facts in favour 
 of the generalisation : 
 
 T/te atomic heat of all solid elements is nearly a con- 
 stant, the mean value of which is 6'4> 
 
 If this be granted, we deduce the statement for finding an 
 approximate value for the atomic weight of an element : 
 
 Atomic weight is approximately equal to j ; 
 
 provided always it is remembered that the specific heat is 
 assumed to be determined with the element in the solid form, 
 and for a considerable range of temperature throughout which 
 the value remains nearly constant. 
 
 This method for determining the atomic weights of ele-
 
 CHAP. I. 27] ATOMIC HEATS. 6 1 
 
 merits has been applied in about 14 cases, besides* those 
 cases where the method of specific gravities has also been 
 employed ; the numbers obtained are usually regarded as the 
 true atomic weights of the elements in question. 
 
 It is evident that in determinations of the specific heats of 
 solid elements we have a most valuable means for deciding 
 which multiple of the combining number of an element is 
 to be accepted as most probably expressing the value of 
 the atomic weight of that element. When the element 
 cannot be obtained, or cannot be obtained in sufficient quan- 
 tity, in the solid form, then measurements of the specific 
 heats of a series of its solid compounds will afford more or 
 less valuable guidance in attempts to find the atomic weight 
 of the element in question. 
 
 The following statements fairly sum up the results of 
 atomic heat determinations. 
 
 I. Solid elements, forty-five in number, whose specific Jieats 
 have been directly determined, and zvhose atomic heats are all 
 nearly equal to 6^4. 
 
 Li Na Mg Al P S K Ca Ti Mn Fe Co Ni Cu Zn As 
 Se Br Zr Mo Rh Ru Pd Ag Cd In Sn Sb Te I La 
 Ce Di W Os Ir Pt Au Hg Tl Pb Bi Th U (Cr) 
 
 II. Solid elements, six in number, wlwse specific heats Jtave 
 been directly determined, and whose atomic heats appear to be 
 about 5*5. 
 
 Ga [? inaccurately determined] Be B C Si Ge. 
 
 III. Solid elements, five in number, whose specific heats 
 have been indirectly determined, and whose atomic heats are 
 probably nearly equal to 6'4. 
 
 V Rb Sr Cs Ba. 
 
 IV. Gaseous elements ; atomic heats very doubtful, appa- 
 rently variable. 
 
 H (F) N O Cl. 
 
 Of the elements whose atomic heats are decidedly less 
 than 6-4, all, except gallium beryllium and germanium, are 
 non-metallic and have atomic weights smaller than 33: indeed 
 if the elements are arranged in order of increasing atomic 
 weight, it is found that, with the exception of lithium, all 
 having an atomic weight less than 23 have also an atomic
 
 62 ATOMS AND MOLECULES. [BOOK I. 
 
 heat less than 6, and that these elements, except beryllium, 
 are non-metallic. 
 
 28 The data concerning the specific heats of beryllium, boron, 
 carbon, and silicon, must be examined in some detail. 
 
 Beryllium. R. E. Reynolds (Phil. Mag. (5) 3. 38) deter- 
 mined the specific heat of this metal at 100 to be '642 : the 
 metal used was however impure. 
 
 Nilson and Pettersson (Ber. 11.351) determined the specific 
 heat of a mixture of metallic beryllium with known quantities 
 of beryllium oxide, ferric oxide, and silica ; they also deter- 
 mined the specific heat of pure beryllium oxide, and, the 
 specific heats of ferric oxide and silica being known, they 
 calculated the specific heat of the metal beryllium to be '4079, 
 for the temperature interval o 100. 
 
 The same chemists (Ber. 13. 1456: see also Chem. News, 
 42. 297) made a second series of determinations with a sample 
 of the metal containing only about 5 per cent, of beryllium 
 and ferric oxides. The following table gives their more 
 important results : 
 
 Specific heat of Beryllium. (NlLSON and PETTERSSON.) 
 
 Temperature interval. 
 
 Specific heat. 
 
 Sp.hLx 13-65. 
 
 o 46 -5 
 
 0'3973 
 
 5 '4 
 
 100 
 
 0-4246 
 
 5-8 
 
 o 214 
 
 0*475 
 
 6-4 
 
 o 300 
 
 0-5055 
 
 6-9. 
 
 Hence these chemists concluded that the atomic weight 
 of beryllium ought to be taken as I3'65, and not 9-1, the value 
 usually assigned to this constant 
 
 The results tabulated above shew that the value of the 
 specific heat of beryllium for the interval o 300 is 
 
 27 per cent, greater than the value for the interval o 50 ; is 
 7 o 200 ; and is 
 
 19 o 100. 
 
 Using the data of Nilson and Pettersson, L. Meyer (Ber. 
 13. 1780) calculated the values of the specific heat of beryllium 
 at various temperatures, with the following results :
 
 CHAP. I. 28-29] ATOMIC HEAT OF BERYLLIUM. 63 
 
 True specific heat of Beryllium at various temperatures, (MEYER.) 
 
 7 = true specific heat at temperature /. 
 Ay = increase in value of y per iC. 
 
 t. 
 
 y- 
 
 Ay. 
 
 ^=9-1 
 
 ^=13-65 
 
 20'2 
 73'2 
 
 0-3973 
 0-4481'" 
 
 O'OOIOI 
 
 0-00085 
 
 3-62 
 
 4-08 
 
 5'43 
 6-12 
 
 157 
 
 0-5193'" 
 
 0*00063 
 
 473 
 
 7-10 
 
 256-8 
 
 0-5819 
 
 
 5-29 
 
 8-94. 
 
 Hence, Meyer concluded that the specific heat of beryllium 
 increases rapidly as temperature increases, but that the rate 
 of this increase diminishes ; and that the specific heat pro- 
 bably attains a constant value, equal to about O"6, at 300 or so 1 . 
 
 Humpidge 2 , working with a specimen of beryllium con- 
 taining 99-2 per cent, metal and 7 per cent, beryllium oxide, 
 obtained the following numbers : 
 
 Specific heat of Beryllium. (HUMPIDGE.) 
 
 Temp. Specific heat. 
 
 100 '4702 
 
 200 -540 
 
 400 '6172 
 
 500 '6206. 
 
 The value approximates to a constant (= about '62) some- 
 where between 400 and 500. 
 
 Boron, Carbon, and Silicon. Very varying values have 
 been obtained for the specific heats of these three ele- 
 ments. The following table summarises the principal data 
 previous to the publication of Weber's papers [see Phil. Mag. 
 (4) 49. 161 & 276]. 
 
 Specific heats of Boron, Carbon, Silicon. (Weber's numbers not included.) 
 (Temperature may be taken as about 35 55.) 
 
 Boron amorphous 
 crystalline 
 
 Sp. ht. 
 
 Sp. ht.Xat. wt, 
 
 Observer. 
 
 
 0-254 
 
 2-8 
 
 Kp. 
 
 1864 
 
 0-230 
 
 2-6 
 
 
 
 
 
 0-252 
 
 2-8 
 
 M.D. 
 
 1873 
 
 0*262 
 
 2-9 
 
 Rg. 
 
 1869 
 
 0'225 
 
 2-5 
 
 Rg. 
 
 1869 
 
 0-257 
 
 2-8 
 
 
 
 
 
 0-235 
 
 2-6 
 
 
 
 
 
 graphitic 
 
 1 For a discussion of the value to be assigned to the atomic weight of beryllium 
 see chapter in. par. 1 1 1. 
 
 2 Proc. R. S.3B. 137: 38. 1 88 : and specially 39. I,
 
 S P . ht. 
 
 Sp. ht. X at. wt. 
 
 Observer. 
 
 
 0-143 
 
 17 
 
 B.W. 
 
 1868 
 
 0-147 
 
 r8 
 
 Rg- 
 
 1841 
 
 0-165 
 
 2"O 
 
 Kp. 
 
 1864 
 
 0-186 
 
 2'2 
 
 B.W. 
 
 1868 
 
 0-197 
 
 2'4 
 
 Rg. 
 
 1841 
 
 0-174 
 
 2'I 
 
 Kp. 
 
 1864 
 
 0-188 
 
 2'3 
 
 B.W. 
 
 1868 
 
 O'2OI 
 
 2'4 
 
 Rg- 
 
 1866 
 
 0-138 
 
 3'9 
 
 Kp. 
 
 1864 
 
 0-166 
 
 4-6 
 
 Rg. 
 
 1861 
 
 0*165 
 
 4-6 
 
 Kp. 
 
 1864 
 
 0'I7I 
 
 4-8 
 
 M.D. 
 
 1873 
 
 0-173 
 
 4'8 
 
 Rg. 
 
 1861. 
 
 64 ATOMS AND MOLECULES. [BOOK I. 
 
 1 Carbon diamond 
 
 j> 
 
 gas-carbon 
 
 >i . 
 i> 
 
 graphite 
 
 > 
 
 > 
 
 Silicon fused 
 
 ii 
 
 crystalline 
 
 Weber (loc. at.} found that the specific heats of carbon, 
 boron, and silicon, increase rapidly as the temperature is 
 raised, but that at high temperatures the rate of the increase 
 becomes much smaller. The following table gives a synopsis 
 of Weber's results : 
 
 Specific heats of Boron, Carbon, and Silicon. (WEBER.) 
 
 Temp. Spec. heat. Spec. ht. x at. wt. 
 
 Boron crystallised 40 0-1915 2-11 
 
 > +77 0-2737 3-01 
 
 ; 177 0-3378 372 
 
 ii 2 33 0-3663 4-03. 
 
 These numbers shew that the specific heat of boron in- 
 creases with increase of temperature, and that the value of 
 this increase, for a given interval, is considerably less at high 
 than at low temperatures. The variations in the rate of 
 this increase are almost identical with the variations noticed 
 in the case of carbon ; hence at temperatures above 233 
 this identity will probably remain. Calculated on this as- 
 sumption, the specific heat of boron at about 1000 is 0*50. 
 
 It must however be observed that Weber did not prove 
 the purity of the specimen of crystalline boron with which he 
 worked. The crystals were prepared by reducing boric oxide 
 
 1 Dewar (Phil. Mag. [4] 44. 461) found for the specific heat of gas-carbon 
 between 20 and 1040 the number 0-32, for diamond the number o'366; and, 
 between 20 and a temperature estimated to be 2000, for 'carbon' the number 
 0-42.
 
 CHAP. I. 29] ATOMIC HEAT OF CARBON. 65 
 
 by aluminium ; according to Hampe (Annalen, 183. 75) the 
 substance thus obtained is a definite boride of aluminium, 
 A1 12 B. 
 
 Specific heats of Boron, Carbon, and Silicon. (WEBER) continued. 
 
 Temp. Spec. heat. Sp. ht. x at. wt. 
 
 Carbon diamond -50 0-0635 0-76 
 
 +10 0-1128 1-35 
 
 85 0-1765 2'12 
 
 250 0-3026 3-63 
 
 606 0-4408 5-29 
 
 985 0-4589 5-50 
 
 graphite - 50 0-1138 1*37 
 
 +10 0-1604 1-93 
 
 61 0-1990 2-39 
 
 201 0-2966 3-56 
 
 250 0-325 3-88 
 
 641 0-4454 5'35 
 
 978 0-467 5-60 
 
 Porous wood carbon o 23 0-1653 1*95 
 
 o 99 0-1935 2-07 
 
 o 223 0-2385 2-84. 
 
 These numbers shew that the specific heat of carbon 
 increases from 50 upwards, the value found at 600 being 
 about seven times as great as that found at 50 ; but that 
 the rate of this increase is very small at high temperatures ; 
 from a red heat upwards the rate is about one-seventeenth 
 of that from o to 100. 
 
 The specific heats of diamond and graphite differ at tem- 
 peratures below about 600, but from this point upwards they 
 are practically identical ; the numbers given for porous wood 
 carbon are almost the same as those for graphite for the same 
 temperature-intervals ; hence it may be said that at high 
 temperatures (above 600) the various modifications of carbon 
 have probably all the same specific heat. 
 
 Table continued. 
 
 p. Temp. Spec. heat. Sp. ht. x at. wt. 
 
 Silicon crystallised -40 0*136 3-81 
 
 +57 ' Q'i833 5'i3 
 
 128 0-196 5-50 
 
 184 0-20 1 I 5-63 
 
 232 0-2029 5-68 
 
 M.C. 5
 
 66 ATOMS AND 'MOLECULES. [HOOK I. 
 
 The specific heat of silicon attains an almost constant 
 value at about 200. 
 
 30 It is evident that the specific heat of an elementary 
 body is not a constant number, but varies with the tem- 
 perature, and that the relation between the variation of 
 specific heat and that of temperature differs for each element. 
 The following formulae calculated from experimentally deter- 
 mined numbers, express the relation in question for some of 
 the elements : 
 
 1 Carbon diamond sp. ht. = 0-4408 + 0-0000405 /, where / varies from 
 
 6oo 800 
 
 = 0-4408 + 0-000056 1 1 8oo 1000 
 
 graphite = 0*4454 + 0*0000472 / 600 800 
 
 =0-4454 + 0-0000840 / 8oo 1000 
 
 2 Copper = 0-0910 + 0*000023 1 o 250 
 
 2 Zinc =0-0865 + 0*000044 1 
 
 2 Lead =0-0286 + 0-000019 1 
 3 Platinum = 0*03 1 7 + o'ooooo6 / o 1200 
 
 The specific heat of any substance also varies with varia- 
 tions in the physical state of that substance, thus : 
 
 Sp. heat. 
 
 Bromine solid ... ... 0-0843 
 
 liquid ... ... OTIIO 
 
 Soft copper 0-0948 
 
 Hard copper ... ... 0*0934 
 
 Iron sulphide as strahlite 0-1332 
 
 Sp. heat. 
 
 Iron sulphide as pyrites ... 0-1279 
 
 Chlorine solid ... ... o'i8o 
 
 4 gaseous ... 0*093 
 
 Mercury solid ... ... 0*032 
 
 4 gaseous ... 0-015 
 
 The specific heats of the elementary bodies have gener- 
 ally been determined at temperatures situated at very varying 
 intervals from the melting points of these elements ; the 
 physical aggregation of the specimens examined has also 
 varied much ; hence the values found for the specific heats 
 of the elements cannot be regarded as strictly comparable. 
 
 There appears to be a certain interval of temperature 
 within which the value of the specific heat of a solid element 
 becomes nearly constant, and for this interval only can the 
 element be said approximately to obey the law of Dulong 
 
 1 Weber (loc. fit.). 
 
 2 Bede, Mem. Couronn. de FAcad. Brux. 27. 3 (1855). 
 
 3 Violle, Compt. rend. 85. 543. 
 
 4 Calculated for constant volume.
 
 CHAP. I. 30-31] ATOMIC HEATS. 67 
 
 and Petit, as stated on p. 60. This temperature-interval 
 varies for each element, especially for the nonmetallic ele- 
 ments with small atomic weights ; for many elements it may 
 be roughly taken as from o to 100 ; but for several it is only 
 attained at high temperatures. 
 
 Kopp (loc. tit.} has supposed that the atoms of certain 
 elements more especially of boron, carbon, and silicon are 
 built up of simpler parts, have themselves a grained structure, 
 and that at high temperatures the atoms of these elements 
 are composed of a smaller number of those little parts than at 
 lower temperatures. Heat added at low temperatures is 
 supposed, on this hypothesis, to be used in separating the 
 atomic groups. With regard to Kopp's hypothesis it may be 
 observed, that the facts of spectroscopy seem to point to the 
 existence of a more complex structure in the nonmetallic than 
 in the metallic molecules ; that allotropy occurs distinctly 
 only among the non-metals ; that the molecules of the five 
 metallic elements whose vapour-densities have been deter- 
 mined are monatomic ; that the atomic heat of tellurium, a 
 metal-like non-metal belonging to the oxygen group, is 6 - o, of 
 the less metal-like selenion about 5'8, of the decidedly non- 
 metallic sulphur about 5'5, and of the typical non-metal oxygen 
 probably not more than 4; and finally that the molecular 
 structures of oxygen, sulphur, and selenion, vapours are more 
 complex than that of tellurium vapour. Now as carbon, 
 boron, and silicon are distinctly non-metallic elements, these 
 facts lend support to the view that a part of the heat added 
 to carbon, boron, or silicon, at low temperatures is spent in 
 separating complex molecular groups into their constituent 
 parts, rather than in separating the hypothetically complex 
 atoms of these elements into smaller atoms. 
 
 31 A consideration of the data summarised in the preceding 
 paragraphs shews, I think, that the application of Avogadro's 
 law is of more value to the chemist as a means of determining 
 the atomic weights of elements than the law of Dulong and 
 Petit. From a general consideration of the molecular theory 
 of matter it is also apparent that a deduction which does not 
 necessitate an exact hypothesis as to the internal structure of 
 
 52
 
 68 ATOMS AND MOLECULES. [BOOK I. 
 
 molecules is more trustworthy and more appropriate, in the 
 present state of knowledge, than another which does necessi- 
 tate some such hypothesis. 
 
 The molecular explanation of the gaseous laws expressing 
 relations between volume, pressure, and temperature, and of 
 Avogadro's law, may be considered as fairly complete ; but in 
 order to give a molecular explanation of the law of specific 
 heats more knowledge of the internal structure of molecules 
 than we now possess is necessary 1 . For the specific heat of a 
 substance depends on the rate at which the whole energy of 
 the molecule increases with increase of temperature : but this 
 energy is made up of two parts, (i) the energy of agitation, 
 that is, the energy the molecule would possess if it moved as a 
 whole with the motion of its centre of mass, or in other words 
 without rotation ; and (2) the energy of rotation, that is, the 
 energy the molecule would possess if its centre of mass were 
 reduced to rest, in other words the energy due to the motion 
 of the parts relatively to the centre of mass of the molecule 2 . 
 If it is assumed that the energy due to the rotational motions 
 of the parts of the molecule tends towards a value having a 
 constant ratio to the energy of agitation of the molecule, 
 then a simple expression is found for the whole energy ; but 
 this expression contains a factor which varies in different 
 gases, and the value of which has been determined only in a 
 few cases 3 . And moreover it is probable that when the energy 
 due to the rotational motions of the parts of a molecule 
 becomes greater than a certain quantity, the molecule separates 
 into parts ; hence when heat is imparted to a mass of mole- 
 cules work is probably in many cases done in destroying 
 some of the molecules as such 4 . Hence the molecular expla- 
 nation of specific heat is not at present in so advanced a state 
 as that of the relations between the volumes, pressures, and 
 temperatures, of gases 5 . If this be true concerning gases, still 
 
 1 Clerk Maxwell, C. S. Journal [2] 13. 507. 
 
 3 Clerk Maxwell, lot. cit. p. 502. 
 
 8 See Clerk Maxwell's Heat, pp. 317319 (6th ed.). 
 
 4 See Hicks, Phil. Mag. (5). 4. 80, and 174. 'On some effects of Dissocia- 
 tion on the Physical Properties of Gases. ' 
 
 5 See in connexion with this subject Strecker, Wied. Ann. 13. 20; and Bolt;;-
 
 CHAP. I. 31-32] ISOMORPHISM. 69 
 
 more is it true concerning solid bodies. Our knowledge of 
 the molecular phenomena of solids is very small ; but the law 
 of Dulong and Petit is applicable to solid elements only. 
 Finally, when heat is added to a solid only a portion of it is 
 used in raising the temperature; another part is spent in 
 increasing the volume of the solid, and a third part is em- 
 ployed in doing work against the external pressure on the 
 solid. 
 
 32 The so-called ' law of isomorphism ' affords a basis on 
 which is founded another method for determining the atomic 
 weights of elementary bodies. 
 
 The views of Abbe Haiiy were dominant in crystallo- 
 graphy in the early days of this century ; he admitted 
 a close connexion between crystalline form and chemical 
 composition, but he thought that each chemically dis- 
 tinct body must be characterised by a definite and peculiar 
 form. 
 
 In 1816 Gay-Lussac noticed that the growth of crystals 
 of potash alum was not affected by placing them in a solution 
 of ammonia alum. 
 
 Various observations of this kind were made from time to 
 time 1 until 1819, when E. Mitscherlich propounded the law of 
 isomorphism, which, modified and developed, was stated by 
 him in 1821 in the following terms: " Equal numbers of atoms 
 similarly combined exhibit tJie same crystalline form ; identity 
 of crystalline form is independent of t/te chemical nature of 
 the atoms, and is conditioned only by the number and configura- 
 tion of the atoms." 
 
 Since this date various observers have advanced the know- 
 ledge of the relations between crystalline form and chemical 
 composition 2 . The more important generalisations are as 
 follows. 
 
 mann, Jo. 13. 544: and 18. 309: also art. Aggregation, States of, in the new 
 edition of Watts' s Dictionary. 
 
 1 For a full historical account of the development of the conception of Iso- 
 morphism, with copious references, see the article 'Isomorphie' in the Neues 
 Handivortcrbuch der Chemie, Bd. ill. p. 844 el seq. 
 
 * See especially ffandworterbuch, loc. at. and Kopp's Lchrbuch der physikal- 
 ischcti und thcorctischcn Chcinic (2nd Ed.), Bd. II. pp. 136155.
 
 70 ATOMS AND MOLECULES. [BOOK I. 
 
 Similar chemical constitution 1 is not necessarily accom- 
 panied by identical crystalline form ; 
 e.g. PbCrO 4 monoclinic, and PbMoO 4 quadratic ; 
 
 AgCl and AgBr regular, and Agl hexagonal ; 
 
 KNO 3 and (NH 4 )NO 3 rhombic but not identical, CsNO 3 and 
 RbNO 3 hexagonal. 
 
 Unlike chemical constitution may be accompanied by 
 similar or identical crystalline form : thus Marignac 2 shewed 
 that the following salts crystallise in identical forms ; 
 
 K 2 TiF 6 . H 2 O, K 2 NbOF 5 . H 2 O, K 2 WO 2 F 4 . H 2 O, are isomorphous ; 
 andCuTiF 6 .4H 2 O, CuNbOF 5 .4H 2 O, CuWO 2 F 4 . 4 H 2 O, are isomorphous. 
 Klein 3 has shewn that the complex compounds 
 9WO 3 . B 2 O 3 . 24H 2 O and I2WO 3 . SiO 2 .33H 2 O, and 
 9\VO 3 . B 2 O 3 . Na 2 O . 23H 2 O, are isomorphous. 
 
 Klein has modified the statement of the law of isomor- 
 phism thus : 
 
 " Isomorphous bodies have either a similar chemical constitution or 
 exhibit only slight differences in percentage composition ; there is always a 
 group of elements which is either common to all the isomorphous bodies, 
 or exhibits identical chemical functions in these bodies, and which 
 constitutes by far the greater part of each of the isomorphous bodies." 
 
 It would appear that all the constituents of a compound 
 exert an influence on the form of that substance. Isomorphism 
 may not be exhibited in comparatively simple analogous 
 compounds of two elements, but may appear in more complex 
 compounds of the same elements ; e.g. many of the simpler 
 compounds of cadmium are not isomorphous with the analo- 
 gous compounds of the metals of the magnesium group (Mg, 
 Mn, Fe, Co, Ni, Zn, Cu, Ca), but comparatively complex 
 cadmium salts such as CdSO 4 . K 2 SO 4 .6H 2 O are generally 
 isomorphous with the corresponding compounds of the mag- 
 nesian metals. Again, many simple salts of sodium and 
 potassium are not isomorphous although their composition is 
 similar, but the alums are isomorphous. 
 
 1 This phrase must not be interpreted too strictly. Closely allied compounds 
 the formula; of which contain the same number of elementary atoms, or groups of 
 atoms, may be said, for the purposes of the present argument, to exhibit a ' similar 
 chemical constitution.' 
 
 2 Ann. Chim. Phys. 60. 257. 3 Compt. rend. 95. 781.
 
 CIIAIM.32] ISOMORPHISM. 71 
 
 One may suppose that the presence of a large number of 
 isomorphous atoms exerts a dominating influence over a 
 smaller number of non-isomorphous atoms. 
 
 The constituents of isomorphous compounds are not them- 
 selves always isomorphous. Thus, the sulphates of nickel, 
 magnesium, and zinc, crystallise in rhombic forms, but the 
 oxides of the same elements are not isomorphous. 
 
 In other cases the constituents of isomorphous bodies are 
 themselves isomorphous ; e.g. the compound 3Ag 2 S . Sb 2 S 3 has 
 the same crystalline form as the compound 3Ag 8 S . As 2 S 3 , 
 Sb 2 S 3 and As 2 S 3 are isomorphous in rhombic forms, and 
 arsenic and antimony form almost identical rhombic crystals. 
 Hence we must distinguish strict isomorphism as applied to 
 bodies which, with similar composition, exhibit the same or 
 nearly the same crystalline form ; and isomorphism as more 
 loosely applied to bodies which, although not themselves 
 crystallising in the same form, nevertheless combine with 
 other bodies to produce strictly isomorphous compounds into 
 which they enter as corresponding groups 1 . 
 
 A certain latitude is generally allowed in the application of 
 the term ' isomorphous crystals.' This latitude has gradually 
 been more and more advanced until it has become difficult to 
 give an exact meaning to the expression. Absolute identity 
 of the angles of two bodies occurs only when the bodies 
 crystallise in the regular system. Chemically analogous com- 
 pounds sometimes crystallise in forms closely resembling one 
 another, yet belonging to different systems; e.g. potassium 
 dichromate crystallises in monoclinic forms, where a : b : c 
 = roii6 : i : rSi45, and ammonium dichromate crystal- 
 lises in triclinic form the relations of the axes of which are 
 nearly the same as those of the monoclinic crystals, viz. a\b:c 
 = 1-0271 : i : 17665. Salts with identical crystalline form 
 sometimes exhibit optical differences 2 . Are all such salts to 
 be called truly isomorphous ? Kopp 3 proposes that only those 
 salts any one of which is capable of growing in unmodified 
 
 1 Lehrbuch der physikalischen und theoretischeii Chemie, 2. 139. 
 
 2 See Baker, C. S. Journal Trans, for 1879. 760. 
 
 3 Ber. 12. goo et seq.
 
 72 ATOMS AND MOLECULES. [BOOK I. 
 
 form when immersed in a solution of any other should be 
 regarded as strictly isomorphous 1 . 
 
 33 As we know the crystalline form of comparatively few 
 elements 2 , the statement that such or such elements form 
 an isomorphous group, generally means only that the 
 analogous compounds of these elements are for the most part 
 isomorphous. 
 
 The more important groups of isomorphous elements, as 
 thus understood, are as follows 3 : 
 
 GROUP I. Fluorine, Chlorine, Bromine, Iodine, [Cyanogen]; in all 
 compounds : 
 
 partially Manganese; in compounds of the type RMnO 4 . 
 
 GROUP II. Sulphur, Selenion; in all compounds and as elements in 
 monosymmetric forms : 
 
 partially Tellurium; in compounds of the type RTe : 
 
 Chromium, Manganese, Tellurium; in salts of their acids 
 
 belonging to the type H 2 RO 4 : 
 Arsenic, Antimony; in compounds of the type RS 2 . 
 
 GROUP III. Arsenic, Antimony, Bismuth, Tellurium; as elements, 
 and the three first-named in all corresponding compounds : 
 
 partially Phosphorus and Vanadium; in salts of their acids : 
 
 Nitrogen with phosphorus, arsenic, and antimony ; in 
 organic bases. 
 
 GROUP IV. Lithium, Sodium, Potassium, Rubidium, Cizsium, \Arn- 
 moniutti\ ; in most compounds : 
 
 partially Thallium; in some compounds : 
 
 ,, Silver, in some compounds (especially with sodium}. 
 
 GROUP V. Calcium, Strontium, Barium, Lead; Magnesium, Zinc, 
 Manganese, Iron; e.g. in carbonates : 
 
 partially Nickel, Cobalt, Copper; with iron in some compounds, e.g. 
 sulphates : 
 
 1 Lehmann, Zeitschr. f. Physikal. Chemie, 1. 15, 49, has recorded a few 
 cases of non-isomorphous compounds crystallising together, e.g. CuCl 2 .2H 2 O and 
 NH 4 C1. Many precautions must be taken in the practical application of this 
 criterion of isomorphism (s. ' Isomorphie ' in Ladenburg's Handuwrterbuch der 
 Chemie, 5. 385). 
 
 2 See, for the crystalline forms of elements in the free state, Watts's Dictionary 
 [ist Ed.], vol. in. p. 429. 
 
 3 From article ' Isomorphie ' in Neues Handivorterbuch, loc. cit. For a much 
 fuller account of the isomorphism of elements, see Ladenburg's Hand-war terbuch 
 dcr Chenric, 5. 394.
 
 CHAT. I. 33] ISOMORPHOUS ELEMENTS. 73 
 
 partially Lanthanum, Cerium, Didymium, Yttrium, Erbium; with 
 
 calcium, in compounds of type RO: 
 Copper, Mercury; with lead, in oxy-compounds : 
 Beryllium, Cadmium, Indium; with zinc, in some com- 
 pounds: 
 Thallium; with lead, in some compounds. 
 
 GROUP VI. Aluminium, Chromium, Manganese, Iron; in the sesqui- 
 oxides [R 2 O 3 ] and salts derived therefrom : 
 
 partially Cerium, Uranium; in their sesquioxides. 
 
 GROUP VII. Copper, Silver; in compounds of the type R 2 O : 
 partially Gold; with silver, 
 
 GROUP VIII. Ruthenium, Rhodium, Palladium, Iridiiim, Platinum, 
 Osmium; in most compounds : 
 partially Iron, Nickel, Gold: 
 Tin \? Tellurium~\. 
 
 GROUP IX. Carbon, Silicon, Titanium, Zirconium, Tin, Thorium; 
 partially in compounds of the type RO 2 , and salts derived from the 
 type H 2 RO 3 : carbon with silicon in many correspond- 
 ing so-called organic compounds. 
 Iron; with titanium. 
 GROUP X. Niobium, Tantalum; in all their compounds. 
 
 GROUP XI. Molybdenum, Tungsten; in all their compounds: 
 partially Chromium; in salts of acids of the type H 2 RO 4 . 
 
 The terms dimorphous, trimorphous, polymorphous were 
 used by Mitscherlich. Many examples of the phenomena to 
 which these names are applied are now known : thus calcium 
 carbonate crystallises in hexagonal forms as calcspar, and in 
 rhombic forms as arragonite; titanium oxide assumes two 
 distinct quadratic forms, one being known as rutile the other as 
 anatasc, and it also crystallises as brookite in rhombic prisms ; 
 arsenious oxide crystallises in octahedral, antimonious oxide 
 in rhombic, forms, but if amorphous arsenious oxide is 
 heated in a sealed tube so that one part of the tube is at 400 
 and the rest below this temperature, the oxide deposited in 
 the middle part of the tube is found to be isomorphous with 
 rhombic antimonious oxide; the latter oxide is also known in 
 octahedral forms, so that the isodimorpJiism of these two 
 oxides is complete 1 . 
 
 1 s. Lehmann, Zeitsch r. f. physikal. Chetttie, 1. 15.
 
 74 ATOMS AND MOLECULES. [BOOK I. 
 
 34 If it is assumed that, as a general rule, those masses of 
 two substances which are crystallographically equivalent 
 have similar chemical constitutions 1 ; and if we suppose 
 that the atomic weights are known of the elements which 
 compose one of two compounds exhibiting identical or nearly 
 identical crystalline form, it is evident in what way deter- 
 minations of crystalline form may aid in fixing atomic 
 weights. 
 
 To take an example : from determinations of the specific 
 gravities of gaseous compounds and analyses of these com- 
 pounds, the value 52*4 is assigned to the atomic weight of 
 chromium ; this number is verified by measurements of the 
 specific heat of the same metal. The green oxide of chromium 
 exhibits the same crystalline form as ferric oxide, hence 
 these oxides should probably be represented by similar for- 
 mulae. On comparing the compositions of crystallographically 
 equivalent quantities of the two oxides, it is found that one is 
 composed of 52^4 x 2 parts by weight of chromium and 
 1 5 '96 x 3 parts of oxygen, and the other of the same mass of 
 oxygen combined with SS'9 x 2 parts by weight of iron. Now 
 the atomic weight of chromium has been determined to be 
 52-4, and the atomic weight of oxygen is known to be I5'96; 
 hence the simplest formula that can be given to the green 
 oxide of chromium is Cr 2 O 3 ; and hence the probable formula 
 of ferric oxide is Fe 2 O s . But if the latter formula is correct it 
 follows that 2 atoms of chromium are replaced from one 
 reacting weight of the oxide Cr 2 O 3 by 2 atoms of iron. If this 
 conclusion is granted, the atomic weight of iron is 55-9. As 
 the specific heat of iron multiplied into 55*9 gives the product 
 6'4, 5 5 '9 is almost certainly the true atomic weight of iron. 
 Again, the formulae of potassium perchlorate and permanga- 
 nate were at one time written KO . C1O 7 and KO . Mn 2 O 7 . 
 Berzelius proposed the formulae KO.C1O 7 and KO.MnO 7 , 
 which on the system of notation now adopted become KC1O 4 
 and KMnO 4 respectively; these formulae represent crystallo- 
 graphically equivalent quantities of the two salts; if it is 
 assumed that Cl (35'37) represents the weight of the atom of 
 1 See note i. p. 70.
 
 CHAP. I. 34] APPLICATION OF ISOMORPHISM. 75 
 
 chlorine, then Mn (55) probably represents the weight of the 
 atom of manganese. 
 
 Observations of crystalline form have sometimes led the 
 way to correct determinations of atomic weights, or to changes 
 in the received values of such weights. Thus H. Rose 1 gave 
 the name of hyponiobium to a supposed allotropic form of 
 the metal niobium; but Marignac 2 shewed that compounds 
 of the hypothetical metal were identical in crystalline form 
 with certain compounds of tin and titanium, and concluded 
 that Rose's hyponiobium was itself isomorphous with the 
 atomic groups SnF and TiF, and was therefore probably a 
 compound. Further experiments shewed that the hypo- 
 niobium of Rose was really composed of niobium and oxygen 
 in the proportions expressed by the formula NbO (Nb = 94) ; 
 now if it was admitted that the groups of atoms NbO, SnF, 
 and TiF, were crystallographically equivalent, it followed, 
 from the analyses of the various compounds, that one atom 
 of tin or titanium (117*8 or 48 parts by weight respectively) 
 was replaced by 94 parts by weight of niobium, and that this 
 number therefore represented the weight of the atom of 
 niobium 8 . 
 
 Again, the isomorphism of the double compound of gal- 
 lium and ammonium sulphates with ordinary ammonia-alum 
 shewed that the former salt was a true alum ; hence the 
 formula X 2 3SO 4 . (NH 4 ) 2 SO 4 .24H 2 O was applicable to the 
 salt in question. But in the case of common alum X 2 = A1 2 = 
 2. x 27'O2; and in the case of gallium alum X 2 = 138 : hence, as 
 two atoms of aluminium were replaced by 138 parts by weight 
 of gallium, it followed that the atomic weight of gallium was 
 J-|p = 69. This number was confirmed by the analysis of 
 gaseous gallium chloride. 
 
 1 PSg' Ann. 108. 273. 
 
 8 Ann. Chim. Phys. 60. 257. 
 
 3 Marignac's conclusions were afterwards confirmed by determinations, by 
 Deville and Troost, of the specific gravity of gaseous chloride and oxychloride of 
 niobium: see Compt. rend. 69. 1221. 
 
 Roscoe's researches on the atomic weight of vanadium afford a very in- 
 structive example of the employment of the results of crystallographic measure- 
 ments in fixing atomic weights. Phil. Trans, for 1868, I. et seq.
 
 76 ATOMS AND MOLECULES. [BOOK I. 
 
 The facts of which an outline has been given shew that 
 until more extended and precise knowledge of the connexions 
 between crystalline form and chemical constitution is ob- 
 tained, that method for determining the atomic weights of 
 elements which is founded on these connexions can be applied 
 only tentatively and in a limited number of cases. The 
 method may however now be of considerable service in 
 suggesting lines of research bearing on the problems con- 
 nected with atomic weight determinations. 
 
 It appears probable that the crystalline form of a sub- 
 stance is connected at once with the internal structure of the 
 molecules of the substance and with the configuration of the 
 molecules themselves. No attempt has been made, nor can 
 in the present state of knowledge hopefully be made in any 
 but the broadest manner, to apply to the facts of crystallo- 
 graphy the theory of the molecular structure of matter. 
 35 Many attempts have been made to determine molecular 
 weights by other physical methods than the three already 
 described. Of these attempts, that made by Raoult has 
 led to important results 1 . This chemist has determined the 
 amount of lowering of the freezing point of water, and various 
 other solvents, produced by dissolving quantities of various 
 compounds proportional to the formula-weights, or reacting 
 weights, of these compounds ; he has found that chemically 
 similar compounds generally produce equal lowerings of the 
 freezing points of water and some other solvents. 
 
 Let P grams of a compound be dissolved in 100 grams of 
 water, or other solvent, and let the observed lowering of the 
 
 freezing point be C\ then -p = coefficient of lowering of freezing 
 
 point for the compound in question. If M= molecular weight, 
 or better, formula-weight, of a specified compound, then the 
 
 product -p M is called by Raoult the molecular lowering of 
 
 freezing point. M -pis constant for all the members of the same 
 
 class of compounds ; thus Raoult finds the following values, 
 water being the solvent : 
 
 1 s. especially Ann. Chim. Phys. [6] 8. 317.
 
 CHAP. I. 35] DETERMINATION OF ATOMIC WEIGHTS. 77 
 
 19 for organic compounds, except oxalic acid and compound 
 
 ammoniums ; 
 35 for all salts of monovalent metals with monobasic acids, 
 
 e.g. NaCl, NaC 2 H 8 O 2) NaNO 3 ; 
 
 40 for all normal salts of monovalent metals with dibasic acids, 
 e.g. (NH 4 ) 2 S0 4 , K 2 C0 3) K 2 CrO 4 ; 
 
 etc. etc. etc. 
 
 When benzene was the solvent, Raoult found the values: 
 
 49 for all organic compounds except acids, alcohols, and 
 
 phenols ; 
 25 for the lower members of homologous series of alcohols. 
 
 Raoult found other constant values when other solvents, 
 e.g. acetic acid, were employed. 
 
 If the value of M -= for a group of compounds is known, it 
 
 is possible to find the formula-weight of a member of the group 
 from observations of the coefficient of lowering of freezing 
 point of that compound. Thus to take the case of ether. 
 
 (i) 4'47 grams of ether were dissolved in 100 grams 
 of water, and the freezing point of the water was lowered by 
 
 - ' 
 4'47 
 
 ganic compounds dissolved in water is 19; therefore in the 
 present case M -^ = 82. 
 
 (ii) 2721 grams of ether dissolved in 100 grams of 
 benzene lowered the freezing point by i'826 ; therefore the 
 
 coefficient of lowering was - = '671. Now as M -p = 49 
 for the class of compounds of which ether is a member, it 
 follows that M= -^- = 73. 
 
 (iii) The coefficient of lowering of freezing point of 
 acetic acid for ether was determined to be '529. 
 
 i'O5 ; hence -75= - = '23. But the value of M -~ for or- 
 r '
 
 78 ATOMS AND MOLECULES. [BOOK I. 
 
 Experiments had shewn that M p = 39 for all organic and 
 many inorganic compounds ; hence in the present case 
 
 The mean of the three results gives the value 76-6 for the 
 formula-weight of ether ; the correct value is 74. 
 
 This method is of wide application for determining the 
 reacting (or formula) weights of compounds, and is especially 
 useful as it is applicable to bodies which cannot be gasified 
 without decomposition. 
 
 36 I have endeavoured to shew that the most trustworthy 
 method for determining molecular and atomic weights is 
 founded on Avogadro's law, which is itself an outcome of 
 the application of dynamical reasoning to a physical theory. 
 Formerly it was supposed that strictly chemical evidence 
 must be of paramount importance in determining these quan- 
 tities. Although the superior importance of Avogadro's law 
 is now admitted, this law can only be applied to a limited 
 number of substances, hence we are frequently obliged to 
 have recourse to purely chemical evidence in support of this 
 or that molecular weight. The nature of such chemical 
 evidence, and the modifications in the physical conception of 
 molecular weight to which it leads, must now be shortly 
 illustrated. 
 
 In 1850 Brodie 1 endeavoured to shew that there is no 
 difference of kind between those reactions wherein elementary 
 bodies are produced, or react, and those in which compound 
 bodies are alone concerned. He supposed that the small 
 particles of elementary substances set free during reactions, 
 or taking part in reactions, are composed of smaller parts 
 which exhibit certain mutual polar relations. Silver chloride 
 is not decomposed by oxygen, but it readily interacts 
 with potassium oxide with production of silver oxide and 
 potassium chloride ; hydriodic and iodic acids decompose 
 one another with production of free iodine ; silver oxide 
 decomposes hydrogen peroxide to form silver, water, and free 
 
 1 Phil. Trans, for 1850, 759, and also C. S. Journal, 4. 194.
 
 CHAP. I. 36] DETERMINATION OF ATOMIC WEIGHTS. 79 
 
 oxygen, half of the oxygen coming from the silver oxide and 
 half from the peroxide ; iodine decomposes barium peroxide 
 with production of barium iodide and oxygen. These re- 
 actions were thus written by Brodie (translating into the new 
 notation): 
 
 (i) AgAgClCl + KKO = AgAgO + KKClCl 
 
 (+nd 
 
 (2) 
 
 (3) 
 (4) 
 
 That part of Brodie's hypothesis which supposed a polar 
 condition of atoms in molecules was not generally adopted 
 by other chemists, but it was admitted that his researches 
 established a general similarity of function and composition 
 between elementary and compound molecules. 
 
 In the same year Williamson 1 distinguished between the 
 atom of zinc in combination, and the free metal zinc (that is 
 to say, he recognised that the atom of an element is not 
 possessed of the same properties as the molecule of that 
 element) : he said it is not quite accurate to speak of ' zinc ' 
 as existing in zinc sulphate. 
 
 Recognising then that chemical reactions took place be- 
 tween molecules, chemists defined the molecule as the smallest 
 part of a substance capable of taking part in a chemical 
 change, or as the acting chemical unit. Supposing the atomic 
 weights of the elements forming a compound to be known, 
 the best method of determining the molecular weight of the 
 compound appeared to be to find that formula which should 
 express the atomic composition in the simplest manner. 
 Thus ammonia is formed by the combination of hydrogen 
 and nitrogen in the proportion of 3 parts by weight of the 
 former to 14 of the latter ; assuming the atomic weights of 
 these elements to be I and 14 respectively, the atomic com- 
 position of ammonia may be represented by the formula NH,. 
 As the reactions in which this substance takes part might 
 all be represented as involving 17, or a whole multiple of 17, 
 
 1 C. S. Journal, 4. 355.
 
 80 ATOMS AND MOLECULES. [BOOK I. 
 
 parts by weight of this compound, and moreover as hydrogen 
 could be removed from 17 parts by weight of ammonia in 
 three separate and equal parts by chemical reactions, 17 was 
 taken to be the molecular weight of ammonia. 
 
 An instructive illustration of this method of fixing a 
 minimum molecular weight is furnished by Williamson's 
 famous researches on ethers '. The formulae generally adopted 
 for common alcohol and ether, previous to Williamson's work, 
 were C 4 H fi O 2 and C 4 H 5 O respectively (C = 6 ; O = 8). William- 
 son allowed ethylic iodide to react on potassium alcoholate, 
 expecting that ethylated alcohol would be produced thus 
 C 4 H 5 KO 2 + C 4 H 5 I should give C 4 H 5 (C 4 H 5 )O 2 + KI but the 
 product was ordinary ether. If the generally accepted formula 
 for ether were doubled the reaction would be explained, and 
 ether would be regarded as an oxide of ethyl (C 4 H 5 ) 2 O 2 . 
 Again, Williamson found that when sulphuric acid acts on 
 ethylic alcohol, and methylic alcohol is added to the mixture, 
 a single substance having the properties of an ether, and the 
 formula C 3 H 4 O or a whole multiple of this formula, distils 
 over. If the formula of ether is C 4 H 5 O, then that of methylic 
 ether is C 2 H 3 O, and a mixture of these ought to be obtained 
 in the reaction just mentioned ; but if ether is (C 4 H 5 ) 2 O 2 , then 
 the single ether obtained is probably methyl-ethyl oxide 2 , 
 i.e. C 4 H 5 (C 2 H S )O 2 (=2C 3 H 4 O). Thus was shewn, on purely 
 chemical grounds, the necessity of doubling the generally 
 accepted molecular formula for ether. 
 
 No purely chemical method capable of general application 
 has been found for determining molecular weights ; each com- 
 pound must be considered as a separate problem. The more 
 important methods may however be roughly classified. 
 
 There is the method of analogies, which is well illustrated 
 by the example of ether already considered. The smallest 
 amount of sulphuretted hydrogen which takes part in chemi- 
 cal changes is represented by the formula H 2 S (assuming 
 S = 32), the hydrogen in this compound is replaceable in two 
 
 1 See C. S. Journal, 4. 106, and 229. 
 
 2 Translated into modern notation, these formulae become (C 2 H 5 ),O and 
 C 2 H 5 (CH 3 )0 respectively.
 
 CHAP. I. 36] ATOMIC WEIGHTS. 8 1 
 
 parts with production of KHS and KKS hence the mole- 
 cular formula is not less than H 2 S. But compounds of selenion 
 and tellurium with hydrogen, analogous in general properties 
 to sulphuretted hydrogen, are known ; from the marked 
 similarity between these two elements and sulphur it is very 
 probable that the molecular formulae of the two compounds 
 in question are H 2 Se and H 2 Te respectively: as these formulae 
 satisfy the analytical numbers, they may be adopted. The 
 simplest formula that can be given to acetic acid con- 
 sistently with the values H = i, C = 12, and O = 16 is CH 2 O. 
 But if this acid is neutralised by soda and the sodium salt 
 thus produced is analysed, it is found that this salt contains 
 one atom of sodium (the atomic weight of sodium is assumed 
 to be known, = 23) in combination with three-fourths of the 
 quantity of hydrogen present in the original acid, the quan- 
 tities of carbon and oxygen being unchanged. Hence, it is 
 argued, one-fourth of the total hydrogen of the acid has been 
 replaced by sodium ; but not less than one atom of hydrogen 
 (or another element) can be removed from a molecule ; hence, 
 as one atom of hydrogen out of four atoms has been replaced 
 by sodium, it follows that the molecule of acetic acid contains 
 at least four atoms of hydrogen. But, in order to express 
 this conclusion, the formula of the acid must be written 
 C 2 H 4 O 2 ; and therefore the minimum molecular weight of 
 acetic acid is 60. This conclusion is confirmed by the pre- 
 paration of thiacetic acid, which is composed of 16 parts by 
 weight of oxygen (i.e. one atom) less than enters into the 
 composition of acetic acid, the quantities of carbon and 
 hydrogen remaining the same, and 32 parts by weight of 
 sulphur. Now if the atomic weight of sulphur is known to 
 be 32, it follows that the minimum molecular weight of acetic 
 acid is expressed by the formula C 2 H 4 O 2 , and that of thiacetic 
 acid by the formula C 2 H 4 OS. 
 
 The formula for water was once written HO. If potas- 
 sium is thrown on to water hydrogen is evolved, and the 
 solid product of the reaction is a white salt whose compo- 
 sition may be expressed by the formula HO.KO(O = 8). 
 But this substance is undecomposed by heat, and it exhibits 
 none of the reactions which a compound of water with a 
 M. C. 6
 
 82 ATOMS AND MOLECULES. [BOOK I. 
 
 metallic oxide might be expected to possess, nevertheless it 
 is composed of hydrogen, oxygen, and potassium ; when it is 
 fused with potassium, hydrogen is evolved and potassium 
 oxide remains. The oxygen of this compound cannot be 
 removed in parts. If the molecular formula of water is 
 written H 2 O(O=i6) these facts are explained; the white 
 solid then becomes KOH, and this formula as the minimum 
 molecular formula of the compound is confirmed by the 
 close analogies which exist between the properties of this 
 body and those of alcohol, the molecular formula of which 
 has been determined to be (C 2 H 5 ) OH. If steam reacts with 
 chlorine or bromine oxygen is evolved, and a compound of 
 hydrogen and chlorine (or bromine) is produced, the simplest 
 formula for which is HC1 (or HBr); no compound of oxygen, 
 hydrogen, and chlorine (or bromine) is formed and oxygen at 
 the same time evolved. Hence, it is argued, the hydrogen in 
 the molecule of water is divisible in chemical changes into 
 two parts, but the oxygen is not divisible, and hence, the 
 simplest molecular formula for water is H 2 O ; but if this is so, 
 the atomic weight of oxygen cannot be less than 16. 
 
 The following generalisation is quoted from Horstmann 1 . 
 
 " When we know that - of a constituent of a molecule can be replaced 
 
 ft 
 
 by another constituent, the composition of the molecule remaining in 
 other respects unchanged, it follows that the given molecule must contain 
 at least n atoms of the first-named constituent, inasmuch as parts of an 
 atom cannot be removed from a molecule.... If the atomic weight of the 
 replacing constituent is known the minimum molecular weight of the 
 original substance can be found, because it is easy to calculate from the 
 empirical composition of the substance how much of the other constituents 
 must be present in combination with n atoms of the replacing body." 
 
 Assuming the atomic weights of iron and oxygen to be 
 (in round numbers) 56 and 16 respectively, the formula Fe 2 O 3 
 is deduced from analyses of ferric oxide as representing the 
 smallest quantity of this compound which neutralises one or 
 more reacting weights of various acids, forms double com- 
 pounds with other oxides &c. the reacting weights of which 
 
 1 Lehrbuch der physikalischen und theoretischen Chemie. Zweite Abtheilung; 
 Theoretische Chemie (eimchliesslich der Thermochemie) von Dr A. Horstmann 
 (1885), p. 86.
 
 CHAP. I. 36] ATOMIC WEIGHTS. 83 
 
 are known, interacts with chlorine to form Fe 8 Cl 6 , &c. ; hence 
 this formula represents the minimum molecular weight of 
 ferric oxide. But similar reasoning leads to As 2 O 8 as the 
 minimum molecular formula of arsenious oxide; now we 
 know that the gaseous oxide has a molecular weight ex- 
 pressed by the formula As 4 O 6 . Hence the method of ana- 
 logies does not always lead to the adoption of the true 
 molecular weight of a compound. 
 
 It should be noted here however that by ' the true mole- 
 cular weight' is meant the relative weight of the gaseous 
 molecule ; but the chemical methods for rinding molecular 
 weights only profess to determine the relative weights of the 
 chemically reacting units of bodies. 
 
 Sometimes the method of analogies becomes very indirect. 
 Thus, ferric chloride has been gasified and the molecular for- 
 mula of this compound is known to be Fe 2 Cl 6 : the simplest 
 formula that can be given to ferrous chloride is Fed 2 ; is 
 this, or a multiple of this, to be adopted as the molecular 
 formula of ferrous chloride ? Ferric chloride is produced by 
 the action of chlorine on ferrous chloride ; now the general 
 action of chlorine is either to add itself on to other molecules, 
 or to decompose molecules and then substitute itself for some 
 one or more of the atoms formerly constituting these mole- 
 cules. If ferrous chloride is FeCl 2 , the action of chlorine on this 
 molecule is represented by the equation 2FeCl 2 + Cl 2 = Fe 2 Cl 6 ; 
 but such a reaction as this does not often occur. If ferrous 
 chloride is Fe 2 Cl 4 , the action of chlorine is represented by 
 the equation Fe 2 Q 4 + C1 2 = Fe 2 Cl fi , and this reaction is ana- 
 logous to other actions of chlorine ; hence the molecular for- 
 mula of ferrous chloride 1 is probably not smaller than Fe 2 Cl 4 . 
 
 The chemical method of determining minimum molecular 
 weights, as applied to acids and bases, generally resolves itself 
 into determining the basicity of the acid, or the acidity of the 
 base. Thus, the results of analyses of sulphuric acid are 
 satisfied by the formula H^S^O^ ; the fact that this acid is 
 
 1 V. Meyer has obtained results regarding the vapour density of ferrous chloride 
 which seem to him to point to the conclusion that, like stannous chloride, this 
 compound possesses two molecular weights expressed respectively by the formulae 
 FeCl. 2 and Fe 2 Cl 4 ; Ber. 14. 1455; 17. 1335. 
 
 62
 
 84 ATOMS AND MOLECULES. [BOOK I. 
 
 dibasic leads with a fair degree of certainty to the con- 
 clusion that x=\, and that the molecular formula 1 of the 
 compound is therefore H 2 SO 4 . The simplest formula which 
 can be given to citric acid consistently with analytical results, 
 and with the atomic weights C = 12, O = 16, H = I, is C 6 H 8 O 7 ; 
 that the molecular formula 1 is probably not greater than this 
 is shewn by the tribasic character of the acid. Reasons 
 have been already given for adopting NH 3 as the true mole- 
 cular formula of ammonia ; analysis shews that the alkaloid 
 quinine cannot have a smaller molecular weight than that 
 represented by the formula C 10 H 12 NO (C = 12, H = i, N = 14, 
 O = 1 6) ; but the quantity of this alkaloid which neutralises 
 that amount of hydrochloric acid which is neutralised by 
 NH 3 , is 2C, H 12 NO ; therefore the molecular formula 1 of 
 quinine is probably not less than C 20 H 24 N.,O 2 . 
 
 This method may also be applied to determine the formulse 
 of salts. Thus if sulphuric acid has the molecular formula 1 
 H 2 SO 4 , the molecule of sodium sulphate is probably repre- 
 sented by the formula Na 2 SO 4 , because the atom of sodium 
 being very probably monovalent 2 , the amount of sodium 
 'equivalent' to 2H is represented by 2Na. So, although ortho- 
 boric acid is non-volatile, its ethyl salt has been vaporised and 
 found to have the formula (C 2 H 5 ) 3 BO 3 , hence, knowing that 
 ortho-boric acid is tribasic, we deduce for it the probable 
 molecular formula 1 H 3 BO 3 . 
 
 The so-called 'law of even numbers' enunciated by Ger- 
 hardt led to the revision of many molecular formulae : 
 Gerhardt stated that the sum of certain elementary atoms 
 (hydrogen, chlorine and its analogues, nitrogen and its ana- 
 logues) contained in any molecule is always an even number 3 . 
 Thus, analysis leads to the formula C 2 H 3 O 3 for tartaric acid, 
 and as the acid is dibasic this formula is apparently mole- 
 cular; but the hydrogen atoms must be expressed by an 
 even number according to Gerhardt's law, therefore the 
 
 1 That is, the formula expressing the smallest mass of the body capable of 
 taking part in a chemical change. 
 
 2 That is, capable of combining directly with not more than one atom of 
 hydrogen, chlorine, bromine, iodine, or fluorine, to form a compound molecule. 
 See chap. II., pars. 56, 57. 
 
 3 See Laurent, Chemical Method, p. 46 et seq.
 
 CHAP. I. 3638] ATOMIC WEIGHTS. 85 
 
 formula was doubled. Similar reasoning applied to the 
 formula of nitric oxide would require this to be written N 2 O 2 ; 
 but we know that the moleculaj formula of this compound 
 is NO ; hence Gerhardt's 'law' must be applied with care 1 . 
 
 37 The chemical methods for determining reacting weights 
 and atomic weights differ in two main particulars from the 
 physical method for determining molecular and atomic weights 
 which is based on the molecular theory. 
 
 The chemical methods as a class do not attempt to 
 distinguish between solids, liquids, and gases ; so far as 
 the application of these methods is concerned the reacting 
 weight of a solid, liquid, or gaseous, substance is the smallest 
 mass of that substance which takes part in a chemical re- 
 action : the physical method for finding molecular weights is 
 strictly applicable only to gases ; but the terms in which the 
 physical definition of molecule is stated are much more 
 precise than those which describe the chemical conception 
 of reacting weight. 
 
 The chemical methods sometimes attempt to determine 
 the atomic weights of the elements which form a specified 
 compound, and from these and other data to deduce the re- 
 acting weight of the compound ; sometimes the reacting 
 weight of the compound is first determined, and then de- 
 ductions are drawn regarding the atomic weights of the 
 constituent elements. The physical method, on the other 
 hand, begins by defining molecule, and then, applying this 
 definition to chemical reactions, arrives at a definition of 
 atom, both definitions being so stated as to indicate the data 
 which are required before the relative weights of either atoms 
 or molecules can be determined. 
 
 38 In the following table I have sought to summarise many 
 facts concerning the atomic weights of the elements: it is well 
 that the student should have placed before him a synopsis of 
 the evidence on which these all-important numbers are based. 
 
 1 For further examples of the application of chemical methods to determina- 
 tions of molecular and atomic weights see Watts's Diet, (ist Ed.) vol. I. pp. 45? 8 
 and 4601 ; also Williamson 'On the Atomic Theory,' C. S. Journal,^. 328. 
 See also Chapter III. of this Book, The Periodic Law.
 
 86 
 
 ATOMS AND MOLECULES. 
 Atomic Weights of the Elements. 
 
 [BOOK T. 
 
 I 
 
 I 
 
 II 
 
 III 
 
 IV 
 
 
 Principal compounds, 
 
 
 
 Element 
 
 vapour densities of 
 which have been 
 
 Specific heat : 
 horu determined 
 
 Isomorphism : 
 compounds compared 
 
 
 determined 
 
 
 
 
 
 
 [See note A, p. 92. 
 
 HYDROGEN 
 
 HF, HC1, HBr, HI, 
 H 2 S, H 2 Se, H 2 Te, 
 H 3 N, H 3 P, H 4 C, &c. 
 
 ndirectly [from sp. heat of H 2 O, 
 NH 4 C1, NH 4 NO 3 ] 
 [atomic heat abnormal?] 
 
 
 
 LITHIUM 
 
 none 
 
 directly 
 
 Li compounds with analogous 
 
 
 
 
 compounds of alkali metals 
 
 BERYLLIUM 
 
 BeBr 2 , BeCl 2 
 
 directly : sp. heat varies much 
 
 a few Be compounds with analo- 
 
 
 
 with temperature 
 
 gous compounds of Cd and Zn 
 
 BORON 
 
 BF 3 , BC1 3 , BBr 3 , 
 
 directly: sp. heat varies much 
 
 
 
 
 B(CH 3 )., 
 
 with temperature 
 
 
 CARBON 
 
 CH 4 , CH 3 F, CH 3 C1, 
 CH 3 Br, CH 3 I, CHCI 3 , 
 CO,CO 2 ,COC1 2 ,COS, 
 
 directlv : sp. heat varies much 
 with temperature 
 
 CN compounds with those of F, 
 Cl, Br and I 
 
 NITROGEN 
 
 CS 2 , CHN, C 2 H 6 O, 
 C 4 H, 0, &c. 
 NH 3 , NO, NO 2 , NOC1, 
 N 2 O, N 2 O 4) &c. 
 
 indirectly: very undecided 
 [from sp. ht. of various com- 
 
 NH 4 compounds with those of 
 alkali metals 
 
 
 
 pounds] 
 
 
 OXYGEN 
 
 OH 2 , ON,, OC, OC1 3 P, 
 2 C, 2 S, 3 S, 4 0s, 
 
 indirectly: very undecided 
 [from sp. ht. of various .com- 
 
 
 
 
 &c. 
 
 pounds] 
 
 
 FLUORINE 
 SODIUM 
 
 FH, F(CH 3 ), F 3 B, F 4 Si, 
 F 5 P, &c. 
 
 indirectly : very undecided 
 [from sp. ht. of CaF 2 , &c.] 
 directly 
 
 metallic fluorides with analogous 
 compounds of Cl, Br and I 
 Na compounds with those of other 
 alkali metals 
 
 MAGNESIUM 
 
 none 
 
 directly 
 
 Mg compounds generally with' 
 
 
 
 
 those of Zn, Mn, and Fe (in fer- 
 
 ALUMINIUM 
 
 A1C1 3 , Al 2 Br 6 , Al.,I e 
 
 directly 
 
 rous salts) 
 with Cr, Mn, and Fe in R 2 O 3 and. 
 
 
 
 
 derivatives 
 
 SILICON 
 PHOSPHORUS 
 
 SiF 4 , SiCl 4 , SiI 4 , 
 Si(CH 3 ) 4 , SiH 3 Cl, 
 Si 2 OCI 6 , SijOCCoH,),, 
 PH 3 . PCI* PI,, PF.. 
 POC1 3 . PSCI 3) P 2 I 4 , 
 
 directly : sp. ht. varies much 
 with temperature 
 
 directly 
 
 with C, Zr, Sn, and Ti in com-> 
 pounds of type RO 2 
 
 phosphates with vanadates andi 
 arsenates, organic compounds! 
 
 SULPHUR 
 
 P 2 H 4 , P 3 N 3 Cl e , &c. 
 SH 2 , SO.,, S0 3 , SOU,, 
 S 2 C, S 2 U 2 , &c. 
 
 directly 
 
 of P with those of N, As, and Sbl 
 with Se compounds, with Te* 
 compounds of type RTe. Saltst 
 of H 2 S0 4 with those of H ,Se0 4 l 
 and H.,TeO 4 
 
 CHLORINE 
 
 C1H, C1(CH 3 ), C1T1, 
 
 indirectly: doubtful 
 
 Chlorides, with analogous conl- 
 
 
 CloZn, CI 2 Hg. C1 3 HC, 
 Cl 3 Bi, Cl 3 Sb, C1 4 C, 
 Cl 4 Si, Cl 4 Ti, Cl/la, 
 
 [from comparison of specific heats 
 of various haloid compounds] 
 
 pounds of Br and I 
 
 
 CI 5 Mo, C1 6 W, &c. 
 
 
 
 POTASSIUM 
 
 KI 
 
 directly 
 
 K compounds with those of other 
 
 
 
 
 alkali metals 
 
 CALCIUM 
 
 none 
 
 directly 
 
 Ca compounds with those of Sr,i 
 
 
 
 
 Ba, and in some cases Pb 
 
 SCANDIUM 
 
 none 
 
 sp. heats of some compounds de- 
 
 [? Sc compounds with those of 
 
 
 
 termined 
 
 other earth metals] 
 
 TITANIUM 
 
 TiCl 4 
 
 directly 
 
 TiO 2 and some derivatives withi 
 
 
 
 
 analogous compounds of C, Si, 
 
 
 
 
 Zr, Sn, and Th 
 
 VANADIUM 
 
 VC1 4 , VOCI 3 
 
 sp. heats of one or two com- 
 
 Vanadates with phosphates aad 
 
 
 
 pounds determined 
 
 arsenates
 
 CHAP. I. 38] COMBINING AND ATOMIC WEIGHTS. 
 
 Atomic Weights of the Elements. 
 
 V VI VII 
 
 VIII 
 
 Atomic weight 
 
 
 
 
 (0 (2) 
 
 
 
 ty vapotn 
 density 
 method 
 
 by sp. heat 
 method 
 
 Compounds analysed, &c. 
 in order to find combining Combining 
 weight of the elemettt , weight 
 
 Remarks 
 
 or more details concern- 1 
 
 
 Tables, pp. 39 44 and [See note B, p. 92.] 
 
 [See note C, p. 92. 
 
 PP- 5I-53-] ^ 
 
 
 
 7 -QI Lithium chloride 
 
 7-01 
 
 
 9-08 9-08 2 Beryllium sulphate 
 
 4'54 
 
 
 io'95 io'9s 3 Borax, boron chloride 
 
 3-65 
 
 
 11-97 
 
 11-97 ! 4 Diamond burnt to CO 2 
 
 2'99 
 
 
 
 5 Ammonium chloride, silver 
 
 4-67 
 
 
 
 
 nitrate 
 
 
 
 '5-96 
 
 
 
 6 Synthesis of water 
 
 7-98 
 
 
 19*1 
 
 1 1 Sodium fluoride, potassium 
 
 I 9' 1 
 
 
 fluoride, calcium fluoride 
 
 
 
 23 
 
 8 Sodium chloride 
 
 23 
 
 
 24 
 
 9 Magnesium sulphate, do. 
 chloride, synthesis of macr- 
 
 12 
 
 
 nesium sulphate 
 
 
 
 27'O2 27'O2 
 
 10 Ammonia alum aluminium 
 
 9 '007 
 
 
 bromide, solution of alumin- 
 
 
 
 ium in soda 
 
 
 2 8'3 28*3 " Silicon chloride; decomposition 
 of silicon bromide by water 
 
 7'o8 
 
 30-96 i 30-96 12 Phosphorus chloride, synthesis 
 of phosphorus pentoxide 
 
 '' 3 ' : 
 
 31-98 31*98 i I3 Synthesis of silver sulphide, 
 
 10-66 
 
 reduction of silver .sulphate 
 
 
 by hydrogen 
 
 
 35'37 
 
 
 
 14 Potassium chlorate, synthesis 
 of silver chloride 
 
 35'37 
 
 
 39 04 394 l5 Potassium chloride, do. bro- 
 
 39 '4 
 
 
 
 mide 
 
 
 
 
 
 39'9 le Calcium chloride, calcium car- 
 
 '9'95 
 
 
 
 
 bonate 
 
 
 
 
 
 
 
 17 Synthesis of scandium sul- 
 
 14-68 
 
 Sc. The atomic weight of this metal 
 
 48 
 
 48 
 
 phate 
 18 Titanium chloride, bromide 
 
 12 
 
 is most probably I4'68X3 = 44'04: if 
 this is so, the oxide is Sc s O 3 , and is 
 
 
 
 and oxide 
 
 
 analogous with the oxides of the 
 
 
 
 
 
 earth metals. 
 
 51 '2 
 
 
 
 19 Vanadium pentoxide, do. oxy- 
 chloride 
 
 . 12-8 

 
 88 
 
 ATOMS AND MOLECULES. 
 Atomic Weights of the Elements. 
 
 [BOOK I. 
 
 I 
 
 11 
 
 III 
 
 IV 
 
 Element 
 
 Principal compounds, 
 vapour densities of 
 which have been 
 determined 
 
 Specific heat : 
 how determined 
 
 Isomorphism : 
 compounds compared 
 
 
 
 
 [See note A, p. 92.] 
 
 CHROMIUM 
 
 CrO 2 Cl 2 , CrCl 3 
 
 directly [? too low] 
 
 Salts of H 2 CrO 4 with those of 
 H 2 Mn0 4 and H 2 TeO 4 , Cr 2 O 3 
 with A1,O 3 Mn 2 O 3 and Fe 2 O 3 
 
 MANGANESE 
 
 MnCl 2 
 
 directly [? too high] 
 
 VIn 2 O 3 with AUO 3 Cr 2 O 3 and 
 Fe 2 3> R,MnO" 4 with R 2 CrO 4 
 and R 2 Te0 4 , RMnO 4 with 
 
 
 
 
 RC1O 4 
 
 IRON 
 
 Fe 2 Cl 6 
 
 directly 
 
 Fe 2 O, and derivatives with Al 2 Oj 
 Cr,6 3 Mn 2 O 3 and derivatives, 
 
 
 
 
 some Fe salts with those of Ni 
 
 
 
 
 Co and Cu 
 
 NICKEL 
 
 none 
 
 directly 
 
 Ni with Co compounds, some Ni 
 
 
 
 
 compounds with those of Fe 
 
 
 
 
 (ferrous salts) 
 
 COBALT 
 
 none 
 
 directly 
 
 Co with Ni compounds, some Co 
 
 
 
 
 compounds with those of Fe< 
 
 
 
 
 (ferrous salts) 
 
 COPPER 
 
 Cu 2 Cl 2 
 
 directly 
 
 most Cu compounds with those of 
 
 
 
 
 Ni and Co, some with Fe (fer- 
 
 
 
 rous) compounds, Cu with Ag , 
 
 ZINC 
 
 ZnCl,, H Zn(CH 3 ) 2) 
 
 directly 
 
 compounds of type R 2 O 
 Zn compounds with those of Mgi 
 and Mn 
 
 GALLIUM 
 
 Ga 2 Cl e 
 
 directly [? too low] 
 
 Ga alum with other alums 
 
 GERMANIUM 
 
 GeCl 4) GeI 4 , GeS 
 
 directly: sp. heat becomes con- 
 
 
 ARSENIC 
 
 AsH 3 , AsCl 3 , AsI 3 , 
 As(CH 3 ) 2 Cl, As 4 O 6 , 
 &c. 
 
 stant only at high temperature 
 directly 
 
 As compounds with those of $> 
 and Bi, organic compounds of 
 As with those of N P and Sb, 
 
 
 
 
 arsenates with phosphates and 
 
 
 
 
 vanadates 
 
 SELENION 
 
 SeH,, SeO 2 
 
 directly 
 
 Se with S compounds 
 
 BROMINE 
 
 BrH. Br(CH 3 ), Br 2 Cd, 
 
 directly 
 
 Bromides with analogous com- 
 
 
 Br 3 B, Br 4 Sn, Br 4 U, &c. 
 
 
 pounds of Cl and I 
 
 RUBIDIUM 
 
 RbCl, Rbl 
 
 indirectly : doubtful 
 [from comparison of specific heats 
 
 Rb compounds with those of other 
 alkali metals 
 
 
 
 of some compounds with those 
 of other alkali metals] 
 
 
 STRONTIUM 
 
 none 
 
 indirectly: doubtful 
 
 Sr compounds with those of Ca 
 
 
 
 [comparison of specific heats ol 
 
 and Ba, and with some Pb salts 
 
 
 
 compounds of Sr, Ca, and Ba] 
 
 
 YTTRIUM 
 
 none 
 
 sp. heats of a few compounds de- 
 
 Yt compounds with those of other 
 
 
 
 termined 
 
 earth metals 
 
 ZIRCONIUM 
 
 ZrCl 4 
 
 directly [? too low] 
 
 ZrO 2 with TiO 2 ThO 2 SnO 2 and 
 
 
 
 
 SiO 2 
 
 NIOBIUM 
 
 NbCIj. NbOClj 
 
 
 
 Nb with Ta compounds, Nb flu- 
 
 
 
 
 orides and oxyfluorides with Mo 
 
 
 
 
 do. do. 
 
 MOLYBDENUM 
 
 MoCl e 
 
 directly [? too high] 
 
 Mo with W compounds, some 
 salts of H 2 MoO 4 with those of 
 HXrO,. Mo with Xb fluorides 
 
 
 
 and oxyfluorides
 
 CHAP. I. 38] COMBINING AND ATOMIC WEIGHTS. 
 Atomic Weights of the Elements. 
 
 V VI VII 
 
 VIII 
 
 Atomic weight 
 
 
 
 
 (i) 
 
 (2) 
 
 
 
 >y vapour 
 density 
 method 
 
 by sp. heat Compounds analysed &~c. 
 * r ,, , in order to find combining 
 weight of the element 
 
 Combining 
 weight 
 
 Remarks 
 
 or more details concern- 
 ing these numbers see 
 
 
 [See note C, p. 92.] 
 
 Tables, pp. 3944 and [See note B, p. 92.] 
 
 
 
 PP- 5I53-] 
 
 
 
 52-4 52-4 j 20 Chromium chloride, silver 
 
 26-2 
 
 
 
 chromate, potassium dichro- j 
 
 
 
 mate 
 
 
 
 55 55 21 Manganese chloride, mangan- 
 
 27-5 
 
 
 ous-manganic oxide, man- 
 
 
 
 ganous oxalate, silver per- 
 
 
 
 manganate, &c. 
 
 
 
 55'9 
 
 55-9 22 Synthesis of ferric oxide, 
 
 27-95 
 
 
 [see p. 60] 
 
 reduction of ferric oxide. 
 
 
 
 j 
 
 analysis of ferrous and ferric 
 
 
 
 J 
 
 chlorides 
 
 
 
 
 
 58-6 
 
 23 Nickel chloride, nickelous ox- 
 
 29*3 
 
 
 
 
 ide, strychnine-nickel cyanide 
 
 
 
 
 
 brucine-nickel cyanide, &c. 
 
 
 
 
 
 59 
 
 21 Ammonium -cobalt cyanide, 
 
 2 9'5 
 
 
 
 
 phenyl-ammonium cobalt cy- 
 
 
 
 
 
 anide, strychnine and bru- 
 
 
 
 
 
 cine-cobalt cyanides 
 
 
 
 63-4 
 
 63-4 
 
 25 Reduction of copper oxide, 
 
 3i '7 
 
 
 [see p. 60] 
 
 
 electrolysis of copper sul- 
 
 
 
 
 
 phate, &c. 
 
 
 
 65-48 
 
 65-48 
 
 26 Synthesis of zinc oxide, analy- 
 sis of potassium-zinc chloride, 
 
 32-74 
 
 
 
 
 solution of zinc in acid 
 
 
 
 69 
 
 69 
 
 27 Oxidation of the metal, analy- 
 
 2 3 
 
 
 [see p. 60] 
 
 
 sis of gallium-ammonia alum 
 
 
 
 72-3 
 
 72'3 
 
 "a Germanium chloride 
 
 18-08 
 
 
 74'9 
 
 74'9 
 
 28 Arsenic bromide, do. chloride, 
 
 24-97 
 
 
 
 
 do. oxide 
 
 
 
 78-8 
 
 78-8 
 
 29 Reduction of selenion dioxide. 
 
 39 '4 
 
 
 
 reduction of silver selenite 
 
 
 
 79'75 
 
 79-75 30 Synthesis of silver bromide, 70/75 
 
 
 
 analysis of potassium bromide 
 
 
 
 85-2 
 
 31 Rubidium chloride 
 
 85-2 
 
 
 
 
 
 
 32 Strontium chloride 
 
 
 
 Sr. The atomic weight of strontium 
 must be taken as 43-65X2 = 87-3 if 
 the formulas of its salts are to be- 
 
 
 
 come analogous to those of the Ba 
 
 
 
 and Ca salts. 
 
 
 
 
 
 33 Synthesis of yttrium sulphate 29-87 ; Yt. Atomic weight probably =20/?7 
 ; x 3 = 80-6 because of analogy orYt 
 
 
 
 
 salts with those of the earth metals. 
 
 90 
 
 90 
 
 34 Zirconium chloride, potassium 45 
 zh-conium fluoride 
 
 
 94 
 
 
 
 3S Niobium chloride, potassium- 31 '32 
 
 
 
 
 niobium oxyfluoride 
 
 
 95'8 
 
 95'8 
 
 3B Molybdenum dichloride, tetra 19-16 
 chloride, and pentachloride 

 
 ATOMS AND MOLECULES. 
 Atomic Weights of the Elements. 
 
 [BOOK i. 
 
 I 
 
 II 
 
 III 
 
 IV 
 
 
 Principal compounds, 
 
 
 
 Element 
 
 vapour densities of 
 which have been 
 
 Specific heat : Isomorphism : 
 how determined compounds compared 
 
 
 determined 
 
 
 
 
 
 [See note A, p. yt.] 
 
 RHODIUM 
 
 none 
 
 directly 
 
 most Rh compounds with those c- 
 Ru, Pd, Ir, Pt, and Os 
 
 RUTHENIUM 
 
 none 
 
 directly 
 
 most Ru compounds with those o 
 
 
 
 
 Rh, Pd, Ir. Pt. and Os 
 
 PALLADIUM 
 
 none 
 
 directly most Pd compounds with those 01 
 
 
 Ru, Rh, Ir, Pt, and Os 
 
 SILVER 
 
 AgCl 
 
 directly ' some Ag compounds with those o 
 
 
 
 Na and other alkali metals. A* 
 
 
 
 
 with Cu compounds of tvp<> 
 
 
 
 
 R 2 O, a few Ag and Au com 
 
 
 
 
 pounds 
 
 CADMIUM 
 
 CdBr 8 
 
 directly 
 
 some Cd compounds with those o 
 
 
 
 
 Be and Zn 
 
 INDIUM 
 
 InCI 3 
 
 directly 
 
 some In compounds with those O* 
 Cd and He 
 
 TIN 
 
 SnClj, SnCl 4 , Sn 2 Cl 4 
 
 directly 
 
 SnO 2 with TiO 2 ZrO 2 and ThO t , 
 
 ANTIMONY 
 
 SbCl 3 , SbI 3> SbBr 3 , 
 Sb(CH 3 )3, Sb 4 0, 
 
 directly 
 
 Sb compounds with those of A* 
 and Bi 
 
 TELLURIUM 
 
 TeH 2 , TeCl 4 , TeCl 2 
 
 directly 
 
 most Te compounds with those* 
 
 
 
 
 ofSandSe 
 
 IODINE 
 
 IH, Id, KCHj), \^t, 
 
 directly 
 
 Iodides with analogous conw 
 pounds of Cl and Br 
 
 CAESIUM 
 
 CsCl, 2 CsI C ' 
 
 indirectly: doubtful 
 [comparison of specific heats of 
 
 Cs compounds with those of others 
 metals of alkalis 
 
 
 
 compounds with those of other 
 
 
 
 
 alkali metals] 
 
 
 BARIUM 
 
 none 
 
 indirectly : doubtful 
 
 Ba compounds with those of QU 
 
 
 
 [comparison of specific heats of 
 
 andSr 
 
 LANTHANUM 
 
 none 
 
 compounds of Ca, Sr, and Ba] 
 directly ^j 
 
 
 CERIUM 
 
 none 
 
 directly 
 
 most La compounds with those 
 
 DIDYMIUM 
 
 none 
 
 directly 
 
 Ce, Di, Kr and Yt, some coift- 
 pounds of these metals with Ca 
 
 ERBIUM 
 
 none 
 
 sp. heats of a few compounds 
 
 compounds 
 
 
 
 determined 
 
 
 YTTERBIUM 
 
 none 
 
 sp. heats of a few compounds 
 determined 
 
 [? a few Yb compounds with those*, 
 of other earth metals] 
 
 TANTALUM 
 
 Tads 
 
 
 Ta with Nb compounds 
 
 TUNGSTEN 
 IRIDIUM 
 
 WOCI 4> WClj, WC1 6 
 none 
 
 directly 
 directly ^ 
 
 W with Mo compounds, some 
 salts of H 2 WO 4 with those of' 
 H 2 CrO 4 and H 2 TeO 4 
 
 OSMIUM 
 
 OsO 4 
 
 directly t 
 
 Os, Ir, and Pt, compounds withf 
 those of Ru, Rh, and Pd 
 
 PLATINUM 
 
 none 
 
 directly ) 

 
 CHAP. I. 38] COMBINING AND ATOMIC WEIGHTS. 
 Atomic Weights of the Elements. 
 
 V 
 
 VI 
 
 VII 
 
 VIII 
 
 Atomic weight 
 
 
 
 
 (i) 
 
 (2) 
 
 
 
 
 y vapour 
 density 
 method 
 
 by sp. heat 
 method 
 
 Compounds analysed, &>c. 
 in order to find combining 
 weight of the element 
 
 Combining 
 weight 
 
 Remarks 
 
 or more details concern- 
 
 
 
 
 ing these numbers see 
 
 
 
 [See note C. p. 92.] 
 
 Tables, pp. 3944 and 
 
 [See note B, p. 92.] 
 
 
 
 PP- 5I53-] f 
 
 
 
 
 
 
 104 
 
 37 Potassium-rhodium chloride 
 
 26 
 
 
 
 (103) 
 
 (37 a Purpureo-rhodium chloro-and 
 
 (25-75) 
 
 
 
 
 bromo-compounds) 
 
 
 
 
 
 I0 4'5 
 106-2 
 
 39 Palladium chloride 
 
 26-55 
 
 
 107-66 
 
 107 '66 
 
 40 Silver chlorate, bromate, iodate, 
 
 107-66 
 
 
 
 
 synthesis of silver bromide 
 
 
 
 
 
 and iodide 
 
 
 
 112 
 
 112 
 
 41 Cadmium bromide 
 
 56 
 
 
 "3 '4 
 
 "3'4 
 
 42 Synthesis of indium oxide 
 
 37-8 
 
 
 117-8 
 
 II 7 -8 
 
 43 Synthesis of stannic oxide 
 
 58-9 
 
 
 120 
 
 120 
 
 44 Antimony bromide, reduction 
 
 4O 
 
 
 
 
 of antimony oxide, also analy 
 
 
 
 
 
 sis of antimony sulphide 
 
 
 
 125 
 
 125 
 
 45 Oxidation of tellurium, analy- 
 
 62-5 
 
 
 
 
 sis of potassium- tellurium 
 
 
 
 
 
 bromide, synthesis of basic 
 
 
 
 126-53 
 
 126-53 
 
 tellurium sulphate and of cop- 
 per telluride 
 "Silver iodate, silver iodide, 
 
 126-53 
 
 
 
 
 synthesis of do. 
 
 
 
 I32-7 
 
 
 
 47 Caesium chloride 
 
 3--7 
 
 
 
 
 
 
 48 Barium chloride 
 
 68-43 
 
 Ba. Atomic weight probably 68-43 
 X2= 136-86 because of analogies be- 
 
 
 
 
 
 tween salts of Ba, Sr, and Ca. 
 
 
 
 I38-5 
 
 49 Lanthanum sulphate, do. ox- 
 
 46-17 
 
 
 
 
 ide, do. oxalale 
 
 
 
 
 
 1 39 '9 
 
 50 Cerium oxalate, do. chloride, 
 
 46-66 
 
 
 
 
 do. sulphate 
 
 
 
 
 
 144 
 
 51 Didymium oxide and sulphate 
 
 48 
 
 
 
 (142) 
 
 
 (47-6) 
 
 
 
 
 
 52 Erbium sulphate 
 
 55^3 
 
 Er. This metal belongs to the earth 
 group, hence the atomic weight is 
 
 
 
 
 
 taken as 55 -33X3 = 166. 
 
 
 
 
 
 53 Ytterbium sulphate 
 
 57-69 
 
 Yb. For similar reasons to those 
 which apply in cases of Sc, Yt, and 
 
 182 
 
 
 
 54 Potassium -tantalum fluoride. 
 
 60-67 
 
 Er, the atomic weight of Ytterbium 
 is regarded as 3 times its combining 
 
 183-6 ; 183-6 
 
 55 Reduction of tungstic oxide. 
 
 30-6 
 
 weight (=173). 
 
 
 analysis of tungsten hexachlor- 
 
 
 
 
 ide 
 
 
 
 
 
 HP'S 
 
 56 Potassium-iridium chloride 
 
 48-13 
 
 
 *93 
 
 T 93 
 
 57 Osmium tetroxide 
 
 48-25 
 
 Os. The number given is calculated 
 
 
 
 
 
 from 2 determinations of vapour 
 
 
 I94-3 
 
 58 Potassium -platinum chloride, 48-57 
 platinum tetrachloride and ' 
 
 density of OsO 4 by Deville and 
 Debray, other experimenters have 
 
 
 
 bromide, &c. 
 
 ! found numbers for the atomic weight 
 
 
 
 
 of this metal varying from 195 to 199.
 
 9 2 
 
 ATOMS AND MOLECULES. 
 Atomic Weights of the Elements. 
 
 [BOOK I. 
 
 I 
 
 II 
 
 III 
 
 IV 
 
 Element 
 
 Principal compounds, 
 vapour densities of 
 which have been 
 
 Specific heat: 
 how determined 
 
 Isomorphism : 
 compounds compared '. 
 
 
 determined 
 
 
 
 
 
 [See note A, p. 92.] 
 
 GOLD ! none 
 
 directly 
 
 some Au compounds with those o 
 Ag, a few Au compounds witV 
 
 
 those of Ni and Fe 
 
 MERCURY |[HgC,] H Hga 2( HgI 2 , 
 
 directly 
 
 Hg and Cu compounds of typ 
 
 THALLIUM 
 
 T1C1 
 
 directly 
 
 Tl compounds with those of PI 
 of type RC1 2 , Tl compounds 
 type T1C1 with those of alkal 
 
 
 
 
 metals 
 
 LEAD 
 
 PbCl 2 , Pb(CH 3 ) 4 directly 
 
 some Ph with Tl compounds, man* 
 Pb with Cu and Hg compouS 
 
 BISMUTH 
 
 BiCl 3 directly 
 
 Bi compounds with those of 
 
 
 
 
 andSb 
 
 THORIUM 
 
 ThCl 4 
 
 directly 
 
 ThO a with SiO 2 TiO 2 SnO, M 
 
 URANIUM 
 
 UC1 4 , UBr 4 directly 
 
 some compounds of type Ufl 
 with those of Al, Cr, Mn, all 
 
 
 
 
 Fe 
 
 Notes to Table of Atomic Weights. 
 
 A. As the method based on isomorphism of compounds is chiefly used as 
 a means of verifying values assigned to atomic weights by other methods, no 
 numbers are given in column IV., but merely an indication of the various com- 
 pounds which have been compared crystallographically, and on which arguments 
 for or against a given value for the atomic weights in column V. have been, or 
 may be, based. 
 
 B. This column (vi.) is not to be regarded as containing anything like a 
 complete summary of the processes employed for determining the combining 
 numbers of the elements ; only the more important processes are indicated ; 
 references are given to the original papers. References to the papers on the 
 spec, heats of the elements will be found on pp. 5354. 
 
 A complete account of all researches on this subject will be found in A Re- 
 calculation of the Atomic Weights, by F. W. Clarke [Part V. of the Constants of 
 Nature published by the Smithsonian Institution], and also in Die Atomgewichte 
 der Elemente, by L. Meyer and K. Seubert [Leipzig, 1883]. 
 
 C. When the atomic weight given in column v. section (2) is a multiple of 
 the combining number in column vn., no number being given in section (i) of 
 column v., it is to be inferred that, besides the argument drawn from the value 
 of the specific heat of the element in question, there are other chemical reasons 
 for adopting the special multiple which appears in V. (2). These reasons may be 
 broadly described as based on analogies between salts of the given element and 
 salts of other elements the atomic weights of which have been established by the 
 two leading physical methods.
 
 CHAP. I. 38] COMBINING AND ATOMIC WEIGHTS. 
 Atomic Weights of the Elements. 
 
 93 
 
 V 
 
 VI 
 
 VII 
 
 VIII 
 
 Atomic weight 
 
 
 
 
 (i) (=) 
 
 
 
 
 ; /Sy 7 by sp. heat 
 
 Compotinds analysed, &^c. 
 in order to find combining 
 weight of the element 
 
 Combining 
 weight 
 
 Remarks 
 
 >r more details concern- 
 
 
 
 
 ing these numbers see 
 
 
 
 [See note C, p. 92.] 
 
 Tables, pp. 39 44 and 
 
 [See note B, p. 92.] 
 
 
 
 PP- 5i 53-1 f 
 
 
 
 
 199-8 
 203-64 
 
 199-8 
 
 203-64 
 
 59 Gold chloride, potassium-gold 65-66 
 
 chloride, potassium-gold bro 
 mide 
 
 60 Mercuric chloride, do. oxide ! 99*9 
 
 Synthesis of thallium nitrate 
 
 203-64 
 
 206-4 
 208 
 
 231-87 
 240 
 
 62 Synthesis of lead nitrate, do. | 103-2 
 
 do. sulphate 
 
 63 Synthesis of bismuthous oxide, 69-33 
 
 &c., analysis of bismuthous 
 chloride 
 
 64 Thorium sulphate 
 
 65 Uranium acetate, do. oxalate 
 
 57'97 
 60 
 
 References to Table of Atomic Weights. 
 
 1 Li. J. W. MALLET, Sill. Amer. Journal (2) 22. 349. STAS, Nouvelles 
 Recherches, pp. 268 and 274. 
 
 2 Be. NILSON and PETTERSSON, Ber. 13. 1451. 
 
 3 B. BERZELIUS, Pogg. Ann. 2. 129. DEVILLE, Ann. Chim.Phys. (3)55. 180. 
 
 4 C. DUMAS and STAS, Ann. Chim. Phys. (3) 1. 5. ERDMANN and 
 MARCHAND, J. fur prakt. Chemie. 23. 159. ROSCOE, Compt. rend. 94. 1180. 
 
 5 N. STAS, Rapports, pp. 50, 87, 92; and Nouvelles Recherches, pp. 57, 281. 
 
 6 0. ERDMANN and MARCHAND, J. fiir prakt. Chemie, 26. 468. DUMAS, 
 Ann. Chim. Phys. (3) 8. 189. KEISER, Ber. 20. 2323. COOKE and RICHARDS, 
 Proc. Amer. Acad. of Arts and Sci. 23. 149. 
 
 7 F. LOUYET, Ann. Chim. Phys. (3) 25. 291. DUMAS, do. (3) 55. 170. 
 DE LUCA, Compt. rend. 51. 299. 
 
 8 Na. PELOUZE, Compt. rend. 20. 1050. DUMAS, Ann. Chim. Phys. (3) 55. 
 182. STAS, Rapports, p. 78; and Nouvelles Recherches, p. 248. 
 
 9 Mg. JACQUELAIN, Ann. Chim. Phys. (3) 32. 202. BAHR, J. fiir prakt. 
 Chemie, 56. 310. DUMAS, Ann. Chim. Phys. (3) 55. 187. MARIGNAC, Archiv. 
 Scien. Phys. nat. (3) 10. 5, 193. 
 
 10 Al. J. W. MALLET, Phil. Trans, for 1880. 1003 et seq. 
 
 11 Si. PELOUZE, Compt. rend. 20. 1052. DUMAS, Ann. Chim. Phys. (3) 55. 183. 
 J. SCHIEL, Annalen, 120. 94. THORPE and YOUNG, C. S. Journal, 51. 576. 
 
 12 P. PELOUZE, Compt. rend. 20. 1053. SCHROTTER, Ann. Chim. Phys. (3) 
 38. 131. DUMAS, Ann. Chim. Phys. (3) 55. 172. 
 
 13 S. STAS, Rapports, p. 53.
 
 94 ATOMS AND MOLECULES. [BOOK I. 
 
 14 Cl. STAS, Rapports, pp. 38, 42, 44, 118; and Nouvelles Recherches, p. 208. 
 
 15 K. STAS, Rapports, pp. 69, 91, 118; and Nouvelles Recherches, p. 244. 
 
 16 <Ta. BERZELIUS, Pogg. Ann. 8. 189. DUMAS, Ann. Chim. Phys. (3) 55. 
 190. ERDMANN and MARCHAND, ^<z/<?, 44. 216: 62. 210: 76. 219. SALVETAL, 
 Compt. rend. 17. 318. 
 
 17 Sc. NILSON, ^r. 13. 1439. 
 
 18 Ti. H. ROSE, Pogg. Ann. 15. 145. J. PIERRE, Ann. Chim. Phys. (3) 20. 
 257. THORPE, A?r. 16. 3014; and (in full) C. S. Journal, Trans, for 1885. 
 108. 
 
 19 V. ROSCOE, Phil. Trans, for 1868. 8, 23. 
 
 20 Cr. E. PELIGOT, Ann. Chim. Phys. (3) 12. 528. BERLIN, Annalen, 56. 
 207: 60. 108 et seq. F. KESSLER, Pogg. Ann. 95. 211. SIEWERT, Zeitschrift 
 
 fur die gesammten Naturwissenschaflen, 17. 530. 
 
 21 ^/w. DUMAS, Ann. Chim. Phys. (3) 55. 150. SCHNEIDER, Pogg. Ann. 
 107. 605 : Id. Annalen, 113. 78. DEWAR and SCOTT, Proc. R. S. 35. 44. 
 MARIGNAC, Archiv. Scien. Phys. not. (3) 10. 5, 193. 
 
 22 Fe. BERZELIUS, Annalen, 50. 432. ERDMANN and MARCHAND, Annalen, 
 52. 212. L. E. RIVOT, Annalen, 78. 214. DUMAS, Ann. Chim. Phys (3) 55. 157. 
 
 23 Ni. DUMAS, Ann. Chim. Phys. (3) 55. 149. RUSSELL, C. S. Journal (2) 
 1. 51: 7. 294. SOMARUGA, Fresenius's Zcitschr. 6. 347. R. H. LEE, Ber. 4. 789. 
 BAUBIGNY, Compt. rend. 97. 951. 
 
 24 C0. WESELSKY, Ber. 2. 592. R. H. LEE, Ber. 4. 789. RUSSELL, loc. cit. 
 
 25 C~#. BERZELIUS, Pogg. Ann. 8. 182. ERDMANN and MARCHAND, J.fiir 
 prakt. Chemie, 31. 391. W. HAMPE, Fresenius's Zeitschr. 13. 352. BAUBIGNY, 
 CVwz/A rend. 97. 906. RICHARDS, /V0<r. Atner. Acad. 23. 177. 
 
 26 Zn. GAY-LUSSAC and THENARD, Gilbert's Annalen, 37. 460. BERZELIUS, 
 Pogg. Ann. 8. 184. ERDMANN, Berzelius's Lehrbuch, (5th ed.) 3. 1219. P. A. 
 FAVRE, Ann. Chim. Phys. (3) 10. 163. MARIGNAC, Archiv. Scien. Phys. nat. 
 (3) 10. 5, 193. REYNOLDS and RAMSAY, C. S. Journal, Trans, for 1887. 854. 
 
 - 7 Ga. LiiCOQ DE BOISBAUDRAN, Compt. rend. 86. 941. 
 27a Ge. WINKLER, J.fiir prakt. Chemie, (2) 34. 177. 
 
 28 As. W. WALLACE, Phil. Mag. (4) 18. 279. DUMAS, Ann. Chim. Phys. 
 (3) 55. 174. F. KESSLER, Pogg. Ann. 95. 204. 
 
 29 Se. PETTERSSON and EKMAN, Ber. 9. 1210. 
 
 30 Br. STAS, Nouvelles Recherches, pp. 158, 170 and 199. 
 
 31 Jib. BUNSEN, Pogg. Ann. 113. 339. PICCARD, J. fiir prakt. Chemie, 
 86. 453. GODEFFROY, Annalen, 181. 189. 
 
 32 Sr. MARIGNAC, Annalen, 106. 168. DUMAS, Ann. Chim. Phys. (3)66. 191. 
 
 33 Yt. CLEVE, ^<?r. 6. 1467. RAMMELSBERG, Ber. 9. 1580. 
 
 34 Zr. HERMANN, J.fiir prakt. Chemie, 31. 77. MARIGNAC, Ann. Chim. 
 Phys. (3) 60. 257. 
 
 35 Nl>. MARIGNAC, Fresenius's Zeitschr. 5. 480. 
 
 36 Mo. P. LIECHTI and B. KEMPE, Annalen, 169. 344. 
 
 37 Rh. BERZELIUS, Pogg. Ann. 13. 437. 
 
 37 Rh. JORGENSEN, J '. fiir prakt. Chemie (2) 27. 433. 
 
 38 Ru. CLAUS, Pogg. Ann. 65. 218. 
 
 39 Pd. BERZELIUS, Pogg. Ann. 13. 442. 
 
 40 Ag. STAS, Rapports, pp. 38, 42, 44; and Nouvelles Recherches, pp. 109, 
 158, 171, 189, 193, 208.
 
 CHAP. I. 38] COMBINING AND ATOMIC WEIGHTS. 95 
 
 41 Cd. O. W. HUNTINGTON, Proc. Amer. Acad. of Arts and Sd. 17. 28 
 \_Chcm. News, 44. 268]. 
 
 42 /;/. C. WINKLER, J.fiir prakt. Chemie, 94. 8: 102. 282. BUNSEN, Pogg. 
 Ann. 141. 28. 
 
 43 Sn. DUMAS, Ann. Chim. Phys. (3) 55. 154. 
 
 44 Sb. R. SCHNEIDER, Uber das Atomgewicht des Antimons (Berlin), 1880. 
 J. P. COOKE, Proc. Amer. Acad. of Arts and Sci. 13. i : 17. 13. J. BONGARTZ, 
 Ber. 16. 1942. 
 
 45 Te. W. L. WILLS, C. S. Journal, Trans, for 1879. 704. BRAUNER, Ber. 
 16. 3055. 
 
 46 /. STAS, Nouvelles Recherches, pp. 135, 152, 189, 193. 
 
 47 Cs. BUNSEN, Pogg. Ann. 119. i. JOHNSON and ALLEN, Sill. Amer. 
 Journal, (2) 35. 94. R. GoDEFFROY, Annalen, 181. 185. 
 
 48 Ba. MARIGNAC, Annalen, 68. 215. DUMAS, Ann. Chim. Phys. (3) 55. 137. 
 
 49 La. MARIGNAC, Ann. Chim. Phys. (4) 30. 67. CLEVE, Bull. Soc. Chim. 
 50. 212: (2) 39. 151, 289. BRAUNER, C. S. Journal, Trans, for 1882. 75. 
 
 50 Ce. MARIGNAC, Annalen, 68. 212. H. BUHRIG, J.fiir prakt. Chemie (2) 
 12. 222. ROBINSON, Proc. R. S. 37. 150. BRAUNER, C. S. Journal, Trans. 
 for 1885. 879. 
 
 51 Di. B. BRAUNER, C. S. Journal, Trans, for 1882. 68. 
 51a Di. P. T. CLEVE, Bull. Soc. Chim. (2) 39. 289. 
 
 52 Er. P. T. CLEVE, Compt. rend. 91. 381. NILSON, Ber. 13. 1459. 
 5:J Yb. NILSON, Ber. 12. 550: 13. 1430. 
 
 54 Ta. MARIGNAC, Annalen, Supplbd. 4. 351. 
 
 55 IV. ROSCOE, Chem. Neivs, 25. 61, 73. 
 
 56 Ir. K. SEUBERT, Ber. 11. 1767. 
 
 57 Os. DEVILLE and DEBRAY, Ann. Chim. Phys. (3) 56. 403. 
 
 58 Pt. K. SEUBERT, Ber. 14. 865. [Annalen, 207. 29.] W. HALBERSTADT, 
 Ber. 17. 2962. 
 
 59 Au. BERZELIUS, Lehrbruch, (5th ed.) 3. 1212. JAVAL, Ann. Chim. Phys. 
 17. 337. LEVOL, Ann. Chim. Phys. (3) 30. 355. THORPE and LAURIE, C. S. 
 Journal, 51. 565. 
 
 60 fig. ERDMANN and MARCHAND, J. fur prakt. Chemie, 31. 392. SVAN- 
 BERG, J.fiir prakt. Chemie, 45. 468. MILLON, Ann. Chim. Phys. (3) 18. 345. 
 
 C1 77. W. CROOKES, Phil. Trans, for 1873. 277. 
 K - Pb. STAS, Rapports, pp. 101 and 106. 
 
 63 Bi. SCHNEIDER, Pogg. Ann. 82. 303. DUMAS, Ann. Chim. Phys. (3) 55. 
 176. MARIGNAC, Archiv. Scien. Phys. nat. (3) 10. 5, 193. Id. Ann. Chim. 
 Phys. (6). i, 289. LOWE, Zeitschr. anal. Chemie, 22. 498. SCHNEIDER, J.fiir 
 prakt. Chemie, (2) 30. 237. 
 
 64 Th. NILSON, Ber. 15. 2527. KRUSS and NILSON, Ber. 20. 1665. 
 
 65 U. PELIGOT, Ann. Chim. Phys. (3) 20. 329. 
 
 Note. The full titles of Stas's treatises which are referred to in this table 
 are : ( i ) Recherches sur les rapports redproques des poids atomiques, par J. S. Stas, 
 Bruxelle;, 1860. (2) Nouvelles recherches sur les lots des proportions chimiques, 
 sur les poids atomiques et leurs rapports mutuels, par J. S. Stas, Bruxelles, 1865. 
 A translation into German of both treatises was published in 1867 under the title 
 Untersuchungen liber (fie Gcsetze der chemischen Proportionen, uber die Atomge- 
 li'ichte and ihre gegenscitigen Verhdltnisse.
 
 [BOOK i. 
 
 CHAPTER II. 
 
 ATOMIC AND MOLECULAR SYSTEMS. 
 
 SECTION I. Nascent Actions. 
 
 39 WE have now gained the conception of chemical change 
 as consisting in the interaction of molecules, or atomic 
 aggregates. The molecules are sometimes shattered into 
 parts which rearrange themselves to form new molecules, 
 or aggregates of atoms ; sometimes new and more complex 
 molecules are formed by the coalescence or combination of 
 less complex molecules. 
 
 We have then to examine the properties which the atoms 
 of elements, and the molecules, or the atomic aggregates, of 
 elements and compounds, exhibit in their mutual actions and 
 reactions. 
 
 Can a distinction be based on chemical facts between the 
 atoms and the molecules of elements ? 
 
 What are the chemical properties of the atoms, as dis- 
 tinguished from the molecules, of elements ? 
 
 When answers have been found to these questions, it will 
 then be necessary to examine the relations between the 
 properties of molecules and the properties of the atoms which 
 compose them. 
 
 Brodie applied his hypothesis regarding the structure 
 of elementary molecules (see ante, p. 78, par. 36) to explain a 
 number of phenomena generally grouped together under the
 
 CHAP. II. 39,40] NASCENT ACTIONS. 97 
 
 name nascent actions. That explanation, somewhat simplified 
 and also developed by subsequent research, is usually regarded 
 as the most satisfactory that can be given in the present state 
 of knowledge, when regard is paid to the configurations of 
 the systems exhibiting the phenomena in question. 
 
 When hydrogen is passed into water containing silver 
 chloride in suspension no chemical change occurs ; when 
 hydrogen is generated in the vessel which contains the silver 
 chloride decomposition of this salt proceeds rapidly with pro- 
 duction of silver and hydrochloric acid. Nitrobenzene is con- 
 verted into aniline by the action of hydrogen produced in 
 contact with it, but not by hydrogen produced in another 
 vessel and conducted into that containing the nitrobenzene. 
 Carbon, hydrogen, and nitrogen do not combine directly; 
 but if electric sparks are passed through a mixture of benzene 
 vapour and nitrogen, hydrocyanic acid is produced. Sulphur 
 dioxide and water when heated with oxygen are only very 
 partially changed into sulphuric acid ; but if the oxygen is 
 produced in contact with the moist dioxide (e.g. by decompo- 
 sition of nitrogen trioxide) the change into sulphuric acid is 
 rapidly completed. Sulphur is not oxidised to sulphuric acid 
 by bromine in presence of water ; but if the sulphur is pro- 
 duced from a compound in presence of bromine water, it is 
 then oxidised, e.g. sulphuretted hydrogen passed into bromine 
 water gives hydrobromic acid and sulphur, and also sul- 
 phuric acid. Metallic chlorides (e.g. aluminium chloride) 
 produced by the action of metals with chlorine only at very 
 high temperatures, and in small quantities for a given time 
 of action, are sometimes much more easily prepared by the 
 action of chlorine on a mixture of the metallic oxide and 
 carbon. The general reaction of metals with dilute cold sul- 
 phuric acid is to produce a sulphate and evolve hydrogen, 
 but with nitric acid to produce a nitrate and evolve oxides of 
 nitrogen, nitrogen, or ammonia ; many metals when heated 
 with concentrated sulphuric acid evolve sulphur dioxide, either 
 alone, or in some cases mixed with hydrogen and sulphuretted 
 hydrogen. 
 
 40 These phenomena, and many others of the same class, 
 M. C. 7
 
 98 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 find a partial explanation in terms of the molecular theory, 
 that explanation being based on the distinction, already in- 
 sisted on, between molecules and atoms. Any mass of a 
 gaseous element under ordinary conditions is built up of 
 molecules, but if we assume that when a compound molecule 
 undergoes decomposition a short but appreciable time elapses 
 before the greater number of the elementary atoms which 
 composed it have rearranged themselves to form new mole- 
 cules, we have the materials for a fairly satisfactory explana- 
 tion, from one point of view, of the phenomena of nascent 
 actions. This explanation does not necessitate, as some of 
 its opponents say it does, the assumption of strange and in- 
 explicable properties as belonging to the elementary atoms. 
 Indeed the occurrence of the phenomena of ' nascent action ' 
 seems to follow as a necessary deduction from the molecular 
 theory applied to chemical phenomena. When a chemical 
 reaction occurs between two molecules, the first step in that 
 process must in very many cases consist in a breaking up of 
 the molecular structures, and the second, in a rearrangement 
 of the parts of the molecules, i.e. of the atoms, to form a con- 
 figuration stable under the conditions of the experiment : and 
 although these changes occur almost simultaneously, neverthe- 
 less, if, by the presentation of molecules of a third chemical 
 substance, there is rendered possible the adoption by the 
 various atoms of another configuration, more stable than 
 that just supposed to be assumed, this, the most stable con- 
 figuration, will be adopted. But if the earlier stable con- 
 figuration has been assumed by the atoms, it does not follow 
 that the introduction of the third class of molecules will now 
 cause this configuration to become unstable \ 
 
 1 It may be urged that the energy or part of the energy which is set free 
 during the mutual actions of the molecules of the reacting bodies, instead of 
 being run down to the form of heat and so lost to the system, becomes available 
 for performing chemical work ; and that the only difference between e.g. ordinary 
 and 'nascent' hydrogen is to be found in the greater chemical energy of the 
 latter. The importance of this point of view is of course admitted by the up- 
 holders of the atomic explanation of nascent actions, but they would supplement 
 this by the statement that the configuration with which the greater quantity of 
 energy is associated is atomic, and they contrast this with a molecular and com- 
 paratively inactive configuration.
 
 CHAP. II. 41] NASCENT ACTIONS. 99 
 
 41 Following out this line of argument, it would appear 
 probable that compounds should present phenomena some- 
 what analogous to those exhibited by elements when in the 
 nascent, i.e. on the hypothesis now adopted the atomic, state. 
 Let it be supposed that no chemical change occurred 
 when the compound molecules a and b were brought into 
 contact, nevertheless if the atoms constituting these molecules 
 were allowed to react a chemical change might occur. In a 
 reaction wherein any given compound is produced there must 
 be a moment of time when this compound can only be said 
 to exist potentially, when the atoms which constitute its 
 molecules have not settled down into stable configurations; 
 at this moment the compound may be said to exist in the 
 nascent state. If the atomic vibrations and interactions are 
 allowed to run what may be called their normal course, the 
 compound molecules are certainly produced, but if these 
 interactions are interfered with, a new set of molecules may be 
 formed, which molecules bear a more or less simple genetic 
 relation to those produced in the normal process of the 
 chemical change '. 
 
 The following among other cases of chemical change find 
 a partial explanation in terms of this hypothesis. Nitrous 
 acid has no action on the primary mononitroparaffins 
 (C n H 2n+1 . NCX), but these compounds are converted into 
 nitrolic acids (C B H 2n . N 2 O 3 ) by the action of potassium 
 nitrite and sulphuric acid, i.e. by the action of reagents which 
 by their mutual decomposition produce nitrous acid. Nitric 
 
 The experiments of Victor Meyer on iodine give direct evidence of the 
 separation of elementary molecules into atoms by the addition of energy in the 
 form of heat. (See ante, p. 33 par. 15.) 
 
 In Book II. chapter II. par. 189, will be found some facts regarding dis- 
 sociation which bear on the subject of nascent actions. 
 
 1 In all such considerations we can deal with molecular phenomena only by a 
 statistical method, we can reason only as to the average condition of the mass of 
 molecules constituting a substance at any moment of time. 
 
 It seems not improbable that there may sometimes be nearly as great 
 differences between the properties of a number of elementary atoms all of one 
 kind and the elementary molecules which are produced by the union of these 
 atoms, as between the properties of a number of atoms of different kinds and the 
 compound molecules produced by the union of these atoms. 
 
 72
 
 IOO ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 acid does not act on napthol to produce dinitronapthol, but 
 if napthol be produced in contact with nitric acid e.g. by 
 boiling diazonapthalene hydrochloride in presence of nitric 
 acid dinitronapthol is formed. Carbon monoxide and 
 ethylene do not react to form acrolei'n even under the influence 
 of electric sparks, but if ethylene is exploded with a quantity 
 of oxygen less than sufficient for complete oxidation, carbon 
 monoxide is produced and simultaneously acrolei'n is formed, 
 i.e. the chemical change proceeds partly in its normal way 
 and at the same time the 'nascent' carbon oxide interacts 
 with the ethylene with production of acrolei'n. When para- 
 iodophenol is fused with potash at 163 hydroquinone is pro- 
 duced, but at higher temperatures only resorcin is formed : 
 now as fusing potash does not act on hydroquinone it seems 
 necessary to conclude, that in the fusion of paraiodophenol at 
 high temperatures hydroquinone is produced, but is imme- 
 diately changed into resorcin. 
 
 42 Whether the course of a chemical action is or is not to be 
 regarded as an example of the particular application of the 
 molecular theory now under consideration, must be decided 
 by the nature of the change in question. Some of the changes 
 which occur when metals and acids interact probably belong 
 to this class of chemical actions. 
 
 The products of the mutual actions of metals and sul- 
 phuric and nitric acid, respectively, have already been 
 broadly stated. That no hydrogen is evolved in the case of 
 nitric acid is generally said to be due to the oxidation, by 
 the nitric acid, of the atoms of hydrogen, assumed to be pro- 
 duced by the interaction of the metal and acid, with a corre- 
 sponding reduction of the acid to oxides of nitrogen, nitrogen, 
 and sometimes ammonia. 
 
 Direct proof in favour of this hypothesis, in the case of the 
 interaction of nitric acid and magnesium, has been given by 
 Gladstone and Tribe 1 , who have shewn that when a small 
 piece of magnesium is placed in a large excess of nitric acid 
 (strengths I : I and I : 2. acid to water were employed) the 
 gas at first evolved consists of nearly pure hydrogen, but 
 
 1 C. S. Journal Tram, for 1879. 178.
 
 CHAP. II. 42] REACTIONS OF ACIDS WITH METALS. IOI 
 
 that oxides of nitrogen are very quickly produced. The same 
 chemists 1 have established a close relation between the reac- 
 tion with sulphuric and nitric acids of the hydrogen produced 
 by electrolysis of these acids, and the hydrogen occluded by 
 platinum or palladium ; they have also shewn that hydrogen 
 evolved by the action of the copper zinc couple is very 
 analogous in general reducing actions to hydrogen occluded 
 by platinum or palladium. 
 
 When concentrated nitric acid is subjected to electrolysis 
 no hydrogen is evolved, but the acid is reduced; when more 
 dilute acid is used hydrogen is evolved, reduction of the acid 
 also occurs, and the more rapid the electrolysis the greater is 
 the quantity of hydrogen evolved. Concentrated nitric acid 
 rapidly acts on hydrogen occluded by platinum or palladium, 
 with oxidation of the hydrogen and reduction of the acid. 
 In the electrolysis of concentrated sulphuric acid sulphur is 
 produced, and also sulphur dioxide with traces of sulphuretted 
 hydrogen, a portion of the hydrogen formed is oxidised and a 
 portion escapes, and the stronger the battery power the 
 greater is the quantity of hydrogen evolved. When the 
 electrolysis is extremely slow, no hydrogen is evolved, and 
 sulphur dioxide is produced in small quantity unmixed with 
 free sulphur. Hydrogen occluded by palladium or platinum 
 also reduces sulphuric acid, with production of sulphur 
 dioxide and escape of a portion of the hydrogen. 
 
 Gladstone and Tribe regard the metal (platinum or palla- 
 dium) present in their experiments as instrumental in the 
 chemical change. They think that the hydrogen produced is 
 occluded by the metal and again given off to the. acid, and 
 that if the gas is produced more quickly than it can be 
 occluded the excess escapes oxidation by the acid : it is 
 probable that occluded hydrogen forms a compound with the 
 occluding metal, and that therefore hydrogen coming from 
 this source is for the most part in the nascent, i.e. on the 
 present hypothesis the atomic, state. Their experiments cer- 
 tainly establish the fact that maximum reduction of either 
 acid is obtained when hydrogen is evolved therein near an 
 
 1 C. S. Journal Trans, for 1878. 139 and 306.
 
 102 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 electro-negative metal ; but a comparison of the results with 
 occluded and electrolytically evolved hydrogen shews that 
 the reducing action of the latter on sulphuric acid is more 
 complete than that of the former. 
 
 There are two hypotheses regarding the mechanism of the 
 changes which occur when metals and aqueous solutions of 
 nitric acid interact. One hypothesis asserts that these 
 changes generally proceed in two stages, taking place simul- 
 taneously ; in the first stage the metal and acid react to pro- 
 duce a nitrate and hydrogen ; in the second stage the hydro- 
 gen, or a portion of it, interacts with another portion of the 
 acid..to produce oxides of nitrogen, ammonia, or nitrogen, and 
 water. The other hypothesis regards the various gaseous 
 products as direct results of the deoxidation of the acid by 
 the reaction with the metal, and denies that hydrogen is pro- 
 duced at any stage of the process. The facts, taken as a 
 whole, seem to me to be more in keeping with the first than 
 with the second of these hypotheses. Indeed to formulate the 
 reaction of zinc and nitric acid on the latter hypothesis 
 requires that nitric acid should be regarded as a variable 
 compound of nitrogen pentoxide and water, and necessitates 
 considerable skill in the manipulation of formulae 1 . 
 
 The interaction of copper and concentrated sulphuric acid 
 has been studied by Pickering' 2 . The ease with which this 
 acid undergoes deoxidation is shewn by the slow production 
 of cuprous sulphide even at 20; the equation 
 
 which represents the change as consisting in deoxidation of 
 part of the acid, and does not involve, nor according to 
 Pickering's experiments allow, an intermediate stage wherein 
 hydrogen reacts with the acid, is nearly realized at this tem- 
 perature. At higher temperatures sulphur dioxide is evolved, 
 until at about 270 the action consists entirely of a change 
 which may be formulated as 
 
 1 Deville, Compt. rend. 70, 20 and 550; or in abstract, Watt's Diet. Suppl. 2, 
 304. See also Acworth and Armstrong, C. S. Journal, vol. 2. for 1877, 54 et seq. 
 
 2 C. S. Journal TOM. for 1878. U2.
 
 CHAP. II. 42] REACTIONS OF ACIDS WITH METALS. 103 
 
 and which is most readily explained as consisting of two 
 parts proceeding simultaneously 
 
 f(i) Cu + H 2 SO 4 = CuSO 4 +H 2 \ 
 \(') H 2 +H 2 S0 4 = 2H 2 + S0 2 J ' 
 
 Tin and lead are dissolved by hot concentrated sulphuric 
 acid, with production of sulphates and evolution of hydrogen 
 and sulphur dioxide, sometimes accompanied by sulphuretted 
 hydrogen, and with separation of sulphur. With more dilute 
 acid tin evolves hydrogen, and as temperature is increased, 
 sulphuretted hydrogen also. The reaction of zinc with sul- 
 phuric acid is broadly analogous to that of tin: with pure zinc 
 and very concentrated hot acid, the products are hydregen 
 and sulphur dioxide; with less pure zinc, sulphuretted hydro- 
 gen and sulphur are also formed, the sulphur compounds (SO 2 
 and SH 2 ) appearing even when the acid is very dilute and is 
 kept cold ; with moderately dilute pure acid and pure zinc 
 hydrogen is the only gaseous product (s. Pattison Muir and 
 Adie, C. S. Journal, Trans. 1888, 47). 
 
 Quantitative analyses of the products of reduction of 
 nitric acid by magnesium, zinc, and cadmium, respectively 
 shew that reduction is carried furthest by magnesium, and 
 further by zinc than by cadmium. Now the 'heats of for- 
 mation ' (see Chap. IV.) of the oxides of these metals are, 
 for Mg 147,132, for Zn 88,244, and for Cd 30,364 thermal 
 gram-units; hence in these cases that reaction in which the 
 greatest amount of heat is produced is accompanied by the 
 greatest reduction of the acid. 
 
 The following numbers representing quantities of heat 
 produced in the chemical changes formulated were obtained 
 by Thomson*: 
 
 [H 2 , S, O 4 , Aq] = 2 10,760 gram-units +. 
 
 [H, N,0\Aq] = 34,270 +. 
 
 [Zn, H 2 SO 4 Aq]= 106,090 +. 
 
 [Zn, 2 HNO 3 Aq]= 1 36,340 +. 
 
 1 These equations tell that e.g. when 2 grams of hydrogen, 32 grams of 
 sulphur, and 64 grams of oxygen interact in presence of a large quantity of water 
 to form a dilute aqueous solution of 98 grams of sulphuric acid, 210,760 gram- 
 units of heat are produced. (For fuller explanations s. Chap. IV.)
 
 IO4 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 Berthelot gives the thermal value 21,500 gram-units to the 
 chemical change 
 
 HNO 3 Aq (dilute) + 8H = NH,Aq (dilute) + 3H 2 O. 
 
 From these numbers we should expect sulphuric acid 
 to be more stable, towards heat, than nitric acid, and we 
 should expect the reaction of zinc with these acids to result 
 in a more complete deoxidation of nitric than of sulphuric 
 acid. 
 
 In the interaction of a metal with nitric acid in aqueous 
 solution at ordinary temperatures, we have then, an unstable 
 acid, a considerable quantity of heat produced, and the 
 formation of hydrogen in contact with the acid ; we have 
 conditions eminently favourable to deoxidation. In the 
 interaction of a metal with dilute sulphuric acid, on the other 
 hand, we have a more stable acid and a smaller quantity of 
 heat produced ; the hydrogen escapes unchanged ; but when 
 the acid is so concentrated that addition of heat from with- 
 out is required to start the reaction, and when the acid is 
 therefore in a condition more comparable with that of nitric 
 acid at ordinary temperatures, a portion of the hydrogen 
 then evolved undergoes oxidation at the expense of the 
 oxygen of the acid. If however hydrogen is evolved, as in 
 the experiments of Gladstone and Tribe, in contact with the 
 concentrated acid at ordinary temperatures, a part of this 
 hydrogen is always oxidised ' ; this shews that all the reacting 
 substances, and also the conditions of the reaction, must be 
 considered, and that attention must not be confined to the 
 hydrogen only. 
 
 The facts, that hot sulphuric acid is deoxidised by carbon, 
 and apparently by phosphorus also 2 , and that .it is possible 
 by heat alone to decompose this acid into sulphur dioxide, 
 oxygen, and water, have caused some chemists to regard the 
 reactions of metals with this acid as simply cases of direct 
 deoxidation: but it seems to me that the facts enumerated 
 both chemical and physical, with regard to the interactions of 
 
 1 When however vapour of sulphuric acid mixed ivith hydrogen is 
 through a hot tube, sulphuretted hydrogen is produced. 
 
 2 Cross, C. S. Journal Trans, for 1879. 253.
 
 CHAP. II. 42] NASCENT ACTIONS. 105 
 
 metals with this acid and with nitric acid are more in 
 keeping with that hypothesis according to which hydro- 
 gen plays an essential part in the series of changes, than 
 with any other hitherto advanced. There may be, indeed 
 there undoubtedly is, more than one process of chemical 
 change resulting in the deoxidation of sulphuric acid ; in some 
 cases direct deoxidation preponderates, in others hydrogen 
 plays the more important part. 
 
 Experiments conducted by Thorpe 1 on the reducing 
 action of zinc, magnesium, and tin, on acidulated solutions 
 of ferric sulphate, shewed that whatever condition tends to 
 give greater chances of contact between the hydrogen pro- 
 duced in the liquid and the ferric sulphate in solution, 
 increases the rate of reduction; that increase of the rate 
 at which hydrogen is evolved, other conditions remaining 
 constant, is accompanied by decrease of the amount of re- 
 duction in unit of time; and that the presence of certain 
 salts, e.g. zinc sulphate, causes a decrease in the rate of 
 reduction. Thorpe's results also established a distinct 
 connexion between the nature of the metal used and the 
 influence on the rate of reduction of the varying conditions 
 under which the experiments were conducted. 
 
 These experiments, and indeed all experiments oh the 
 interactions of metals and acids, emphasise the necessity that 
 exists for considering all the reacting substances which take 
 part in a process of reduction by hydrogen, and not confining 
 attention to the hydrogen alone. The results of experiments 
 by Tommasi 2 also shew this need: Tommasi found that po- 
 tassium chlorate was not deoxidised by hydrogen evolved by 
 the action of sodium-amalgam, but was reduced by hydrogen 
 evolved by the action of zinc on diluted sulphuric acid, 
 but that the latter agents failed to remove oxygen from 
 potassium perchlorate. Experiments conducted in my la- 
 boratory have shewn that an aqueous solution of potassium 
 chlorate is reduced by the action of magnesium or sodium, 
 and by that of the copper-zinc couple; and that an aqueous 
 
 1 C. S. Journal Trans, for 1882. 289. 
 
 2 See especially Pogg. BeiWitter, 2. 205.
 
 106 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 solution of potassium perchlorate is very slightly reduced (to 
 chloride) by the action of sodium, and by the prolonged action 
 of magnesium, but is not reduced by the action of the copper- 
 zinc couple, by that of zinc dust and potash, or by electrolysis. 
 43 The conception which underlies such expressions as nascent 
 actions, action of nascent hydrogen, &c., is that implied in the 
 distinction drawn between atom and molecule. That this 
 distinction is not one merely of terminology but is based on 
 actual reactions, is rendered apparent by the results of ex- 
 periments by Traube 1 on the electrolysis of water, using 
 electrodes of different materials. For instance, he found that 
 when palladium is charged with hydrogen and made the 
 positive pole of the battery no hydrogen peroxide is produced, 
 but the oxygen which is being evolved is absorbed by the 
 palladium and is combined with the occluded hydrogen to 
 form water. When however the hydrogenised palladium is 
 made the negative pole a little hydrogen peroxide is pro- 
 duced; and the quantity of this compound may be con- 
 siderably increased by causing bubbles of air to rise through 
 the liquid near the negative pole. If however no air is passed 
 through the water, and at the same time the transference of 
 oxygen from the positive pole (where it is being liberated) 
 through the liquid to the negative pole is mechanically pre- 
 vented, no hydrogen peroxide, or only a trace of this com- 
 pound, is produced. Further, if hydrogenised palladium is 
 made the positive pole, and bubbles of air are at the same 
 time caused to rise through the liquid around the pole, a little, 
 but only a little, hydrogen peroxide is produced. 
 
 Finally if the electrodes are made of palladium uncharged 
 with hydrogen the maximum yield of hydrogen peroxide is 
 obtained (entirely at the negative pole) by arranging the rate 
 of electrolysis so that the whole of the hydrogen produced is 
 occluded by the palladium; the more rapid the evolution of 
 hydrogen from the liquid the smaller is the quantity of 
 hydrogen peroxide produced 2 . Now it is generally supposed 
 
 1 er,15. 659, 2421, 2434: 16. 1201. 
 
 2 These results are confirmatory of those obtained by Gladstone and Tribe in 
 their electrolytic experiments on the reduction of acids. See ante, p. 100.
 
 CHAP. II. 43, 44] NASCENT ACTIONS. IO/ 
 
 that the greater part of the oxygen or hydrogen liberated 
 during the electrolysis of water is at the moment of its pro- 
 duction in the state of atoms, and that the greater part of the 
 oxygen in ordinary air is composed of molecules ; if this be 
 granted, it follows that Traube's experiments establish a 
 marked difference between the reactions of oxygen atoms and 
 oxygen molecules : by their reaction with hydrogen occluded 
 by palladium, the former produce water, the latter produce 
 hydrogen peroxide; if a few atoms and many molecules of 
 oxygen are present much peroxide and little water are the 
 products, while if many atoms and few molecules of oxygen 
 are brought into contact with the hydrogen, much water and 
 little peroxide is the result. 
 
 44 But the experiments of Traube also shew that the direction 
 and final goal of the chemical change depends not only on the 
 structure of the particles of oxygen, but also on the source 
 and conditions of supply of the hydrogen. If the hydrogen 
 is produced by rapid electrolysis little peroxide is formed; 
 indeed if the hydrogen is produced, rapidly or slowly, by 
 electrolysis with carbon poles no peroxide is obtained. The 
 chemical nature and the mass of each of the members of the 
 changing system influence the final configuration. The im- 
 portance of considering the conditions under which hydrogen 
 is produced when we are attempting to explain any of the 
 phenomena classed together as nascent, is emphasised by the 
 fact that the metals which decompose water in absence of oxy- 
 gen do not give rise to the production of hydrogen peroxide 
 by their action on water in presence of oxygen; for instance, 
 hydrogen peroxide is never produced by the action of sodium 
 on water. It is not enough then that oxygen molecules 
 should be present in contact with atoms of hydrogen as these 
 are liberated from water. The peroxide results from the 
 mutual interactions of the three substances, metal, water, and 
 oxygen; if the water is decomposed by the metal alone, 
 hydrogen is evolved rapidly and escapes the pursuit of the 
 oxygen molecules; the peroxide appears to be a product of 
 the joint action of the metal and oxygen on the molecules of 
 water.
 
 IO8 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 The conception of a joint action of metal and oxygen with 
 water may be used to explain some of the phenomena ex- 
 hibited when metals and acids interact. Traube seeks to 
 explain many of these reactions in this way. 
 
 Copper does not remove oxygen from an aqueous solution 
 of potassium nitrate as zinc does: but if copper is brought 
 into contact with dilute sulphuric acid in presence of oxygen, 
 hydrogen peroxide is produced. The joint action of copper 
 and potassium nitrate is not sufficient to decompose water- 
 molecules ; but copper and oxygen aided by a little sulphuric 
 acid suffice to complete this change. The reaction in question 
 is represented thus by Traube : 
 
 rOH \H] ..... 7o H-0 
 
 (a) Cu + \ I \+\ | = Cu(OH) 2 + | 
 
 (OH j HJ lO H-0 
 
 (b) (when a certain amount of H 2 O 2 is produced) 
 
 Cu + H 2 2 =Cu(OH) 2 
 (0 Cu(OH) 2 + H 2 S0 4 =CuSO 4 + 2H 2 0. 
 
 If some compound which is readily acted on by hydrogen 
 is substituted for oxygen in this series of changes, then 
 copper and dilute sulphuric acid form a reducing agent; 
 ferric sulphate e.g. is reduced under these conditions to 
 ferrous sulphate: 
 
 OH fti" ...... 
 
 Cu + 
 
 Similarly the interaction of copper with dilute nitric acid 
 would be represented thus : 
 
 (OH ; H) 
 
 ] U 3 (0 i NO,H 
 
 (OH i HJ i 
 
 [but 3 NO 2 H rapidly decomposes to give HNO 3 + 2NO + H 2 O]. 
 
 As thus regarded, these reactions of metals with acids are 
 
 complex changes; at one stage or other of the complete 
 
 change hydrogen plays an important part, and it does this in 
 
 virtue of being itself a product of another part of the whole
 
 CHAP. II. 44, 45] NASCENT ACTIONS. IOQ 
 
 reaction. Hydrogen imported from without the system fails 
 to accomplish actions which are brought about by hydrogen 
 generated within the system, provided this hydrogen be pro- 
 duced at the proper rate and under conditions generally 
 favourable to the action it is to perform. 
 
 The investigation of Divers 1 'On the production of hy- 
 droxylamine from nitric acid' is an interesting and instructive 
 example of the need of considering all the members of a 
 changing system in attempting to find an explanation of the 
 change. Hydroxylamine is produced in very small quantities 
 during the reaction of tin, zinc, and some other metals, with 
 nitric acid; but if hydrochloric or sulphuric acid is added to 
 the zinc and nitric acid a marked increase in the yield of hy- 
 droxylamine is noticed. When a mixture of nitric and sul- 
 phuric acids reacts with zinc it is probable, from the experiments 
 made by Divers, that the ammonia which is produced in con- 
 siderable quantities is a product of the direct mutual action of 
 the zinc and nitric acid, and that the hydroxylamine is a 
 product of the reduction of the nitric acid by the combined 
 interaction with that acid of zinc and sulphuric acid. Zinc 
 and sulphuric acid in presence of nitric acid, according to 
 Divers, form an hydrogenising mixture; the chief products of 
 this action are hydrogen and hydroxylamine, besides sulphate 
 and nitrate of zinc. Zinc and aqueous nitric acid alone also 
 form an hydrogenising mixture; but the chief product of this 
 action, other than zinc nitrate, is ammonia. Hydroxylamine 
 is not therefore an invariable product of the reaction of hy- 
 drogen with nitric acid even when that hydrogen is evolved in 
 contact with the acid ; it is rather to be regarded as a product 
 of the combined interaction of nitric acid and sulphuric acid 
 with zinc, this reaction being such that the nitric acid is sup- 
 plied with hydrogen whereby it is reduced to hydroxylamine. 
 45 The expression 'nascent action' has probably been at once 
 helpful and harmful to the progress of chemistry. By classing 
 under a common name many phenomena that might other- 
 wise have been lost in the vast mass of facts with which the 
 
 1 C. S. Journal, Trans, for 1883. 443 : also Divers and Shimidzu, C. S. Journal, 
 Trans, for 1886. 597.
 
 110 ATOMIC AND MOLECULAR SYSTEMS. [HOOK I. 
 
 science has to deal, the expression has, I think, done good 
 service; but in so far as its use has tended to prevent in- 
 vestigation for it is always easier to say of any unusual 
 reactions, 'these are cases of nascent action,' than to examine 
 carefully into their course and conditions and also in so 
 far as it has favoured the impression that 'nascent' hydro- 
 gen or 'nascent' oxygen, &c. is ordinary hydrogen or oxygen, 
 &c. with certain indefinite properties which always belong 
 to the hydrogen, or other element, when in this peculiar con- 
 dition the use of the expression has, I think, been unfavour- 
 able to the best interests of chemical science. 
 
 A study of the reactions in which nascent substances play 
 important parts appears to me to keep before the student 
 that all-important distinction between the atom and the 
 molecule which is so vital in chemical considerations, and also 
 to draw attention in a marked way to the complexity of all 
 chemical changes. We find, or think we find, that when atoms 
 of hydrogen are presented to another substance in a given 
 chemical reaction, certain definite products result; and we 
 are apt to conclude that the interaction of hydrogen atoms 
 with this substance will always give this result; but investi- 
 gation discovers that not only the course of the reaction, but 
 also the final configuration of the changing system, is de- 
 pendent on the whole previous history of the reacting bodies. 
 Hydrogen as it is produced by the action of sodium-amalgam 
 appears to possess properties different from those which 
 characterise hydrogen produced by the reaction of zinc with 
 dilute sulphuric acid. Attempts to explain these apparent 
 differences lead to fresh researches; the results of these re- 
 searches shew the danger of using such an expression as tJie 
 properties of Jiydrogen produced by the action of sodium-amalgam, 
 and contrasting these with the properties of hydrogen produced 
 by the reaction of zinc with dilute sulphuric acid; they teach 
 that every chemical change is composed of parts, and that the 
 occurrence of one part is dependent on the occurrence of the 
 other parts, that we cannot, except occasionally, alter one part 
 of the complete change and expect the other parts to proceed 
 as before, The change of hydrogen and potassium chlorate
 
 CHAP. II. 45,46] USE OF TERM 'NASCENT.' Ill 
 
 in aqueous solution to potassium chloride and water, for 
 instance, is dependent not only on the interaction of the 
 chlorate and hydrogen but also on the interaction whereby 
 the hydrogen is itself produced. It is not that hydrogen 
 produced in one way has certain properties and hydrogen 
 produced in another way has other properties, but rather that 
 the members of the system composed of potassium chlorate, 
 water, and sodium-amalgam, interact to produce potassium 
 chlorate, soda, water, mercury, and hydrogen, whereas the 
 members of the system composed of potassium chlorate, 
 water, zinc, and sulphuric acid, interact to produce potassium 
 chloride, water, zinc sulphate, and hydrogen. We thus be- 
 come impressed with the conviction that chemistry is not the 
 study of this element or that, regarded as a kind of matter 
 with certain fixed physical properties, but that processes of 
 change are the subject-matter of the science, and that to 
 explain any one of these we must take into account each and 
 all of the reacting bodies, and each and all of the conditions 
 under which the total change is proceeding. 
 
 If the expression 'nascent action' does in any way help to 
 emphasise such considerations as these, I think it ought to be 
 retained in chemical nomenclature 1 . 
 
 SECTION II. The Dualist ic and Unitary Hypotheses. 
 
 We must now examine the relations between the chemical 
 properties of atoms and of the molecules, or atomic aggregates, 
 which are formed by the union of these atoms. We must in- 
 quire whether the properties of the molecule are the sum of 
 the properties of its constituent atoms ; or whether the latter 
 properties are modified by the mutual interactions of the 
 atoms. We must endeavour to learn something regarding the 
 structure of molecules. 
 
 46 Partly from his definition of element, partly from his study 
 of the products of combustion in oxygen, of phosphorus, 
 carbon, sulphur, &c., Lavoisier was led to regard every salt 
 1 See also Book II. chapter n.
 
 112 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 as formed by the union of an acid with a radicle, the latter 
 being itself either simple or compound. 
 
 Davy began his electro-chemical researches in the early 
 years of the present century. In the Philosophical Transactions 
 for 1807*, and in his Elements of Chemical Philosophy*, he 
 regards chemical combination as accompanied by an ex- 
 change of quantities of electricity of opposite sign between 
 the combining bodies. He found that when sulphur and 
 copper are rubbed together the sulphur is negatively, the 
 copper positively, electrified; and that when the sulphur is 
 heated the electrical activities become more apparent, until 
 the sulphur melts, when chemical combination occurs, and 
 the product, copper sulphide, exhibits neither positive nor 
 negative electricity. If the quantity of electricity lost in the 
 act of chemical union is restored, e.g. by the passage of a 
 current through the compound formed, chemical decom- 
 position occurs and the original components are again ob- 
 tained. Davy regarded the primary cause of chemical and 
 electrical effects as possibly the same force; when this force 
 is exerted between masses of matter, electrical phenomena, he 
 said, result; when it is exerted between the smallest particles 
 of bodies chemical phenomena result. Thus in his Elements 
 of Chemical Philosophy* Davy says, 
 
 "Electrical effects are exhibited by the same bodies when acting as 
 masses, which produce chemical phenomena when acting by their par- 
 ticles ; it is not therefore improbable that the primary cause of both may 
 be the same, and that the same arrangements of matter, or the same 
 attracting powers, which place bodies in the relations of positive and 
 negative, i.e. which render them attractive of each other electrically, and 
 capable of communicating attractive powers to other matter, may likewise 
 render their particles attractive, and enable them to combine, when they 
 have full freedom of motion." " That the decomposition of the chemical 
 agents is connected with the energies of the pile, is evident from all the 
 experiments that have been made; as yet no sound objection has been 
 urged against the theory that the contact of the metals destroys the 
 electrical equilibrium, and that the chemical changes restore it; and, in 
 
 1 'On some chemical agencies of electricity,' p. i. 
 
 3 Collected Works, vol. iv. (see also Ladenburg's Entwickelungsgeschichte der 
 Chemie, pp. 7581). 
 
 3 Pp. 119 1 20, and p. 125.
 
 CHAP. II. 47] BERZELIUS' ELECTRO-CHEMICAL WORK. I 13 
 
 consequence, that the action exists as long as the decompositions con- 
 tinue." 1 
 
 17 At once a brilliant theoriser and a thorough-going experi- 
 menter, Davy did not attempt to found a general scheme of 
 chemical classification on his electro-chemical work. This 
 was however done by Berzelius, who developed a consistent 
 and definite, although narrow, theory which for a time seemed 
 to explain all chemical phenomena. 
 
 All chemical actions were regarded by Berzelius as brought 
 about by electrical force 2 . "Die Elektricitat...scJieint die erste 
 Thatigkeits- Ursache in der ganzen, uns umgebenden Natur zu 
 sem." Electrical actions, according to Berzelius, were not to 
 be described as consequences of contact, or of mutual action, 
 between heterogeneous bodies. Each elementary atom, he 
 held, is endowed with two kinds of electricity, it has two 
 electric poles ; but these poles differ in strength, so that 
 each atom considered as a whole is positively or negatively 
 electrified ; in some elementary atoms positive electricity 
 predominates and gives a positive character to the whole 
 atom; in others negative electricity overpowers the positive. 
 When a positively electrified atom attracts a negatively elec- 
 trified atom, opposite electricities neutralise one another, but 
 the electricities formerly masked in the separate atoms now 
 come into play, and so the new group of atoms, as a whole, 
 exhibits positive or negative electricity, in virtue of which it 
 is capable of chemically combining with other atoms or groups 
 of atoms. But as the stronger poles are first neutralised, it 
 follows that the more complex a compound is, the less polarity 
 does it exhibit, and hence the less readily does it combine 
 with other substances. Berzelius moreover regarded the quan- 
 tity of electricity on either pole as to some extent variable 
 with variations of temperature. By the Berzelian theory 
 
 1 It is interesting to observe how similar this view, stated by Davy in the 
 beginning of the present century, is to the latest views regarding the connexion 
 of chemical and electrical forces. Compare especially Helmholtz's ' Faraday 
 Lecture.' (C. S. jfournal, Trans, for 1881, 277 et seq.: see particularly pp. 300 
 302.) [See /to/, Book II.] 
 
 2 Lehrbuch (ist Ed.), in. part I. p. 77. 
 
 M.C. 8
 
 114 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 atoms are regarded as essentially unipolar ; one polarity so 
 predominates over the other that each atom acts as a posi- 
 tively or negatively electrified whole. 
 
 The electro-chemical properties of oxidised compounds, 
 Berzelius taught, depend chiefly on the unipolarity of the 
 electro-positive radicles they contain. Of two oxides, that 
 which contains the more electro-negative radicle is generally 
 itself electro-negative; thus sulphuric acid (regarded as SO 3 ) 
 is electro-negative to all metallic oxides, because sulphur is 
 itself electro-negative to all metals: on the other hand the 
 oxides of potassium and sodium are electro-positive to all 
 other oxides (excepting those of caesium and rubidium) be- 
 cause potassium and sodium are themselves electro-positive 
 to all other elements 1 (except caesium and rubidium). 
 
 Polarity and chemical affinity are closely connected in the 
 system of Berzelius: the 'specific unipolarity' 2 however does 
 not alone determine the greater or less affinity of one atom 
 for another. Some atoms have a more intense polarity than 
 others and therefore exhibit a greater striving (Bestreben] to 
 neutralise the electricity divided between their poles, in other 
 words, have a greater affinity for a given substance than 
 other atoms. 
 
 Chemical affinity appears to have been regarded by Ber- 
 zelius as nearly synonymous with intensity of atomic polarity 3 . 
 Thus, oxygen combines with sulphur rather than with lead, 
 although oxygen and sulphur have the same unipolarity (viz. 
 negative); but, the Berzelian view asserts, the positive pole of 
 the sulphur atom neutralises more negative electricity on the 
 oxygen atom than can be neutralised by the positive pole of 
 the lead atom. 
 
 1 An important deduction made from these considerations is, that as oxygen 
 occurs both in markedly electro-positive and electro-negative compounds, and as 
 acids are as a group electro-negative, oxygen cannot be the acidifying element, as 
 Lavoisier said it was. 
 
 2 Specifische Unipolaritat. Berzelius, loc. cit. p. 73. 
 
 3 This might perhaps be regarded as equivalent to the modern conception of 
 higher and lower potential ; as if one atom might have a smaller electrical charge 
 but at a higher potential than another, and would therefore exhibit greater 
 chemical affinity than the other.
 
 CH. II. 48] THE DUALISTIC THEORY. 115 
 
 Double decompositions were readily explained in terms of 
 this theory: 
 
 "Every chemical action," says Berzelius 1 , "is an electrical pheno- 
 menon depending on the electrical polarity of the particles ; everything 
 that appears to be due to the action of affinity is caused by the possession 
 by some bodies of an electrical polarity stronger than that of others. If 
 the compound AB is decomposed by the substance C which has a greater 
 affinity for A than B has, then C must possess a more intense electrical 
 polarity than B ; on this account there results more complete neutralisa- 
 tion between A and C than between A and B.... If two bodies, AB and 
 CD, so react as to produce two new bodies, AD and BC, it follows that 
 the electrical polarities are better neutralised in the latter pair of bodies 
 than in the former." 
 
 48 On the basis of this conception Berzelius raised the struc- 
 ture of the dualistic chemistry, which asserted that every 
 compound, whether simple or complex, must be constituted of 
 two parts, of which one is positively, and the other negatively, 
 electrified. 
 
 The doctrine of dualism is thus introduced by Berzelius 2 : 
 " If these electro-chemical conceptions are just, it follows that every 
 chemical compound is dependent on two opposing forces, positive and 
 negative electricity, and on these alone ; and that every compound must 
 be composed of two parts held together by their mutual electro-chemical 
 reactions. Therefore it follows that every compound body, whatever be 
 the number of its constituents, can be separated into two parts, whereof 
 one is positively and the other negatively electrified. Thus, for example, 
 sodium sulphate is put together, not from sulphur, oxygen, and sodium, 
 but from sulphuric acid and soda, which again can themselves be separated 
 into positive and negative constituents. So also alum cannot be regarded 
 as immediately built up from its elements, but must rather be looked on 
 as the product of a reaction between sulphate of alumina and sulphate of 
 potash, the former acting as a negative, the latter as a positive element." 3 
 
 In support of his theory Berzelius appealed to the facts of 
 electrolysis. A solution of sodium sulphate containing a little 
 blue vegetable colouring matter is electrolysed ; the colouring 
 matter is reddened around the positive electrode and rendered 
 
 1 Lehrbuch (ist Ed.), III. part I. p. 77. 
 
 8 Ibid. p. 79. 
 
 3 See also Berzelius, Theorie des proportions chimiques, et de ^influence 
 chimiqtie de V electricity dans la nature inorganique ; 3rd Ed. Paris, 1835. Also, 
 for a condensed account of the electro-chemical theory of Berzelius, see Laden- 
 burg, Enhvickelutigsgcschichtc dcr Chemie, pp. 89 93. 
 
 82
 
 Il6 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 more distinctly blue around the negative. What can this 
 experiment teach but that the salt is separated by the electric 
 current into alkali and acid ? And can the inference be 
 avoided that the salt is composed of, or contains in itself, 
 these two compound radicles, soda (Na 2 O), and sulphuric 
 acid (SO 3 )? All salts were to be regarded as dualistic struc- 
 tures. Given the composition of a salt, a dualistic formula, or 
 rather a series of formulae, was at once devised for it. The 
 following formulae were employed by various dualistic chemists 
 to express the structure of acetic acid : 
 
 (i) C 4 H 6 3 . H 2 (2) C 4 H 6 4 . H 2 (3) C 4 H 6 O . O 2 . H 2 O 
 
 (4) (C 2 H 6 )C 2 3 .H 2 (5) (C 2 H 6 )C 2 4 .H 2 (6) (C 3 H 6 O)CO 2 . H 2 O 
 
 (7) C 4 H 8 . 4 (8) C 2 H 4 . 2 (9) C 4 H 6 O 2 . H 2 O 2 
 (10) C 4 H 2 .0 4 H 6 
 
 To choose the proper formula from such a chaos, was a task 
 possible only for one whose foible was omniscience. That 
 formula which had the weight of authority on its side was 
 accepted as correct. 
 
 49 Lavoisier had regarded oxygen as the ' acidifying prin- 
 ciple.' Hydrochloric acid was undoubtedly an acid sub- 
 stance ; therefore, in accordance with the dictum of Lavoisier, 
 it contained oxygen. Davy's study of this compound, and 
 of its analogue hydriodic acid, nevertheless established the 
 fact that an acid can exist which contains no oxygen. The 
 further fact, that so many of the oxides then called acids 
 exhibited acidic properties only in presence of water, led Davy 
 to the belief that very many acids are compounds of hydrogen. 
 Shaking off the trammels of that older philosophy which re- 
 garded the introduction of undefined 'principles' as affording 
 explanations of natural phenomena, Davy said that acids are 
 not characterised by the invariable presence of any one ele- 
 ment, but that certain compounds of very diverse elements 
 belong to this group 1 . 
 
 Dulong 2 in 1815 further advanced Davy's conception of 
 acids by recognising no essential difference between those 
 
 1 For an account of the important work of Davy on the non-oxygenised acids, 
 and the arguments of his opponents, see Ladenburg, loc. cit. pp. 81 87. 
 
 2 Mtm. de FAcad. 1813 15, p. 198: and Schweigger's Journal, 17. 229.
 
 CHAP. II. 49 51] THE DUALISTIC THEORY. 117 
 
 acids which contain oxygen and those which do not. 
 Lavoisier's hypothesis was not however generally abandoned 
 until many years later. 
 
 In 1837 38 Liebig 1 , following up Graham's work on 
 phosphoric acid 2 , distinctly recognised the existence of 're- 
 placeable hydrogen' in acids, whether oxy-acids or acids 
 containing no oxygen, and defined salts to be compounds be- 
 longing to the same class as acids, and formed by putting 
 a metal in the place of an equivalent quantity of hydrogen in 
 acids 3 . 
 
 This view of the structure of salts was altogether opposed 
 to the dualistic theory of Berzelius. 
 
 50 Another severe blow was inflicted on the prevailing theory 
 by Faraday's researches on electrolytic decompositions. 
 
 Faraday shewed that the quantities of various elements 
 set free from different electrolytes, by the same electric 
 current, were chemically equivalent to one another : thus 
 for each two parts by weight of hydrogen set free from 
 water, there were obtained 16 parts of oxygen, 78*2 parts 
 of potassium, 63-5 parts of copper from persalts and 127 
 parts of copper from protosalts. But the affinities of the 
 atoms of the various electrolytes were undoubtedly different 
 in each combination. According to Berzelius, the quantity 
 of electricity collected on any group of atoms is greater, the 
 greater the mutual affinity of these atoms ; but Faraday's 
 experiments shewed, that in so far as this electricity was 
 measurable by electrolytic decomposition, (and that at least 
 comparative measurements should be thus obtained followed 
 from the terms of the dualistic theory itself), the quantity 
 of it was in no way dependent on the affinities of the com- 
 bining atoms 4 . 
 
 51 A bold and partially successful attempt, such an attempt 
 
 1 Compt. rend. 5. 863 (with Dumas): and Annalen, 26. 113, see especially 
 p. 181. 
 
 2 Phil. Trans, for 1833. 253. 
 
 3 See, in connexion with acid generally, Laurent, Chemical Method, pp. 
 
 3945- 
 
 4 See Helmholtz, 'The Faraday Lecture.' C. S. Journal, Trans, for 1881. 
 pp. 2846.
 
 Il8 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 as could be made only by a man of preeminent power, 
 had been made by Berzelius to found chemical classification 
 on the study of composition alone, almost wholly divorced 
 from the study of function or power of doing. As his au- 
 thority became greater Berzelius led chemistry further from 
 the only true path by which she could advance, that namely 
 wherein experiment, and reasoning on experimental data, go 
 hand in hand. And yet no single chemist has enriched the 
 science by the addition of so great a mass of laboriously and 
 accurately determined experimental data as he. The intense 
 concentration of his great intellectual powers upon one view 
 of chemical phenomena led Berzelius to disparage the reason- 
 ing of those who sought to view these phenomena from stand- 
 points other than his own. 
 
 Among those who recalled chemistry to the true scientific 
 method, Dumas, Laurent, and Gerhardt stand preeminent. 
 
 In I839 1 Dumas described trichloracetic acid, obtained by 
 the action of chlorine on acetic acid. The new compound, 
 although containing chlorine in place of hydrogen, was a 
 monobasic acid and resembled acetic acid in its general 
 reactions. Dumas said there are certain types in organic 
 chemistry which are maintained even when a volume of 
 chlorine, bromine, or iodine, is put in the place of an equal 
 volume of hydrogen in the parent substance 2 . 
 
 Berzelius, and the defenders of the dualistic chemistry, 
 violently opposed the idea that the electrically negative 
 chlorine could be substituted for the positive hydrogen, and 
 the identity of type yet be maintained. In Dumas' succeed- 
 ing papers 3 the conception of types was more fully developed. 
 All compounds composed of the same number of equivalents 
 of simple substances, combined in a similar manner, and ex- 
 hibiting broad analogies of properties, were regarded as be- 
 longing to the same type. Such compounds were also, as a 
 
 1 Compt. rend. 8. 609: and Annalen, 32. 101. 
 
 2 Compt. rend. 8. 621. 
 
 3 Annalen, 33. 259: 35. 129 (with Stas), and 289 (with Peligot) : or Compt. 
 rend. 9. 813, and 10. 149.
 
 CHAP. II. 52] THE UNITARY THEORY. 119 
 
 rule, simply related to one another by reactions of formation 
 and decomposition : thus acetic and chloracetic acids ; chlo- 
 roform, bromoform, and iodoform ; ethylene and its chloro- 
 derivatives, &c.; belonged to the same types, or as Dumas 
 said to the same 'natural families'. Dumas regarded car- 
 bonyl chloride as derived from carbonic anhydride by substi- 
 tuting one oxygen by two chlorine atoms ; thus COO gives 
 COC1 2 : this was utterly opposed to the dualistic view, ac- 
 cording to which the formula of carbonyl chloride was 
 written CO . CC1 4 because every compound must be com- 
 posed of two parts, one of which is electrically positive and 
 the other negative. 
 
 52 The new school of chemists naturally opposed the con- 
 ception of compound radicles, a conception too closely asso- 
 ciated with those dualistic theories they were leaving behind 
 to find favour in their sight. But these chemists found that, 
 unless substitution of simple atoms by groups of atoms were 
 regarded as possible, identity of type could not be maintained 
 through groups of compounds undoubtedly belonging to the 
 same natural family. 
 
 Inasmuch as the new chemistry based its claims to re- 
 cognition on an appeal to actual reactions, it was impossible 
 that it should long refuse to recognise the conception of 
 compound, as well as simple, radicles, without proving false 
 to its own method. Liebig and Wohler, in their researches 
 on oil of bitter almonds, explained the observed reactions 
 of the bodies they obtained by assuming the existence of 
 the compound radicle benzoyl (= C U H 10 O 2 ) in these bodies 
 (see Annalen, 3. 249). 
 
 But -what are these compound radicles which the chemists 
 who upheld the unitary system were obliged to recognise, 
 equally with their opponents who supported a dualistic theory? 
 Are they definite groups of atoms always existing as such 
 in compound molecules, or are they only convenient methods 
 of expressing and generalising reactions ? 
 
 As chemistry advanced, compound radicles came to be 
 generally recognised as certain groups of atoms, in com- 
 pound molecules, which remain undecomposed throughout
 
 120 ATOMIC AND MOLECULAR SYSTEMS. [BOOK 1 
 
 a series of reactions undergone by those molecules 1 . Thus 
 we find Kekule in 1857 citing the case of sulphuric acid, 
 H 2 SO 4 , which when acted on by zinc gives ZnSO 4 , and 
 may therefore be said to contain the radicle SO 4 ; but when 
 acted on by phosphorus pentachloride, the compound SO 2 C1 2 
 is produced, hence the acid may be said to contain the 
 radicle SO.,. 
 
 53 The conception of types was destined to bear much fruit. 
 Let us briefly trace its development. 
 
 Liebig and Dumas had regarded salts as substituted 
 metallic derivatives of acids ; they had spoken of a quantity 
 of metal as taking the place of an equivalent quantity of 
 hydrogen : Dumas had even ventured to regard the negative 
 chlorine as capable of replacing an equivalent amount of the 
 positive hydrogen. In doing this, these chemists had returned 
 to the old conception too much forgotten by the Berzelian 
 school of equivalents as quantities to be determined by the 
 study of reactions ; but they had given this conception fresh life 
 by engrafting on to it the notion of natural families or types. 
 
 In writing the formulae of sulphates, selenates, and chro- 
 mates, as MO . SO 3 ; MO . SeO 3 ; and MO . CrO s ; Berzelius had 
 undoubtedly recognised the principle of types ; but so long as 
 this principle was dominated by the necessities of the dual- 
 istic system it was unfruitful. The idea of the chemically 
 reacting unit as one whole, one structure with parts capable 
 of replacement by other parts without the necessary de- 
 struction of the building, gave meaning to what was before 
 but a form of words. 
 
 From its earliest beginnings to its present form the theory 
 of types has been interwoven with the atomic theory ; with- 
 out the latter, the former had never had being. If the value 
 of a scientific idea is to be measured by its fruitfulness, then 
 is Dalton's New System of Chemical Philosophy the most im- 
 portant work yet produced by any chemist. 
 
 1 See especially Laurent's Chemical Method, pp. 276 300 Also Ladenburg, 
 loc. cit. 9th and roth Lectures. The modern development of the conception of 
 compound radicle will be better understood by considering pars. 7074 in 
 Section 4 of this chapter.
 
 CHAP. ii. 53] TYPES. 121 
 
 Now if the reacting unit of any substance is possessed 
 of a definite atomic structure, only those bodies can be said 
 to belong to the same type, or natural family, whose re- 
 acting units are built on a similar atomic plan : but our 
 only method of discovering similarity of structure is by study- 
 ing reactions ; hence only those bodies which are charac- 
 terised by similarity of chemical function ought to be 
 classified under the same type 1 . And as modification of 
 structure has been recognised as not necessarily implying 
 destruction of type, it follows that those quantities of radi- 
 cles, simple or compound, are equivalent, which can perform 
 similar functions in similarly constituted compounds. 
 
 At last a method of chemical classification has been found 
 by Dumas, Liebig, Gerhardt, and Laurent, which when more 
 fully developed will reconcile those who regard composition 
 as all important, with those for whom function is supreme ; 
 which will preserve the fundamental conception of equiva- 
 lent, but interpret it in terms of the wider theory of atoms ; 
 and which will recognise the connexion, while yet empha- 
 sising the importance of the difference, between the atom of 
 Dalton and the molecule of Avogadro. 
 
 But in its development the theory of types must neces- 
 sarily be largely modified. Classification by types cannot be 
 final in a science which has advanced so far towards be- 
 coming an abstract science as chemistry. 
 
 " By the classification of any series of objects is meant the actual, or 
 ideal, arrangement together of those which are like and the separation of 
 those which are unlike ; the purpose of this arrangement being, primarily, 
 to disclose the correlations or laws of union of properties or circumstances, 
 and, secondarily, to facilitate the operations of the mind in clearly con- 
 ceiving and retaining in the memory the 'character of the objects in 
 question'." 2 
 
 Those ' properties or circumstances ' which are correlated 
 must be such as are really characteristic of the objects clas- 
 sified, they must be essential properties of these objects, not 
 mere surface appearances ; they must be capable of accurate 
 
 1 See especially Laurent's Chemical Method, pp. 298 300. 
 
 2 W. Stanley Jevons (modifying the words of Huxley), Principles of Science, 
 2. p. 348.
 
 122 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 definition, and at the same time of fairly easy recognition ; 
 and that property, or properties, chosen as the mark of 
 a class must belong to all the members of that class. 
 
 But the properties of a type are necessarily somewhat 
 vague: properties regarded by one observer as essentially 
 belonging to the type may by another be regarded as acci- 
 dental ; a given substance may possess so many of the 
 properties of the type as at one time suffices to ensure its 
 admission into the class, but at a future time new proper- 
 ties may be discovered which necessitate the removal of the 
 substance to a class whose type shews considerable diver- 
 gence from that under which the substance was originally 
 placed. 
 
 The very elasticity, and even vagueness, of the theory 
 of types ensured it an important place in the development 
 of chemical science. 
 
 SECTION III. Equivalency of atoms, 
 
 54 Dualism had reigned supreme, but only because it was 
 despotic; when the rebellion, headed by Dumas, once got a 
 footing the fate of the older theory was sealed. The new 
 system succeeded because it was not too systematic. 
 
 In attempting to preserve unity of type through large 
 series of compounds, the builders of modern chemistry were 
 obliged to make free use of the conception of compound 
 radicles as substituting simple radicles ; they thus became 
 familiarised with the general notion of each radicle pos- 
 sessing a definite substituting power. 
 
 In 1852 Frankland 1 extended this conception to the 
 atoms of the elementary bodies; in 1855 Odling 2 introduced 
 the use of dashes placed over the atomic symbols to express 
 what he called ' the replaceable, or representative, or substitu- 
 
 1 Phil. Trans. 142. 417, see especially p. 440. 
 
 2 C. S. Journal, 1. i . (The recognition of two ' replaceable values ' for the 
 iron atom, and other atoms, shews the close connexion between the theory then 
 coming into existence and the older theory of equivalents.)
 
 CHAP. II. 54] EQUIVALENCY OF ATOMS. 12$ 
 
 tion value ' of these atoms, he also recognised that an ele- 
 mentary atom may have more than one 'replaceable value'. 
 Odling applied this fruitful conception to the formulae of 
 many salts, especially the phosphates, and succeeded in 
 shewing analogies until then overlooked. 
 
 The inherent fascination of the idea of the compound 
 radicle may be realised, by considering that in less than 
 twenty years after Dumas' discovery of the chloracetic acids, 
 a discovery which marks the beginning of the revolt against 
 the compound radicles of dualism, Kekule 1 , and inde- 
 pendently of him Couper 2 , (in papers of the greatest im- 
 portance) found it necessary to recall chemists to the con- 
 sideration of elementary atoms as being the true units by the 
 combinations of which all compound molecules are built up, 
 and by whose properties those of the compounds are deter- 
 mined. Couper criticised Gerhardt's development of types, 
 objecting to the vagueness of the idea as a basis for classifi- 
 cation ; and especially opposing Gerhardt's opinion that the 
 molecular constitution of bodies can never be ascertained by 
 chemists. " Would it not be rational," says Couper, " in ac- 
 cepting this veto to renounce chemical research altogether?" 
 This dictum of Gerhardt is to be traced, in Couper's opinion, 
 to the overdue employment of compound radicles, to for- 
 getting that these can have no properties which are not 
 "a direct consequence of the properties of the individual 
 elements of which they are made up," and hence to endow- 
 ing these radicles with some " unknown and ultimate power 
 which it is impossible to explain." Returning then to a 
 study of the elements, Couper finds chemical affinity as a pro- 
 perty inherent in, and common to, them all ; he distinguishes 
 ' affinity of kind ' and ' affinity of degree ;' applying the latter 
 to carbon, he cites the oxides CO and CO 2 (in his notation 
 C 2 O 2 and C 2 OJ, the former expressing the first, the latter the 
 second and last, degree: CO 2 is "the ultimate affinity, or 
 combining unit, for carbon." 
 
 Kekule in 1857, an d more especially in a paper published 
 
 1 Annalen (1857), 104. 129. 
 
 2 Phil. Mag. (1858) [4], 16. 104.
 
 124 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 in March 1858*, a paper the importance of which can hardly 
 be overrated, distinguishes more clearly than Couper 'affi- 
 nity of kind' from 'affinity of degree'; or rather he distin- 
 guishes chemical affinity from what he calls the 'basicity of 
 atoms'; both conceptions being needed, he says, for the 
 explanation of chemical combinations. Kekule clearly dis- 
 tinguishes, and this distinction has been too much forgotten 
 in recent developments of chemical theory, between equi- 
 valent weights of elements, and equivalency (or basicity) of 
 elementary atoms; he shews that the new theory deals 
 with definite entities, called atoms, having defined properties, 
 and not with 'unit weights,' and that it is these atoms which 
 he proposes to compare as to their substituting power for the 
 .hydrogen atom. Having shewn that one atom of carbon, 
 so far as our knowledge goes, is never combined with more 
 than four atoms of hydrogen in a compound molecule, Kekule 
 also shews that two atoms of carbon do not bind to them- 
 selves more than six atoms of hydrogen, three atoms of 
 carbon not more than eight atoms of hydrogen, and so on. 
 
 The tetravalency of the carbon atom, and the power 
 which two, or more, atoms of carbon possess of binding them- 
 selves together in a molecule, are enunciated by Kekule in 
 this paper, which forms the foundation stone of the modern 
 hypothesis of 'atom-linking.' 2 
 
 Kekule and Couper insisted, that if a definite conception of 
 the connexions between the properties and the structure of 
 compounds is to be obtained, it must be based on the study 
 of the combining powers of the elementary atoms: 'The 
 whole is simply a derivative of its parts,' said Couper. 
 55 An hypothesis which shall attempt to explain the atomic 
 structure of compound molecules, must, in the present state 
 of knowledge, be based on the consideration of gaseous 
 bodies. We do not know how to determine the relative 
 
 1 Annalen, 106. 129. 
 
 2 In comparing Couper's paper with Kekule's it may be well to notice how 
 Couper attempts to trace a close connexion between the basicity of atoms and 
 chemical affinity; his statements are here much vaguer than Kekule's, yet this 
 dynamical method of regarding 'valency' at the very outset of the theory is 
 important.
 
 CHAP. II. 55, 56] VALENCY OF ATOMS. 125 
 
 weights of the molecules of solid or liquid substances ; indeed 
 the term molecule is used with a strictly definite meaning 
 only when applied to gases. We have reason to believe that 
 the ultimate structure of a mass of a solid or liquid is much 
 more complex than that of a mass of a gaseous substance; 
 no generalisations have yet been made regarding the mo- 
 lecular phenomena of solids or liquids comparable with those 
 which under the names of the laws of Boyle, Charles, and 
 Avogadro have been made regarding the molecular phe- 
 nomena of gases. We must recognise the limits within which 
 an hypothesis regarding atomic structure can assist advance; 
 if it be pushed too far it will become, with some a dogma, 
 with others a thing to be scorned. 
 
 Consider these four molecular formulae HC1, H 2 O, H 3 N, 
 H 4 Si. It is seen that one atom of chlorine is combined with 
 one atom of hydrogen in the molecule HC1, that one atom of 
 oxygen is combined with two atoms of hydrogen in the mole- 
 cule H 2 O, that one atom of nitrogen is combined with three 
 atoms of hydrogen in the molecule H 3 N, and that one atom 
 of silicon is combined with four atoms of hydrogen in the 
 molecule H 4 Si. Considering the molecular formulae C1H, 
 Cl 2 Hg, Cl 3 Bi, and Cl 4 Sn, it is seen that one atom of hydrogen 
 is comb'ned with one atom of chlorine, one atom of mercury 
 with two atoms of chlorine, one atom of bismuth with three 
 atoms of chlorine, and one atom of tin with four atoms of 
 chlorine, in these compound molecules. 
 
 These facts may be expressed by saying that the atoms of 
 oxygen and mercury are divalent, the atoms of nitrogen and 
 bismuth are trivalent, and the atoms of silicon and tin are 
 tetravalent; i.e. so far as the data at present before us are con- 
 cerned, the atom of oxygen, and that of mercury, combines 
 with two atoms of hydrogen or of chlorine ; the atom of 
 nitrogen, and that of bismuth, combines with three atoms of 
 hydrogen or of chlorine; the atom of silicon, and that of tin, 
 combines with four atoms of hydrogen or of chlorine, to 
 form compound molecules. 
 
 56 But these terms monovalent, divalent, &c., atoms must be 
 more strictly defined.
 
 126 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 Let us begin by attempting to define the expression, a 
 monovalent atom. Let those atoms which combine each with 
 one, and not more than one, atom of hydrogen to form 
 gaseous molecules, be placed together and called monovalent 
 atoms. Then the atoms of hydrogen, chlorine, bromine, iodine, 
 and probably fluorine, are monovalent ; the evidence is the 
 existence of the gaseous molecules HH, HC1, HBr, HI, and 
 HF 1 , and the non-existence of any gaseous molecules com- 
 posed of a single atom of hydrogen, chlorine, bromine, iodine 
 (or ? fluorine), and more than one atom of hydrogen. The 
 term monovalent strictly implies that all the atoms to which 
 it is applied are equivalent, or of equal value in exchange. 
 It is important to observe that as regards combination with 
 one atom of hydrogen to produce gaseous molecules, the 
 atoms of chlorine, bromine, iodine, and probably fluorine, 
 are equivalent ; but that it is quite possible that these atoms 
 may not be equivalent, or of equal value in exchange, in 
 other respects. 
 
 If it is assumed that an atom which combines with not 
 more than two atoms of chlorine, bromine, iodine, or fluorine, 
 is equivalent to another atom which combines with not more 
 than two atoms of hydrogen, then we arrive at the definition 
 of a divalent atom as an atom which combines with not more 
 than two monovalent atoms (i.e. atoms of hydrogen, chlorine, 
 bromine, iodine or fluorine) to form gaseous molecules. Simi- 
 larly, definitions of trivalent, 'tetravaleut, &c. atoms are found. 
 Applying these definitions to the data contained in the table 
 on pp. 39 43 we arrive at the following classification of 
 atoms. 
 
 1 Mallet [Amer. Chem. Journal 3. 189] has shewn that at low temperatures 
 the molecule of hydrofluoric acid must be represented by the formula H 2 F 2 ; at 
 higher temperatures however the formula HF represents the molecule of this 
 gas. It is possible that hydrofluoric acid is a 'molecular compound' at low 
 temperatures (see Section 5 of the present chapter) : determinations of the spec, 
 gravity of this gas for a considerable range of temperature and pressure would 
 throw light on this question.
 
 CHAP. II. 56] VALENCY OF ATOMS. 127 
 
 STANDARD MONOVALENT ATOMS; H, F, Cl, Br, I. 
 
 I. Monovalent atoms ; i.e. 
 
 atoms which combine with one standard monovalent atom to form 
 gaseous molecules ... K, Rb, Ag, Cs, Hg, Tl. 
 
 II. Di i <alen t atoms ; i.e. 
 
 atoms which combine with two standard monovalent atoms to form 
 gaseous molecules O, S, Se, Te, Be, Cd, Zn, Hg, Sn, Pb, Mn. 
 
 III. Trivalent a toms ; i.e. 
 
 atoms which combine with three standard monovalent atoms to form 
 gaseous molecules B, N, Al, P, Cr, As, Sb, Bi, In. 
 
 IV. Tetravalcnt atoms ; i.e. 
 
 atoms which combine with four standard monovalent atoms to form 
 gaseous molecules. ..C, Si, Ti, Ge, Zr, V, Sn, Te, Th, U, Pb (s. p. 128). 
 
 V. Pentavalent atoms ; i.e. 
 
 atoms which combine with Jive standard monovalent atoms to form 
 gaseous molecules P, Nb, Ta, Mo, W. 
 
 VI. Hexavalent atoms ; i.e. 
 
 atoms which combine with six standard monovalent atoms to form 
 gaseous molecules W. 
 
 The data on which this classification of atoms rests are 
 presented in the following list of formula:: which shew the 
 compositions of all gaseous molecules composed of one of 
 the standard monovalent atoms combined with a single atom 
 of any other element : 
 
 KI, RbCl, Rbl, AgCl, CsCl, Csl, HgCl, T1C1 ; BeCl 2 , 
 BeBr 2 , OH 8 , OC1 2> SH 2 , MnCl 2 , SeH s , TeH 2 , TeCl 2 , CdBr 2 , 
 ZnCl 2 , HgCl 2 , HgBr 2 , HgI 2 , SnCl 2 , PbCl 2 ; BF 3 , BC1 3 , BBr 3 , 
 NH 3 , A1C1 3 , PH 3 , PC1 3 , CrCl 3 , AsH 3 , AsCl 3 , AsI 3 , SbCl 3 , 
 SbI 3 , BiCl 3 , InCl 3 ; CH 4 , CC1 4 , SiF 4 , SiCl 4 , SiI 4 , GeCl 4 , GeI 4 , 
 TiCl 4 , ZrCl 4 , VC1 4 , SnCl 4 , SnBr 4 , TeCl 4 , ThCl 4 , UBr 4 , UC1 4 ; 
 PF 5 , NbCl 5 , TaCl 5 , MoCl 8 , WC1 6 ; WC1 8 . 
 
 When it is said that one atom is combined with a certain 
 number of standard monovalent atoms, direct interaction 
 between these atoms in the molecule is assumed. Thus the 
 statement that one atom of bismuth is combined with three
 
 128 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 monovalent atoms of chlorine in the gaseous molecule BiCl 3 
 implies, that in this molecule there is direct action and 
 reaction of some kind between the atom of bismuth and 
 each of the atoms of chlorine. It might be that the atom 
 of bismuth interacts directly with one, or two, atoms of 
 chlorine and only indirectly with the other atoms ; but con- 
 sidering that one atom of chlorine is never found combined 
 with more than a single atom of hydrogen, bromine, or iodine, 
 in gaseous molecules composed of any two of these elements, 
 considering, that is to say, that the atom of chlorine is by 
 definition monovalent, the simplest hypothesis is that the 
 atom of bismuth interacts directly with each of the chlorine 
 atoms in the gaseous molecule BiCl s , in other words, that the 
 atom of bismuth is trivalent in this molecule. 
 
 The groups of atoms, methyl CH 8 , and ethyl C 2 H 5 , may 
 be regarded as monovalent, inasmuch as each combines 
 with one and not more than one of the standard monovalent 
 atoms to form gaseous molecules 1 . If the formulae of those 
 gaseous molecules which are composed of a single atom of 
 an element combined with one of the groups of atoms methyl 
 or ethyl are tabulated, we find that the atom of lead is tetra- 
 valent as well as divalent 2 . 
 
 The table on p. 127 contains 37 elements (besides the 
 five standard monovalent elements); the atoms of six of these 
 are found each in two classes. The atom of mercury is 
 monovalent and divalent, the atoms of tellurium, tin, and 
 lead are divalent and tetravalent, the atom of phosphorus 
 is trivalent and pentavalent, and the atom of tungsten is 
 pentavalent and hexavalent. This variation in the valency of 
 certain atoms is not surprising when we recall the fact that 
 an element has frequently more than one equivalent weight, 
 and we consider that the object of the classification of atoms 
 in accordance with their valencies is to place together those 
 atoms which are equivalent, that is of equal value in exchange. 
 
 1 These molecules are (CH 3 )H, (CH^F, (CH 3 )C1, (CH 3 )Br, (CH 3 )I, (C 2 H 8 )H, 
 (C 2 H 6 )C1, (C 2 H 6 )Br, (C 2 H 5 )L 
 
 2 The molecules in question are these; Hg(CH 3 ) 2 , Hg(C 2 H 5 ) 2 , Zn(CH 3 ) 2 , 
 B(CH :) ) 3 , Sh(C 2 H 5 ) 3 , Si(C 2 H 5 ) 4 , Sn(C 2 H 5 ) 4 , Pb(CH 3 ) 4 .
 
 CHAP. II. 5 7] VALENCY OF ATOMS. 1 29 
 
 57 We have now gained definitions of the terms monovalent, 
 divalent, trivalent, &c. as applied to atoms. The atoms of 
 hydrogen, chlorine, bromine, iodine, (and fluorine) are equi- 
 valent in this respect that each combines with one and 
 only one atom of hydrogen to form gaseous molecules ; 
 these atoms are therefore taken as the standard mono- 
 valent atoms. 
 
 The valency of any other atom is determined by finding 
 the number of standard monovalent atoms with which it 
 combines to form gaseous molecules, the maximum valency 
 being measured by the maximum number of these standard 
 monovalent atoms. It is certain that some atoms com- 
 bine now with one number, and now with another number, 
 of standard monovalent atoms, to form gaseous mole- 
 cules. 
 
 The valency of the atom of an element cannot be accu- 
 rately determined except at least one gasifiable compound 
 has been obtained composed of a single atom of the element 
 in question combined with standard monovalent atoms, and 
 with such atoms only. Thus the valencies of the atoms 
 of aluminium, iron, copper, and gallium cannot be defi- 
 nitely determined from considering the compositions of the 
 following gaseous molecules ; Al 2 Br d , A1 2 I 6 , Fe 2 Cl 6 , Cu 8 Cl 2 , 
 Ga 2 Cl, 
 
 We might now define the valency of an atom to be the 
 maximum number of atoms of hydrogen, fluorine, chlorine, 
 bromine, or iodine, with which the specified atom combines 
 to form gaseous molecules ; but when we apply this definition 
 we find it too limited. An examination of the composi- 
 tions of the gaseous molecules tabulated on p. 127 leads to 
 the notion of a limit to the number of atoms between which 
 direct interaction occurs in gaseous molecules. This con- 
 ception may be put into a definite form of words, thus ; each 
 atom in a gaseous molecule can directly interact with a 
 limited number of other atoms. From this conception the 
 definition of valency easily follows : the valency of an atom 
 is a number which expresses the maximum mimber of oilier 
 atoms between which and the specified atom tiiere is direct inter- 
 M. c. 9
 
 130 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 action in any gaseous molecule. This definition furnishes an 
 excellent working hypothesis in all attempts to learn anything 
 of the arrangement of the parts of molecules. 
 
 But while the definition of valency of an atom is widened, 
 we must, I think, always determine the valency of any 
 specified atom by considering the compositions of gaseous 
 molecules composed only of that atom and the standard 
 monovalent atoms, hydrogen, fluorine, chlorine, bromine, 
 and iodine. If a specified atom combines with not more 
 than n standard monovalent atoms, then we conclude that 
 this atom will not directly interact in any gaseous molecule 
 with more than n atoms of any element. The greater the 
 number of gaseous molecules composed of the specified atom 
 and atoms of hydrogen, fluorine, &c. which have been ex- 
 amined, the greater is the probability that the value of ;/ 
 expresses the true maximum valency of the atom in question. 
 Thus, suppose that the gaseous molecules SnCl 4 and SnBr 4 
 were unknown, the existence of the molecule SnCl 2 would 
 lead us to place the atom of tin in the class of divalent 
 atoms. 
 
 As only six of the 37 atoms whose valencies have been 
 accurately determined (excluding the standard monovalent 
 atoms) shew variations of valency, we may provisionally re- 
 gard the value found for the valency of an atom from the 
 composition of even a single molecule composed of that 
 atom and any of the standard monovalent atoms as the 
 true valency of the specified atom. At any rate we must 
 make use of this value in all discussions regarding the 
 arrangement of the parts of molecules into which this atom 
 enters so long as no direct proof is forthcoming that the 
 value is erroneous; and the only direct proof is the forma- 
 tion and analysis of gaseous molecules composed of the 
 specified atom and a number of standard monovalent atoms 
 different from the number present in the gaseous molecule 
 on the composition of which the value originally adopted 
 for the valency of the atom in question was based. If we 
 allow ourselves to vary the valencies of atoms without 
 cogent proof endless confusion arises, and the applications
 
 CHAP. II. 57 59] VALENCY OF ATOMS. 131 
 
 of the hypothesis of valency become merely amusing exer- 
 cises of fancy. 
 
 When therefore it is said in this book that the atom of 
 a certain element is n valent, the statement is to be un- 
 derstood as asserting, (i) that one or more gaseous molecules 
 are known composed of a single atom of the specified element 
 combined with n atoms of hydrogen, fluorine, chlorine, bro- 
 mine, or iodine ; (2) that no gaseous molecule is known 
 composed of a single atom of the specified element and 
 more than n atoms of hydrogen, fluorine, &c. ; and (3) that 
 in discussions regarding the arrangement of the parts of 
 molecules of which the specified atom forms a constituent, 
 we shall assume that direct interaction occurs between the 
 specified atom and not more than n other atoms of any kind. 
 58 Such a statement as ' the atom of phosphorus is trivalent 
 in the molecule PC1 3 ,' or ' the atom of carbon is trivalent in 
 the molecule C 2 H 4 ,' asserts that the atom named directly 
 interacts in the specified molecule with three other atoms; 
 such statements do not assert that the maximum valency 
 of the specified atom is defined by its actual valency in the 
 particular molecule referred to. Such a statement as ' the 
 atom of arsenic is trivalent' implies that the maximum 
 valency of this atom is three. 
 
 9 The atoms of hydrogen, fluorine, chlorine, bromine, and 
 iodine were placed in one class and said to be equivalent, 
 because each combines with a single atom of hydrogen to 
 form gaseous molecules. The atoms of 37 other elements 
 were then arranged in classes, and the members of each class 
 were said to be equivalent because they all combine with 
 the same number of atoms of hydrogen, or fluorine, or 
 chlorine, or bromine, or iodine, to form gaseous molecules. 
 The conception of equivalency has evidently been widened ; 
 an atom of hydrogen is regarded as equivalent to an atom 
 of chlorine not only as regards the combination of each with 
 hydrogen atoms, but also as regards the combination of 
 each with certain other atoms. Then the notion of equiva- 
 lency was yet further widened, and it was said that all atoms 
 which are equivalent in respect that they combine with 
 
 92
 
 132 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 atoms of hydrogen, fluorine &c. are also equivalent in respect 
 that they directly interact with n atoms of any kind in 
 gaseous molecules. The words equivalent to have been used 
 with an ever widening meaning. It might be, and it has 
 very often been, urged that to say that an atom is divalent 
 is the same thing as to say that the atom is equivalent to 
 two monovalent atoms. Thus, to say that the atom of oxygen 
 is divalent, it may be argued, is an assertion that one atom 
 of oxygen is equivalent to two atoms of hydrogen, fluorine, 
 &c. If we are careful to recall the exact meaning of the 
 words equivalent to in this statement, then, it seems to me, 
 that no valid objection can be brought against the statement. 
 Now the words equivalent to here mean, combines with the 
 same number of standard monovalent atoms as; no other 
 kind of equivalency between one atom of oxygen and two 
 atoms of hydrogen, &c. is asserted. But the limitation of 
 the meaning of the term equivalent in connexion with the 
 valencies of atoms has been too much forgotten. Thus, it 
 has been argued that because an atom of oxygen is divalent, 
 and because the gaseous molecules CO and CO 2 exist, there- 
 fore the atom of carbon is divalent in the molecule CO and 
 tetravalent in the molecule CO 2 . To say this appears to 
 me to be using a phrase which has no accurate meaning. 
 60 As there has been much discussion regarding such phrases 
 as this, it behoves us to consider some of them more closely. 
 The valency of an atom is generally expressed by a Roman 
 numeral placed over the symbol of the element, thus C IV , P 111 ; 
 
 or by lines proceeding from the symbol, thus C-, P . 
 
 i i 
 
 It required but a short time from the introduction of this 
 notation for chemists to forget that these lines are only a 
 form of language. From speaking of the valency of an atom, 
 they soon came to speak of each line as a valency, or a unit 
 of affinity, and to assert that such or such an atom has four 
 (or three or two &c.) units of affinity or valencies. Then 
 they went a step farther, and asserted that in the molecule 
 CO two of the four valencies or units of affinity of the 
 tetravalent carbon atom are satisfied by the two valencies
 
 CHAP. ii. 60,61] USE OF 'BONDS' OR 'LINKS.' 133 
 
 of the divalent oxygen atom, and that in the molecule CO 2 
 all the affinities of the carbon atom are satisfied by the four 
 valencies of the two oxygen atoms. These assertions were 
 embodied in the symbols C = O and O = C = O. Similarly, 
 the^ symbols H 2 = C = C = H 2 and H C = C H were used 
 to represent the distributions of the units of affinity, or the 
 valencies, of the atoms of carbon and hydrogen in the mole- 
 cules C 2 H 4 and C 2 H 2 . Then such phrases as '-carbon atoms 
 linked by double and treble bonds ' and ' doubly and singly 
 linked carbon atoms ' were employed. 
 61 What definite meanings can be given to such expressions 
 and such symbols ? 
 
 (1) The statement 1 that an atom of carbon has four 
 valencies or four units of affinity cannot mean that the force 
 of affinity of a carbon atom is divided into four parts within 
 that atom, for 'force' has no meaning apart from two or 
 more reacting bodies : force is a name given by one of the 
 parties to a transaction, but a transaction involves at least 
 two transacting parties. The force between a carbon atom 
 and another atom must vary with external conditions, prob- 
 ably with the distance, the mass, and the chemical nature, 
 (a vague term but perhaps as good as can be given at present) 
 of both atoms. 
 
 (2) The carbon atom has four equivalencies, or four units 
 of affinity. This cannot mean that four parts of the carbon 
 atom are chemically active, and the other parts inactive : such 
 a hypothesis leads at present to contradictions (see appendix 
 to Section 4); moreover in the present state of knowledge it 
 is inadvisable to hazard hypotheses as to the inner structure 
 of atoms in order to explain chemical phenomena. Atoms 
 may not be homogeneous, but at present they are the ulti- 
 mate particles to be considered in chemical changes. 
 
 (3) The expression under consideration cannot mean 
 that the chemical energy of a carbon atom is divided, or js 
 
 1 A paper of the greatest importance entitled ' Ueber die Vertheilung der 
 Atome in der Molekel,' by W. Lessen, appeared in Annalen, 204. 265. I have 
 made free use of this paper in the present chapter. (See also Claus, Ber. 14. 
 432 ; and Lessen, ibid. 760.)
 
 134 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 always divisible, into four parts. What is to be the unit of 
 chemical work ? the mass of matter fixed by a given atom ? 
 where then is the equivalency between one atom of oxygen 
 with the mass 1 6 and two atoms of chlorine with the mass 7 1 ? 
 Let a carbon atom combine with four hydrogen atoms, the 
 total chemical energy of the atoms disappears ; let a carbon 
 atom combine with two atoms of oxygen, the total chemical 
 energy of the atoms again disappears : but if the carbon atom 
 possesses four ' units of affinity,' the oxygen atom two ' units 
 of affinity.' and the hydrogen atom one ' unit of affinity,' the 
 heats of formation of the two compound molecules ought to 
 be equal; assuming, of course, that the heat produced when the 
 molecules CH 4 and CO 2 are formed from atoms of carbon and 
 hydrogen, and carbon and oxygen, respectively, measures the 
 total loss of chemical energy which occurs in these processes. 
 But the differences between the heats of formation of carbon 
 compounds shew that the expression ' the carbon atom has 
 four units of affinity' cannot mean that the chemical energy 
 of the carbon atom is divisible into four parts, unless indeed 
 the unit of affinity is variable, and is varied for each com- 
 bination of carbon with other atoms 1 . 
 
 (4) The carbon atom has four equivalencies. Can this 
 mean that the atom exerts force in four directions ? A so- 
 called 'valency' is then a direction. But there is no force 
 exerted till the mutual atomic transaction begins; the carbon 
 atom considered alone has therefore no ' valencies.' Take the 
 molecule CO; force is exerted by the carbon on the oxygen 
 atom; the remaining 'valencies' are sometimes said to be 
 ' mutually satisfied,' i.e. on the present hypothesis, the carbon 
 atom in the molecule CO exerts force in two directions on 
 itself; but here again we have the hypothesis of the non- 
 homogeneity of the carbon atom, and the existence of active 
 and inactive parts in that atom. 
 
 (5) In the vibration of a carbon atom there are four 
 points, at each of which mutual action can occur between 
 this atom and another atom. On this supposition, a 'double 
 
 1 For a view analogous to this see appendix to Section 4 of the present 
 chapter, par. 98.
 
 CHAP. 1 1. 6 1, 62] ATOMIC 'BONDS.' 135 
 
 link' would mean that mutual action occurs between the two 
 atoms thus linked at two of these positions; e.g. the formula 
 O = C = O would mean that in performing a vibration the 
 carbon atom acts twice on, and is twice acted on by, each 
 oxygen atom. But if so, surely a 'double link' would imply 
 molecular stability, whereas it frequently means the reverse 1 . 
 62 But although we cannot form a clear physical conception 
 of the meaning of the phrase 'the carbon atom has four 
 bonds,' and although such formulae as C = O, O = C = O, 
 H 2 C = CH 2 , and HC = CH, which spring from the notion of 
 atomic bonds, fail to call up in the mind clear images of the 
 things they are meant to represent, nevertheless it may be 
 urged that inasmuch as the properties of such molecules as 
 CO, CO 8 , C a H 4 , and C 2 H 2 , shew that the chemical functions 
 of the atoms of carbon vary in different molecules all of 
 which are composed of carbon and hydrogen atoms only 
 or of carbon and oxygen atoms only, it is convenient to 
 express such variations of function in our nomenclature and 
 notation, and that the expressions ' singly, doubly, and trebly, 
 linked carbon atoms,' and the symbols C C, C = C, and 
 C = C, are convenient for this purpose. 
 
 The importance of expressing undoubted chemical facts 
 in simple terms and of representing these facts in consistent 
 
 1 A view different from any of the preceding has been suggested by Pickering 
 (C. S. Proc. 1885. 122), and also by Armstrong (Proc. . S. 1886. 268; Nature, 
 35. 570) ; but the view appears to me to involve the use of the term valency as 
 synonymous with affinity of atoms, and therefore to call for discussion rather in the 
 chapter on affinity than in the present place. In his Ansichten iiber die organische 
 Chemie (part I., pp. 2 5), van't Hoff regards the chemical interactions of atoms as 
 a consequence of gravitation. He shews that if the form of an atom is not spherical 
 the intensity of the attraction of that atom for other atoms must be marked by a 
 definite number of maximum points on the surface of the atom, which maxima 
 depend on the form of the atom, and may have different values. The number of 
 these maxima is regarded by van't Hoff as expressing the valency of the atom. As 
 the atom vibrates its form will undergo change; hence the valency of an atom may 
 vary with variations in the state of motion of the atom, and these variations will be 
 conditioned by temperature, nearness to other atoms, &c. On this view, a combina- 
 tion of atoms, that is a molecule, must possess a certain valency, which is conditioned 
 by the special arrangement of its parts, but is not necessarily the same as the 
 valency of any of these parts. On the subject of 'double bonds ' see also appendix 
 to Section 4 of this chapter.
 
 136 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 formulae is admitted by all chemists. Those chemists who 
 oppose the use of formulae and terms based on the hypothesis 
 of atomic bonds assert, and I think rightly assert, that the 
 facts supposed to be expressed by single, double, and treble 
 .linkings are more simply and as forcibly expressed by for- 
 mulae arising out of the three fundamental notions of atomic 
 valency; which are (i) that each atom in a molecule directly 
 interacts with a limited number of other atoms ; (2) that the 
 maximum number of atoms with which any specified atom 
 directly interacts is measured by the maximum number of 
 atoms of hydrogen, fluorine, chlorine, bromine, or iodine, 
 with which the atom in question combines to form a gaseous 
 molecule; and (3) that an atom may, and frequently does, 
 directly interact with a smaller number of other atoms than 
 is expressed by its maximum valency. Instead of saying, 
 'the two carbon atoms in the molecule of ethane (C 2 H 6 ) are 
 singly linked, the two carbon atoms in the molecule of 
 ethylene (C 2 H 4 ) are doubly linked, and in the molecule of 
 acetylene (C 2 H 2 ) the two carbon atoms are trebly linked,' 
 these chemists say, ' the molecule of ethane contains a 
 pair of tetravalent carbon atoms, the molecule of ethylene 
 contains a pair of trivalent carbon atoms, and the molecule 
 of acetylene contains a pair of divalent carbon atoms'; and 
 instead of the symbols H 2 C = CH 2 and HC = CH, they use 
 the symbols H 2 C - CH 2 and HC - CH. All that is expressed 
 or suggested by the first pair of formulae is expressed and 
 suggested by the second, and the latter have the great 
 advantage of being based on a definite and self-consistent 
 hypothesis of atomic valency, whereas the former rest to a 
 great extent only on words and phrases. 
 
 The expressions ' single, double, and treble linkings,' 
 ' mutual satisfaction of units of affinity,' and the like, imply 
 the possession of knowledge which at present we do not 
 possess. 
 
 The notion of units of affinity, or valencies 1 , or bonds, 
 has been carried too far. It appears at first sight to give 
 
 1 It is important to distinguish between the expression 'valency' and 'a 
 valency.'
 
 CHAP. II. 62, 63] EQUIVALENCY OF ATOMS. 137 
 
 a dynamical explanation of the structure of molecules, but 
 it has forgotten the two-sidedness of atomic transactions; it 
 apparently affords a means of measuring atomic forces, but 
 it has used a unit, undefined except as a quantity changeable 
 at pleasure; it appears to simplify chemical formulae, but it 
 has really made them harder to understand by grafting on to 
 the definite conception of atom the vague and unnecessary 
 notion of 'bond.' 
 
 63 The valencies of the atoms of about three-fifths of the 
 elements can be regarded as fairly well established. The 
 data required for determining the valency of an elementary 
 atom are, the analysis, and determination of the molecular 
 weight, of more than one gasifiable compound, the molecule 
 of each of which compounds is composed of a single atom of 
 the specified element combined with monovalent atoms only, 
 that is combined with atoms of hydrogen, chlorine, bromine, 
 iodine, or fluorine, only. 
 
 Many non-gasifiable compounds containing monovalent 
 atoms combined with atoms of a single other element are 
 known (e.g. many metallic haloid compounds): if the reacting 
 weights of these solid compounds, as deduced by the aid of 
 considerations such as those sketched on pp. 78 85, are 
 assumed to be the true relative weights of the molecules of 
 these compounds ; and if those generalisations which have 
 been made concerning the arrangement of atoms in gaseous 
 molecules are assumed to hold good for the reacting weights 
 of solids also ; then the valency of many elementary atoms 
 not included in the table on p. 127 can be determined. 
 Thus, if we assume that the general formula MX represents 
 the atomic structure of the molecules of the solid haloid 
 salts of the alkali metals, (M = K, Na, Li, &c. and X = F, 
 Cl, Br, or I) then the atoms of these metals are most 
 probably monovalent. Most of the generally accepted for- 
 mulae for salts of alkali metals may be written with the 
 atoms of these metals represented as each in direct com- 
 bination with only one other atom ; but whenever this 
 arrangement has become somewhat unsatifactory chemists 
 have not hesitated to assume that the atoms of the alkali
 
 138 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 metals may be tri- penta- or even heptavalent, i.e. may each 
 act on, and be acted on by, 3, 5, or 7 other atoms. So with 
 other elements ; from a consideration of solid or liquid com- 
 pounds only no trustworthy conclusions as to the valencies of 
 the atoms in the molecules of these compounds can be deduced. 
 It is so easy, after making the two fundamental assumptions 
 stated above, to make an indefinite number of further assump- 
 tions; it becomes so pleasant to manipulate formulae on 
 paper, that it is certainly better, in the present state of 
 knowledge, to determine the valencies of atoms altogether 
 from the study of gaseous molecules. It is very probable 
 that the valency of the elementary atoms varies periodically 
 with variations in the relative weights of these atoms : if this 
 general statement is thoroughly established, the exact nature 
 of the periodic function is determined, and the true atomic 
 weights of all the elements are fixed, we shall have in the 
 Periodic Law a most important method for determining 
 atomic valencies. But a great deal of work must be done 
 before this ' law ' can be applied otherwise than generally and 
 tentatively to questions of valency (see chap. III. par. 1 14). 
 
 SECTION IV. Allotropy and Isomerism. 
 
 64 Having gained the conception of a molecule as composed 
 of atoms each directly interacting with a definite number of 
 other atoms, we at once regard the molecule as a structure ; 
 we recognise what Frankland in 1852 happily called 'limited 
 molecular mobility.' A structure involves arrangement of 
 parts and subordination of less to more important parts ; it 
 supposes the existence of definite actions for fulfilling which 
 the structure is adapted ; in a word, structure means cor- 
 relation of properties with material configuration 1 . 
 
 1 When 'arrangement of atoms in the molecule' is spoken of, or when a 
 similar phrase is used, it is to be taken as implying only a rough approximation 
 to a knowledge of atomic arrangements. Structural formulas sum up facts of 
 formation and decomposition, and, assuming the fundamental positions of the 
 molecular and atomic theory, and also the hypothesis of valency, these formulae 
 exhibit, in a rough and general way, connexions between these facts and the 
 directions of the mutual interactions of the atoms in the molecules of the compounds
 
 CHAP. II. 64 66] MOLECULAR STRUCTURE. 139 
 
 And when we consider the properties of individual mole- 
 cules the justness of thus regarding each as a definite atomic 
 structure becomes more apparent. We find many compound 
 molecules composed of the same number of the same atoms 
 and yet exhibiting markedly different chemical and physical 
 properties, i.e. we find the phenomenon of Isomerism: how can 
 we account for this except by assuming (i) that each mole- 
 cule has a definite atomic structure, and (2) that the same 
 atoms may be differently arranged in different molecules? 
 
 65 A knowledge of the atomic configurations of series of 
 molecules, supposing this to be gained, must be supplemented 
 by a knowledge of the way in which the energy of each 
 molecule varies with variations in the configuration and 
 motion of its constituent atoms, before a complete knowledge 
 of the dynamical properties of these molecules is possible. 
 But chemistry is yet far from this goal ; she is obliged to be 
 content with a very partial and sometimes very vague know- 
 ledge concerning the atomic configurations of a few mole- 
 cules ; she has hardly entered on the second part of her task. 
 
 66 Granting then that variations in the properties (chemical 
 and physical) of molecules accompany variations in the con- 
 figurations of the atoms which build up these molecules, it is 
 conceivable that the latter variations may consist in 
 
 (i) variations in the relative positions of the atoms, 
 or (2) variations in the distances between the atoms, their 
 relative positions being constant. 
 
 To illustrate this point let us take the molecule C a H 6 O. 
 More than one compound exists the molecules of which 
 have the atomic composition expressed by this formula. On 
 the first assumption, viz. that variation of properties is to be 
 correlated with variations in the relative positions of the 
 atoms in the molecule, the atoms being represented as arranged 
 all in the same plane, we find that there are two possible 
 arrangements of two carbon, six hydrogen, and one oxygen, 
 
 formulated, the atoms being represented in the formulae as situated all in the same 
 plane. No attempt is made in these formulae to express quantitative measure- 
 ments of atomic interactions.
 
 140 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 atoms (assuming the valency of the carbon, hydrogen, and 
 oxygen atom to be 4, i, and 2 respectively), viz. ; 
 
 (a) H H (b] H H . 
 
 II II 
 
 H C C O H, H C O-C H. 
 
 II I I 
 
 H H H H 
 
 Hence, on the first assumption, two compounds each 
 having the composition expressed by the empirical formula 
 C 2 H 6 O may exist. 
 
 But if we make the second assumption, viz. that variation 
 of properties is to be correlated with variations in the dis- 
 tances between the atoms in the molecule, the relative posi- 
 tions of these atoms remaining unchanged, we may have 
 an apparently unlimited number of compounds of the for- 
 mula C 2 H 6 O ; such compounds might perhaps be repre- 
 sented in this way : 
 
 (a) H H () H H 
 
 II II 
 
 H C C O H, H C C O H, 
 
 II II 
 H H 
 
 H H 
 
 (c) H H 
 
 H C C O H, 
 
 I 
 H H 
 
 and so on. 
 
 Now as only two compounds having the composition 
 C 2 H 6 O are known to exist, we have a presumption in favour 
 of the first supposition : much stress cannot however be laid 
 on this argument. Moreover if the second of the two suppo- 
 sitions is correct, then any molecule composed of two atoms 
 should be capable of existing in more than one modification ; 
 in other words, every diatomic molecule should be capable 
 of shewing isomerism. But there is no certainly-established 
 instance of isomerism exhibited by a molecule composed 
 of less than three atoms ; therefore, as the assumption that 
 variations of properties exhibited by compounds having the
 
 CHAP. II. 66, 67] ALLOTROPY AND POLYMERISM. 141 
 
 same composition and the same molecular weight are con- 
 nected with variations in the relative positions of the atoms 
 composing the molecules of these compounds suffices to 
 explain the vast majority of well-authenticated cases of iso- 
 merism among gaseous molecules, we conclude that it is 
 better, at any rate at present, to build the general theory 
 of isomerism on this hypothesis 1 . 
 
 67 But before more fully considering this subject, it will be 
 well to glance at the allied phenomena of allotropy and 
 polymerism. 
 
 The table on p. 45 shews that of the sixteen elements 
 whose molecular weights have been determined by the help 
 of Avogadro's law, six, viz. oxygen, sulphur, selenion, iodine, 
 phosphorus, and arsenic (probably bromine also), possess a 
 smaller molecular weight at high than at lower tempera- 
 tures : the number of atoms in the molecule of oxygen 
 at temperatures below about 300 and under special con- 
 ditions is 3, at temperatures above 300 it is 2 ; the molecule 
 of sulphur at temperatures not much higher than the boiling 
 point of that element is composed of 6 atoms, and at some- 
 what higher temperatures of 2 atoms; the number of atoms in 
 the molecule of selenion varies from 3 to 2, in the molecule 
 of iodine (and probably also in that of bromine) from 2 to I, 
 and in the molecules of phosphorus and arsenic from 4 to 2, 
 according to temperature. We know that the properties of 
 the triatomic molecule O 3 differ much from those which cha- 
 racterise the diatomic molecule O 2 ; no experiments have 
 been made to compare the properties of the hexatomic with 
 those of the diatomic molecules of sulphur, of the triatomic 
 with the diatomic molecules of selenion, of the diatomic with 
 the monatomic molecules of iodine, or of the tetratomic 
 with the diatomic molecules of phosphorus or arsenic. 
 
 Of the 15 or 16 nonmetallic elements, phosphorus and 
 
 1 The supposition that isomerism may be due to variations in the distances 
 between atoms the relative positions of which remain unchanged, appears to be 
 opposed to the results of physical experiments which are in agreement with 
 deductions made from the kinetic theory of gases. See Lessen, Annalen, 204, 
 p. 269.
 
 142 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 arsenic, boron, carbon and silicon besides sulphur and sele- 
 nion exhibit marked variations in physical and chemical 
 properties when in the solid state. We are not justified 
 in unconditionally asserting that these variations of pro- 
 perties accompany differences in the atomic configurations 
 of the molecules, or differences in the numbers of atoms in 
 the molecules, of red and yellow phosphorus, or of octahe- 
 dral and prismatic sulphur, &c. When the differences in 
 properties are chiefly physical (e.g. differences in crystalline 
 form, in specific gravity, in melting points, &c.), they very 
 probably may be correlated with differences in the molecular, 
 rather than in the atomic, configurations of the various modi- 
 fications of the element in question \ 
 
 Be this however as it may, the differences experimentally 
 shewn to exist between the properties of the molecules of 
 gaseous oxygen and ozone are explicable in terms of the 
 molecular theory only by admitting that the properties of 
 a molecule are dependent not only on the nature but also 
 on the number of the atoms which compose it 2 . 
 68 The names allotropy and polymerism are applied to ana- 
 logous phenomena exhibited by elements and compounds 
 respectively 3 . In the preceding paragraph we have had 
 
 1 See Section 5 of present chapter. 
 
 - It ought to be noted that change from one allotropic form to another is 
 accompanied by production or disappearance of heat; se&post, chap. IV., par. 125. 
 There are some interesting observations bearing on the subject of allotropy by 
 W. Spring in the Berichte [see especially 16. 1002 3]. Spring finds that when an 
 element which exhibits allotropy is subjected to great pressure, that modification 
 which has the greatest specific gravity is produced. Yellow phosphorus is changed 
 into red by compression : red phosphorus and sulphur do not combine until heated 
 to 260, i.e. to the temperature at which red is changed to yellow phosphorus; red 
 phosphorus does not combine with sulphur when the two are subjected to a 
 pressure of 6500 atmospheres, at which pressure many metallic sulphides are 
 produced. Hence Spring concludes that red phosphorus is less chemically ener- 
 getic than yellow; and generally that the more a solid substance is rendered 
 dense the more is its chemical activity decreased. Red phosphorus he regards as 
 a polymeride of yellow phosphorus. 
 
 3 The term allotropy is sometimes applied to compounds as well as to elements, 
 to express the existence of two or more forms of the same solid compound ; thus 
 arsenious oxide crystallises in two distinct forms, and the change from one of these to 
 the other is sometimes said to be an allotropic change. Allotropy as thus applied 
 to compounds is synonymous with physical isomerism (s. post, par. 101). The
 
 CHAP. II. 68, 69] POLYMERISM. 1 43 
 
 examples of allotropy, let us now consider a few examples 
 of polymerism. 
 
 If two molecules exist consisting of the same elementary 
 atoms but one heavier than the other, the heavier molecule is 
 said, in certain cases, to be a ' polymeric modification' or 
 a ' polymeride ' of the other : thus C^H^ is a polymeride of 
 C 8 H 10 , C ]5 H 24 is a polymeride of C 10 H, a , H 3 C 3 N 3 O 3 is a poly- 
 meride of HCNO, C 6 H ]2 O 3 is a polymeride of C 2 H 4 O. Glu- 
 cose, .rC 6 H 12 O 6 , is not however regarded as a polymeride of 
 acetic acid, C 2 H 4 O a : the name is restricted to those mole- 
 cules whose mass is a multiple of that of other molecules, 
 and which are obtained by simple reactions from these other 
 molecules. Thus ethaldehyde, C a H 4 O, is easily polymerised 
 (e.g. by the action of a very little hydrochloric or sulphuric 
 acid) with formation of parethaldehyde, C 6 H 12 O 8 : but the 
 latter body is not directly obtainable from ethylene oxide, 
 although the molecule of this compound, like that of ethalde- 
 hyde, is composed of 2 atoms of carbon, 4 of hydrogen, and 
 I of oxygen ; therefore parethaldehyde is not called a poly- 
 meride of ethylene oxide. 
 
 But few examples of undoubted polymerism are fur- 
 nished by compounds of the elements other than carbon : 
 one of the most marked cases is the molecule N 2 O 4 which 
 is a polymeride of NO 2 ; another instance is furnished by the 
 molecules Sn 2 Cl 4 and SnCly 
 
 69 Let us now turn to the subject of isomerism. This term 
 is applied to the existence of molecules characterised by 
 different properties but composed of the same number of 
 the same atoms. 
 
 Isomeric compounds are generally said to be metameric 
 when they belong to different chemical types. This state- 
 ment does not of course furnish a definition of metameric 
 compounds; but it is sufficient. Various hydrocarbons, all 
 possessed of the general properties of paraffins but each 
 differing in some properties, chemical and physical, from the 
 others, are represented by the formula C 6 H 14 : various hydro- 
 art. Allotropy in ihe new edition of Waltz's Dictionary should be read by the 
 student.
 
 144 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 carbons, all benzenes, but each characterised by its own special 
 properties, are represented by the formula C 8 H 10 : the different 
 paraffins (C 6 H 14 ) or the different benzenes (C 8 H 10 ) are said to 
 be isomerides one of the other. But although two molecules 
 are represented by the formula C 2 H 6 O yet these belong to 
 very different types or groups of compounds, one is a pri- 
 mary alcohol, the other is an ether ; so again allylic alcohol 
 and dimethyl ketone have both the formula C 3 HgO, but these 
 bodies are altogether distinct in their chemical properties: 
 such compounds are said to be metameric. Metamerides 
 are thus seen to be a sub-class included in the larger class of 
 isomeric compounds. 
 
 A few inorganic compounds exhibit phenomena which 
 may be explained by supposing the existence of isomeric 
 molecules, but it is only when we study the compounds 
 of carbon that we are obliged to admit that molecules may 
 be composed of the same numbers of the same atoms but 
 differ in chemical and physical properties. 
 
 70 The hypothesis of atomic valency having led to the re- 
 cognition of the molecule as a structure may be carried 
 further ; it may guide us in determining the probable relative 
 structures of isomeric molecules (see note to p. 138). 
 
 If it be granted that isomerism is correlated with different 
 relative positions of atoms, but not with different distances 
 between atoms in the same relative positions in the molecule, 
 (see p. 139) it follows that a molecule composed of not more 
 than two atoms cannot exhibit isomerism 1 . 
 
 The maximum number of monovalent atoms which can 
 be combined with polyvalent atoms in a molecule is found 
 by the formula 2 
 
 n \ H 3 + 2W 4 + 3 ;/ 5 + 4 W 6 + 2 > 
 
 where t , 3 , 4 , &c. represent the numbers of monovalent, 
 trivalent, tetravalent, &c. atoms in the molecule. In any mole- 
 cule in which the value of , agrees with that deduced by 
 this formula each polyvalent atom must necessarily directly 
 
 1 Such formulae as O = N - and = N - O - are really at present the same. 
 
 2 See Lothar Meyer, Die Modernen Theorien der Chemie (4th Ed.), p. 218 
 et sef., or English Edition [Modern Theories of Chemistry}, p. 198 et seq., of which 
 pages free use has been made in these paragraphs.
 
 CHAP. II. 70, 71] ISOMERISM. 145. 
 
 interact with the maximum number of monovalent atoms. 
 Such molecules are said to be saturated; they cannot directly 
 combine with monovalent atoms. Examples of saturated 
 molecules are furnished by C 2 H 6 , C 8 H 8 , C 2 H 5 C1, C 3 H 6 C1 2 , &c. 
 But in the molecules C 2 H 4 , C 2 H 2 , C 6 H 6 , and in many other 
 molecules, the number of monovalent atoms is less than that 
 expressed by the formula just given. In these molecules 
 each polyvalent atom directly interacts with less than the 
 maximum number of monovalent atoms. Such molecules 
 are said to be unsaturated. Unsaturated molecules are 
 generally able to combine directly with monovalent atoms. 
 
 The language in which the facts of isomerism are generally 
 expressed speaks of some of the polyvalent atoms in unsatu- 
 rated molecules as being ' linked by double or treble bonds ' ; 
 the language which springs from the view of valency adopted 
 in this book (the view is essentially that of Lessen) speaks 
 of some of the polyvalent atoms in unsaturated molecules 
 as exhibiting in these molecules less than their maximum 
 valency. 
 
 Thus to take the unsaturated molecules C 2 H 4 and C 2 H 2 : 
 the expression in common use is 'the carbon atoms in the 
 molecule C 2 H 4 are joined by a double bond, and in the mole- 
 cule C 2 H 2 by a treble bond'; and this expression is embodied 
 in the formulae H 2 C = CH 2 and HC = CH: the expression 
 used by the upholders of Lossen's conception of atomic 
 valency is ' the carbon atoms in the molecule C 2 H 4 are tri- 
 valent, and in the molecule C 2 H 2 the carbon atoms are di- 
 valent ' ; and this expression is embodied in the formulae 
 H 2 C CH 2 and HC CH. The expressions 'a pair of doubly 
 linked carbon atoms ' and ' a pair of trebly linked carbon 
 atoms ' are respectively synonymous with the expressions ' a 
 pair of trivalent carbon atoms ' and ' a pair of divalent carbon 
 atoms ' : each term used in the latter expressions has an 
 accurate meaning defined once for all ; the meanings given 
 to the terms ' doubly linked ' and ' trebly linked ' atoms 
 depend upon the views of the chemist who employs them. 
 71 The number of ways in which the atoms comprising a 
 complex molecule may be arranged, in accordance with the 
 M. c. 10
 
 146 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 limitations imposed by the hypothesis of atomic valency, is 
 evidently very great ; to determine the maximum number of 
 possible isomerides of a given formula is a purely mathe- 
 matical problem 1 . At present we seem justified in con- 
 cluding that many atomic configurations which are mathe- 
 matically possible are physically impossible; this is equivalent 
 to saying that the stability of molecules does not depend 
 solely on the valencies of their constituent atoms. To deter- 
 mine which of the possible configurations of a given number 
 of atoms are stable ; to generalise the connexions undoubtedly 
 existing between molecular structure and stability, and also 
 between this structure and the functions of the molecule or 
 of parts thereof; this is the task that chemists are now 
 elaborating. 
 
 72 The molecular formula of a compound sometimes of itself 
 gives us a considerable amount of information regarding the 
 structure of the molecule of that compound. Thus we appear 
 justified, at present, in making the following assertions : 
 (i) molecules composed of monovalent atoms only cannot 
 exhibit isomerism ; (2} molecules composed of a single poly- 
 valent atom united with monovalent atoms only cannot ex- 
 hibit isomerism ; (3) isomerism cannot be exhibited by mole- 
 cules composed of two polyvalent atoms united with mono- 
 valent atoms, provided the latter are all atoms of the same 
 element, or all but one atoms of the same element, when the 
 two polyvalent atoms are themselves atoms of the same 
 element. 
 
 73 Any molecule composed of more than two atoms and not 
 belonging to one of the classes above defined may exhibit 
 isomerism. The possible variations of structure even in mole- 
 cules composed of a small number of atoms may be large. 
 Thus N 2 O may have any of the structures 
 
 (i) N N, or (2) N N O, or (3) N O N ; 
 
 1 Prof. Cayley, Brit. Ass. Reports for 1875. 257, examined the relations between 
 the number of carbon atoms in the molecules of paraffins and the number of 
 isomeric modifications of each molecule allowed by the hypothesis of valency ; thus 
 
 number of carbon atoms in molecule of paraffin, i. 4. 7. 10. 12. 13. 
 
 number of possible isomerides ...... i. 2. 9. 75. 357. 799.
 
 CHAP. IT. 72, 73] STRUCTURAL FORMULAE. 147 
 
 neither the nitrogen nor the oxygen atom can directly inter- 
 act with more than two atoms, i.e. neither can be more than 
 divalent 1 . NO can be regarded only as N O. NO 2 may be 
 (i) O N O, or (2) O N O, or (3) N O O. 
 
 N 2 O 4 may have many structures ; e.g. 
 
 (i) O N N O, or ( 2 ) O N N O, 
 
 I I ^Q' x o x 
 o o 
 
 or ( 3 )O N O O N O, or (4) O N O O N O, 
 or (5) N O O O O N, or (6) N N O O O O, &c. 
 
 The compounds of carbon present the best field for the 
 study of isomerism 2 . 
 
 It has been already stated that a molecule composed of 
 two carbon (tetravalent) atoms united with five monovalent 
 atoms of one element and one monovalent atom of another 
 element, (i.e. a molecule of the form C^X 6 X) cannot exhibit 
 isomerism. If however there are four monad atoms of one 
 kind, and two of another kind, in the molecule (if the form of 
 the molecule is represented by the symbol C 2 X 4 JQ isomerism 
 becomes possible ; thus C 2 H 4 C1 2 may have the structure 
 
 H H H H 
 
 II II 
 
 Cl C C Cl, or H C-C Cl 
 
 II II 
 
 H H H Cl 
 
 (or more shortly, C1H 2 C - CH 2 C1 and H 8 C - CHC1 2 ). But 
 when three carbon atoms combine with monovalent atoms, 
 the existence in the molecule thus produced of a single 
 monad atom different in kind from the other monad atoms 
 renders isomerism possible ; thus C S H 7 C1 (which belongs to 
 the general form C S X 7 X) may have the structure 
 
 H 2 H Cl 
 
 II \/ 
 
 H 3 C C CH 2 C1 or H 3 C C CH 3 . 
 
 1 Lossen's nomenclature and notation are used here and generally throughout 
 the rest of this book. 
 
 2 The subject of the constitution of compounds is considered very fully and 
 clearly in the 3rd edition of Remsen's Theoretical Chemistry. 
 
 10 2
 
 148 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 So also four molecules C 3 H 6 C1 2 , five molecules C 3 H 6 C1 8 , six 
 C 8 H 4 C1 4 1 , five C 3 H 3 C1 S , &c. may exist. Molecules composed 
 of four, or more than four, atoms of carbon combined with 
 monovalent atoms may exhibit isomerism even when all the 
 monad atoms are of one kind, (i.e. molecules of the general 
 form C 4 X 10 ) ; thus C 4 H 10 may have the structure 
 
 H 2 H 2 H CH 3 
 
 II II I / 
 
 H 3 C-C C-CH 3 or H 3 C C 
 
 X CH 3 
 
 Molecules composed of five carbon atoms combined with 
 other atoms may have the carbon atoms arranged in three 
 ways, as represented by the formulae 
 
 C 
 
 C C C C C, C C C C, and C C C. 
 
 I I 
 
 C C 
 
 When six carbon atoms are present in the molecule these 
 atoms may be arranged in five ways, viz. 
 
 C C C C C C, C C C C C, C C C C C, 
 
 I I 
 
 C C 
 
 C 
 
 I 
 
 C C C C, C C C C. 
 
 I I I 
 
 C C C 
 
 When eight carbon atoms are present, they may be arranged 
 in 1 8 different ways, &c. The maximum number of mono- 
 valent atoms which can be combined with any of these 
 arrangements of carbon atoms is found by the formula 
 j = 2 4 + 2 where n 4 = number of carbon atoms 2 . But all 
 the carbon atoms in a molecule are not necessarily tetrava- 
 lent in that molecule (in the ordinary nomenclature some of 
 
 1 Viz. CH 2 C1 CHC1 2 CC1 3 CHC1 2 CC1 3 CH 3 
 
 CC1 2 CH 2 CHC1 CHC1 CH 2 CC1 2 
 
 CH a Cl CHC1 2 CH 3 CH 2 C1 CH 2 C1 CHC1,. 
 
 2 See Lothar Meyer, loc. cit. pp. 240 242.
 
 CHAP. II. 73] STRUCTURAL FORMULA. 149 
 
 the carbon atoms may be doubly or trebly linked to one 
 another, or there may exist ' free affinities '). Now the gene- 
 ral formula given on p. 144, viz. 
 
 shews that the maximum number of monad atoms in such 
 a molecule is dependent only on the number of trivalent 
 and tetravalent, and is independent of the number of diva- 
 lent, carbon atoms in the molecule. But in applying this 
 formula it is assumed that the number of carbon atoms 
 which are actually trivalent, and of those which are actually 
 tetravalent, in any given molecule, can be determined. It 
 is better to represent the molecule of a carbon compound, if 
 possible, as containing only tetravalent carbon atoms: in 
 many cases however this cannot be done ; in any case the 
 reactions of the compound must be studied before a formula 
 is given to it. 
 
 Let us suppose we are required to assign formulae to 
 compound molecules containing carbon, hydrogen, and oxygen 
 atoms. When the equation t = 2# 4 + 2 is satisfied, the struc- 
 tural formula assigned to the molecule must evidently con- 
 tain only tetravalent carbon atoms ; several such formulae 
 may however be possible ; thus for the molecule C 3 H 8 O two 
 structural formulas fulfil the conditions required : 
 
 Hg ri2 Hg Ho Ho Ho 
 
 III II II III II III 
 
 C C C O H and C C O C. 
 
 In accordance with generalisations which have been made 
 correlating structure and properties the first of these for- 
 mulae belongs to a primary alcohol, the second belongs to 
 a mixed ether : two and only two compounds having the 
 composition C 3 H 8 O are known ; one exhibits the properties of 
 a primary alcohol, the other those of a mixed ether. 
 
 When however n^ < 2U 4 + 2, and divalent atoms are also 
 present in the molecule, the formula may contain only 
 tetravalent carbon atoms, or it may contain tetravalent, and 
 also di- or trivalent, carbon atoms. Thus in C 3 H a O t = 2 4 ;
 
 ISO ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 two structural formulae are possible for this molecule wherein 
 each carbon atom is tetravalent, viz. 
 
 (i) H 2 C CH 2 CH 2 and (2) H 3 C CH CH 2 . 
 
 V 
 
 Each of these is the formula of an ether ; in propylene 
 oxide we have an ether the properties of which shew 
 that it is probably described by the first of these formulae. 
 Six structural formulae are possible for the molecule 
 C 3 H 8 O, provided some of the carbon atoms may be tri- or 
 divalent. Three compounds having this formula (besides 
 propylene oxide) are known ; of these, one is a ketone, i.e. 
 belongs to a class of compounds the molecules of which are 
 generally regarded as containing a carbon and an oxygen 
 atom in direct union ; another is an aldehyde, i.e. belongs to 
 a class of compounds the molecules of which are regarded as 
 containing a carbon atom in direct combination with one 
 oxygen and one hydrogen atom ; and the third is an alcohol, 
 probably a primary alcohol. The six possible formulae are 
 
 (I) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 CH 3 
 
 CH, 
 
 CH 2 
 
 CH 3 
 
 CH 3 
 
 CH 3 
 
 1 
 
 1 
 
 1 
 
 
 1 
 
 1 
 
 c o 
 
 CH S 
 
 CH 
 
 CH 2 
 
 C 
 
 CH 
 
 1 
 
 1 
 
 | 
 
 1 
 
 | 
 
 1 
 
 CH 3 H- 
 
 -C O 
 
 CH 2 
 
 C O H 
 
 CH 2 
 
 CH 
 
 
 
 1 
 
 
 1 
 
 1 
 
 
 
 O H 
 
 
 O H 
 
 O H 
 
 The first and second formulae contain each one trivalent carbon 
 atom and the oxygen atom is monovalent in both, the fourth 
 and fifth contain each one divalent carbon atom, and the 
 third and sixth each two trivalent carbon atoms. Formulae 
 (i) and (2) are appropriated by dimethyl ketone and pro- 
 paldehyde respectively ; of the remaining four, (3) and (5) 
 represent allylic alcohol as a primary, (6) as a secondary, and 
 (4) as a tertiary, alcohol. Judging from the general reactions 
 of allylic alcohol this compound is probably a primary 
 alcohol. Formula (3) is preferable to (5), because the latter 
 would lead us to expect acetic acid (H 3 C - CO 2 H) as one 
 of the products of oxidation of allylic alcohol ; inasmuch as
 
 CHAP. II. 73, 74] STRUCTURAL FORMULAE. 151 
 
 acetic acid is not produced in this oxidation, formula (3) more 
 probably expresses the structure of the molecule of allylic 
 alcohol than any other possible formula. 
 
 74 In these examples of the method adopted for determining 
 the structural formula of a compound several generalisations 
 concerning the connexion of structure with properties have 
 been assumed. For instance, it has been assumed that if a 
 given compound exhibits aldehydic properties the structural 
 formula of the molecule is to be written as containing the 
 atomic group CHO ; but it has also been assumed that two 
 structures are possible for this group, one in which the carbon 
 atom interacts directly with the oxygen and the hydrogen 
 atoms (H C O), and the other in which the carbon atom 
 directly interacts with the oxygen atom only (C O H) ; 
 further, the first of these structures is assumed to be corre- 
 lated with the group of properties connoted by the word 
 'aldehydic,' and the second with the properties connoted 
 by the expression ' tertiary alcoholic.' When therefore a 
 new carbon compound is discovered, it is necessary to de- 
 termine, as far as possible, to what group of compounds it 
 belongs ; the existence of a certain atomic group (or groups) 
 in the molecule of the compound may then generally be 
 predicated, and the number of possible structural formulae 
 may thus be considerably diminished. But the classification 
 of the carbon compounds is certainly not yet complete ; 
 hence arise two difficulties ; (i) a new compound may belong 
 to a class no other member of which has been previously 
 examined, in which case no class-group can be assigned to 
 the formula of the new compound ; or (2) a compound may 
 be prepared whose properties indicate that it belongs to one 
 of the known classes, and yet the atomic group which 
 generally marks this class may not be present in the molecule 
 of this particular compound. The following cases may be 
 taken as illustrations of these difficulties. 
 
 (i) It was known that the interaction of nitrous acid 
 with carbon compounds the molecules of which contained the 
 group NH 2 (amido-derivatives) resulted in the production of 
 compounds differing from the original by containing OH
 
 152 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 in place of NH 2 ; but when nitrous acid acted on certain 
 amido-derivatives of benzene, compound molecules containing 
 one nitrogen atom more and two hydrogen atoms less 
 than the original molecule were obtained. The reaction ap- 
 peared to be abnormal. Several of the new compounds were 
 prepared, their properties were studied, and the existence of a 
 new class of carbon compounds was recognised, the relations 
 of which to other classes could be summarised in formulae 
 containing the characteristic group N 2 . 
 
 (2) As the result of long and varied experience 
 the generalisation has been made that the molecules of 
 very many carbon acids contain the characteristic group 
 H O C O ; but from time to time compounds have 
 been prepared exhibiting acidic properties, but possessed of 
 a molecular structure from which the characteristic group 
 is absent. Thus C 3 H 8 yields C 3 H 7 NO 2 , and from this 
 compound two isomerides C 8 H 6 BrNO 2 are obtained, one of 
 which is a monobasic acid, while the other does not shew 
 acidic properties ; the possible formulae for these isomerides are 
 NO 2 H 2 H 
 
 i I I 
 
 (i) H 3 C C CH 3 , and (2} H 3 C C C NO 2 . 
 
 Br Br 
 
 From a consideration of the general properties of the two 
 isomerides and their relations to other compounds the second 
 formula is assigned to the acid. Hence we are obliged to 
 conclude that although most known carbon acids are charac- 
 terised by the atomic group H - O - C - O, yet a carbon 
 compound in the molecule of which this group is not present 
 may nevertheless be a true acid. 
 
 A very instructive example of the difficulties to be over- 
 come before a general structural formula can be assigned to a 
 group of carbon compounds, is afforded by the investigations 
 which have been and are being made into the constitution 
 of the quinones; and also into the constitution of the 
 compounds allied to indigo 1 . 
 
 1 See Armstrong and Groves, Organic Chemistry, pp. 812, 813. Also art. 
 "Indigogruppe" in Ladenburg's Handivorterbuch der Chemie, Bd. 5, p. 248.
 
 CHAP. II. 74] STRUCTURAL FORMULAE. 153 
 
 These examples (and others might easily be added) shew 
 how undesirable it is to regard the present system of classifi- 
 cation of carbon compounds as final. As facts are accumu- 
 lated the atomic grouping which was regarded as a class- 
 group sometimes becomes the group of a larger class, 
 sub-classes being formed each characterised by its special 
 group and yet each containing the class-group. Thus, from 
 the analogy between metallic hydroxides and alcohols, and 
 for other reasons, the group O H was assigned to alcohols 
 (e.g. C 2 H 5 .OH, C 3 H 7 .OH, &c., &c.); but it became evident 
 that a sub-division of this great class was required ; facts 
 were amassed and formulae devised to generalise these facts, 
 until most chemists are now agreed that the molecules of 
 those alcohols called ' primary ' (which yield certain defi- 
 nite products when oxidised, &c.) contain the atomic group 
 H O CH 2 , the molecules of those called 'secondary' (and 
 which yield other but also definite products when oxidised) 
 contain the group H - O C - H, and the molecules of those 
 called ' tertiary' (which yield a third distinct set of products 
 when oxidised) contain the group C O H. 
 
 Each of these 'alcoholic groups' itself contains the group 
 O H; but the 'acid group' H O-C O also contains 
 this group ; now we know that the function performed by 
 hydrogen in an alcoholic molecule is not the same as that 
 performed by hydrogen in an acid molecule ; e.g. all, or 
 some, of the hydrogen in the latter, but none of that in 
 the former, is replaceable by metal when the compound is 
 acted on by a metallic carbonate ; hence we infer that the 
 function discharged by a given atom in a molecule depends 
 not only on the nature of that atom, but also on the nature of 
 the atoms with which it is directly, and indirectly, connected 
 in the molecule. 
 
 In all the alcoholic groups (viz. H 2 C - OH, HC - OH, 
 and C OH) an atom of hydrogen is directly connected 
 with an oxygen atom which is again directly connected with 
 an atom of carbon, which directly interacts with either 
 hydrogen atoms and atoms belonging to the other part of 
 the molecule always either carbon or hydrogen atoms or
 
 154 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 only the latter. In the acid group (O C OH) the carbon 
 atom with which the hydrogen atom is indirectly connected 
 (through an atom of oxygen) is itself directly connected 
 with an oxygen atom, as well as with an atom, or atoms, 
 belonging to the other part of the molecule. Now oxygen is 
 a markedly electro-negative element ; from the facts enume- 
 rated and from other similar facts, the generalisation has 
 been made, that when an atom of hydrogen is in direct 
 connexion with an atom of carbon which also directly binds 
 negative atoms, or negative groups of atoms, that hydrogen 
 is, as a rule, 'replaceable by metal' &c. ; i.e. that hydrogen 
 fulfils the function of 'acidic hydrogen.' 1 
 
 75 In thus trying to use the hypothesis of valency as a guide 
 towards determining the structures of isomeric molecules, we 
 have found it on the whole advantageous to limit the appli- 
 cation of this hypothesis in various ways. 
 
 I. The hypothesis is applied in strictness only to the 
 molecules of bodies in the gaseous state. 
 
 II. The valency of an atom of any specified element 
 is defined as a number which expresses the maximum number 
 of other atoms between which and the given atom there is 
 direct action and reaction in a molecule ; this number is 
 determined by the study of certain defined classes of mole- 
 cules, viz. molecules composed of a single atom of the specified 
 element combined with atoms of hydrogen, fluorine, chlorine, 
 bromine, or iodine. 
 
 III. Isomerism is regarded as correlated with varying 
 
 1 I am aware that such expressions as are used in these paragraphs, ' a carbon 
 atom is directly connected with, or directly binds to itself, an atom of hydrogen,' 
 &c., are very easily misunderstood; they appear, at first sight, to convey much 
 more precise information than they really do convey. I have more than once 
 insisted on the importance of clearly remembering that these and similar ex- 
 pressions are attempts to summarise facts concerning the reactions of compounds 
 in the language of a special theory of the structure of compounds. Nor should 
 it be forgotten that, granting the fundamental hypotheses of the molecular and 
 atomic theory, and also granting that each' atom can directly interact with a 
 limited number of other atoms in a molecule, we are obliged to regard the 
 atoms which form any molecule as performing constant but regulated movements, 
 and not, as might be supposed by a careless or superficial reader of the atomic 
 explanation of isomerism, as in absolutely fixed positions within the molecule.
 
 CHAP. II. 75] STRUCTURAL FORMULA. 155 
 
 relative positions of the atoms, not with variations in the 
 distances between identically arranged atoms, forming a 
 molecule. 
 
 IV. The atoms which form a molecule are regarded 
 as arranged in the same plane; no attempt is made to con- 
 nect the facts of isomerism with the arrangement of the 
 atoms in different dimensions in space. 
 
 Applying the hypothesis as thus limited, and for the most 
 part to compounds of carbon, we found that the structural 
 formulae of classes of carbon compounds can be general- 
 ised so far as to admit of the assertion that the molecules 
 of the members of any one class are characterised by the 
 presence of a special atomic group which may be called the 
 class-group : and hence that the first step in assigning a 
 structural formula to a new compound is to determine the 
 class to which it belongs by comparing the reactions of 
 this compound with those of known substances belonging 
 to various classes; having done this, we then eliminate 
 from the possible structural formulae those which do not 
 contain the characteristic group of the class in which our 
 compound is placed. Finally, we choose from the remaining 
 formulae that one which best summarises the reactions of the 
 compound molecule under consideration and its relations to 
 other molecules. 
 
 We found that a wide knowledge of the characters of 
 classes of compounds is required on the part of him who 
 would employ this method with success, and also that the 
 chemist has constantly to be on his guard against drawing 
 too rigid conclusions. A new compound may represent a 
 new class, hence a new class-group has to be determined by 
 comparing the reactions of the new compound with those 
 of others the classification of which is fairly settled, and also 
 by seeking to obtain other representatives of the new class. 
 The discovery and study of new compounds apparently 
 belonging to a known class may lead to a revision of the 
 general formula assigned to the class, and perhaps to a 
 division of the class into sub-classes each characterised by 
 its own group.
 
 156 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 76 The application of the hypothesis of valency to determine 
 the most probable of many possible formulae is evidently 
 a matter of no little difficulty. Certain generalisations are 
 usually adopted as guides in interpreting the results of the 
 study of the chemical properties of molecules. The principal 
 generalisations are these. 
 
 (1) Those atoms which are obtained as an undecom- 
 posed group in reactions resulting in the splitting up of a 
 compound are present in the molecule of that compound as 
 a group of directly combined atoms. 
 
 (2) When a group of atoms passes from one com- 
 pound molecule to another, the relative arrangement of these 
 atoms, as a rule, is not altered. 
 
 (3) When an atom, or group of atoms, replaces another 
 atom or group of atoms of equal valency with itself, the re- 
 placing atom, or group, occupies (as a rule) the same position 
 relatively to the other atoms in the molecule as was occupied 
 by the atom, or group of atoms, which it has replaced ' ; 
 or it may be better to say, the relations of the replacing 
 atom, or group, to the rest of the molecule are generally the 
 same as those of the atom, or group of atoms, which it has 
 replaced. 
 
 77 Many of the reactions given on pp. 149 154, as illus- 
 trative of methods for assigning structural formulae to given 
 compounds also serve as illustrations of the use of these 
 generalisations ; one or two further illustrations will be given 
 here. 
 
 Two isomerides each having the composition C 2 H 6 O are 
 theoretically possible; viz. 
 
 (i) H 3 C C O H and (2) H 3 C O CH 3 . 
 
 Two compounds having this formula are known. One of 
 these (alcohol) interacts with potassium or sodium thus, 
 
 (a) C 2 H 6 O + K = C 2 H 5 KO + H; 
 potassium (or sodium) does not react with the substance thus 
 
 1 L. Meyer, loc. cit. pp. 252 et seq, (English Ed. pp. 230 31) slightly modified.
 
 CHAP. II. 76, 77] STRUCTURAL FORMULA. 1 5 7 
 
 formed : alcohol interacts with phosphorus pentachloride 
 thus, 
 
 (b) C 2 H 6 O'+ PC1 5 = C 2 H 5 C1 + POC1 3 + HCL 
 
 The second isomeride (methyl ether) does not interact with 
 potassium or sodium but reacts with phosphorus penta- 
 chloride thus, 
 
 C 2 H 6 O + PC1 6 =2CH 3 C1 + POC1 3 . 
 
 The first formula generalises the reactions of alcohol, the 
 second generalises the reactions of methyl ether : thus 
 
 (a) H 3 C-CH 2 -OH + K = H 3 C-CH 2 -OK + H; 
 
 one, and only one, hydrogen atom is represented in the 
 formula as indirectly bound (through an oxygen atom) to 
 a carbon atom ; 
 
 (ff) H 3 C-CH 2 -OH + PC1 5 =H 3 C-CH 2 -C1 + POC1 3 +HC1; 
 
 the group OH is replaced by the atom Cl, which being of 
 equal valency is regarded as occupying the place in the 
 molecule relatively to the other atoms formerly occupied by 
 the group OH. 
 
 The second formula H 3 C O CH 3 assigned to methyl 
 ether represents all the hydrogen atoms as directly reacting 
 with atoms of carbon, it represents them as having all the 
 same function ; hence either none, or all, will be replaced by 
 the action of potassium. But the second formula represents 
 the atom of oxygen as in direct union with atoms of carbon 
 only ; if the oxygen atom should be replaced by two mono- 
 valent atoms, e.g. by two atoms of chlorine, the molecule 
 could no longer hold together but would separate into two 
 molecules, each having the structure Cl CH 3 ; this is what 
 happens when methyl ether is acted on by phosphorus penta- 
 chloride. 
 
 When the molecule HO-CH 2 -CH S is oxidised it loses 
 two atoms of hydrogen, producing C 2 H 4 O, which is then 
 changed, by taking up one atom of oxygen, into the mono- 
 basic acid C 2 H 4 O 2 . Probably the simplest way in which 
 these changes can be represented in structural formulae is
 
 158 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 ([) CH 3 CH 3 (2) CH 3 CH 3 
 
 CH 2 - H., = C C + O = C O. 
 
 I I I I 
 
 OH OH OH OH 
 
 Now are the properties of the acid molecule C 2 H 4 O 2 such 
 as we should expect if we assumed it to have the formula 
 H 3 C CO OH ? Two important reactions of the compound 
 in question are these : 
 
 (1) By reacting with phosphorus pentachloride it yields 
 C 2 H 3 OC1, and this does not interact with the same reagent ; 
 
 (2) When the sodium salt of this acid is heated with 
 caustic soda it is decomposed thus, 
 
 C 2 H 3 NaO 2 + NaHO=Na 2 CO 3 + CH 4 . 
 
 These reactions are expressed by the formula O C CH 3 
 
 I 
 
 OH 
 
 which is therefore adopted as the structural formula for acetic 
 acid 1 . 
 
 Now let us turn to the compound C 2 H 4 O, intermediate 
 between alcohol and acetic acid. Is this molecule well repre- 
 sented by the formula H 3 C C OH provisionally assigned 
 to it? When the compound in question interacts with phos- 
 phorus pentachloride it yields C 2 H 4 C1 2 , and not C 2 H 3 C1 as 
 might be expected if the formula H 3 C C OH were correct. 
 From synthetical and analytical reactions, C 2 H 4 C1 2 may be 
 shewn to be best represented by the structural formula 
 C1 2 = CH CH 3 ; assuming this formula, and remembering 
 that the reaction to be explained, viz. formation of C 2 H 4 C1 2 
 from C 2 H 4 O, consists in the replacement of one divalent 
 oxygen atom by two monovalent chlorine atoms, we apply 
 generalisation (3) par. 76, and conclude that the structure of 
 
 i Thus, 
 (i) CH 3 CH 3 (2) CH 3 CH 3 
 
 C + PC1 6 = C + &c. C 04-Na-OH = H + Na 2 CO 3 . 
 
 OH Cl ONa 
 
 One of the carbon atoms in the original molecule remains associated with 3 atoms 
 of hydrogen throughout both processes of change, hence we conclude that the 
 molecule of acetic acid contains the group CH 3 .
 
 CHAP. II. 77] STRUCTURAL FORMULA. 159 
 
 the molecule C 2 H 4 O is best represented by the formula 
 0-CH-CH 8 . 
 
 The oxidation of alcohol is then best represented thus in 
 structural formulae : 
 
 (i) CH 3 CH 3 (2) CH 3 CH 3 
 
 ! i I I 
 
 CH 2 - H 2 = C H C-H + O = C OH. 
 
 O H O O O 
 
 Another and somewhat more complex illustration, taken 
 from the so-called ' aromatic ' (or better ' benzenoid ') carbon 
 compounds, will serve to shew that the generalisations stated 
 in par. 76, although widely applicable, must yet be used with 
 great caution. Assuming the generally adopted structural 
 formula for the molecule of benzene 1 (C 6 H 6 ), viz. 2 
 
 H 
 
 I 
 
 ' 
 
 H 
 
 the existence of three, and only three, isomeric dichloro- or 
 dibromo- &c. benzenes, becomes possible, viz. 
 
 (0 (2) (3) 
 
 C-C1 C Cl C Cl 
 
 /\ / \ /\ 
 
 H C C Cl H C C H H C C H 
 
 H C C H H C C Cl H C C H 
 
 \ / \/ \/ 
 
 C C C 
 
 I I I 
 
 H H Cl 
 
 1 See Armstrong and Groves, Organic Chemistry, pp. 260 63; also pp. 270 
 74. See also post, par. 81. 
 
 2 The fact that this formula is generally used rather than the more complex 
 formula originally proposed byKekule with alternate 'doubly' and 'singly-linked' 
 carbon atoms, and that most chemists are content meanwhile to overlook the 
 contradiction involved in employing such a formula and yet using the language of 
 ' bonds,' is indicative of the unsatisfactory nature of this language when rigidly 
 applied.
 
 l6o ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 In (i) both chlorine atoms are in direct connexion with 
 carbon atoms which are directly bound to one another ; in (2) 
 one carbon atom intervenes, and in (3) two carbon atoms 
 intervene, between the atoms of carbon which directly interact 
 with the chlorine atoms. 
 
 These three isomeric compounds 1 are usually distinguished 
 as i : 2, i : 3, and i : 4, dichlorobenzene ; it is evident that 
 1:6=1 : 2, and i : 5 = i : 3. Each of these dichloroben- 
 zenes when acted on by chlorine yields one or more isomeric 
 trichlorobenzenes (C 6 H 3 C1 3 ). Korner has formulated a simple 
 method of proving that I : 2 dichlorobenzene can yield two, 
 i : 3 can yield three, and i : 4 can yield only one, trichloro- 
 benzene 2 . 
 
 Now if the generalisations we are considering are applic- 
 able to the benzenoid hydrocarbons, it follows that any 
 di-derivative of benzene C 6 H 4 JT 2 where X is a monovalent 
 atom or group of atoms which, by a simple series of reac- 
 tions can be obtained from, or can be converted into, i : 2 
 dichloro- (or dibromo- or dinitro-) benzene, must be itself a 
 i : 2 derivative; i.e. the two X groups or atoms must be in 
 direct interaction with carbon atoms between which there is 
 direct mutual action within the molecule. A similar conclu- 
 sion is drawn regarding the structure of those compounds of 
 the formula C 8 H 4 JT 2 which can be obtained from or reduced 
 to i : 3, or i : 4, dichloro dibromo or dinitro-benzene. 
 
 Thus i : 3 dinitrobenzene, by the action of zinc and 
 hydrochloric acid, yields nitramidobenzene C 6 H 4 NO 2 NH 2 ; 
 by the further action of nascent hydrogen this yields 
 diamidobenzene C 6 H 4 (NH 2 ) 2 ; and diamidobenzene, by the 
 
 1 The carbon atoms in the hexagon are numbered thus : 
 
 /c\ 
 
 6 C C 2 
 
 l (ch 
 
 4 
 
 2 i : 2 yields 1:2:3, an ^ I : a : 4, ( i : 2 : 3 = i : 2 : 6, and i : 2 : 5 = i : 2 :4) 
 i : 3 yields 1:2:3, and 1:3:4 (which= i : 3 : 6), and 1:3:5. 1:4 yields i 2:4 
 { which = 1:3:4=1:4:5 = 1:4:6). See Armstrong and Groves, loc. cil. pp. 
 4678.
 
 CHAP. II. 77] FORMULAE OF BENZENE COMPOUNDS. l6l 
 
 ' diazo reaction' 1 (or 'Griess' reaction'), yields bromohydroxy- 
 benzene C e H 4 Br. OH; this bromohydroxybenzene is therefore 
 assumed to be a I : 3 derivative of benzene. Now when this 
 body is fused with caustic potash it yields one of the three 
 isomeric dihydroxybenzenes C 6 H 4 (OH) 2 ; in accordance with 
 generalisation (3) par 76 this dihydroxybenzene ought to be 
 regarded as a I : 3 derivative. But I : 4 bromohydroxy- 
 benzene obtained by a method similar to that sketched 
 above from i : 4 dinitrobenzene yields, by fusion with 
 potash, the same dihydroxybenzene as just mentioned ; hence 
 this dihydroxybenzene is now shewn to be probably a I : 4 
 derivative of benzene. Again, this same dihydroxybenzene 
 is the sole product of the fusion with potash at a high tem- 
 perature of i : 4 iodohydroxybenzene C 6 H 4 I . OH; but when 
 this iodohydroxybenzene is fused with potash at 165 none of 
 the dihydroxybenzene already mentioned is obtained but 
 only one of the dihydroxybenzenes isomeric with it 2 . 
 
 Another example, shewing how necessary it is to apply 
 such generalisations as those under consideration only in a 
 tentative manner, is furnished by some reactions of i : 4 
 nitrobromobenzene C 6 H 4 NO 2 Br. By the action of alcoholic 
 ammonia on this compound nitramidobenzene C 6 H 4 NO 2 NH 2 
 is produced ; that this nitramidobenzene is, as we should 
 expect, a i : 4 derivative of benzene, can be proved by trust- 
 worthy evidence. But if the same i : 4 C 6 H 4 NO 2 Br is acted 
 on by potassium cyanide, and the product of this action, 
 C 6 H 4 CNBr, is boiled with dilute acid, bromobenzoic acid, 
 C 8 H 4 Br(CO 2 H), is obtained, and the reactions of this acid 
 prove beyond doubt that it is a i : 3, and not as we should 
 expect a 1:4, derivative of benzene. Similarly the product 
 of the action of potassium cyanide followed by that of dilute 
 acid on i : 3 C 6 H 4 NO 2 Br is i : 2 bromobenzoic acid, 
 C 6 H 4 Br (CO 2 H), and not, as a strict application of the state- 
 ment in par. 76 would lead us to expect, the i : 3 derivative. 
 
 1 For an account of these ' diazo-reactions,' which are much used in the 
 synthesis of benzene derivatives, see Armstrong and Groves, loc. cit. pp. 
 298-9. 
 
 * See, for more details, Armstrong and Groves, loc. cit. pp. 5212. 
 
 M. C. II
 
 162 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 And finally, when I : 2 C 6 H 4 NO 2 Br is subjected to the action 
 of potassium cyanide 1 no replacement of NO 2 by CN occurs 2 . 
 
 78 The application of the hypothesis of valency to the phe- 
 nomena of isomerism has rendered more definite that general 
 conception of the molecule as a structure which arose so soon 
 as it was recognised that each atom in a molecule could di- 
 rectly interact with a limited number of other atoms. Analy- 
 ses of reactions, and comparisons of classes of reactions, have 
 led to the adoption of certain rules which, when applied with 
 caution, have proved of very considerable service in researches 
 on molecular structure. These researches have served to 
 emphasise the fundamental connexion which exists between 
 composition and properties, between function and quality of 
 material : but chemistry is not now contented with connecting 
 the reactions of compounds with their elementary composi- 
 tions, or even with the atomic compositions of their molecules, 
 she attempts, and is gradually succeeding in the attempt, to 
 connect certain definite arrangements of atoms in molecules 
 with certain definite properties and actions of these molecules. 
 
 79 In his remarkable paper published in 1858, Kekule recog- 
 nised that the function performed by an atom in any molecule 
 depends on the nature of the other atoms, as well as on the 
 nature of the given atom, and also on the arrangement of all 
 the atoms. Since 1858 the nature of the dependence in 
 question has been more fully elucidated ; and although it 
 cannot be said that we have at present much knowledge, 
 capable of being generalised in statements at once accurate 
 and wide, of the connexions between the functions of parts 
 of molecules and the atomic compositions and structures of 
 these molecules, yet we are certainly gathering facts which 
 will doubtless prove the basis for far-reaching generalisations. 
 
 1 In Armstrong and Groves, loc. cit. pp. 334 6, will be found an account of 
 the action of potassium cyanide on benzene derivatives ; this action, although 
 abnormal, may be expressed by a tolerably simple generalisation. 
 
 8 Further examples of the point under discussion will be found in the change of 
 normal propyl to isopropyl, by (i) the action of Al 2 Br 6 [see Kekule, Ber. 12. 2279], 
 or (2) the action of zinc dust [see Jacobsen, Ber. 12. 1512]: also in the change of 
 C n H 2n+ iCN to C n H 2n+1 NC by the action of heat : and also in the action of 
 reducing agents on phenanthraquinone (see Japp, C. S. Journal, Trans, for 1883. 
 13, note].
 
 CHAP. II. 78-80] FUNCTIONS OF ATOMS IN MOLECULES. 163 
 
 Numerous illustrations have already been given of the 
 existence of a connexion of some kind between the functions 
 of parts of a molecule and the composition, using this term in 
 its widest sense, of the whole molecule. But the existence of 
 such a connexion is so important that I shall devote a 
 paragraph to its illustration. 
 
 The relation to be illustrated is that between the function 
 performed by an atom, or atomic group, in a molecule, 
 
 and 
 
 I. the nature, and arrangement relatively 
 to the given atom (or group), of the 
 
 other atoms ; 
 
 otner atoms ; 
 II. the general relative arrangement of 
 
 all 
 
 the parts ; 
 
 of the 
 mole- 
 cule. 
 
 80 I. That the function performed by an atom of hydrogen 
 in a molecule varies according to the nature and arrangement 
 relatively to the hydrogen of the other atoms, has already 
 been shewn (see par. 74, pp. 151 154). Hydrogen which is 
 associated with negative atoms or groups is as a rule 'replace- 
 able by metals,' in other words, performs acidic functions in 
 the molecule. Thus of the two compounds, potassium-nitro- 
 propane and bromonitropropane, the latter is much more 
 decidedly acidic than the former : if the formulae are com- 
 pared, 
 
 K Br 
 
 H 5 C 2 C NO 2 with H 6 C 2 C NO 2 , 
 
 I I 
 
 H H 
 
 it is seen that, in the markedly acidic compound the carbon 
 atom with which the sixth atom of hydrogen is represented 
 as directly connected is itself directly bound to the negative 
 group NO 2 and to the negative atom Br ; but that in the less 
 acidic compound this carbon atom is represented as directly 
 bound to the negative group NO 2 and to the positive atom K. 
 Again C1 3 C - H is not an acid, but (NO 2 ) 3 C - H is ; the 
 influence of the very negative NO 2 group seems to be im- 
 pressed through the carbon atom on the hydrogen atom of 
 the molecule.
 
 1 64 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 In these cases the atom of ' acidic hydrogen ' is represent- 
 ed as directly bound to a carbon atom within the binding- 
 sphere of which come negative atoms or groups. But the 
 case of the nitrolic acids, assuming the usually accepted for- 
 mula (C n H 2n+1 ) C - NO 2 to be correct, shews that 
 
 I 
 N-OH 
 
 an atom of hydrogen which is indirectly bound to carbon 
 itself binding negative groups may react as acidic hydrogen. 
 Glyoxaline and tribromoglyoxaline also furnish examples 
 in point; each of these molecules contains one atom of acidic 
 hydrogen 1 . 
 
 A portion of the hydrogen in monohydric alcohols is re- 
 placeable by metal, but only by the very positive metals ; e.g. 
 C 2 H 5 .OH + K = C 2 H 5 OK+H; but by the introduction of 
 an atom of sulphur into the molecule in place of oxygen a 
 thio-alcohol is obtained which readily exchanges hydrogen 
 even for comparatively negative metals 2 , e.g. 
 
 2C 2 H 5 SH + HgO = (C 2 H s S) 2 Hg + H 2 O. 
 
 Again, the experiments of R. Meyer appear to prove that an atom of 
 hydrogen in the molecule of a carbon compound can be replaced by the 
 group OH, by the action of oxidising agents, only when the carbon atom 
 with which the hydrogen is directly connected does not directly bind any 
 other hydrogen atoms; thus isobutyric acid is oxidised by potassium 
 permanganate to isohydroxybutyric acid, but normal butyric acid yields 
 acetic, oxalic, carbonic, and other acids, under the same conditions. 
 
 O 
 [In structural formulae ; H 3 C CH 2 CH 2 C^ does not yield 
 
 OH 
 
 O^ ^CH 3 O^ X CH 3 
 
 a hydroxy-acid ; but C CH yields C COH .] 
 
 HO^ X CH 3 ' HO/ X CH 3 
 
 1 The most probable formulae are, 
 
 CH CH CH NH CBr CBr CBr NH 
 
 \N/ \N/ 
 
 (see Armstrong and Groves, loc. cit, p. 769). Some reactions of water are con- 
 sistent with the statement that one of the hydrogen atoms performs the functions 
 of acidic hydrogen ; e.g. 
 
 HOH + CH 3 ONa = CH 3 OH + NaOH. 
 
 2 For details concerning these reactions see Armstrong and Groves, loc. cit., 
 pp. 660 i.
 
 CHAP. II. 8 1] FUNCTIONS OF ATOMS IN MOLECULES. 165 
 
 81 II. A good illustration of the influence exerted by the 
 arrangement of all the atoms in a molecule on the functions 
 of one, or some, of these atoms, is afforded by a comparative 
 study of the two groups of carbon compounds, more especially 
 the hydrocarbons, generally known as 'fatty' (or 'paraffinoid') 
 and 'aromatic' (or 'benzenoid') respectively 1 : a few, but only 
 a few, of the more important points will be briefly stated. 
 
 Comparing the interaction between concentrated nitric 
 or sulphuric acid and a paraffin, e.g. C 2 H 6 , with the inter- 
 action of the same acid with a benzene, e.g. C 6 H 6 , it is 
 noticed that while one or more hydrogen atoms in the 
 molecule of the latter are readily replaced by the groups NO 2 
 or SO 8 H, the acids are without action on the former hydro- 
 carbon. When the homologues of benzene are oxidised, they 
 generally yield quinones, the molecule of any one of which 
 contains the same number of carbon atoms as the parent 
 hydrocarbon but has two atoms of oxygen in place of two 
 atoms of hydrogen in the original molecule. When the 
 paraffinoid hydrocarbons on the other hand are oxidised 
 they do not yield derivatives analogous to the quinones, 
 but rather afford mixtures of acids the molecule of each of 
 which contains fewer carbon atoms than were present in the 
 original hydrocarbon molecule. 
 
 When chlorine reacts with the molecule of a paraffinoid 
 hydrocarbon containing only tetravalent 8 carbon atoms it 
 produces chloro-substitution derivatives containing tetravalent 
 carbon atoms, the whole of the hydrogen in the hydrocarbon 
 being eventually replaced by chlorine ; the further action of 
 chlorine then frequently results in a separation of the mole- 
 cule into two or more molecules, each containing a smaller 
 number of carbon atoms than the original molecule. When 
 however chlorine reacts with the molecule of a paraffinoid 
 hydrocarbon containing two or more trivalent 3 carbon atoms 
 it generally combines with it and so produces a molecule 
 containing tetravalent carbon atoms, which then reacts with 
 
 1 See Armstrong and Groves, loc. cit. pp. 391 402. 
 
 2 In ordinary nomenclature it would be said ' singly-linked carbon atoms." 
 
 3 In ordinary nomenclature it would be said ' doubly-linked carbon atoms.'
 
 1 66 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 chlorine as hydrocarbons with tetravalent carbon atoms 
 usually do. Thus when propane, H 3 C CH 2 CH 3 , reacts 
 with chlorine, chloro - derivatives H 3 C - CH 2 - CH 2 C1, 
 H 3 C CH 2 CHC1 2 , &c. and finally octochloropropane 
 C1 3 C CC1 2 CC1 3 , are produced ; and when this octo- 
 chloropropane is caused to interact with iodine chloride, 
 two compounds, viz. C1 3 C CC1 3 and CC1 4 , are formed. On 
 the other hand when propylene, H 2 C CH 2 CH 2 , the 
 molecule of which contains two trivalent atoms of carbon, 
 reacts with chlorine propylene chloride, C1H 2 C-CH 8 -CH 2 C1, 
 is produced ; and this compound, which contains only te- 
 travalent carbon atoms in its molecule, is decomposed by 
 the action of iodine chloride, first into C 3 C1 8 , and then into 
 C 2 C1 6 and CC1 4 . 
 
 The interaction of chlorine with the hydrocarbon benzene, 
 C 6 H 6 , finally results in the formation of hexachloro-benzene 
 C 6 C1 6 , in which, it may be safely asserted from the formula 
 and from a study of the properties of the compound, the 
 carbon atoms directly interact with the same number of 
 atoms as in the original C 6 H 6 molecule. So far then benzene 
 behaves like a paraffin: but IC1 has no action on C 6 C1 6 ; the 
 molecule refuses to separate into parts ; the six atoms of 
 carbon are apparently more firmly joined together, and form 
 a more stable group, than the carbon atoms in the molecule 
 of a paraffin. 
 
 The functions both of the hydrogen and the carbon atoms 
 in the molecules of a benzene and of a paraffin say in C 6 H 6 
 and in C 6 H U evidently depend to some extent on the general 
 arrangement of all the atoms in these molecules. 
 
 The arrangement of carbon atoms supposed to characterise 
 the molecule of a fatty hydrocarbon, e.g. a paraffin, is usually 
 spoken of as an arrangement in 'an open chain? while that 
 supposed to characterise the molecule of an aromatic hydro- 
 carbon, e.g. a benzene, is called 'a closed ring.' 1 If the inter- 
 
 1 Ring-formed molecules resemble . unsaturated molecules in that they can 
 directly combine with monovalent atoms without loss of any of their constituent 
 atoms, e.g. benzene forms C 6 H 6 C1 6 ; but they resemble saturated molecules in 
 that the assumption of monovalent atoms is possible only when preceded by
 
 CHAP.'II.8l] FUNCTIONS OF ATOMS IN MOLECULES. l6/ 
 
 action between atom and atom be supposed to begin at one 
 of the carbon atoms, then in a closed ring molecule it returns 
 to that atom ; in other words each carbon atom acts on, and 
 is acted on by, at least two other carbon atoms in the 
 molecule : but in an open chain molecule the action does not 
 return to the carbon atom at which it started ; in other words, 
 there are two carbon atoms in the molecule, each of which 
 acts on, and is acted on by, only one other carbon atom. 
 
 The ring-formed molecule containing six carbon atoms 
 may be represented thus : 
 
 C 
 
 / \ 
 
 C C C or thus C C 
 
 II I I 
 
 C C C C C 
 
 v/ 
 
 C 
 
 and the open chain molecule thus : 
 
 C C C C-C C. 
 
 As the six carbon atoms in the molecule of benzene ap- 
 pear to form a very stable group, they are sometimes spoken 
 of as the ' six-carbon-nucleus' of the molecule. Now if the 
 monochloro-derivative of xylene, C 8 H 10 , produced by the 
 reaction of chlorine with that hydrocarbon when cold is 
 compared with the monochloro-derivative produced by the 
 reaction of chlorine with the same hydrocarbon when hot, 
 it is found that the latter readily exchanges its chlorine atom 
 for the group OH with production of an alcohol, C 8 H 9 (OH), 
 but that the chlorine atom in the former can scarcely be 
 replaced by other radicles. If we assume the ordinarily 
 accepted structural formulae for the two isomeric mono- 
 chloroxylenes we at once see how profoundly the functions 
 
 a redistribution of the mutual actions between some of the polyvalent atoms. 
 (Lossen.) 
 
 The number of molecules produced in any reaction wherein only saturated 
 molecules take part is equal to or greater than the number of molecules taking 
 part in the reaction : when the number produced in any reaction is smaller than 
 the number of molecules originally taking part in the reaction, at least one of the 
 reacting molecules must be either unsaturated or ring-formed. (Lossen.) 
 
 It is evident that a ring-formed molecule must contain at least three polyvalent 
 atoms, and that for such molecules j < 3 + 2 4 + &c.... + 2.
 
 168 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 of the chlorine atoms depend on the relative arrangement of 
 all the atoms in the molecule. The formulae in question are 
 
 (a) monochloroxylene from hot xylene 
 
 H H 2 
 
 / c \ II 
 HC C C CH 2 C1, 
 
 I I 
 HC CH 
 
 ^C^ 
 H 
 
 (b] monochloroxylene from cold xylene 
 
 HC H 2 
 
 / \ II 
 HC C C CH 3 . 
 
 HC C Cl 
 \ / 
 CH 
 
 The chlorine atom in (a) is said to be in ' the side chainl 
 and in (b) in the ''central nucleus! In the hydrocarbon C 8 H 10 
 we have the properties both of a paraffin and a benzene ; part 
 of the molecule, the six-carbon-nucleus, behaves as a ben- 
 zenoid group ; the other part, the side chain C 2 H 5 , as a paraffi- 
 noid group. 
 
 A comparison of some of the reactions of metallic hy- 
 droxides, alcohols, and phenols, will serve to illustrate the 
 dependence of the functions of part of a molecule at once on 
 the nature, and arrangement relatively to this part, of the 
 other atoms, and also on the general arrangement of all the 
 atoms, in the molecule. 
 
 The interactions of acids with metallic hydroxides and 
 alcohols result in the formation of salts : 
 Zn(OH) 2 +2HCl = Zn 
 
 But phenols do not yield analogous products by their reactions 
 with acids. Alcohols and some metallic hydroxides, e.g. 
 Zn(OH) a and Al 2 (OH) a , yield unstable metallic derivatives by 
 reacting with markedly positive metals or their hydroxides ; 
 phenols however yield much more stable metallic derivatives 
 by reacting with the same metals, or their hydroxides. The 
 hydrogen atom (or atoms) which is indirectly connected,
 
 CHAP. II. 8l] FUNCTIONS OF ATOMS IN MOLECULES. 169 
 
 through oxygen, with the metal or hydrocarbon-radicle of 
 the molecules of alcohols, certain metallic hydroxides, and 
 phenols evidently fulfils more or less acidic or basic functions 
 according to the nature of the other part of the molecule. 
 When that other part is a strongly positive metallic atom (or 
 atoms) the hydrogen is basic; when the metallic atom (or 
 atoms) is not markedly positive the hydrogen as a rule is at 
 once basic and acidic in function ; when the nonhydroxylic 
 part of the molecule is composed of carbon and hydrogen 
 atoms arranged in an ' open chain ' the hydrogen appears to 
 be more or less analogous to the hydrogen of metallic hy- 
 droxides; and when the carbon and hydrogen of the nonhy- 
 droxylic part of the molecule are arranged in a ' closed ring ' 
 the hydrogen appears to be more distinctly acidic in function 1 . 
 
 The following facts and generalisations concerning the 
 action of reagents on various benzene derivatives afford further 
 examples of the influence exerted by the relative position, 
 and nature of the parts, of a molecule, and the general ar- 
 rangement of all the atoms in a molecule, on reactions wherein 
 atoms, or atomic groups, in the molecule are substituted by 
 other atoms or groups. 
 
 In the production of certain di-substituted derivatives of 
 benzene C 6 H 4 JTJr', from mono- substituted derivatives C 6 H 5 ^f, 
 it is found that whether the di-derivative shall belong to the 
 i : 2, I : 3, or i : 4 series 2 , depends on the nature of the atom 
 or atomic group X in C 6 H 6 Jf, and also on the nature of the 
 atom or group X' in C 6 H 4 XX'. When X = Cl, Br, I, OH, 
 CH 3 , CH.C1, CHC1 2 , CC1 3 , or NH 2 , and X' = C\, Br, I, NO 2 , 
 or SO 3 H, the di-derivative C e H t XX' generally belongs to the 
 i :4 series: when ^=NO 2 ,SO 3 H, CN, CHO, COCH 3 , or 
 CO 2 H, and X 1 =Cl, Br, I, NO 2 , or SO 3 H, then C 6 H<XX' 
 generally belongs to the i : 3 series 8 . 
 
 When derivatives of benzene containing paraffinoid radicles 
 as ' side chains ' are oxidised they yield mono-, di-, tri-, &c., 
 
 1 See Armstrong and Groves, loc. dt. p. 566. 
 
 2 See par. 77, p. 160, for an explanation of this notation. 
 
 3 See table in Armstrong and Groves, loc. cit. p. 337 : also Armstrong, C. S. 
 Journal, Trans, for 1887. 258.
 
 I/O ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 basic acids, according to the number of side chains in the 
 original molecule; thus C 6 H 4 .C 2 H 5 .CH 3 yields C 6 H/CO 2 H) 2 , 
 C 6 H 4 .CH,.C0 2 H also yields C 6 H 4 (CO 2 H) 2 , &c.: but if a 
 negative atom or group is introduced into the benzene deri- 
 vative and the oxidation is then effected, the paraffin-radicle 
 which forms the side chain nearest to 1 the negative atom (or 
 group) is protected by that atom (or group) and does not un- 
 dergo oxidation. Thus C 6 H 4 .CH 3 .C 2 H 5 [1:4] when oxidised 
 produces C 6 H 4 (CO 2 H) 2 ; but C 6 H 3 .Br.CH 3 .C 2 H 5 [i : 2 -.4] pro- 
 duces C 6 H 3 Br.CH 3 .CO 2 H [1:2: 4]. So again C 6 H 4 (C 2 H 5 ) 2 
 [i : 4] oxidises to C 6 H 4 (CO 2 H) 2 ; but C 6 H 3 .C 2 H 8 .SO 2 NH 2 .C 2 H 5 
 [1:2:4] oxidises to C 6 H 3 .C 2 H 5 .S0 2 NH 2 .CO 2 H [1:2:4]; in the 
 latter case 2 the C 2 H 5 nearest to the negative group is protected, 
 while the other C 2 H 5 group undergoes oxidation to CCXH. 
 So also if i : 3 : 4, i : 4 : 5, or i : 2 : 4, dimethylnitroxylene 
 (C 8 H 7 .CH 3 .CH 3 .NO 2 ) is oxidised, in each case the CH 3 group 
 nearest to the NO 2 group is unchanged, and the other CH 3 
 group is oxidised to CO 2 H ; but if 1:3:5 dimethylnitro- 
 xylene is oxidised, both the CH 3 groups are converted into 
 CO 2 H groups : now in a 1:3:5 derivative the substituting 
 groups are equally distributed ; in the case before us each 
 methyl group is situated in exactly the same position relatively 
 to the NO 2 group 3 . 
 
 1 'Nearest to': compare the structural formulae for the three methylbromo- 
 benzenes 
 
 CH 3 CH 3 CH 3 
 
 C] 
 
 
 
 * 
 
 Br 
 1:2 1:3 1:4 
 
 the Br atom is said to be nearer to the CH 3 group in the i : i than in the i : 3, 
 and nearer in the i : 3 than in the i : 4 compound. 
 
 2 See Remsen and Hall, Amer. Chem. yournal 2. 50 ; and Remsen and Noyes, 
 ibid. 4. 197. 
 
 3 See E. Wroblewsky, er. 15. 1021. Compare the following formulae where 
 X represents the group CH 3 and A the group NO 2 : 
 
 SL .A. 
 
 0' .0:
 
 CHAP. II. 8 1, 82] MOLECULAR STRUCTURE. I/ 1 
 
 Again, when thiophene, C 4 H 4 S, is acted on by nitric acid 
 the thiophene is completely oxidised ; but when negative 
 groups are introduced into the thiophene molecule the pro- 
 ducts react with strong nitric acid to produce nitro-derivatives 1 . 
 Thus moniodothiophene, C 4 H 3 IS, yields nitriodothiophene 
 C 4 H 2 I(NO. 2 )S ; and dibromothiophene, C 4 H 2 Br 2 S, yields dini- 
 trodibromothiophene, C 4 Br.,(NO 2 ) 2 S. 
 
 : From these considerations it would appear that the 
 readiness to undergo this reaction or that, or, as might be 
 said, the chemical stability of a molecule, depends largely 
 on the balance of properties of the parts of the molecule, such 
 balance being itself connected with the nature and relative 
 arrangements of these parts. Many of the reactions cited 
 in the foregoing paragraphs (80 and 81) may serve as 
 illustrations of the meaning of the expression ' chemical 
 stability', and of the conception of a dependence between this 
 and the balance of functions of parts of the molecule ; let 
 one more illustration suffice. 
 
 The conditions under which an atom of hydrogen ap- 
 parently fulfils alcoholic functions have been already sum- 
 marised [pp. 168 169]. In some molecules the acid and 
 alcoholic functions of the hydrogen atoms seem to be equally 
 balanced, so that for some purposes the compound may be 
 classed as an alcohol, for other purposes as an acid ; thus, when 
 an atom of hydrogen in the benzene molecule is replaced 
 by the group OH, the product, phenol C 6 H 5 .OH, exhibits 
 some of the properties of an acid and also some of the 
 properties of an alcohol; e.g. an atom of hydrogen is 
 replaceable by metal when the compound is acted on by 
 an alkali metal or alkaline hydroxide, but not when it is 
 acted on by an alkaline carbonate 2 . By replacing three 
 hydrogen atoms in the phenol molecule, C 6 H 5 . OH, by 
 NH 2 and NO S groups, compounds are obtained which ex- 
 hibit both basic and acidic properties; e.g. the molecule 
 
 1 H. Kreis, Ber. 17. 2073. 
 
 2 In these actions phenol presents an analogy to aluminium hydroxide- 
 
 Ala (OH) 8 .
 
 172 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 C 6 H 2 . (NH 2 ) . (NO 2 ) 2 . OH combines with HC1, but the 
 product is not very stable ; the same molecule however readily 
 exchanges an atom of hydrogen for metal by the action of 
 alkaline carbonates, thus forming well-marked stable metallic 
 derivatives, e.g. C 6 H 2 (NH 2 )(NO 2 ) 2 ONa. If however two NH 2 
 groups and one NO 2 group are introduced in place of 
 three hydrogen atoms in the phenol molecule, the product 
 C 6 H 2 (NH 2 ) 2 (NO,)OH is distinctly basic, combining readily 
 with HC1, but yielding only unstable metallic derivatives. 
 
 83 Not only is the general chemical stability of a molecule 
 dependent, in part, on the balance of functions of the atoms 
 and atomic groups in the molecule, but many of the 
 properties generally called physical are correlated with a 
 similar balance of parts. Thus Witt l has shewn that there 
 exists a definite connexion between the tinctorial proper- 
 ties of many derivatives of azobenzene, C 6 H 5 N 2 C 6 H 5 , 
 and the atomic composition and structure of these mole- 
 cules. By introducing the group NH 2 in place of hydrogen 
 in the azobenzene molecule salt-forming molecules are 
 produced, possessed of considerable dyeing properties; if 
 negative groups, as OH, HSO 3 , &c. are introduced into 
 the molecule the products are also strongly coloured ; 
 but the best dyes are formed by compounds which are 
 neither markedly basic or acidic. Thus C 6 H S - N 2 - C 6 H 4 (NH 2 ) 
 dyes a light yellow, but the colour is very fugitive; 
 the colour of (NH 2 )C 6 H 4 - N 2 - C 6 H 3 (NH 2 ) 2 is too dull; 
 but when an azotised or a di-azotised base is combined 
 with a negative phenolic or naphtholic group, good dyes 
 are usually obtained; e.g. C 6 H 6 - N 2 -C 10 H 5 (SO 3 H)(OH) or 
 C 6 H 5 - N 2 - C 6 H 4 - N, - C 6 H 4 O H. 
 
 84 We have already learned (pars. 32 34) that a general 
 relation exists between the crystalline form of a compound 
 and the number and arrangement of the atoms in the molecule 
 of that compound. Groth 2 , and others, have shewn that the 
 
 1 C. S. Journal, Trans, for 1879. 179 and 357 : also Hartley, C. S. Journal, 
 Trans, for 1887. 152. 
 
 " Pgg- Ann. 141. 31. See also C. Hintze, Pogg. Ann. ErgzM. 6. 195; 
 C. Bodewig, Pogg. Ann. 158. 239; P. Friedlander, Zeitschr. Krystall. 3. 168;
 
 CHAP. II. 83, 84] MORPHOTROPIC RELATIONS. 173 
 
 substitution of Cl, Br, NO 2 , or OH &c., for hydrogen in the 
 molecules of benzene derivatives is accompanied by definite 
 changes in the crystalline forms of the compounds. The 
 relations existing between crystalline form and chemical 
 structure, so far as the latter is modified by processes of 
 substitution, are called by Groth morphotropic relations. The 
 change of crystalline form in any given case depends on 
 (i) the chemical nature of the parent substance; (2) the 
 crystalline system to which it belongs ; (3) the chemical nature 
 of the substituting atom (or group); and (4) the chemical 
 nature of the product of the reaction, using the expression 
 ' chemical nature' in its widest sense as including the con- 
 ceptions of atomic composition and atomic structure. 
 
 When the parent substance belongs to a crystalline system 
 in which the relations of the axes are not invariable, substitu- 
 tion of Cl, Br, &c., generally only produces changes in these 
 relations, without total changes to other systems ; but if the 
 parent substance belongs to the regular system, the substituted 
 product is found to belong to one of the other five systems. 
 
 Groth's researches lead to the following generalisations 
 concerning the derivatives of benzene : 
 
 (1) Substitution of H by OH or NO 2 , is accompanied 
 by changes in the relations of the axes, but not by changes 
 from one system to another. 
 
 (2) Substitution of H by Cl or Br, is accompanied by 
 changes from one crystalline system to another, less sym- 
 metrical, system; but further substitution by the same atoms is 
 sometimes accompanied by a return to a more symmetrical 
 system. 
 
 (3) Substitution of H by CH 3 is also accompanied by 
 marked changes in crystalline symmetry. 
 
 (4) Chemically similar derivatives of benzene belonging 
 to zpara [i : 4] series shew greater crystallographic analogies 
 with one another than with the members of a meta [i 13] or 
 an ortlw [1:2] series. 
 
 and the article ' Isomorphie ' in the Nates Handivorterbwh dcr Chemie, 3. especially 
 pp. 854 9; also 'Isomorphie' in Ladenburg's Handworterbzich der Chemie, 5. 
 pp. 4015.
 
 174 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 The general conclusion to be drawn from these facts is, 
 that, in some compounds at any rate, crystalline form is 
 more or less closely connected with the nature and arrange- 
 ment, as well as with the number, of the atoms and groups of 
 atoms in the compound molecules. 
 
 85 Very many measurements have been made of the 
 quantities of heat which are produced or disappear during 
 processes of chemical change. This subject will be con- 
 sidered more fully in a future chapter 1 ; at present I wish to 
 insist on the fact that the data of thermal chemistry establish 
 an undoubted connexion between the thermal changes which 
 accompany chemical reactions and the nature and arrange- 
 ment of the atoms, and groups of atoms, forming the 
 molecules which take part in these reactions. Especial 
 reference must be made here to the experiments of J. 
 Thomsen 2 , from which the conclusion can be drawn that 
 the change from a material system of isolated atoms say 
 x carbon atoms, x 1 hydrogen atoms, and x" oxygen atoms 
 to a molecular system in which these atoms are combined so 
 that all the carbon atoms are tetravalent (i.e. each acts on 
 and is acted on by four other atoms) and all the oxygen 
 atoms are divalent, is attended with the loss to the system of 
 a quantity of energy different from that which accompanies 
 the change from the same system of isolated atoms to a 
 molecular system in which some, say (x-2], carbon atoms 
 are trivalent, and some, say (x" i), oxygen atoms are 
 monovalent. 
 
 86 The measurements which have been made of the quantities 
 of heat that are produced or disappear during similar chemical 
 changes undergone by isomeric compounds shew that in many 
 cases at any rate the quantity of energy associated with one 
 isomeride is different from that associated with another. 
 Thus, the heat produced during the complete combustion 
 of dipropargyl (C 6 H 6 ) is about 850,000 gram-units, while that 
 produced during the combustion of the isomeric molecule 
 
 1 See Chapter iv. Section i. 
 
 2 Ber. 13. 1321 ; Journal fiir prakt. Chemie. 23. 157 and 163 ; and Zeitschr. f, 
 physikal. Chemie. 1, 369. See also/w/, chap, iv., par. 134.
 
 CHAP. II. 85-87] THERMAL WORK ON TSOMERISM. 175 
 
 benzene is about 800,000 gram-units ; hence the amount of 
 energy associated with the arrangement of six atoms of 
 carbon and six atoms of hydrogen in the molecule of 
 benzene is less than that associated with the arrangement 
 of the same numbers of the same atoms in the molecule 
 of dipropargyl. But in the molecule of benzene each carbon 
 atom is at least trivalent (and possibly tetravalent), while in 
 that of dipropargyl some of the carbon atoms are certainly 
 divalent 1 : hence, it might apparently be concluded, that more 
 energy is degraded in the formation, from atoms of carbon and 
 hydrogen, of a molecule in which all the carbon atoms act as 
 tri- or tetravalent atoms, than of an isomeric molecule in 
 which some of the carbons act as divalent atoms. But it 
 must be remembered that in the benzene molecule each 
 carbon atom directly interacts with not more than one atom 
 of hydrogen, and with at least two other atoms of carbon ; 
 whereas in the molecule of dipropargyl it is very probable 
 that two of the carbon atoms directly interact each with a 
 single other carbon atom, and also that some of the atoms 
 of carbon interact each with two atoms of hydrogen. Hence, 
 if we may provisionally draw a general conclusion from the 
 very limited data before us, it might be inferred that the 
 differences between the quantities of energy associated with 
 different isomeric atomic systems depend, among other con- 
 ditions, on 
 
 (1) whether each atom directly interacts with the 
 
 maximum number of other atoms; in other 
 words, on the actual valencies of the atoms in 
 the molecules ; and 
 
 (2) on the nature of the atoms between which direct 
 
 interaction occurs ; in other words, on the dis- 
 tribution of the interatomic reactions. 
 
 87 The following data, in addition to the numbers already 
 given for the heats of combustion of benzene and dipro- 
 
 1 The usually adopted formula for the dipropargyl molecule is 
 
 HC C CH a CH 2 C CH, 
 which contains 2 tetra- and 4 divalent carbon atoms.
 
 176 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 pargyl, serve to illustrate the existence of a relation between 
 the quantities of energy, and the valencies of the atoms, in 
 isomeric molecules. 
 
 Empirical formula 
 C 3 H 6 
 
 (i) propaldehyde 
 
 Heat of combustion. 
 
 420,000 gram-units. 
 
 H,C CH, c; 
 
 (2) allylalcohol 442,000 gram-units. 
 
 H 2 C CH CH 2 OH 
 
 Assuming the correctness of these structural formulae, it 
 is seen that the propaldehyde molecule contains two tetra- 
 and one trivalent carbon atoms, and also one monovalent 
 oxygen atom, whereas the molecule of allylic alcohol con- 
 tains two tri- and one tetravalent carbon atoms, and also one 
 divalent oxygen atom. 
 
 88 The data of thermal chemistry furnish more numerous 
 examples of the existence of a connexion between greater 
 or less molecular energy and the distribution of the atomic 
 interactions in isomeric molecules. 
 
 Empirical formula 
 C 3 H 6 2 
 
 (i) ethyl formate 
 
 H/ 
 
 (2) methyl acetate 
 C> 
 
 H, 
 
 C 2 H, 
 
 O CH. 
 
 Heat of combustion. 
 
 390,000 gram-units. 
 
 395,000 gram-units. 
 
 If the structural formulae given are correct, then in each 
 of these molecules we have two tetra- and one trivalent 
 carbon atoms, and one mono- and one divalent oxygen 
 atoms; but the trivalent carbon atom in ethyl formate inter- 
 acts directly with two oxygen and one hydrogen atoms, and 
 in methyl acetate with two oxygen and one carbon atoms : in- 
 spection of the formulas will disclose other differences in the 
 distribution of the atomic interactions. 
 
 Alcohol and methylic oxide afford another example of the 
 relation we are discussing :
 
 I. 
 
 Empirical formula 
 C 3 H 
 
 CHAP. II. 88, 89] THERMAL WORK ON ISOMERISM. 177 
 
 Heat of combustion. 
 
 (i) alcohol, 330,000 gram- units. 
 
 Empirical formula H 3 C CH 2 OH 
 
 C H O 
 
 2 6 (2) methylic oxide 344,ooo gram-units. 
 
 H 3 C-0-CH 3 
 
 We have here two molecules each containing a pair of tetra- 
 valent carbon atoms, one divalent oxygen atom, and six 
 monovalent hydrogen atoms, but in one of the molecules 
 each carbon atom directly interacts with three hydrogen and 
 one oxygen atoms, while in the other the arrangement of 
 the atomic interactions is less symmetrical. 
 
 Other examples are afforded by the following groups of 
 compounds : 
 
 Heat of combustion. 
 
 (1) allyl alcohol 443,000 gram-units. 
 
 CH 2 .CH.CH 2 OH 
 
 (2) propaldehyde 426,000 
 
 CH,.CH 2 .CHO 
 
 (3) acetone 424,000 
 
 CH 3 .CO.CH 3 
 
 f(i) methyl formate 252,000 
 H . COOCH 3 
 , . 
 
 C H O. (2) acetic acid 210,000 
 
 ( CH 3 .COOH 
 
 /( i ) ethyl acetate 554,ooo 
 
 IH. CH 3 .CO.OCH 2 .CH 3 
 
 Empirical formula ] 
 
 C 4 H,O 2 (2) butyric acid 497,ooo 
 
 ( CH(CH 3 ) 2 .COOH 
 
 1(1) i : 4 hydroxybenzoic acid, 
 C H 4 (OH)C0 2 H 752,000 
 
 -r--- --,(2) ! : 3 754,000 
 
 1(3) i =2 759,ooo 
 
 89 The data are not sufficient to warrant any precise state- 
 ment as to the relations between greater or smaller quantities 
 of energy and molecular structure. It is possible that the 
 case of benzene and dipropargyl is typical, and that of two 
 M. C. 12
 
 178 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 isomeric molecules one of which belongs to the class of 
 ring-formed and the other to that of open-chain molecules, 
 the former always contains relatively less energy than the 
 latter. It is also possible that of two isomeric carbon com- 
 pounds the molecules of which belong to the open-chain 
 class, and in which n l < 2 4 + ... 2, that containing the greater 
 number of tetravalent carbon atoms contains the smaller 
 quantity of energy, provided that the distribution of the 
 atomic interactions is the same, or nearly the same, in the 
 two molecules. Or again it may be that when the actual 
 valencies of the atoms in two or more isomeric molecules 
 are the same, that molecule in which the atomic interactions 
 are distributed so as to produce the greatest degree of sym- 
 metry is marked by the smallest amount of energy 1 . But 
 we have as yet no accurate knowledge which may enable us 
 to test the applicability of these suggestions. 
 
 Even if it could be asserted (as seems possible in a few 
 cases) that this isomeride contains relatively less energy than 
 that, and is therefore more stable, the question would arise, 
 what do we mean by stability ? For although of two mole- 
 cules one may be the more stable as stability is measured by 
 thermal changes, it may nevertheless be impossible to say 
 that this molecule is possessed of greater chemical stability 
 than the other. But a discussion of the meaning and appli- 
 cation of the expression chemical stability, requiring as it 
 does a knowledge of the facts and theories of chemical affinity, 
 will find a fitter place in that part of this book which deals 
 with chemical kinetics 2 . 
 
 Inasmuch as variations in the physical properties of ma- 
 terial systems accompany variations in the energies of these 
 systems, it follows, if the two very general assumptions made 
 on p. 175 concerning the connexion between the energy and 
 the structure of isomeric molecules are granted, that physical 
 phenomena, other than thermal, may be expected to exhibit 
 variations in isomeric molecules. 
 
 1 This view is put forward tentatively by Carnelley, Phil. Mag. [5] 13. 180. 
 The data given on p. 177 for alcohol and methylic oxide are not in keeping with 
 this suggestion. 
 
 2 See Book n.
 
 CHAP. II. 89,90] PHYSICAL WORK ON ISOMERISM. 1/9 
 
 An attempt will be made in a future chapter to summarise 
 the more important physical phenomena between which and 
 molecular structure in general there is an established con- 
 nexion (Chapter IV.). Here I would only remark that the 
 researches of various chemists on the ' specific volumes ' of 
 liquid compounds seem to shew that the influence of any 
 atom on the 'specific volume' of a compound molecule is 
 dependent, not only on the nature and the actual valency 
 of that atom, but also on the nature of the other atom, or 
 atoms, between which and the given atom there is direct 
 interaction. It is also probable that while the influence 
 exerted by a polyvalent atom on the ' molecular refraction ' 
 of isomeric carbon-containing molecules is to a large extent 
 dependent on the actual valency of that atom, nevertheless 
 this influence is also sometimes connected with the nature of 
 the other atoms between which and the given atom there is 
 direct interaction in the molecule (j. Chapter IV. Sect. 2). 
 i Much is to be expected from researches into the phe- 
 nomena which occupy the border-land between chemistry 
 and physics. If the knowledge chemists already have of the 
 structure of molecules, meagre though that knowledge be, can 
 be supplemented by definite dynamical conceptions, obtain- 
 able in part by the methods of thermal chemistry, then we 
 may hope that chemistry will enter on a new stage of advance 
 as a branch of the science of matter and motion. It seems to 
 me that a most important step will be made by abandoning 
 the vague conception of atomic valency which finds ex- 
 pression in such phrases as 'single and double bonds,' ' satis- 
 faction of one, two, or more valencies/ and the like; with this 
 will go all those quasi-dynamical expressions, the offspring 
 of loose and slipshod ways of thinking, which have gathered 
 round that strange anomaly, a ' unit of affinity,' employed as 
 a variable standard for measuring nothing. 
 
 If it is decided that the valency of an atom expresses 
 the maximum number of other atoms between which and the 
 given atom there is direct interaction in any molecule, and 
 if it is agreed to measure this valency by the maximum 
 number of monovalent atoms (i.e. atoms of hydrogen, fluorine, 
 
 122
 
 180 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 chlorine, bromine, or iodine) which combine with the specified 
 atom to form a molecule, then we are put in possession 
 of a definite conception which may be applied to actually 
 occurring phenomena, and the application of which will 
 gradually lead to more precise knowledge regarding the 
 distribution of the atomic interactions in various molecules. 
 But at the same time that we are classifying molecules in 
 accordance with the valencies of their constituent atoms and 
 the distribution of the interactions of these atoms, i.e. in 
 accordance with their structure, we are also becoming more 
 impressed with the inadequacy of this classification ; we see 
 a vast field opening for investigation, we see that measure- 
 ments of losses or gains of energy are required, and that 
 determinations of many physical constants are called for. 
 We begin, I think, to perceive that this knowledge, when 
 gained, will supplement and not supplant that which is 
 already possessed by us, and that it will do this by leading to 
 an exact knowledge of the way in which the variations in 
 the energies of molecules are connected with changes in the 
 configurations and motions of the atoms which constitute 
 these molecules. 
 
 91 Granting that the definition of valency given by Lessen 
 furnishes a better working hypothesis than any other, we 
 must nevertheless admit that several compounds present 
 phenomena which seem to find no explanation in terms of the 
 hypothesis of isomerism which arises out of the notion of 
 valency, if that hypothesis is limited as was done in par. 75. 
 If the best studied examples of these exceptional compounds 
 are classified 1 it will, I think, be apparent ; that structural 
 formulae in keeping with reactions may be assigned to some 
 of the isomeric compounds mentioned provided we cease to 
 regard the conventional method of expressing valency by one 
 or more straight lines, as affording any quantitative measure- 
 ments, even relative measurements, of atomic interactions ; 
 that some cases of unexplained isomerism 2 are probably 
 
 1 See especially the article Isomerism in Watts's Dictionary [ist Ed.], Suppl. 
 m. (1881). 
 
 2 That optical properties are not always dependent on the structure of the
 
 CHAP. II. 91,92] GEOMETRICAL ISOMERISM. l8l 
 
 illustrations of modifications in properties being correlated 
 with variations in mutual actions between groups of molecules 
 rather than between the atoms constituting each molecule; 
 and that the remaining cases are true residual phenomena, 
 at present inexplicable in terms of the generally accepted 
 hypothesis but not therefore of necessity destructive of this 
 hypothesis. 
 
 92 One of the limitations almost universally placed on the 
 application of the molecular and atomic theory to explain 
 the facts of isomerism consists in simplifying the phenomena 
 to be explained by assuming that the atoms which form a 
 molecule are arranged in one plane. 
 
 Chemists have always recognised that a complete me- 
 chanical conception of the atomic structure of a molecule was 
 impossible unless the conception included the spatial arrange- 
 ment of the atoms which form the molecule. Attempts have 
 been made from time to time to formulate such a conception, 
 van't Hoff 1 , following Le Bel 2 , in 1875 tried to gain a definite 
 notion of the spatial arrangement of the atoms forming the 
 molecules of certain carbon compounds. Considering the 
 molecule CRRRR, where each R represents a different mono- 
 valent atom or atomic group, van't Hoff supposed the carbon 
 atom to be placed at the centre of a regular tetrahedron and 
 each monovalent radicle to be placed at one of the summits ; 
 two different tetrahedra would thus result, bearing to each 
 other the relation of an object to its reflected image, and 
 incapable of being superposed in whatever position they may 
 be placed. 
 
 The more immediate object of this conception was to 
 connect the power of rotating the plane of polarisation of a 
 ray of light possessed by certain compounds of carbon with 
 the atomic structure of the molecules of these compounds 
 (for more details s. Chap. iv. par. 416). Wislicenus has 
 
 molecule is shewn by the ease with which optically active amylic alcohol and 
 valeric acid are converted into the inactive alcohol, and acid, without change of 
 chemical properties. See Armstrong and Groves, Organic Chemistry, p. 449. 
 
 1 La Chitnie dans I ' 'space. 
 
 - Bull. Soc. Chim. 22. 337 ; 23. 395.
 
 1 82 ATOMIC AND MOLECULAR SYSTEMS. [BOOK 1- 
 
 recently extended the notions of van't Hoff and Le Bel 
 regarding the spatial arrangement of atoms ; he has en- 
 deavoured to shew that the greater number, if not all, of the 
 well-established facts of isomerism which lie outside of the 
 ordinary hypothesis find an explanation in terms of the geo- 
 metrical conception of the molecule suggested by van't Hoff 1 . 
 93 Although atomic valencies can be accurately determined 
 only by the examination of a certain class of gaseous mole- 
 cules, yet we may carry over the general conception of 
 limited direct atomic interactions from gaseous molecules and 
 apply it to the reacting atomic aggregates of solid and liquid 
 compounds. This is done by Wislicenus. Most of the phe- 
 nomena to be explained are exhibited by compounds of 
 carbon which cannot be gasified without decomposition. 
 Wislicenus assumes that in the molecules or atomic aggregates 
 of these compounds no carbon atom can directly interact 
 with more than four other atoms. 
 
 The geometrical conception which Wislicenus forms of the 
 molecule of a carbon compound is that each carbon atom is 
 situated at the centre of a regular tetrahedron, and that each 
 can directly interact with four other atoms or radicles situated 
 relatively to the carbon atom as the four summits of a regular 
 tetrahedron are situated relatively to the centre. A molecule 
 containing a pair of tetravalent ('singly linked') carbon atoms 
 of the general form C^g, where = amonovalent atom or radicle, 
 is represented by two tetrahedra with one pair of common 
 summits; a molecule containing a pair of trivalent ('doubly 
 linked ') carbon atoms C^ 4 is represented by two tetrahedra 
 with two pairs of common summits ; and a molecule con- 
 taining a pair of divalent (' trebly linked ') carbon atoms 
 C^ 2 is represented by two tetrahedra with three pairs of 
 common summits. Figures I, 2, and 3 represent these geo- 
 metrical conceptions. 
 
 In a molecule of the composition C^&j, where a^ repre- 
 
 1 ttber die raumliclie Anordnung der Atome In organischen Molekulen 
 und ilire Bestimmung in geometrischen-isomeren ungesattigten Verbindungen. 
 Konigl. Siichsischen Gesellschaft der Wissenschaften (inath-physische Classe) Bd. 
 l-l. i.
 
 CHAP. 1 1. 93] 
 
 GEOMETRICAL ISOMERISM. 
 
 sents two identical monovalent atoms or radicles, and # 2 repre- 
 sents two monovalent atoms different from a, chemical iso- 
 
 merism may arise because of different arrangements of the 
 atoms ; thus we may have 
 
 b a a a 
 
 (0 
 
 C C 
 
 c c 
 
 but the second of these isomerides may exist in two forms 
 which are geometrically different although structurally the 
 same, and either of these geometrical isomerides will bear to 
 the other the relation of an object to its image. The three 
 forms of C^/2 are represented in figs. 4, 5, and 6. 
 
 Fig. 4 . Fig. 5. Fig. 6. 
 
 1* 
 
 Similarly a molecule of the composition C 2 
 chemical isomerism ; 
 
 b a a 
 
 C C 
 
 and 
 
 \ 
 
 C C : 
 
 ' \ 
 
 may shew
 
 184 
 
 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 but the second isomeride may also exhibit geometrical iso- 
 merism. A molecule of the form C^abcd may exist in three 
 isomeric modifications, each of which may exist in two geo- 
 metrically different forms. Figs. 7 to 15 represent these 
 isomerides. 
 
 Fig. 7. Fig. 8. Fig. 9. 
 
 Fig. 10. 
 
 Fig. 13- 
 
 Fig. 14. 
 
 Fig. 15- 
 
 The terms axially symmetric and plane-symmetric are used 
 to distinguish geometrical isomerides of the composition 
 Cotfj^. A molecule the configuration of which is shewn in fig. 
 1 6 is called by Wislicenus axially symmetric, because the 
 atoms a and b are represented as arranged symmetrically 
 about an axis passing between the two pairs of common
 
 CHAP. II. 93, 94] GEOMETRICAL ISOMERISM. 185 
 
 summits ; the geometrically isomeric molecule shewn in fig. 
 17 is called plane-symmetric because the atoms a and b are 
 
 Fig. 16. Fig. 17. 
 
 it 
 
 represented as arranged symmetrically about a plane passing 
 through the two pairs of common summits. 
 
 94 Wislicenus developes these conceptions chiefly for mole- 
 cules containing two carbon atoms. When the molecule 
 contains a pair of divalent ('trebly linked') carbon atoms 
 geometrical isomerism cannot occur; when the molecule 
 contains a pair of trivalent ('doubly linked') carbon atoms geo- 
 metrical isomerism may occur in the manner illustrated in 
 the preceding paragraph ; when the molecule contains a pair 
 of tetravalent (' singly linked ') carbon atoms geometrical iso- 
 merism may occur by the rotation of one part of the molecule 
 relatively to the other. This last kind of isomerism is illus- 
 trated by figs. 1 8 and 19. The cause of this rotation of one part 
 
 Fig. 1 8. 
 
 Fig. 19. 
 
 of a molecule containing a pair of tetravalent carbon atoms 
 is supposed by Wislicenus to be the affinities 1 of the atoms 
 
 1 The term affinity is here used to express the unknown property of atoms by 
 reason of which they chemically interact.
 
 186 ATOMIC AND MOLECULAR SYSTEMS. [BOOK 1. 
 
 other than carbon ; the configuration of the molecule tends 
 to become that in which the atoms with the largest affinities 
 are situated nearest to each other. 
 
 But besides the affinities of the atoms, heat will probably 
 produce rotation of the parts of a molecule containing only 
 tetravalent carbon atoms. The most stable atomic configura- 
 tion will be that caused by the mutual atomic affinities ; but 
 besides this, some configurations will probably exist, and will 
 likely increase in number as temperature rises, which con- 
 figurations are caused by the action of heat ; at high tem- 
 peratures therefore a given compound will probably be 
 composed for the greater part of molecules the atomic con- 
 figuration of which is determined by the atomic affinities, but 
 other and less stable configurations will also be present. 
 
 If a molecule containing a pair of divalent ('trebly linked') 
 carbon atoms combines with two monovalent atoms of the 
 same kind, or of different kinds, only one geometrical isomer- 
 ide can be produced. If a molecule containing a pair of 
 trivalent ('doubly linked ') carbon atoms, one or both of which 
 atoms is in direct union with two monovalent atoms of the 
 same kind, combines with two new atoms two geometrical 
 isomerides may be produced ; in some cases the isomerides 
 so produced will contain an asymmetric carbon atom, i.e. 
 an atom in direct union with four different atoms or groups. 
 Thus if the original molecule is of the form 
 
 a a 
 
 \ / 
 
 C C 
 
 / \ 
 a b 
 
 and the new molecule is of the form 
 
 a a 
 
 \ / 
 a C C b, 
 / \ 
 
 c c 
 
 the italicised C represents an asymmetric carbonation. In 
 such a case the compound thus produced should exhibit optical 
 
 1 See Chap. iv. par. 146.
 
 CHAT. II. 94- 95] GEOMETRICAL ISOMEKISM. 
 
 18; 
 
 activity, if the hypothesis of van t Hoff is adopted (s. Chap. IV.) 
 But such reactions are sometimes known to produce com- 
 pounds which do not shew optical activity. Wislicenus sup- 
 poses that in these cases the two geometrical isomerides are 
 produced in equal quantities, and that as one is dextrorota- 
 tory and the other laevorotatory the compound as a whole is 
 optically inactive. The foregoing statements are rendered 
 clearer by examining figs. 20 to 27. 
 
 Fig. 20. 
 
 Fig. 21. 
 
 Fig. 23- 
 
 Fig. 24. Fig. 25. Fig. 26. Fig. 27. 
 
 95 Wislicenus developes these conceptions and applies them 
 to many cases of isomerism which do not find an explanation 
 in terms of the hypothesis of valency when it is limited by 
 the condition that the atoms which form a molecule must be 
 represented as arranged in a single plane. 
 
 Thus to take the cases of fumaric and maleic acids, 
 C 2 H 2 (CO 2 H) 2 . Fumaric acid is probably the axially sym- 
 metric, and maleic acid the plane-symmetric, isomeride ; figs. 
 28 and 29 represent these compounds. When malic acid 
 C 2 H 3 (OH)(CO 8 H) a is heated to about 150 water is separated 
 and fumaric acid is formed; this change is represented in
 
 1 88 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 figs. 30 and 31. But at 170 180 malic acid is partly 
 changed to maleic anhydride ; if we suppose that rise of 
 
 Fig. 29. 
 
 COOJl 
 
 Fig. 30. 
 
 Fig. 31- 
 
 temperature causes rotation of the parts of the molecule of 
 malic acid with the production of a geometrical form less 
 stable than the original form, and that water is then separated 
 from this less stable form, we can explain the production of 
 maleic anhydride along with fumaric acid by heating malic 
 acid. Figs. 32 and 33 (taken with fig. 30) represent this process. 
 Fig. 32. Fig. 33. 
 
 Maleic acid is changed almost wholly to fumaric acid by 
 interacting with hydrochloric or hydrobromic acid. Wis-
 
 CHAP. II. 95] GEOMETRICAL ISOMERISM. 
 
 I8 9 
 
 licenus supposes that an additive compound is produced, 
 that rotation of the parts of this molecule then occurs caused 
 by the affinities of the atoms H and Br and the group 
 COOH, and that HBr is then split off; the mechanism of 
 the change as thus imagined is shewn in figs. 34 to 37. 
 
 Fig- 34- Fig. 35. 
 
 COOH 
 
 Fig- 36- 
 
 Fumaric acid combines with bromine forming dibromo- 
 succinic acid, which when boiled with water yields hydro- 
 bromic and bromomaleic acids. Maleic acid combines with 
 bromine forming isodibromosuccinic acid, and this when 
 boiled with water yields hydrobromic and bromofumaric 
 acids. These changes are easily explained in terms of Wisli- 
 cenus' conception, by supposing that in each case an additive 
 compound is formed, that the atomic affinities then cause 
 rotation of the parts of the molecules, and that hydrobromic 
 acid is then split off. Figs. 38 to 45 represent the changes. 
 
 Other reactions of fumaric and maleic acid are considered 
 and explained by Wislicenus. The only reaction of these 
 acids which is inexplicable in terms of the geometrical hypo- 
 thesis of isomerism is that of bromine with acetylene di-
 
 1 9 o 
 
 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 carboxylic acid, C 2 (CO 2 H) 2 , whereby dibromofumaric acid is 
 said to be produced. The geometrical hypothesis requires 
 
 Fig. 38- 
 
 Fig. 40. 
 
 the production of dibromomaleic acid. But Wislicenus' ex- 
 periments have proved that hydrobromic acid is always pro- 
 duced in this reaction, and that if care is taken to limit the 
 yield of this acid as much as possible, some dibromomaleic 
 acid is produced. The production of dibromofumaric acid 
 is easily explained by the interaction of the hydrobromic 
 and bromomaleic acids produced in the principle reaction.
 
 CHAP. II. 95, 96] RECAPITULATION. 191 
 
 There can be no doubt as to the ingenuity of the ex- 
 tension of van't HofFs geometrical conception made by Wis- 
 licenus. One point which appears to me to be gained by 
 this hypothesis is the possibility of keeping separate the two 
 conceptions of atomic valency and atomic affinity, and of 
 using both in explaining the configurations and chemical 
 properties of molecules. 
 E)6 We have thus found that to trace the connexions between 
 the compositions and the properties of changing material 
 systems has always been regarded as the fundamental problem 
 of chemistry. Attention has sometimes been almost confined 
 to the composition of substances forming such systems, at other 
 times the properties of the systems and their components 
 have been regarded as chiefly important. We found that as 
 chemistry advanced it became necessary to know more than 
 the mere elementary composition of bodies ; having gained 
 the atom and the molecule, chemists were soon convinced 
 'that the arrangement of the same atoms might vary, and that 
 properties might therefore be correlated not only with atomic 
 composition but also with atomic configuration. We traced 
 this conception through the dualism of Berzelius and the 
 unitary system of Dumas, Laurent, Gerhardt and others, 
 through the hypothesis of compound radicles and that of 
 types, to the time when Frankland and Kekul6 gave it 
 greater precision by arranging the elementary atoms in 
 groups according to the maximum number of other atoms 
 with which each was found to combine. 
 
 But we saw that the expression equivalency, or valency, 
 of atoms gradually came to be used in a loose and inexact 
 manner. We found that the comparison of monovalent with 
 divalent, &c. atoms, when unchecked by accurate dynamical 
 knowledge, led to the belief that the terms in question ex- 
 pressed in some vague way quantitative measurements of 
 interatomic forces, and to the conclusion that, inasmuch as 
 one divalent atom could directly bind to itself two other 
 atoms, while one monovalent atom could directly interact 
 with only a single other atom, in a molecule, therefore the 
 divalent atom was capable of exerting twice as much force
 
 192 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 as the monovalent atom. The latter part of the foregoing 
 sentence may I think be taken as fairly representative of the 
 loose and slipshod way in which dynamical language has too 
 often been used in chemistry. 
 
 We found that attempts were made to build a general 
 conception of atomic valency on a shifting quasi-dynamical 
 foundation ; but the account given in this section of Lossen's 
 criticisms of the expressions 'a bond,' 'a valency,' 'a unity of 
 affinity,' &c. has I think been sufficient to shew how inexact, 
 while apparently precise, and how narrow, while apparently 
 far-reaching, the conception in question really is. 
 
 The objections raised against the atomic theory in recent 
 years by some chemists, who nevertheless made free use of 
 the essentially atomic conceptions of modern chemistry, led, 
 it seems to me, to a looseness of thinking about atoms, mole- 
 cules, and equivalents, which has done no little harm. Parts 
 by weight were spoken of as if the expression were synony- 
 mous with atom; equivalents were regarded as acting and 
 reacting with one another ; there appeared to be a possibility 
 of chemistry retracing her steps to the time when no precise 
 meaning was attached to any of the terms atom, molecule, 
 combining weight, equivalent, but each was used as nearly 
 synonymous with the others. From the possibility of such 
 retrogression we have been saved by the general advance of 
 physical science. As the molecular theory of matter became 
 more precise and its applications more far-reaching, it was 
 impossible for chemists to employ conceptions essentially 
 molecular and atomic and at the same time to express 
 chemical changes in a notation based on the notions of a 
 pre-molecular era. It became necessary to choose definitely 
 between the atom and the equivalent, and the great body of 
 chemists has certainly chosen the former. 
 
 But as soon as attempts to found a conception of chemical 
 actions on the basis of equivalents were abandoned, it was 
 seen that the conception of equivalency might be retained 
 and applied to the elementary atoms. To keep distinct the 
 conceptions implied in the terms equivalent and atom, and at 
 the same time to arrange the atoms in equivalent groups, is
 
 CHAP. II 96] RECAPITULATION. 193 
 
 one of the problems of modern chemistry. On this distinction 
 and on this resemblance is based the molecular explanation 
 of isomerism. We have found that the study of isomerism 
 has done much to render precise the conception of the mole- 
 cule as a structure with properties dependent on the nature, 
 the number, and the arrangement, of the constituent atoms. 
 
 We endeavoured to subdivide the conception expressed in 
 the words ' arrangement of atoms in a molecule ' into parts, 
 and to demonstrate by illustrations the existence of a con- 
 nexion between each of these parts and the properties of the 
 molecule. These illustrations led to clearer notions concern- 
 ing the valencies of atoms, and the meaning of structural 
 formulae: these formulae we regarded as expressing the actual 
 valencies of the atoms in the molecule, i.e. the number of atoms 
 directly acting on and acted on by each atom, and as ex- 
 pressing also the distribution of the atomic interactions, i.e. 
 the nature of the atoms in direct mutual connexion ; but we 
 tried not to attach any quantitative meaning to the symbols 
 used for expressing atomic valencies and the distributions of 
 atomic interactions. We also glanced at the geometrical con- 
 ception by which van't Hoff and Wislicenus have sought to 
 picture the connexion between the properties of isomeric 
 molecules and the configurations of the atoms which form 
 these molecules. 
 
 The hypothesis of valency as thus used leads to dynamical 
 conceptions but regards these as outside its sphere : it points 
 the way along which progress will be made. Attempts must 
 be made to apply thermal, optical, and other physical, methods 
 of research to the investigation of chemical problems ; thus 
 we may hope to gain clear and precise knowledge regarding 
 the connexion between the structure and the stability of mole- 
 cules, in so far as the latter is measured by variations in the 
 quantities of energy associated with different molecules. 
 
 APPENDIX TO SECTION IV. 
 
 To have given a detailed account of Lossen's criticisms of the 
 
 generally accepted views regarding 'valencies' or 'units of affinity' in 
 
 the text of the section on isomerism, would have involved too great 
 
 an interruption of the main argument of that section. But as Lossen's 
 
 M.C. 13
 
 194 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 criticisms seem to me of great importance I propose to give some account 
 of them here. 
 
 The many and varied hypotheses concerning valency set forth by 
 chemists of acknowledged authority may be divided, says Lessen, into 
 three groups : 
 
 I. Those hypotheses which regard 'an affinity' as a definite quantity 
 of matter, or as an action of some kind proceeding from a definite 
 quantity of matter. 
 
 II. Those which regard 'an affinity' as a part of an atom, or at 
 least as something connected with a part of an atom. 
 
 III. Those which regard the 'affinities' of an atom as definite 
 forms of motion of the atom. 
 
 I. Erlenmeyer 1 has developed the conception of ' Affinivalencies? 
 He states, as a rule without exceptions, that "in all chemical combi- 
 nations a constant quantity of one element always attracts a constant 
 quantity of another." These constant quantities are the ' affinivalencies ' 
 of the elements: one affinivalency of element a always binds to itself 
 one affinivalency of element b. The affinivalency of carbon = 3, of 
 oxygen = 8. Now in CO 2 we have 3 parts by weight of carbon com- 
 bined with 8 of oxygen, but in CO the same amount of carbon with 
 only 4 parts by weight of oxygen ; Erlenmeyer's general law does not 
 therefore always hold good. If it be said that a constant quantity of 
 one element attracts (not combines with) a constant quantity of another, 
 then, as in CO 2 6 parts by weight of carbon attract 16 of oxygen, we 
 must suppose that in CO 16 parts by weight of oxygen are attracted 
 by 6 of carbon, and that the remaining 6 of carbon have no attractive 
 action on the oxygen. 
 
 Atoms and relative quantities of matter are compared by Erlenmeyer ; 
 but relative quantities do not attract each other. In the molecule CO 
 there is one atom of carbon and one atom of oxygen, and these atoms 
 attract one another; half an atom cannot attract because it has no 
 existence. The hypothesis that an atom is non-homogeneous, although 
 indivisible, might be made, but is not made, by Erlenmeyer. If an 
 equivalent is regarded as a constant quantity, this quantity attracts 
 sometimes one, sometimes two (or more) equivalents of other elements. 
 The molecule CH 4 is composed of one atom of carbon and four atoms 
 of hydrogen, we may say that 3 parts by weight of carbon here attract 
 i part by weight of hydrogen ; so in CC1 4 it may be said that 3 parts 
 of carbon attract 35-5 parts of chlorine. But in CH 3 C1 12 parts of 
 carbon attract 3 parts of hydrogen and 35-5 parts of chlorine ; in place 
 of 12 parts of carbon we may, if we choose, say 9 + 3 parts, just as we 
 might say that 7 + 5 = 12, or Vi44=i2; but we cannot say that 9 parts 
 
 1 For references to the work of the various chemists mentioned, see Lessen, 
 Annalen, 204. 265 et seq.
 
 CHAP, ii.] LOSSEN'S CRITICISM OF ' BOND' HYPOTHESIS. 195 
 
 of carbon attract 3 parts of hydrogen and the remaining 3 parts of 
 carbon attract the 35-5 parts of chlorine. If we suppose the carbon 
 atom to be perfectly homogeneous, then the whole atom interacts with 
 the chlorine atom and with each of the hydrogen atoms ; if we suppose 
 that the atom of carbon is possessed of a structure, it remains to 
 explain in what respect one part of the atom differs from the other 
 parts : but a part of an atom is not the same thing as a fraction of the 
 relative weight of an atom. 
 
 Hofmann speaks of 'an affinity' as a force proceeding from a con- 
 stant mass of an element, which mass he regards as the equivalent and 
 defines as 'the minimum atom-binding quantity' of the element. He 
 nevertheless uses an equivalent as a varying quantity. By an arbitrary 
 choice of certain values for the equivalents of the elements it is possible 
 that the number obtained by dividing the atomic weight by the equiva- 
 lent weight of any element should be the same as the number expressing 
 the maximum number of hydrogen atoms which can be bound by one 
 atom of the given element. 
 
 L. Meyer also speaks of the action of quantities by weight of one 
 element on atoms of another element. In one place he defines equiva- 
 lent quantities of elements as those quantities which are able to bind 
 to themselves, directly and without the intervention of a third substance, 
 equal quantities of other substances. We should expect 16 parts by 
 weight of oxygen to be equivalent to 12 parts by weight of carbon, and 
 to 14 parts by weight of nitrogen, because 16 parts of oxygen directly 
 bind 16 of oxygen in O 2 , 14 of nitrogen in NO, and 12 of carbon in 
 CO ; but Meyer supposes two free affinities in the last named molecule, 
 i.e. he supposes that * parts of carbon bind 16 parts of oxygen, although 
 the molecule CO contains one indivisible atom of carbon and one in- 
 divisible atom of oxygen. 
 
 Those hypotheses in which 'affinities' are regarded as constant 
 weights of matter, or as actions proceeding from constant weights, arise, 
 according to Lessen, from not sufficiently marking the distinction be- 
 tween the equivalent and the atom. Equivalent, or combining, weights 
 are relative weights of divisible masses ; atomic weights are relative 
 weights of indivisible masses. If the atomic hypothesis is adopted we 
 must regard atomic weights as relative weights of mutually reacting 
 bodies ; but equivalent weights, in so far as they differ from atomic 
 weights, are relative weights of imagined sums, or fractions, of these 
 bodies. Bodies whose relative weights are equal to these equivalent 
 weights do not mutually react in molecules. To find equivalents, parts 
 by weight should be compared with parts by weight, or atoms with 
 atoms. 
 
 II. Besides the hypothesis of 'affinivalencies' already referred to, 
 Erlenmeyer also speaks of mutual actions between atoms as occurring 
 at certain points of these atoms. This may mean either that contact 
 
 132
 
 196 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 (not of course absolute contact) between the reacting atoms is made 
 at these points, or that mutual atomic action occurs only when these 
 attracting points coincide. The attracting points must be considered 
 as qualitatively different from the rest of the atoms. The form of poly- 
 valent atoms must be such that several points of one can touch the 
 same number of points of another: the positions of the points must be 
 such that when some of these points are in contact it is not necessary 
 that all should be in contact. To fulfil these conditions without sup- 
 posing the form of the atoms, or at any rate the positions of the points, 
 changeable, is exceedingly difficult. This hypothesis of Erlenmeyer 
 tends to foster the notion of an attractive force proceeding from different 
 parts of elementary atoms ; Kekule"'s graphic formulae do not, probably, 
 imply this conception, but these formulas may be, and have been, used 
 as if this conception were true. 
 
 A qualitative difference between parts of an atom can only mean 
 that some parts are chemically active while others are chemically inactive. 
 If the inactive parts are composed of imponderable matter then each 
 -valent atom must be made up of n atoms; we thus arrive at atomic 
 weights different from those on which the science of chemistry at present 
 rests. If the inactive parts consist of ponderable matter, then in the 
 case of action between different atoms we have action through the ether, 
 but in the case of action between parts of the same atom we have action 
 through ponderable chemically inactive matter. In either case it appears 
 that the notion of atom must be very different from that at present 
 adopted, and, it would seem, necessarily adopted if facts are to be 
 explained. 
 
 But it may be supposed that the active parts of the atom are in 
 a different electrical condition from the inactive parts. If electricity 
 be a form of motion, then some parts of an indivisible atom must be 
 supposed in motion while others are not ; if electricity be a fluid, then 
 we have a material difference, arising from the partial fixation of this 
 fluid, between the active and inactive parts of the atom. Both of these 
 hypotheses are opposed to the fundamental conception of atom 1 . 
 
 Michaelis has supposed that the attractive force of an atom is exerted 
 in certain fixed directions only. On this hypothesis a straight line 
 joining two atoms which are directly bound together may be regarded 
 as expressing the direction of the mutually exerted force; an -valent 
 atom has n such directions. If this atom is directly bound to fewer 
 than n atoms, say to n - x atoms, then the mutual action is exerted 
 in n x directions. Lessen expresses his general agreement with this 
 interpretation of the hypothesis of Michaelis. But if that chemist sup- 
 
 1 This criticism is rather weak : we know too little as to what electricity is to 
 hazard such criticism as this ; besides, Helmholtz has shewn that there is probably 
 a close and definite connexion between the valency of an atom and the electrical 
 charges on that atom ; see Book n.
 
 CHAP. IL] LOSSEN'S CRITICISM OF * BOND' HYPOTHESIS. 197 
 
 poses that to every atom, regarded as a point, there are always attached 
 a fixed number of such 'lines of force,' then it is asked 'on what does 
 the atom act when it is bound to less than its maximum number of 
 other atoms?' 
 
 The objection urged to van't Hoff's form of the hypothesis now being 
 discussed, is, that by this chemist the 'affinities' of an atom are imagined 
 as arranged in a definite form in space ; but as we cannot define an 
 'affinity,' much less can we assign geometrical figures to the arrange- 
 ment of these 'affinities' 1 . 
 
 III. L. Meyer supposes that there is one position at which a mono- 
 valent atom during its vibration can combine with another atom to 
 form a stable compound, that there are two positions at which a divalent 
 atom can combine with another atom, and so on. In the molecule NH 3 
 we have one trivalent and three monovalent atoms; the nitrogen atom 
 swings through three positions at each of which it can take up one 
 hydrogen atom. In the molecule OH 2 the divalent oxygen atom swings 
 through two such positions. In the molecule NO it appears as if the 
 three positions of possible combination passed through by the triad 
 nitrogen atom must also be touched by the path of the diad oxygen 
 atom, but if so the oxygen atom may, in some circumstances, be 
 trivalent. 
 
 The results of O. E. Meyer's physical and dynamical investigation of 
 the forms of molecules are not in harmony with this view of L. Meyer. 
 The form of a molecule would appear to be dependent more on the 
 number of the constituent atoms than on the valencies of these atoms ; 
 but on L. Meyer's hypothesis the nature of the path of the atoms swinging 
 in the molecule must condition the form of the molecule, and the nature 
 of this path is itself conditioned by the valencies of the atoms. 
 
 Kekule' has advanced hypotheses as to the motion of atoms within 
 molecules, but these hypotheses are not sufficiently definite to admit 
 of detailed criticism. Lessen however objects to applying to the motion 
 of atoms within molecules the conceptions which arise from a study of 
 the motion of molecules in a confining vessel. If the atoms composing 
 a mass of hydrogen molecules undergo mutual collisions, why, when 
 they have separated a certain distance from one another, is the direction 
 of their motion changed until a second collision occurs? There is no 
 confining molecular wall answering to the sides of a containing vessel. 
 If it be supposed that the atoms in molecule a enter into collision with 
 the atoms in molecule b or c, then this is equivalent to asserting that 
 a mass of hydrogen is composed not of diatomic, but of monatomic 
 molecules 2 . 
 
 1 Van't Hoffs hypothesis as recently developed by Wislicenus is discussed in 
 pars. 92 to 95. 
 
 2 Here again, I think Lessen carries his criticism too far. The methods of 
 molecular enquiry are necessarily statistical; a mass of hydrogen may contain
 
 198 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 Among the various developments of the bond-hypothesis of valency 
 not mentioned in the text, is that which concerns itself with the question 
 whether all the bonds of a polyvalent atom are of equal value, or 
 whether one maybe 'stronger' than another. If the criticism applied 
 to the subject of bonds generally is just, it follows, I think, that the 
 question alluded to is meaningless; but as it has been hotly disputed 
 about it may be well briefly to consider it here. 
 
 It is assumed in the bond-hypothesis that the so-called affinities of 
 atoms attract or satisfy one another, and hence those affinities of one 
 atom which are not satisfied by affinities of another must be satisfied by 
 other affinities of the atom itself. No molecule, it is sometimes said, 
 can contain an odd number of atoms of uneven valency. This outcome 1 
 of Gerhardt's 'law of even numbers' (see ante, chap. I. p. 84) is how- 
 ever contradicted by the existence of the molecules I, NO, NO 2 , C1O 2 , 
 WC1 5 , VC1 4 or VOC1 3 , and cannot therefore be accepted as a statement 
 of facts, unless indeed the valency of an atom is a number susceptible 
 of arbitrary variation. That the maximum valency of each atom is 
 fixed is generally admitted. One school however holds that (e.g.) a 
 tetrad atom is always tetrad ; another school asserts that a tetrad may 
 function as a diad atom. The followers of the first school maintain 
 that in the molecule CO, for instance, the carbon atom is tetravalent, 
 but two of its affinities are mutually satisfied; the opponents of this 
 view say that in CO the carbon atom is divalent, and that the other 
 pair of bonds is latent. The dispute has been wholly a battle about 
 words. Whether the two bonds are latent, or are mutually satisfied, 
 as Lessen remarks, 'zwei und zwei geben dock immer vier.' 
 
 But if always existent, are the bonds always of equal value ? Are 
 the two pairs of bonds which hold the two oxygen atoms to the carbon 
 atom in the molecule CO 2 equal in value to twice the pair of bonds 
 by which one oxygen atom is held to a carbon atom in the molecule 
 CO? 
 
 Now if we wish to compare things we must have a standard; 
 but I think sufficient facts have been enumerated to shew that no 
 standard exists in terms of which the expression 'value of a bond' may 
 be stated. Even if the valency of an atom is regarded as expressing the 
 total number of parts into which the chemical energy of that atom is 
 divisible, this must mean that the energy is divisible when there is mutual 
 action between the given atom and other atoms in a molecule. Thus, 
 assume for a moment that the chemical energy of an atom of carbon is 
 divisible into four parts, it does not follow that each part represents a 
 fourth of the whole energy, or always represents the same portion of 
 
 many free atoms (or monatomic molecules) and yet for all practical purposes 
 behave as if composed entirely of diatomic molecules. 
 
 1 The statement is sometimes put in this form ; ' the sum of the valencies, or 
 affinities, of the atoms in any molecule is always an even number.'
 
 CHAP. II. 97] MOLECULAR COMPOUNDS. 199 
 
 that energy. To take an illustration; in the stable molecule CO we 
 must suppose, on this hypothesis, that the whole of the chemical energy 
 of the carbon atom is employed in the transaction symbolised by the 
 formula C O ; again, in the molecule O C S the whole of the energy 
 of the carbon atom is employed, but the energy represented by O - C 
 is probably different from that represented by C S, and the sum of 
 these is probably different from that represented by the expression 
 O C O. The results of thermal measurements made by Thomson 
 (see par. 84, also post, par. 134) render it fairly certain that the quantity 
 of energy which changes form during the process symbolically expressed 
 as 'linking a pair of carbon atoms by a double bond' bears no simple 
 relation to the quantity of energy which changes form when 'a pair of 
 carbon atoms is linked by a single bond.' The number of possible ways 
 in which the energy is distributed is, on this hypothesis, measured by 
 the valency of the atom ; the amount of the energy employed in any 
 atomic transaction depends on the nature of the atom or atoms between 
 which and the given atom there is mutual intramolecular action 1 . 
 
 Even if we adopt this, the most dynamical, view of valency that can 
 be adopted with any safety, the controversy concerning equal and un- 
 equal bonds is seen to be a mere logomachy 2 . 
 
 SECTION V. Molecular Compounds. 
 
 97 In the preceding sections we have learned that some com- 
 pounds can be gasified without decomposition while others 
 are separated by heat into two or more constituent parts. 
 
 The conception expressed in the term molecule can be 
 applied in strictness to the former compounds only, and the 
 fundamental notions regarding the structure of molecules 
 must be gained by the study of such gasifiable compounds. 
 
 1 For a fuller working out of this way of regarding valency see Claus, Ber. 
 14. 432. 
 
 2 It is sometimes said that the hydrogen atoms in the molecule of benzene are 
 of equal value, but when one of these atoms is replaced by a radicle the remaining 
 five are of different values relatively to the radicle introduced into the molecule. 
 To make such a statement as this, it seems to me, is to employ the term value in 
 too loose and vague a way. All the hydrogen atoms in a molecule of a mono- 
 derivative of benzene are monovalent, and therefore of equal value so far as 
 'proportion in exchange' for chlorine, bromine &c. goes. What appears to be' 
 meant by the statement in question is, that more than one mono-derivative 
 (chloro- bromo- or generally X - derivative) can be obtained from the mole- 
 cule CgHjA'; but this is simply a special illustration of the general proposition 
 that the properties of compounds are not wholly dependent on the valencies of 
 their constituent atoms.
 
 2OO ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 But, it may be asked, is there a distinction of kind, or 
 only one of degree, between those compounds which can be 
 gasified, and those which separate into parts when they are 
 heated ? This question has been provocative of much dis- 
 cussion. Kekule 1 and others have employed the term atomic 
 compounds to express those compounds which can be vaporised 
 without decomposition, and they have contrasted these with 
 molecular compounds, meaning thereby those compounds which 
 separate into two or more parts when heated. 
 
 This division of compounds has played an important part 
 in the development of the hypothesis of valency. Kekule 
 has always insisted that facts regarding atomic compounds 
 can alone be employed as data for rinding the valencies of 
 elementary atoms ; his opponents have retorted by de- 
 manding a definition of molecular as opposed to atomic 
 compounds, and by shewing that every proposed definition 
 fails when applied to actual phenomena. 
 
 But it is not so much as it concerns the hypothesis of 
 valency that the distinction implied in the words atomic and 
 molecular compounds ought, I think, to be insisted on ; if the 
 arguments put forward in the preceding section are of any 
 value, we must agree to confine what may be called the non- 
 geometrical hypothesis of valency to gaseous compounds. 
 There are however many and varied phenomena, all more 
 or less belonging to the borderland between chemistry and 
 physics, which may conveniently be considered under the 
 heading of molecular compounds. 
 
 i And I would begin by admitting that no strict definition 
 of molecular, as opposed to atomic, compounds, can be given, 
 which shall enable us to assign every disputed case to its 
 proper class. A substance may yield a vapour which is 
 chemically homogeneous below a certain temperature but 
 heterogeneous above this temperature ; we cannot fix a limit- 
 ing temperature for each group of compounds and say, that 
 those which yield vapours homogeneous above this tempera- 
 ture are atomic, while those in the vapour of which dissocia- 
 tion begins below the temperature-limit are molecular. 
 
 1 See his Lehrbuch, Vol. I. pp. 142, 145, 443, c. : also Compt. rend. 58. 510.
 
 CHAP. II. 98, 99] MOLECULAR COMPOUNDS. 2OI 
 
 I would again urge the importance of remembering that 
 when we say that' a gas consists of molecules of this or that 
 composition, we refer and can refer only to the average com- 
 position of the gas ; many molecules may be dissociated into 
 two or more chemically different kinds of matter, other 
 molecules may be aggregated into complex groups. Even in 
 an elementary gas at moderate temperatures some atoms and 
 many groups of molecules may be present at any moment : 
 the values obtained for the specific gravities of gaseous bro- 
 mine and iodine, and for gaseous nitrogen dioxide, stannous 
 chloride, and acetic acid well illustrate the gradual nature of 
 the passage from one average molecular state to another 1 . 
 99 Some chemists would recognise the existence of molecular 
 compounds in mixtures of two or more liquids, and in solu- 
 tions of salts, and of gases (e.g. CO 2 ), in water. In such cases 
 the proportions in which the substances are supposed to be 
 combined are very variable. It cannot be correct to speak 
 of a molecule of the mixture of alcohol and water, or of a 
 molecule of the solution of salt in water, although it may be 
 permissible to regard these liquids as containing groups of 
 molecules of alcohol and water, or of salt and water. 
 
 As examples of bodies which seem to hold a place between 
 definite chemical compounds and mere mixtures may be noted 
 the products of the fusion together of sulphur and selenion. 
 Rathke 2 fused together sulphur and selenion, dissolved the 
 fused mass in carbon disulphide, and fractionally precipitated 
 by gradual evaporation ; he then redissolved the various pre- 
 cipitates, and again fractionated. The precipitates all con- 
 sisted of monoclinic crystals composed of sulphur and selenion 
 (neither element exhibiting the properties which characterise 
 it in the free state) but varying in quantitative composition 
 between the limits expressed by the formula:; SeS 4 and Se 4 S. 
 Rathke thinks it possible that elements which are chemically 
 very analogous may combine in varying proportions to pro- 
 duce isomorphous bodies. 
 
 There are other actions wherein small changes in physical 
 
 1 See par. 99, pp. 203, 1067. 
 
 s Ber. 18. 1534. See also Lehmann, Zeitschr.f, physikal. Chcmie, 1. 15.
 
 202 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 conditions suffice to cause changes in the relative quantities of 
 substances combined in definite proportions ; for instance, 
 when the substance containing water and sodium phosphate 
 in the proportion Na 2 HPO 4 : I2H 2 O is heated, it very readily 
 loses water and becomes Na 2 HPO 4 . 7H 2 O. If by molecular 
 compound is meant, a loose combination in definite pro- 
 portions of two or more chemically different kinds of matter 
 so as to produce another kind of matter characterised by 
 fairly definite properties but readily undergoing change, then 
 we may certainly say that Na 2 HPO 4 . i2H 2 O is a molecular 
 compound. 
 
 Once more, compounds exist which are characterised by 
 very definite properties, but which, when heated, undergo 
 gradual change into two or more substances, the original 
 compound being gradually re-formed as the vapours cool. 
 Thus the formula PC1 5 expresses the elementary composi- 
 tion of an undoubted chemical compound ; when this solid 
 substance is heated it vaporises, but the vapour can be 
 proved by experiment to contain molecules of PC1 3 and C1 2 , 
 along with undecomposed PC1 5 . The following numbers 
 shew the gradual progress of the change which occurs : 
 
 Calculated sp. gr. of gaseous PC1 5 =7'2 IF * 1 
 
 gas consisting of PC1 3 + C1 2 = 3-6) La 
 
 Number of molecules 
 
 Temperature. Sp. gr. of vapour. decomposed * per too 
 
 molecules of PClj. 
 
 182 5'08 417 
 
 IQO 4-99 44-3 
 
 200 4-85 48-5 
 
 230 4-30 67-4 
 
 250 4-00 80-0 ' 
 
 274 3-84 87-5 
 
 288 3-67 96-2 
 
 300 3-65 97-3 
 
 1 Calculated by means of the formula p= = where /= number of 
 
 molecules decomposed, D= observed sp. grav. of gas, d= theoretical sp. grav. of 
 vapour supposing no dissociation to occur. This formula assumes that each 
 molecule separates into two parts: if each molecule separates into a parts, the 
 
 formula is/=-r-_ . See Naumann, Lehr- und Handbuch der Tliermochemie, 
 
 pp. 114, 115.
 
 CHAP. II. 99] GASEOUS MOLECULAR COMPOUNDS. 203 
 
 The following numbers 1 representing the specific gravities 
 of gaseous nitrogen tetroxide at various temperatures exhibit 
 the gradual dissociation of molecules of N 2 O 4 into molecules 
 ofNO 2 : 
 
 Texture. Sp. *, of vapou, ^^^^ 
 
 267 2-65 19-96 6'5 
 
 35-4 2-53 25-68 8-1 
 
 39*8 2-46 29-23 iro 
 
 49"6 2-27 40*04 1 2- 1 
 
 60-2 2-08 52-84 13-0 
 
 70-0 1-92 65-57 10-4 
 
 80-6 r86 76-61 8-8 
 
 96-0 172 84-83 1-8 
 
 135*0 r6o 98-69 
 
 As N 2 O 4 is dark-red and nearly opaque, and NO 2 is trans- 
 parent and nearly colourless, the change from one compound 
 to the other can be traced by observing the colour of the 
 heated gas. 
 
 A study of the specific gravity of the vapour obtained by 
 heating acetic acid, at different temperatures and pressures, 
 shews that the specific gravity decreases as temperature rises 
 whether pressure be small or great, and that the specific 
 gravity also decreases as pressure falls whether the tempe- 
 rature be high or low; in other words, the vapour of acetic 
 acid becomes specifically heavier by increasing pressure, 
 temperature being constant, or by decreasing temperature, 
 pressure being constant 2 . The most probable molecular ex- 
 planation of these facts is to suppose that the vapour of acetic 
 acid at low temperatures contains molecules, or molecular 
 groups, the parts of which hold together throughout small 
 temperature-intervals, and that these molecules, or groups, 
 
 1 Naumann, loc cit. p. 117. 
 
 - See Ramsay and Young, C. S. Journal, Trans, for 1886. 790 (s. also 
 Book II.). Comparing the variations in the specific gravities of the vapours of 
 acetic acid, alcohol, and ether, Ramsay and Young (Phil, Mag. (5) 23. 129) 
 found that the specific gravities of alcohol vapour and ether vapour increase as 
 temperature falls until a certain point is reached beneath which the specific 
 gravities are unchanged. They conclude that the increase in the specific densities 
 of the vapours of alcohol and ether are probably due to the cohesion of the 
 molecules, and not to the formation of groups of molecules.
 
 204 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 are heavier than those which compose the vapour of the same 
 acid at temperatures considerably above the boiling point of 
 the compound. 
 
 If we define a molecular compound to be one the mole- 
 cules of which may exist in the gaseous state at low tempe- 
 ratures but are gradually decomposed into less dense mole- 
 cules of the same kind of matter as temperature rises, then 
 we must regard acetic acid at temperatures not far above its 
 boiling point as a molecular compound. 
 
 But if this is so, we evidently have a series of substances, 
 beginning with solutions of salts or gases in water, and 
 proceeding through crystallised solid salts to acetic acid 
 vapour at low temperatures, which connects mechanical mix- 
 tures on the one hand with stable gaseous compounds on the 
 other. 
 
 It might be urged that we ought not to distinguish be- 
 tween the particles which compose acetic acid vapour at low 
 temperatures and those which form the vapour of the same 
 acid at high temperatures ; that if a molecule is ' that small 
 part of a gas the parts of which do not part company during 
 the motion of agitation of the gas,' then the reasoning which 
 compels us to say that the molecule of acetic acid vapour at 
 220 is represented by the formula C 2 H 4 O 2 , likewise compels 
 us to say that at 120 the molecule of this gas is represented 
 by the formula C 3 H 6 O 3 (pressure in each case being 760 mm.). 
 The statement that acetic acid at low temperatures is a mole- 
 cular compound does not appear to me to go against this 
 reasoning ; for this statement only implies that at low tempe- 
 ratures the vapour of this acid is composed of particles, of 
 varying masses which may be called molecules or mole- 
 cular groups but that as temperature rises these all tend to 
 separate into particles whose composition is represented by the 
 formula C 2 H 4 O 2 . The particle having the composition C 2 H 4 O 2 
 is stable throughout so large a range of temperature that we 
 may apply to it and to it only the knowledge we have gained 
 regarding the structure of molecules. It is better not to 
 apply the term molecule to the heavier particles, (i) because 
 they so readily separate into lighter, and comparatively stable,
 
 CHAP. II. 99] GASEOUS MOLECULAR COMPOUNDS. 2O5 
 
 particles ; (2) because what we know of molecular structure 
 has been gained from, and can only be strictly applied to, 
 the study of molecules which are stable throughout a con- 
 siderable range of temperature; and (3) because by re- 
 cognising the possibility of the existence in certain vapours 
 of groups of molecules, which are not mere mixtures but on 
 the other hand are not to be classed as true molecules, we 
 have the means of explaining, in a general way, many phe- 
 nomena which at present cannot be explained by any other 
 equally simple hypothesis which is in keeping with the funda- 
 mental conceptions of the molecular theory of matter. 
 
 That the existence of molecular groups in a gas at low tem- 
 peratures is in keeping with this theory can readily be shewn. 
 When two gases are at equal temperatures the mean kinetic 
 energy of agitation of the molecules must be the same in 
 both ; but although the mean kinetic energy is constant for a 
 given temperature, yet the kinetic energy (and hence the 
 temperature) of many molecules may differ from this mean 
 value. If the temperature of the gas is increased, there is an 
 increase not only of the energy of agitation of the molecules 
 as a whole, but also of the energy due to the internal motions 
 of the parts of each molecule ; as the latter energy increases, 
 a point is reached at which the molecule decomposes into 
 its constituent parts, but these may again unite in some other 
 portion of the mass of gas. As temperature continues to rise 
 a point will come at which molecular decompositions and re- 
 compositions are equal in unit of time ; the temperature at 
 which this state of matters is reached has been called (by 
 Naumann and others) the decomposition-temperature; from 
 this point onwards, as temperature rises, the molecular de- 
 compositions will exceed the recompositions, until finally 
 there are no recompositions, or these are so few in number 
 that the average state of the gas is fitly described as that 
 of complete decomposition. 
 
 Now if we suppose that the vapours coming from certain 
 liquids, especially from dissociable compounds, at, or near to, 
 their boiling points consist to a great extent of molecular 
 aggregations, we may trace the gradual decomposition of
 
 2O6 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 these aggregates into true gaseous molecules, just as we have 
 traced the decomposition of molecules of one kind of matter 
 into those of another kind of matter. Many spectroscopic 
 facts almost necessitate the assumption that groups of mole- 
 cules may exist, and behave for certain small changes in 
 physical conditions as definite wholes 1 . 
 
 But it might be asked, why should not all molecules 
 decompose when heated ? It is extremely probable that all 
 molecules are capable of being decomposed by heat. The 
 results of Meyer's experiments on iodine vapour shew that 
 the diatomic molecules of this gas are separated into atoms 
 at high temperatures. The following table exhibits the 
 process of change from I 2 to I. 
 
 Dissociation of Iodine molecules^. 
 
 Temp. 
 
 448 
 680 
 
 Sp. gr. of 
 
 vapour. 
 
 874 
 
 Percentage Rise of Increase in 
 decomposition. temp. d e?omSkfon. 
 
 Mean increase 
 in decomposition 
 for ioo 3 . 
 
 764 
 
 8-28 
 
 
 
 
 
 855 
 940 
 
 8-07 
 7-60 
 
 8-6 
 H'SJ 
 
 85 
 
 . IO3 .. 
 
 10*5 
 
 6-9 
 
 IO'2 
 
 1043 
 
 ( I2 75 
 (approxi-l 
 
 mately) US 
 
 7'01 
 5-82 
 
 5-06 
 
 25-0 ' 
 
 5O* ^ ' 
 
 66-2J ' 
 73-ri ' 
 
 J 
 
 232 
 78 
 
 25-5 .... 
 157 .... 
 
 .. 6-9 .... 
 
 iro 
 
 137 
 8-8 
 
 Somewhat similar results have been obtained with bromine. 
 A fact of much interest is disclosed by studying the specific 
 gravities of gaseous bromine and chlorine at low and at high 
 temperatures ; some of the results of such a study are given 
 in the following table 3 . 
 
 1 In connexion with this subject see especially the article 'Constitution of 
 bodies,' by Clerk Maxwell, in the Encyclopedia Briiannica. (pth Ed.) See also 
 'Report of the B. A. Committee on Spectrum Analysis.' Brit, Ass. Reports for 
 1880, 2581 et seq. See especially pp. 284298. Also the article 'Aggregation, 
 States of in the new edition of Watts' Dictionary of Chemistry. 
 
 8 Naumann, Ber. 13. 1050, using the numbers of Crafts and Meier, do. do. 868. 
 
 3 Jahns, Ber. 15. 1238.
 
 CHAP. II. 99> 1 00] GASEOUS MOLECULAR COMPOUNDS. 2O/ 
 Specific gravities of gaseous Bromine and Chlorine. 
 
 Temp, measured in degrees above Snerifir irravi'tv Deviation of sp. gr. from normal, 
 
 boiling point of in per centages of latter. 
 
 IROMINE. 
 
 CHLORINE. 
 
 BROMINE. 
 
 CHLORINE. 
 
 BROMINE. 
 
 CHLORINI 
 
 40 
 
 4 
 
 57HS 
 
 2-4844 
 
 3-38I 
 
 I '397 
 
 60 
 
 60 
 
 5-6809 
 
 2*4810 
 
 2-872 
 
 1*261 
 
 80 
 
 80 
 
 5-6503 
 
 2-4776 
 
 2-223 
 
 ri22 
 
 IOO 
 
 IOO 
 
 5-6197 
 
 2-4742 
 
 1719 
 
 0-984 
 
 120 
 
 120 
 
 5 -58 9 I 
 
 2-4708 
 
 1*650 
 
 0-845 
 
 160 
 
 160 
 
 5-5279 
 
 2-4641 
 
 0-058 
 
 0*571 
 
 
 2OO 
 
 
 2-4572 
 
 
 0-290 
 
 
 240 
 
 
 2-4504 
 
 
 O'OOO 
 
 We have here a phenomenon very analogous to that pre- 
 sented by acetic acid ; and if an analogous explanation is to 
 be given, we must suppose that bromine vapour at tem- 
 peratures from 40 to 140 degrees above the boiling point of 
 this substance contains molecular groups which are slowly 
 decomposed as temperature increases ; and that the same 
 holds good of chlorine vapour, only that in this case the 
 molecular groups are relatively lighter, but more stable as 
 regards heat, than those of bromine. 
 
 A study of the specific gravities of the gases obtained by 
 heating various liquid compounds shews that in very many 
 cases the specific gravity decreases as the temperature rises, 
 and that a constant value is not obtained until the gas has 
 been heated many degrees above the boiling point of the 
 liquid. 
 
 Facts have now been recounted sufficient I think to 
 warrant the adoption of the hypothesis that gaseous mole- 
 cules may hold together in groups, the members of which 
 do not part company throughout more or less extended 
 ranges of temperature and pressure ; and if this is so in gases, 
 much more should we expect to find the existence of mole- 
 cular groups in liquids and solids. 
 
 100 The hypothesis, by the application of which we hope to 
 find many groups of facts falling into some kind of order, 
 may be broadly stated as consisting in the recognition of a 
 third order of particles more complex, but less stable, than 
 ; ts the molecule, as the molecule is more complex, but less 
 --table, than the atom. This hypothesis affords no definition
 
 2O8 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 of the third order of particles, nor does it always enable us to 
 refer a special case to this, or that, order of particles. It is a 
 general guide and as such only must it be employed. 
 101 Many salts when in solution undergo changes not so 
 marked as those usually called chemical, and yet too definite 
 to be altogether classed as physical. Thus an aqueous so- 
 lution of ferric chloride undergoes partial separation into 
 hydrochloric acid and a colloidal form of ferric hydrate ; 
 aqueous solutions of various alums are partially separated 
 into their constituents when heated. The direction of many 
 of these changes may be partially reversed by altering the 
 conditions of temperature 1 . Again hydrated cobalt chloride 
 crystallises in a rose-red form (CO 2 C1 4 . I2H 2 O), while the 
 colour of the dehydrated crystals (CO 2 C1 4 ) is blue ; if an 
 aqueous solution of the red salt is warmed, the colour slowly 
 becomes darker and finally changes to blue, but the rose 
 red colour gradually reappears as the liquid cools. The 
 temperature at which the change from hydrated to dehydrated 
 salt occurs is the lower, the less the amount of water present 
 relatively to that of salt. A crystal of cobalt chloride grow- 
 ing in a blue-coloured solution is seen under the microscope 
 to be surrounded by a film of pink liquid, which indicates 
 the existence round the crystal of a zone of liquid containing 
 relatively less of the salt than the rest of the solution 2 . 
 
 From the results of Lehmann's microscopic studies 3 on the 
 formation of crystals of hydrated ferrous chloride, cobaltous 
 chloride, and cupric chloride, it appears certain that an aqueous 
 solution of one of these salts from which crystals, now of 
 a more hydrated and now of a less hydrated salt, separate, as 
 temperature varies, does not contain at a fixed temperature 
 only the one hydrate and at another temperature only the 
 other hydrate. As temperature slowly rises the molecular 
 groups tend to fall to pieces and so the liquid becomes poorer 
 in particles of the relatively most hydrated salt ; on cooling, 
 
 1 The expresssion ' dissociation of salts in solution ' is sometimes applied to 
 these processes. See Book II. 
 
 2 See Lehmann, Zeitschr.fiir Krystallog. 1. 99. : see also Potilitzin, Ber. 17. 276. 
 
 3 Zeitschr. fiir Krystallog. 1. 100 103.
 
 CHA1MI. 101] MOLECULAR COMPOUNDS. 2OQ 
 
 the conditions are reversed, and the liquid becomes poorer in 
 particles of the least hydrated salt. Lehman n considers the 
 three cases ; (i) the liquid is equally saturated for the hydrate 
 rich in water and for that poorer in water; (2) the liquid con- 
 tains rather more of one hydrate than of the other; (3) the 
 liquid is concentrated as regards one hydrate, but dilute as 
 regards the other. He shews that, as temperature slowly 
 increases, in the first case crystals of both hydrates grow 
 simultaneously and at the same rate until the spheres 1 of the 
 crystals touch, when growth is almost entirely stopped ; in 
 the second case both kinds of crystals grow, but for a time 
 one kind grows more quickly than the other, then both grow 
 at the same rate, and then the second kind of crystals grow 
 more rapidly than the first ; in the third case those crystals 
 which are present in the liquid in greater quantity grow 
 rapidly, and the others dissolve rapidly, so that the dissolving 
 crystals appear to pass directly into crystals of the other hydrate. 
 
 The definite form, solubility, temperature of formation, &c. 
 of each kind of crystal formed in these experiments conducted 
 by Lehmann prevent us from regarding the various crystalline 
 solids as mere mixtures of ice and salt ; on the other hand, 
 the extremely small variations in temperature, or in the re- 
 lative quantities of water and salt, required to cause change 
 from one crystal to another, equally prevent us from attempt- 
 ing to explain the properties of each hydrate as wholly, or 
 almost wholly, conditioned by the mutual interactions of 
 atoms forming the molecule: we seem forced to adopt the 
 hypothesis of molecular compounds. 
 
 Several compounds exist each in more than one modifi- 
 cation, one form being generally more stable towards heat 
 than the other. A typical case of this kind is presented by 
 antimonious iodide, SbI 3 ; this compound crystallises in red 
 hexagonal forms which are suddenly changed at 1 14 to an 
 aggregation of yellow orthorhombic crystals, the original 
 external form of the mass being preserved 2 . 
 
 1 Lehmann's term is 'der Hof des Krystalles:'' each crystal, he says, can be 
 seen under the microscope to be surrounded by a liquid film, from which it draws 
 Us supplies of solid matter; this is the Ifofor sphere of the crystal. 
 
 2 J. P. Cooke, Proe. Anu-r. Acad. of AHs and Sci. [2]. 5. 72. 
 
 M. C. 14
 
 2IO ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 Several carbon compounds (apparently all belonging to 
 the class of benzenoid compounds) exist in more than one 
 form, each modification being characterised by a definite 
 melting point and generally also by a special crystalline form. 
 Thus chlorodinitrobenzene, C ( ,H 3 C1(NO 2 ) 2 [i : 2 .'4], is said to 
 form monoclinic crystals which melt at 36, and also rhombic 
 crystals which melt at 39. Anthracene, C 14 H 10 , crystallises 
 in monoclinic plates melting at 213 which are easily oxidised 
 by the action of nitric acid to anthraquinone (C 14 H 8 O 2 ) ; when 
 a solution, in benzene, of anthracene is exposed to sunlight 
 small prismatic crystals separate, melting at 244, having the 
 composition C 14 H :o , but not acted on by nitric acid, and not 
 oxidised to anthraquinone by chromic acid 1 . A very re- 
 markable instance of the phenomenon under consideration is 
 presented by the derivative of diphenyl to which the formula 
 (C 6 H 3 BrNHCOC 6 H 5 ) 2 is assigned. This compound melts at 
 195 ; if the melted substance is cooled quickly and again 
 heated its melting point is now 99 ; but if heating is con- 
 tinued the liquid again solidifies at 125 130, and the solid 
 thus obtained melts once more at 195. Finally if the solid 
 which melts at 195 is raised to that temperature and then 
 slowly cooled, the product possesses the normal melting point 2 , 
 viz. 195. When a substance crystallises in more than one 
 system, one crystalline form frequently approaches as nearly 
 as possible to the other ; one form may be said to imitate the 
 other both crystallographically and optically 3 ; thus arsenious 
 oxide crystallises in regular octahedra and also in rhombic 
 prisms, the latter exhibiting an angle identical with the angle 
 of the regular octahedron. 
 
 O. Lehmann 4 has collected and discussed many instances 
 of the exhibition of different physical properties by com- 
 pounds possessing the same elementary composition 5 . The 
 
 1 See Armstrong and Groves, foe. cit. p. 199. 
 
 2 See E. Lellmann, Ber. 15. 2835. 
 
 3 Pasteur, Ann. Chim. Phys. [3] 23. 267. 
 
 4 Zeitschr. fur Krystallog. 1. 97. See also, in connexion with the subject 
 generally, the article 'Isomerie, physikalische ' in Neues Haudivorterbtuh der 
 Chemie, Bd. in. pp. 836843. 
 
 8 On this subject see also Laubenheimer, Ber. 9. 760.
 
 CHAP. II.IOl] PHYSICAL ISOMERISM. 211 
 
 phenomenon, which may be called physical isomerisin 1 , pre- 
 sents analogies with allotropy (see ante, par. 67); in both, 
 temperature is the most important condition affecting the 
 change from one form to another, and this change is accom- 
 panied in both classes of phenomena by disappearance or 
 production of heat. 
 
 Lehmann divides physically isomeric bodies into two 
 classes: (i) those in which change from one form to another 
 occurs at a definite temperature, the direction of the change 
 being dependent on very small differences of temperature; 
 (2) those which exhibit two forms, one more stable than the 
 other, and in which change from one form to the other does 
 not occur at a definite temperature, and is not reversible by 
 heat alone. 
 
 Ammonium nitrate is an example of a substance belong- 
 ing to the first class ; the rhombic crystals of this salt, which 
 separate at ordinary temperatures from an aqueous solution, 
 melt at (about) 168; as the molten mass cools crystals be- 
 longing to the regular system are formed, but at (about) 
 125 these change to rhombohedral forms ; at (about) 87 the 
 rhombohedral forms are converted into rhombic needles, 
 from which, at 36 or so, the original rhombic crystals are 
 produced. If the rhombic crystals are again slowly heated 
 the rhombic needle-shaped crystals form at (about) 36 ; the 
 rhombohedral forms appear at (about) 87; the regular 
 crystals at (about) 125; and finally the solid melts at 198. 
 Again, if a little sulphur is melted on a microscopic slide, 
 under a cover, and the slide is arranged so that temperature 
 can be easily regulated 2 monoclinic crystals are produced, 
 but as temperature falls these change into rhombic forms ; 
 it is possible to regulate the temperature so that definite 
 amounts of each form exist simultaneously, but on the 
 slightest change of temperature the rhombic crystals grow at 
 the expense of the monoclinic, or vice versa. 
 
 The behaviour of dibromopropionic acid when heated 
 
 1 The term physical isomerism seems to have been first used by L. Carius, 
 Annalen, 126. 214 (see also do. 130. 237). 
 
 s Lehmann describes an apparatus for this purpose (loc. cit. pp. 102 3). 
 
 142
 
 212 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 illustrates the nature of the changes which characterise sub- 
 stances belonging to Lehmann's second class of physical 
 isomerides. This substance crystallises in rhombic forms 
 which melt at (about) 64; if the molten mass is heated a 
 few degrees above this point the same rhombic crystals 
 are again produced on cooling; but if the molten substance 
 is heated many degrees above 64 and is then allowed to 
 cool, small flat nearly right-angled tables are obtained 
 which melt at (about) 51. If the less stable form melting at 
 51 is slowly heated growth of the other and more stable 
 crystals is noticed under the microscope ; the growth at first 
 is rapid, then slower, but before the change has gone far the 
 melting point of the less stable crystals is reached and the 
 whole mass becomes liquid. If the more stable form is 
 melted, heated some degrees above 64, and is then brought 
 into contact with crystals of both forms, growth of each 
 modification proceeds until the crystals touch, after which 
 the more stable (higher melting) crystals grow into the others 
 until the latter are completely changed into the stabler forms. 
 
 Another instance of Lehmann's second class is furnished 
 by paranitrophenol. This compound crystallises from hot 
 aqueous solutions in monoclinic crystals, and from cold 
 aqueous (or alcoholic) solutions in crystals belonging to the 
 same system but differing in form and melting point from 
 the others. By fusing either form and allowing the molten 
 mass to cool, only the less stable (lower melting) crystals 
 are produced; but if a little of the substance is melted on a 
 microscopic slide; and a crystal of the second (stabler) form 
 is placed in contact with the edge of the solidified mass, 
 and heating is then again commenced, crystals of the stabler 
 form begin to grow at the expense of the other crystals, at 
 first rapidly and then more slowly, until both forms melt, the 
 less stable at a lower temperature than the more stable. 
 
 Substances of which ammonium nitrate is the type ap- 
 pear to be less profoundly modified by the action of heat 
 than substances belonging to the class represented by dibromo- 
 propionic acid. Substances belonging to the first of these 
 classes shew analogies with many of the molecular com-
 
 CHAP. II. 101] PHYSICAL ISOMERISM. 213 
 
 pounds discussed in the present section ; compare e. g. the 
 action of heat on hydrated cobalt salts, with the action of 
 the same agent on dibromopropionic acid or on paranitro- 
 phenol. Moreover the course of the change brought about 
 by the action of heat on these bodies shews some analogies 
 with the processes of gaseous dissociation. For these rea- 
 sons Lehmann has summarised the phenomena characteristic 
 of bodies of this class under the term physical polymerism, 
 and the phenomena characteristic of bodies of the other class 
 under the term physical metamerism. The former term im- 
 plies that the physically different forms exhibited by a sub- 
 stance belonging to this class are to be regarded as associ- 
 ated with the existence of physical molecules, each formed 
 by the grouping together of a different number of chemical 
 molecules (as defined in Chap. I. par. 13, p. 26). The term 
 physical metamerism on the other hand implies that the 
 physical molecule of each different form of a substance 
 belonging to this class is composed of the same number of 
 chemical molecules, but that the arrangement of these is 
 different in each case. 
 
 Lehmann's classification is certainly based on no fanciful 
 analogies. Pclymerism and metamerism are well marked 
 phenomena among gaseous molecules ; and the hypothesis of 
 the existence of groups of molecules characterised by definite 
 properties, but each of which groups is readily decomposed 
 by heat, appears to be as simple as any other molecular and 
 atomic hypothesis that can be proposed to explain the 
 observed facts. But the analogy between the reactions of 
 gaseous molecules and the changes undergone by solid and 
 liquid substances may be pushed too far; we ought to recog- 
 nise how small and inexact our knowledge is of the mole- 
 cular actions of the latter classes of bodies. Qualification 
 of the terms molecule, polymerism, and metamerism, by the 
 adjective physical, widens the meanings of these terms by 
 making them applicable to a larger class of phenomena, but 
 at the same time it makes the application less precise 1 . 
 
 1 Lehmann considers in considerable detail the phenomena attending the 
 change of one form of a substance into another; he divides the changes into
 
 214 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 The researches of Graham on colloidal and crystalloidal 
 substances are of the utmost importance as regards the 
 hypothesis we are considering ; to understand the import- 
 ance of Graham's work it is necessary carefully to study the 
 whole series of papers on liquid diffusion which he communi- 
 cated to the Royal Society 1 . Graham 2 found that certain 
 substances when in solution pass very quickly through wet 
 
 groups, according as both forms are solid, or one solid and one liquid, c. As the 
 subject is important I give a brief resume of some of Lehmann's results in this 
 note, but the original paper ought to be studied by all who are interested in the 
 subject. 
 
 A. Change of one, more complex, solid form of isomeride to another, less 
 complex, solid form, attended with disappearance of heat; physical mole- 
 cules of both kinds are present simultaneously, but at a certain tempera- 
 ture change will occur. If one modification is heated alone, the normal 
 temperature of change may be largely exceeded without a complete 
 change to the second modification, but at such a high temperature 
 contact with the second modification may determine sudden and complete 
 change. 
 
 B. Change of solid form to liquid form, occurring with disappearance of heat 
 at a definite temperature dependent on the pressure ; the change will not 
 be complete, as molecules of both kinds will exist together. If the specific 
 gravity of the solid form is greater than that of the liquid form, then on 
 heating past the melting point there will be rapid expansion as the physical 
 molecules of the solid form are separated into those of the liquid; this will 
 be followed by a slower regular expansion. If the specific gravity of the 
 solid is less than that of the liquid, expansion will be small, or even 
 negative, until a point of maximum density is reached, after which expan- 
 sion will proceed at the normal rate. 
 
 In some cases a solid form is changed, by the action of heat, into a 
 liquid form, which, at a higher temperature, is again changed into a second 
 solid form; e.g. when selenion is heated till it becomes viscous and is kept 
 at this temperature for some time it changes into a crystalline form. So in 
 the change of yellow to red phosphorus by the action of heat ; in this case 
 it is probable that the molecules which form the liquid phosphorus are kept 
 apart for some time, by the energy added as heat acting against cohesion, 
 and so are allowed to re-arrange themselves in loose groups. 
 
 C. Change of liquid to solid, modification is complex ; a few crystals form 
 and determine the crystallisation of the whole mass; in some cases the 
 liquid, especially if viscous, may be cooled below the temperature at which 
 crystallisation normally begins, and may then pass into an amorphous solid 
 form. 
 
 1 Happily Graham's papers have been collected and published by the late 
 Drs Angus Smith and James Young. 
 - Phil. Tram, for 1861. 185.
 
 CHAP. II.IOl] MOLECULAR COMPOUNDS. 215 
 
 animal or vegetable membranes, while others are scarcely, if 
 at all, diffusible through the same septa. The more diffu- 
 sible bodies Graham called crystalloids, the less diffusible he 
 called colloids. Colloidal substances e. g. albumen, hydrated 
 alumina or stannic oxide, &c. are very inert chemically consi- 
 dered, but at the same time they are affected by the smallest 
 changes in their environment, e.g. slight alterations of tem- 
 perature cause marked changes in their properties ; they are 
 easily permeated by diffusible crystalloidal substances, to 
 which, says Graham, they give up water, 'molecule by mole- 
 cule'; "their existence is a continual metastasis." Ice, which 
 under ordinary conditions of formation is crystalloidal, when 
 formed in contact with water at o possesses those properties 
 which characterise colloids : " Can any facts," says Graham, 
 " more strikingly illustrate the maxim that in nature there 
 are no abrupt transitions, and that distinctions of class are 
 never absolute ?" 
 
 The marked differences between the properties of colloids 
 and crystalloids are associated, in the opinion of Graham, 
 with differences of molecular structure. He regarded the 
 reacting unit of a colloid as probably formed by the coales- 
 cence of a large number of molecules ; hence the marked 
 instability, and at the same time the chemical inertness, 
 which characterise the class of colloidal substances. 
 
 Hittorf 1 has shewn that when a concentrated aqueous 
 solution of cadmium iodide is electrolysed, more iodine is 
 separated at the positive pole than could be the case were 
 the composition of the body undergoing electrolysis repre- 
 sented by the formula CdI 2 . Hittorf suggests that the solu- 
 tion in question contains molecular groups of the composi- 
 tion Cd 3 I e , and that these are separated by the electric cur- 
 rent into Cd and Cd 2 I 6 . 
 
 Some interesting observations have been made by van 
 Bemmelen 2 on the absorption of acids and salts by hydrated 
 oxides. When the hydrated dioxide of tin, silicon, or man- 
 ganese, is shaken with an aqueous solution of a mineral acid, 
 
 1 Pogg. Ann. 106. 337, 513. 
 
 2 7- fiirprakt. CAerniefr] 23. 324; see also 26. 227.
 
 2l6 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 or of a salt such as potassium sulphate or sodium chloride, a 
 definite quantity of the acid or salt is absorbed by the oxide; 
 the amount absorbed is dependent on the nature of the 
 hydrated oxide and that of the acid or salt, on the relative 
 masses of oxide, acid, or salt, and on the amount of water 
 present. The substances which exhibit this absorptive 
 action are characterised by the readiness with which the 
 change from hydrated to dehydrated oxide and vice versa 
 occurs; thus the hydrates SnO 2 .;rH 2 O, SiO 2 .^H 2 O, and 
 MnO 2 .^'H 2 O, part with water when placed over sulphuric 
 acid, and the oxides absorb water when placed in a moist 
 atmosphere. The amount of water absorbed by any one of 
 the dehydrated oxides depends in part on its physical state ; 
 if the oxide is strongly heated it absorbs less water than if 
 dried over sulphuric acid in vactto 1 ; the 'looser' the aggrega- 
 tion of the particles, the greater the quantity of water ab- 
 sorbed by the oxide. 
 
 In some cases, e.g. the hydrate SiO 2< 4H 2 O, the amount 
 of acid or salt withdrawn from an aqueous solution was 
 found to be equivalent to the amount of water removed 
 from the hydrated oxide by drying it over sulphuric acid in 
 vacua. In other cases, e.g. SnO 2 .3H 2 O, 3SnO 2 . 7H 2 O, 
 2SnO 2 .3H 2 O, 2MnO 2 .5H 2 O, MnO 2 .2H a O, the amount of 
 acid or salt withdrawn by the hydrate from solution was 
 greater than the quantity equivalent to the loosely-held 
 water of the hydrate. As the amount of water which some 
 of these oxides absorb from a moist atmosphere was found to 
 vary with the physical aggregation of the oxide, so the 
 amount of salt or acid absorbed by these hydrated oxides 
 was found to shew analogous variations : this is specially 
 worked out in detail by van Bemmelen for the action of 
 metastannic acid on aqueous solutions of HC1, H 2 SO 4 , KC1, 
 K 2 SO 4 , and KNO 3 . 
 
 If these actions are to be classed as purely physical, we 
 
 1 Graham [Brit, Ass. Reports for 1834. 579] called attention to the difference 
 between strongly heated calcium sulphate and the same substance 'in a state for 
 setting:' but, says Graham, "this is a department of corpuscular philosophy which 
 stands much in want of further development."
 
 CHAP.II. IOI] MOLECULAR COMPOUNDS. 2I/ 
 
 should not expect to find a definite limit to the amount of 
 salt or acid absorbed by each hydrated oxide : but van Bem- 
 melen's researches shew that the process tends to the esta- 
 blishment of an equilibrium between acid (or salt), water, and 
 hydrated oxide ; that this condition is attained slowly ; and 
 that it is affected by the relative masses of the reacting sub- 
 stances in the original system. Thus less acid (or salt) is 
 absorbed from a very dilute than from a more concentrated 
 solution, but the amount of acid or salt absorbed increases 
 much more slowly than the increase in the concentration of 
 the solution of acid or salt. The final equilibrium is not 
 disturbed by the addition of a solution of acid or salt of the 
 same degree of concentration as that surrounding the hy- 
 drated dioxide, but if the added solution is relatively richer 
 in acid or salt than the liquid surrounding the dioxide, then 
 the equilibrium is overthrown and the absorption of acid or 
 salt begins again and proceeds till a second condition of 
 equilibrium is established. 
 
 Some hydrated oxides not only absorb, but also par- 
 tially decompose, salts ; for instance, when the hydrate 
 2MnO 2 .5H 2 O is shaken with an aqueous solution of K 2 SO 4 , 
 it absorbs a definite amount of the latter and at the same 
 time separates part of it into KOH and H 2 SO 4 . Again, one 
 salt is sometimes absorbed in preference to another; thus if 
 MnO 2 .;rH 2 O is shaken in contact with H 2 SO 4 , washed, and 
 again shaken in contact with an aqueous solution of K 2 SO 4 , 
 a portion of the H 2 SO 4 which had been absorbed by the 
 hydrated oxide is replaced by K 2 SO 4 ; again, if SiO 2 . 4H 2 O 
 is allowed to absorb A1 2 C1 , is then washed till the washings 
 no longer contain chlorine, and is finally shaken with an 
 aqueous solution of KC1, it is found that some of the KC1 
 has been absorbed and some of the Al a Cl 6 has passed into 
 the surrounding liquid. 
 
 These substances investigated by van Bemmelen, whether 
 they be called compounds or loose combinations of salt (or 
 acid) and hydrated oxide, can scarcely be regarded as com- 
 posed of molecules each built up of atoms of metal, oxygen, 
 hydrogen, and the elements of acid or salt, but rather as
 
 2l8 ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 composed of molecular groups each constituted by the co- 
 alescence of molecules of acid (or salt), water, and metallic 
 oxide, the number of such molecules in each group or re- 
 acting weight being variable within certain limits. The pro- 
 perties of many of the salts of the weaker acids e.g. car- 
 bonic, boric, and sulphurous are regarded by van Bemmelen 
 as explicable in terms of the general hypothesis of molecular 
 compounds ; he would regard the reacting weights of these 
 salts as molecular groups, more stable than those which com- 
 pose the peculiar class of bodies just described, but less stable 
 than the true chemical molecule. 
 
 102 I n ms second paper (loc. cit.} van Bemmelen has more 
 particularly studied hydrated beryllium oxide BeO . ^'H 2 O. 
 He shews that two varieties of this oxide exist, viz. a gela- 
 tinous and a granular form ; that the former alone exhibits 
 the property of absorbing acids and salts from aqueous solu- 
 tions ; and also that the action of heat on the two hydrates is 
 different. After heating to 220 the granular hydrate had 
 lost 0*5 H 2 O, and was now much altered in properties. This 
 fact and others analogous to this are known seems to shew 
 that by the application of energy from without the system the 
 parts of a loose molecular group may be caused to react so 
 as to bring about a marked change in the properties of the 
 body composed of such groups. In other words, the com- 
 parative readiness with which definite chemical changes may 
 be started among the constituents of a molecular group 
 appears to shew that although these constituents are held 
 together but loosely, nevertheless they are not merely mixed. 
 Thus, As(CH 3 ) 2 Cl combines with C1 2 to form As(CH 3 ) 2 Cl 3 ; 
 when this compound is heated it yields As(CH 3 )Cl 2 + CH 3 C1 ; 
 then As(CH 3 )Cl 2 readily takes up C1 2 to form As(CH 3 )Cl 4 , 
 which on being heated separates into AsCl 3 + CH 3 Cl. Now 
 on account of their properties some of these compounds must 
 be classed as molecular, yet under the influence of heat the 
 parts of the molecular groups mutually act and react in a 
 way analogous to, if not identical with, that characteristic of 
 chemical change. But such phenomena as these are exactly 
 what might be expected from the hypothesis of molecular
 
 CH.II.IO2,IO3] ATOMIC AND MOLECULAR COMPOUNDS. 219 
 
 compounds ; if these bodies are formed of groups of mole- 
 cules we should expect that reactions between these groups 
 would, in many cases, easily occur and result in the produc- 
 tion of new, less complex, groups, or, it may be, new mole- 
 cules. That a substance is found to behave in a definite 
 manner under the influence of this or that reagent cannot be 
 regarded as sufficient evidence for classing it among atomic 
 rather than molecular compounds. Thus the observation re- 
 corded by R. W. Atkinson 1 regarding the identity of the salts 
 produced by mixing (i) SbCl 3 and 3KBr, and (2) SbBr 3 and 
 3KC1, cannot be regarded as proving that the product of 
 these actions is built up of molecules represented by the for- 
 mula AfSbCl 3 Br 3 K 3 , the properties of which are conditioned 
 only by the mutual interactions of the atoms Sb, Cl, Br, and 
 K. Regarded however as a contribution towards solving the 
 questions suggested by the term molecular compounds, the 
 observations made by Atkinson are of interest, as shewing 
 how possible it is to obtain substances which behave in some 
 respects as molecular, and in other respects as atomic, com- 
 pounds. 
 
 It cannot be too strongly insisted on that no hypothesis 
 has been proposed regarding molecular compounds which 
 furnishes us with a definition of the class 'molecular', or puts 
 into our hands an instrument for determining whether a 
 given compound belongs to this class or to the class of 
 atomic compounds. What the hypothesis does is to negative 
 the notion that the properties of all compounds are to 
 be explained by the conception of actions and reactions 
 between atoms which together constitute a molecule, and to 
 open a path for future research by insisting on the complexity 
 of chemical phenomena, and the folly of attempting to ex- 
 plain all in terms of a favourite theory. 
 
 103 But the consideration of molecular compounds leads to 
 the discussion of questions which properly belong to chemical 
 kinetics : we cannot separate these bodies from their environ- 
 ment ; they are members of a system which is continually 
 undergoing change and the comparative stability of which is 
 
 1 C. S. Jon mat, Trans, for 1883. 289.
 
 22O ATOMIC AND MOLECULAR SYSTEMS. [BOOK I. 
 
 the result of never ceasing action and reaction between its 
 parts. Chemistry is not a collection of facts regarding the 
 crystalline forms, melting points, boiling points, specific 
 gravities, &c., &c., of elements or compounds ; it is rather 
 the orderly and regulated study of the changes which these 
 kinds of matter undergo and which result in more or less 
 profound modifications in the properties of the changing 
 bodies. 
 
 A great advance has certainly been made by replacing 
 the notion of a molecule as an undefined quantity of matter 
 constructed of groups of atoms more or less loosely and 
 vaguely arranged, by that conception which regards the mole- 
 cule as a definite and definable quantity of matter, built up 
 of atoms arranged in an orderly manner, and exhibiting 
 functions dependent on the nature, arrangement, and mutual 
 interactions, of these atoms. Among the functions of the mole- 
 cule we must, I think, place the power of combining, under 
 proper conditions, with other molecules to form more or less 
 complex groups, less stable than the molecules of a gas, and 
 not so sharply defined from other groups as the molecule of 
 one compound is from that of another. Although the ex- 
 planation of the properties of molecular compounds is not 
 to be brought wholly within the scope of the hypothesis of 
 valency, nevertheless if we regard the formation (or non- 
 formation), and the relative stabilities, of such compounds, 
 as functions of all the molecules concerned in their synthesis, 
 we can see that the valencies of the elementary atoms must 
 be important factors in determining the production of mole- 
 cular compounds 1 . 
 
 Although we can put our conception of the molecule into 
 definite terms, yet the advance of knowledge regarding the 
 properties of molecules warns us against attempting to define 
 the molecule too rigidly. The molecular and atomic theory 
 
 1 In connexion with this subject compare the presidential address to Section 
 B of the British Association at Aberdeen [1885]. In this address Armstrong 
 suggests that the "formation of so-called molecular compounds is mainly due 
 to peculiarities inherent more especially in the negative elements i.e. the non- 
 metals and metalloids, and not in the positive elements the metals." (See 
 Nature, 32. 470.)
 
 CHAP. II. IO3] ATOMIC AND MOLECULAR COMPOUNDS. 221 
 
 presents the chemist with the conception of the gaseous mole- 
 cule ; by applying this to chemical facts he arrives at the 
 conception of the atom, a conception much more definite 
 than that of the molecule ; he then rebuilds the molecule by 
 putting together the atoms of which it is composed ; but he 
 does not always find the molecule thus re-constructed to be 
 the same as the molecule he received from the physicist. 
 The physical definition of the molecule applies in strictness 
 only to perfect gases ; but the chemist has to deal with im- 
 perfect gases, and also with liquids and solids. 
 
 Notwithstanding these difficulties fair progress has been 
 made in the chemical investigation of the molecule. We 
 have endeavoured to trace this progress, as it appears in the 
 methods for finding the relative weights of atoms and mole- 
 cules ; in the distinction between the properties of atoms and 
 the properties of molecules formed by the union of atoms ; 
 in the chemical conception of the molecule as a structure of 
 atoms or groups of atoms, the functions of which structure 
 are dependent on the nature, number, and arrangement, of its 
 parts; in the development of this conception in the hypo- 
 theses of valency and isomerism ; and in the recognition, 
 forced on the chemist by the study of liquid and solid 
 compounds, that although the properties of the molecule are 
 conditioned by the properties of its parts, it has also an 
 individual existence and is capable of interacting as a whole 
 with other molecules.
 
 [BOOK i. 
 
 CHAPTER III. 
 
 THE PERIODIC LAW. 
 
 IN the preceding Chapter we have endeavoured to 
 trace the development of the conceptions of the atom and 
 the molecule. The properties of compounds are regarded 
 in chemistry as the properties of the molecules of these com- 
 pounds, and these again as conditioned by the properties 
 of the atoms which compose the molecules. Can we then 
 trace a definite connexion between the properties of the 
 atoms of the elements and the properties of the compounds 
 formed by the union of these elements? A measurable pro- 
 perty of the atoms is their relative masses. Is there any 
 definite and definable relation between the atomic weights 
 and the properties of the elements, and between the atomic 
 weights of the elements and the properties of their com- 
 pounds ? 
 
 104 Attempts have been made from time to time throughout 
 the preceding 50 or 60 years to trace connexions between 
 the atomic weights and the general properties of groups of 
 elements. 
 
 Soon after the appearance of Dalton's New System of 
 Chemical Philosophy, an hypothesis was promulgated by 
 Prout to the effect that the atomic weights of the elements 
 are whole multiples of that of hydrogen ; but the researches 
 of Berzelius, Marignac, and Stas, shewed that this hypothesis 
 was untenable. A modification of Prout's hypothesis was 
 made by Dumas which appears to have a fair probability in 
 its favour.
 
 CH.III.I04,I05] ARRANGEMENT OF THE ELEMENTS. 223 
 
 Gmelin, Dumas, Gladstone, Cooke, Kremers, Pettenkofer, 
 Odling, and especially Newlands 1 , who was among the earliest 
 workers in this field, have drawn attention to points of 
 connexion between the properties and the atomic weights of 
 elements. In 1864 Newlands arranged a number of elements 
 in order of their atomic weights, and shewed that these 
 elements were divisible into groups of seven, and that the 
 properties of one group were to some extent repeated in the 
 next group. " The eighth element," said Newlands, " starting 
 from a given element is a kind of repetition of the first, like 
 the eighth note of an octave in music." In subsequent papers 
 Newlands insisted on the general applicability of what he 
 called the ' law of octaves.' 
 
 It is however especially to Mendelejeff 2 that we owe the 
 systematic correlation of the atomic weights with the chemical 
 and physical properties of the elements, and the properties of 
 their compounds. 
 
 Lothar Meyer 8 has also made important contributions 
 to the same subject, and in his Modernen Theorien he has 
 gathered together the more important facts which have been 
 established concerning the relation in question. 
 105 We may confidently say that a large probability has been 
 established in favour of the hypothesis that the properties 
 of the elements, and of the compounds of each element, are 
 periodic functions of the atomic weights of the elements. 
 Lothar Meyer puts the general statement of the "Periodic 
 Law" in this form 4 : "If the elements are arranged in order 
 of increasing atomic weights, the properties of these elements 
 I'ary from member to member of the series, but return more or 
 less nearly to the same values at certain fixed points in tlie 
 scries" 
 
 Let the elements be arranged in the order of their atomic 
 weights ; let this list of elements be (broadly) divided into 
 
 3 Chem. News,1. 70; and 10. 59, 94; 12. 83, 94; 13. 113, &c. Newlands' 
 contributions to this subject have been gathered together and published in a' 
 small volume entitled 'On the Discovery of the Periodic Law' [Spon, 1884]. 
 
 2 Annalen, Suppl. Bd. 8. 133. See also Chem. News, Vols. 40 and 41. 
 
 3 Anna/en, Suppl. Bd. 5. 129, and 7. 354 &c. 
 
 4 Die modernen Theorien, 4th Ed. p. 136; English Ed. p. 117.
 
 224 THE PERIODIC LAW. [BOOK I. 
 
 series of sevens; let the members of the second series be 
 placed under those of the first, those of the third under those 
 of the second, and so on : then the elements contained in a 
 vertical column are said to form a group, while those in a 
 horizontal column form a scries. 
 
 In this arrangement of the elements each group cor- 
 responds, for the most part, with a natural family. This is 
 more clearly shewn, and the relations between the atomic 
 weights and the properties of the elements are more distinctly 
 developed, if certain gaps are supposed to exist in the list of 
 elements. The table 1 on p. 225 exhibits the arrangement of 
 the elements in groups and series. 
 
 106 Before giving a detailed explanation of this table let us 
 meanwhile gather together some of the best established 
 generalisations concerning the periodic connexion of pro- 
 perties and atomic weights of the elements. 
 
 A phenomenon is said to be periodic when, if the con- 
 ditioning circumstances vary continuously, it repeats itself at 
 definite intervals. The variable under consideration is the 
 atomic weight, the phenomenon to be examined is the nature 
 of each chemical element and its compounds. Although it 
 is not as yet possible to state quantitatively the nature of the 
 periodic function which connects the atomic weights with 
 the general properties of the elements, it may nevertheless be 
 established that the function in question is periodic. For 
 this purpose it will be necessary to break up the phenomenon 
 'nature of the chemical element and its compounds' and to 
 endeavour to shew that the malleability, ductility, atomic 
 volume, power of forming oxides (or chlorides) of definite 
 composition, position in electrical series, &c , of the elements 
 do vary periodically with variations in the atomic weights of 
 these elements 2 . 
 
 107 Atomic volume. The quotient obtained by dividing the 
 
 1 Taken from a paper by B. Brauner in C. S. Journal Trans, for 1882. 78: 
 atomic weights are stated in round numbers. 
 
 2 For greater details on this point see L. Meyer, Die modernm Thcoricn, 
 4th Ed. pp. 139 173 (English Ed. pp. 117 150), of which this and the few 
 following pages must be regarded as an abstract.
 
 CHAP. III. lO/] ARRANGEMENT OF THE ELEMENTS. 225 
 
 oo en 
 -n\o 
 
 II II 
 
 
 " 
 
 I II 
 
 bo cj 
 
 \o 
 
 
 So 
 
 M. C.
 
 226 THE PERIODIC LAW. [BOOK I. 
 
 atomic weight of an element by its specific gravity in the 
 solid form is called the atomic volume of that element. This 
 quotient expresses the volume, in cubic centimetres, occupied 
 by an amount of the solid element, in grams, proportional to 
 the atomic weight of that element. 
 
 Arranging the elements in order of increasing atomic 
 weights it is found that the value for atomic volume reaches 
 its first maximum at lithium, that it then diminishes through 
 beryllium, boron, &c. and again increases through carbon, &c. 
 reaching a second maximum at sodium ; the other maxima 
 occur at potassium, rubidium, and caesium. 
 
 The periodic nature of the connexion between atomic 
 volumes and atomic weights becomes very apparent when the 
 magnitudes of those quantities are graphically represented as 
 is done on the plate facing this page 1 . 
 
 The maximum points on the curve are seen to be occupied 
 by metals of low specific gravity, while the minimum points 
 are occupied by heavy metals. 
 
 The position of an element on the curve, with reference to 
 the preceding and succeeding elements, appears to be inti- 
 mately connected with the properties of the element in question. 
 Thus phosphorus and magnesium on the one hand, and calcium 
 and chlorine on the other, have nearly equal atomic volumes ; 
 phosphorus and chlorine are followed by elements the atomic 
 volumes of which are larger than their own (i.e. are situated 
 on ascending portions of the curve), whereas magnesium and 
 calcium are followed by elements having atomic volumes 
 smaller than their own (i.e. are situated on descending portions 
 of the curve). 
 
 The ductile metals are placed at or near to maximum and 
 minimum points on the curve ; those of low specific gravity 
 occurring at, and immediately after, maximum points, and 
 those of high specific gravity at, and immediately after, 
 minimum points. The brittle heavy metals occur in sections 
 4, 5, and 7 immediately before the minimum points 2 . 
 
 1 Only those elements the specific gravities of which in the solid state have 
 been directly determined are included in the curve ; want of data is indicated by a 
 broken line. 
 
 2 A section of the curve means the part situated between two maxima; section
 
 THE PERIODIC LAW. 
 
 710 20 30 40 SO 60 70 80 90 100 III 120 130 WO ISO IM 170 ISO 190 200 210 220 230 240 
 
 Thick line curve shews atomic ntumes. 
 
 Thin , melting Dointt 
 
 Dotted lints indicate that data, are wanf/np 
 
 'THIS POINT SHOULD flf PLACED 66 DIVISIONS HICHfP 
 
 IS 2
 
 228 THE PERIODIC LAW. [BOOK I. 
 
 The elements on the descending parts of sections 2 and 3 
 of the atomic volume curve are electropositive and form basic 
 hydroxides; those on the ascending portions of the same sec- 
 tions are electronegative and form acid hydroxides. Each of 
 sections 4 and 5 contains four groups of elements arranged in 
 accordance with their negative or positive character. Electro- 
 positive elements occur on the first portions of the descending 
 curve in each of these sections (K, Ca ; Rb, Sr) ; these are 
 followed by a group of comparatively negative elements 
 (V, Cr, Mn ; Zr, Nb, Mo, Rh, Ru) ; these again by positive 
 elements (Fe, Ni, Co, Cu, Zn, Ga ; Pd, Ag, Cd, In) ; and after 
 these comes a group of negative and acid-forming elements 
 situated on the ascending part of the curve in each section 
 (As, Se, Br; [Sn], Sb, Te, I). Sections 6 and 7 are too 
 incomplete to allow of definite conclusions being drawn 
 regarding the positive or negative character of the elements 
 situated thereon. 
 
 108 Fusibility. The melting points of several elements have 
 been determined by various observers 1 ; of late especially by 
 Carnelley 2 , who has shewn that the fusibility of the elements 
 varies periodically with their atomic weights. The thin line 3 
 curve on the plate on p. 227 graphically exhibits this con- 
 nexion. 
 
 A connexion may be traced between the positions of an 
 element on the curve of atomic volumes and on that of 
 
 i includes hydrogen only, section 2 extends from lithium to sodium, section 3 
 from sodium to potassium, and so on. There are probably several unknown 
 elements with atomic weights greater than that of didymium and smaller than 
 that of tantalum ; the curve, if complete, would probably be marked by a sixth 
 maximum point between csesium and thorium, this part of the curve is therefore 
 said to comprise two sections (6 and 7). 
 
 1 See Constants of Nature, Part I. and Supplement to do. Also L. Meyer, 
 loc. cit. pp. 145, 6. (English Ed. pp. 129, 130.) 
 
 2 Phil. Mag. [5] 8. 315 et seq.: this paper contains a good resume of the 
 periodic law. All well established data concerning melting points are collected 
 in Carnelley's Tables of melting and boiling points (1885 87). 
 
 3 The values of the melting points used in preparing this curve are taken for 
 the most part from Carnelley's paper. The data are meagre, hence many gaps 
 occur in the curve (indicated by the broken lines) ; many of the numbers, especially 
 those for elements at and near to maximum points, must be regarded as only 
 rough approximations to the true values.
 
 CH. III. 108, 109] EXPLANATION OF PERIODIC LAW. 22Q 
 
 fusibility ; as a rule, only those elements which are situated 
 on ascending portions of the former curve, are easily fusible. 
 Generalisations have also been made concerning the con- 
 nexions between the atomic weights of groups of elements 
 and the melting points of these elements and some of their 
 analogous compounds 1 . Thus the melting points of the 
 haloid salts of the metals in Group li. (see table on p. 225) 
 are considerably higher than those of the corresponding salts 
 of the metals of Group III.: 
 
 e.g. MgCl 2 MgBr 2 ; CaCl 2 CaBr 2 CaI 2 ; SrCl 2 SrBr 2 SrI 2 ; 
 
 M.P. 708 695 ; 719 676 631 ; 825 630 507 ; 
 
 but A1 2 C1 6 Al 2 Br 6 A1 2 I 8 . 
 
 M.P. very low 90 185. 
 
 Carnelley 2 found the melting point of beryllium chloride 
 to lie between 585 and 617, hence he concluded that beryl- 
 lium belongs to Group n. and that the formula of its chloride 
 is BeCl 2 (Be = 9'i), and not BeCl 8 or Be 2 Cl 6 (Be= I3'i5) 3 . 
 The data, so far as obtained, concerning the boiling points, 
 crystalline forms, and expansion by heat, of the elements, 
 indicate that the connexion between these constants and the 
 atomic weights of the elements is of a periodic character 4 . 
 
 Hartley 5 has shewn that the ultra-violet spectra of elements 109 
 of the same group shew fairly marked analogies as regards 
 general character ; the spectra hitherto obtained do not permit 
 him to affirm, or deny, the existence of numerical relations 
 between the different groups of lines, sufficient to establish a 
 definite periodic connexion between the atomic weights of the 
 elements and the wave-lengths of the lines in the elementary 
 spectra. 
 
 That there exists a well-marked connexion, of periodic 
 character, between the atomic weights, and the heats of com- 
 bination of the elements with chlorine, bromine, and iodine, 
 
 See Williams and Carnelley, C. S. Journal Trans, for 1879. 563: 1880. 125. 
 
 Proc. R. S. 29. 190. See also Ibid. Ber. 17. 1357. 
 
 See forward, par. in. 
 
 For details see L. Meyer, loc. cit. pp. 150152. (English Ed. pp. 130152.) 
 
 C. . Journal Trans, for 1882. 84 : permanent photographs of the ultra-violet 
 spectra of various elements are given in this paper. See also ibid. Trans, for 1883. 
 390 : and Proc. R. S. 36. 462.
 
 230 THE PERIODIC LAW. [BOOK 1. 
 
 appears to have been first pointed out by Carnelley 1 . A little 
 later Laurie 2 independently drew attention to this subject and 
 exhibited the relation in question by means of a curve. 
 110 Having thus established the existence of a connexion, 
 distinctly of a periodic character, between the atomic weights 
 and the general nature of the elements, we may proceed to 
 consider the more important applications of the periodic law. 
 This consideration will also serve more fully to elucidate the 
 meaning of the law. 
 
 The law has been applied to predict the properties of 
 unknown elements. In the nomenclature of unknown ele- 
 ments Mendelejeff employs as prefixes the Sanskrit numerals 
 eka, dui, tri, &c. Thus if no elements were known with 
 atomic weights equal to about 48 and 90, two gaps would 
 occur in Group IV. (see table, p. 225); from a general in- 
 spection of the table it would be seen that these gaps ought to 
 be filled by elements bearing a more or less close analogy to 
 carbon ; the hypothetical elements would be called eka-carbon 
 and dui-carbon respectively. At the time of MendelejefFs 
 earliest publication there was no element known which could 
 be placed opposite the atomic weight 69 in Group ill., nor 
 any which could be placed opposite the atomic weight 44 in 
 the same group. The former of these hypothetical elements 
 Mendelejeff named eka-aluminium, the latter he called eka- 
 boron. The properties of eka-aluminium were predicted by 
 Mendelejeff from considering the position of the element in 
 the same group as, and interposed between, aluminium and 
 indium, and in the same series as, and following after, zinc. 
 In 1875 a new metal was discovered by L. de Boisbaudran. 
 The following table contains, in parallel columns, the leading 
 properties of this metal, and those enumerated by Mendelejeff 
 as characteristic of eka-aluminium : the hypothetical metal 
 of Mendelejeff and the gallium of de Boisbaudran are one 
 and the same element. 
 
 1 Proc. R. S. 29. 190. 
 
 2 Phil. Mag. (5) 15. 42. For data shewing that some of the physical 
 properties of compounds, e.g. melting and boiling points, vary periodically with 
 variations in the atomic weights of the constituent elements, see Camelley, Phil. 
 Mag. [5] 8. 36870.
 
 CH. III.IIO] PREDICTION OF ELEMENTS. 
 
 231 
 
 Eka-aluininium. 
 
 Atomic weight about 69. 
 
 Readily obtained by reduction. 
 
 Melting point low. Sp. gr. = 5'9. 
 
 Not acted on by air. 
 
 Will decompose water at a red heat. 
 
 Slowly attacked by acids or alkalis. 
 
 Will form a potassium alum more 
 soluble, but less easily crystallis- 
 able, than the corresponding 
 aluminium salt. 
 
 Oxide = E1 2 O 3 . Chloride = E1 2 C1 < ,. 
 
 Gallium. 
 
 Atomic weight = 69. 
 Readily obtained by electrolysing 
 alkaline solutions. 
 
 Non-volatile, and but superficially 
 oxidised in air at bright red heat. 
 Decomposes water at high temper- 
 atures. Soluble in hot hydro- 
 chloric acid, scarcely attacked 
 by cold nitric acid ; soluble in 
 caustic potash. 
 Forms a well-defined alum. 
 I Oxide = Ga 2 O 3 . Chloride = Ga2Cl 6 . 
 
 Eka-boron belongs to Group ill. the members of which 
 group combine with oxygen to produce well-marked oxides 
 having the composition R 2 O 3 . In its properties eka-boron 
 ought to be related to aluminium as calcium is to mag- 
 nesium, and as titanium is to silicon. The atomic weight of 
 eka-boron must be about 43 46, inasmuch as it follows K (39) 
 and Ca (40), and is followed by Ti (48) and V (51). Reason- 
 ing from these data, Mendelejeff 1 predicted certain properties 
 as characteristic of eka-boron and its salts. Some of these 
 are placed in parallel columns with a description of the 
 properties of the metal scandium*, discovered in 1879 by 
 Nilson : 
 
 Eka-boron. 
 
 Atomic weight about 44. 
 
 Oxide Eb 2 O 3 soluble in acids ; sp. 
 gr. about 3-5; analogous to but 
 more basic than A1 2 O 3 ; less basic 
 than MgO ; insoluble in alkalis. 
 
 Salts of Eb colourless, and yield 
 gelatinous precipitates with 
 KOH, K 2 CO 3 , Na 2 HPO 4 , &c. 
 
 Sulphate, Eb 2 .3SO 4 , will form a 
 
 double salt with K 2 SO 4 , probably 
 not isomorphous with the alums. 
 Chloride EbCl 3 or Eb 2 Cl 6 , sp. gr. 
 about 2, less volatile than Al 2 Clg. 
 1 See translation of MendelejefTs paper in Chem. News, 41. pp. 71 72. 
 8 Ber. 14. 1439. See also Cleve, Ber. 12. 2264: and Compt. rend. 89. 419 
 (abstract of latter paper in C. S. Journal for 1880. 8, is useful). 
 
 Scandium. 
 
 Atomic weight = 44. 
 
 Oxide Sc 2 O 3 ; sp. gr. = 3*8 ; soluble 
 in strong acids ; analogous with 
 but more decidedly basic than 
 A1 2 O 3 ; insoluble in alkalis. 
 
 Solutions of Sc salts, colourless and 
 yield gelatinous precipitates with 
 KOH, K 2 CO 3 , and Na 2 HPO 4 . 
 
 Sulphate, Sc 2 .3SO 4 , forms a double 
 salt, not an alum, 
 
 Sc 23 S0 4 . 3 K 2 S0 4 .
 
 232 THE PERIODIC LAW. [BOOK I. 
 
 There was a gap in Group IV. Series 5. Eka-silicon comes 
 in the group which comprises Si, Sn, and Pb, and in the 
 series including Ga and As. This hypothetical element ought 
 also to shew analogies with other elements ; thus, 
 
 Es : Ti : : Zn : Ca : : As : V. 
 
 From the position of eka-silicon^ Mendelejeff concluded that 
 it would be a grey metal, obtained by reducing the oxide by 
 sodium, fusible with difficulty; it would decompose steam 
 very slowly, would be scarcely acted on by acids, but easily 
 by alkalis. The oxide, EsO 2 , (sp. gr. about 47) would be 
 obtainable by burning the metal in air, it would resemble 
 TiO 2 , but would be less basic than this oxide, although more 
 basic than SiO 2 ; the hydroxide would be soluble in acids, 
 but the solution would be easily decomposed yielding an in- 
 soluble metahydroxide. The oxide would yield a series of 
 double fluorides M 2 EsF 6 (M = alkali metal) isomorphous with 
 the corresponding salts of Si, Ti, Zn, and Sn. The fluoride 
 EsF 4 would not be gaseous ; the chloride EsCl 4 would be a 
 volatile liquid boiling at about 100. Eka-silicon would form 
 volatile organo-compounds. 
 
 The discovery and study of germanium, by Winkler 2 have 
 entirely confirmed Mendelejeff's prediction : eka-silicon and 
 germanium are one and the same element. 
 
 Ill The periodic law has also been successfully used as a guide 
 in the comparative study of the properties of elements already 
 known. 
 
 To which group of elements does beryllium belong ? Is 
 the formula of the oxide BeO or Be 2 O 3 , and of the chloride 
 BeCl 2 or BeCl s ? Is the atomic weight of beryllium 9 or 13-5 ? 
 
 The arrangement of the elements in accordance with the 
 periodic law seems to necessitate the placing of beryllium in 
 Group II. ; but Nilson and Pettersson, and also Humpidge, who 
 had made a special study of this metal, were for some time 
 strongly of opinion that beryllium should be classed with the 
 
 1 See Chem. News, 41. 83. 
 
 2 Ber. 19. 210; J.fiir prakt. Chemie [a], 34. 177: s. also Kriiss and Nilson, 
 Ber. 20. 1296: L. de Boisbaudran, Compt. rend. 102. 1291; 103. 452: Kobb, 
 Wied. Ann. 29. 670: also L. Meyer, Ber. 20. 497.
 
 CH.III.IIl] CLASSIFICATION OF ELEMENTS. 233 
 
 elements which form oxides of the composition R 8 O 8 . The 
 atomic weight of beryllium = # . QT : the data regarding the 
 specific heat of this metal have been presented in Chapter I. 
 par. 28, and it has there been shewn that, so far as specific 
 heat data are concerned, the value of n is most probably I. 
 
 Carnelley's determination of the melting-point of beryl- 
 lium chloride (see ante, par. 108) points to the beginning of 
 Group II. as the proper position for beryllium, and hence to 
 the number 9-1 as the atomic weight of this metal. 
 
 The general chemical characters of beryllium salts are 
 summed up in the three statements 1 (Be = 9'i); 
 
 (1) Li : Be=Be : B 
 
 (2) Li : Na = Be : Mg = B : Al 
 
 (3) Li : Mg = Be : Al =B : Si. 
 
 From these considerations we may conclude that there is a 
 large probability in favour of the value 9*1 for the atomic 
 weight of beryllium. This conclusion is supported by 
 Hartley's observations on the spectrum of beryllium and 
 his comparison of that spectrum with those of metals in 
 Groups II. and III.* 
 
 Nilson and Pettersson 3 have succeeded in gasifying beryl- 
 lium chloride; and Humpidge 4 has gasified beryllium chloride 
 and bromide. The determinations of the vapour densities of 
 these compounds shew that the formulae BeCl 2 and BeBr s 
 (Be = 9'i) really represent their molecular weights. 
 
 There can be no doubt that the atomic weight of beryllium 
 is 9' i, and that this metal is to be placed in the same group 
 as magnesium, calcium, zinc, strontium &c., all of which form 
 oxides having the composition RO and chlorides having the 
 composition RC1 8 . 
 
 In the table on p. 225 tellurium and iodine are placed in 
 Series 7. The atomic weight of iodine was for many years 
 supposed to be less than that of tellurium ; nor was this 
 result contradicted by the work of Wills 8 . Nevertheless the 
 
 See Brauner, Ber. 14. 53. 
 
 C. S. Journal Trans, for 1883. 316, 390: also Proc. R. S. 36. 461. 
 
 Ber. 17. 987. 
 
 Proc. R. S. 38. 188. 
 
 C. S. Journal Trans, for 1879. 704.
 
 234 THE PERIODIC LAW. [BOOK I. 
 
 analogies between sulphur, selenion, and tellurium, on the 
 one hand, and chlorine, bromine, and iodine, on the other, 
 are so marked that it would be absurd to place tellurium in 
 the same class as chlorine and bromine, and to classify iodine 
 with sulphur and selenion. But if the grouping indicated 
 by the periodic law is to be adhered to the atomic weight of 
 tellurium must be less than that of iodine. Brauner 1 in 1883 
 made an experimental criticism of the method by which the 
 atomic weight of tellurium had been determined by Berzelius 
 and also by Wills ; he shewed that this method almost neces- 
 sarily gives results which are too high. By converting tel- 
 lurium into the very stable basic sulphate Te 2 O 4 SO 3 , and also 
 by syntheses of copper telluride Cu 2 Te, Brauner obtained a 
 series of values for the atomic weight of tellurium varying 
 from 124*94 to I25'4 with a mean value of 125. We are there- 
 fore justified in placing tellurium in Group VI. and iodine in 
 Group VII. 
 
 Uranium is another element the comparative study of the 
 properties of which has been much advanced by the appli- 
 cation of the periodic law. The atomic weight of this element 
 has been established as = n. 120. If n = i, the three oxides of 
 uranium must be formulated UO, U 2 O 8 , and U 3 O 4 ; but there 
 is no place for an element with this atomic weight and 
 forming these oxides in the periodic arrangement If how- 
 ever n = 2, then (U = 240) the oxides become UO 2 , UO 3 , and 
 U 3 O 8 , and uranium finds a place in VI 12. The preceding 
 members of Group VI. which belong to even series, viz. Cr, 
 Mo, and W, yield oxides of the form RO 3 which are acid- 
 forming. But a comparative study of the relations between 
 the properties of oxides and the atomic weights of the 
 elements in these oxides shews, that as the atomic weight 
 of the elements in a group increases the acidic character of 
 the higher oxides formed by these elements becomes less 
 marked (e.g. CrO 3 is more markedly an acidic oxide than 
 MoO 3 or WO 8 ). Now the highest oxide of uranium is an 
 acid-forming oxide, but its acidic functions are less marked 
 than those of CrO 3 , MoO 3 , and WO 3 ; salts corresponding to 
 
 1 See abstract in Ber. 16. 3055 (original is in Russian).
 
 CH. III. III, 112] LONG AND SHORT PERIODS. 235 
 
 K 2 CrO 4 and K 2 Cr 2 O 7 in which Cr is replaced by U are known. 
 Uranic chloride, UC1 4 if 11 = 240, resembles MoCl 4 in being 
 volatile and decomposable by water. 
 
 /. atomic weight\ 
 
 The atomic volume i.e. - of the four 
 
 V spec, gravity / 
 
 metals, Cr, Mo, W, U, increases as atomic weight increases, 
 the values being Cr = 7'6; Mo= n ; W= 11 ; U= 12*5. 
 
 Hence the comparative study of compounds of uranium, 
 which is suggested by the periodic law, justifies the adoption 
 of the number 240 as the atomic weight of this metal. 
 
 Determinations of the densities of gaseous uranium bromide 
 and chloride, and of the specific heat of pure uranium, have 
 fully confirmed this value. (See ante, Chap. I. pars. 19 and 25 ; 
 also p. 59.) 
 
 The facts enumerated in the preceding pages undoubtedly 11 
 establish the periodic law on a firm basis, and justify the em- 
 ployment of this law as one of the main guides in a general 
 scheme of chemical classification 1 . 
 
 The following arrangement of the elements (the table is 
 taken, with a few alterations, from a paper by Mendelejeff in 
 Ber. 13. 1804) is in the opinion of Mendelejeff himself the 
 best for clearly setting forth the general teaching of the 
 periodic law. (See next page.) 
 
 Each group except Group vill. contains members be- 
 longing to odd and to even series ; or it may be said that 
 each vertical column, or large series, is subdivided into two 
 parts having seven elements in each. The entire column, 
 comprising an odd and an even series, forms a ' long period ' ; 
 the seven members in the even or in the odd series form 
 a 'short period.' The members of Group vill. form 'transition 
 'periods' from series 4 to 5, 6 to 7, (probably 8 to 9), and 
 10 to u. Including the 'transition periods,' each complete 
 ' long period ' should contain 17 elements. 
 
 Because of its peculiar properties, and also because of the 
 
 1 The system of classification of elements and compounds adopted in Ele- 
 mentary Chemistry (Pattison Muir and Slater) is based entirely on the periodic 
 law. 
 
 It is very unfortunate that Mendelejeffs Treatise on Chemistry should not 
 have been translated into one of the languages of Western Europe.
 
 236 THE PERIODIC LAW. [BOOK I. 
 
 
 N O 
 
 2 1 H f ' I I I I | 3 
 
 e * 
 
 i 
 
 
 ro N <* H t-x O rj- fx OO 
 
 S | ii | ii if 2^ 7 1 1 I - l IS 
 
 H &a < S p 
 
 11 
 
 
 
 R P; ?5 5- 3 1 & 
 
 
 
 oo II II II II II | | || I I II I 
 
 u 3 ,3 <3 3 1 w 
 
 
 w 
 
 LA t>G\O'^" v O II II o > i ri ri ri 
 
 CO 
 
 g x 
 
 CO 
 
 f f f H IT F i ^< H ii ii ii H H ii t~ 
 
 ^Q "- 1 4-* .^ .Q O ^*.vo bfl T) C C ^ <u i i 
 
 gjCotxN^^ ^ v 8<U'- | cocoH 
 
 > 2 
 
 H 
 
 CO 
 
 
 do ro 
 
 ^cjcoH^Og^^UNOO^copq 
 H II II 
 
 0) 
 
 
 
 eq II II if li* II li* li" II II II II II II II eo 
 3 j A D O' *! jg^^co^^O 
 
 
 
 S1U3UI313 JBOldXj. 
 
 
 I 
 
 rH II l-l 
 ffi 
 
 
 
 |s>>>^ s ^5^ > >> 

 
 CH. III. 112] ODD AND EVEN SERIES. 237 
 
 anomalous relations between the values of its atomic weight 
 and those of succeeding elements, hydrogen is regarded as 
 the sole representative of Series I, Group I. 
 
 Comparing series, we find closer analogies between corre- 
 sponding members of odd or of even series, than between 
 those of odd and even series : thus, comparing Series 4 and 6, 
 and 4 and 7, potassium and rubidium are seen to be more 
 closely related than potassium and silver; calcium and 
 strontium, than calcium and cadmium ; vanadium and nio- 
 bium, than vanadium and antimony. Again, comparing 
 Series 5 and 7, and also 5 and 6, it is seen that the relations 
 between zinc and cadmium, or between arsenic and antimony, 
 are closer than those between zinc and strontium, or arsenic 
 and niobium. 
 
 Omitting the 'typical' elements (see p. 238) it may be 
 said that, as a rule, the most markedly nonmetallic elements 
 are placed in odd series. Also, that the passage from an 
 even to an odd series is accompanied by a gradual change, 
 but that from an odd to an even series by a more sudden 
 change, in the properties of the elements ; thus chromium 
 and manganese resemble copper and zinc much more than 
 selenion and bromine resemble rubidium and strontium, or 
 than tellurium and iodine resemble caesium and barium. It 
 may also be laid down as a general proposition that volatile 
 organo-metallic compounds are formed only by metals which 
 occur in odd series ; should such compounds be hereafter 
 formed containing metals which belong to even series, the 
 properties of the compounds in question will probably differ 
 much from those of the volatile organo-metallic compounds 
 at present known. (Mendelejeff.) 
 
 The elements which form the 'transition periods' (Group 
 VIII.) possess many characteristic properties. They are very 
 infusible, have small atomic volumes, and occlude oxygen and 
 other gases ; oxides of the form RO 4 are met with in this group 
 only ; the highest oxides are basic or only slightly acidic ; 
 these metals form stable alkaline double cyanides K 4 RCy 6 . 
 K 3 RCy 6 , or K 2 RCy 4 , and also stable ammoniacal compounds 1 . 
 1 See Mendelejeff, Chem, News, 40. 267.
 
 238 THE PERIODIC LAW. [BOOK I. 
 
 The elements in Series 2 (from lithium to fluorine), and 
 perhaps the first member of Series 3, viz. sodium 1 , are grouped 
 together by Mendelejeff as ' typical ' elements. There is no 
 ' transition period ' coming between the even Series 2 and the 
 odd Series 3 as there is between Series 4 and 5, 6 and 7, and 
 10 and II. The mean difference between the atomic weights 
 of two elements in successive even series and in the same 
 group (e.g. between potassium and rubidium, or between 
 rubidium and caesium) is 45 ; but the mean difference between 
 the atomic weight of an element in Series 4 and the corre- 
 sponding element (i.e. the element in the same group) in 
 Series 2 is 35 ; hence we should expect to find the relations 
 of Series 2 to other series different from the general mutual 
 relations exhibited by these other series. As the lower mem- 
 bers of an homologous series of carbon compounds are some- 
 times characterised by the possession of properties which do 
 not belong to the higher members, so the elements with 
 atomic weights ranging from I to 19 (? 23) are characterised 
 by special properties which to some extent mark them off 
 from the other elements. 
 
 As the atomic weight increases in each group, the basic 
 character of the higher oxides formed by the members of the 
 group becomes more marked, and at the same time these 
 oxides become more easily reduced. It is also to be noted 
 that the composition of the more stable haloid and oxyhaloid 
 salts (and in some cases of the more stable salts as a whole) 
 tends, as atomic weight increases, to correspond in form with 
 an oxide containing less oxygen than the highest oxide. 
 These statements hold good more especially for those 
 members of a group which occupy the odd series. Group V. 
 presents a good example. Sb 2 O g is more basic than P 2 O S , and 
 Bi 2 O 6 is marked by an almost complete absence of acidic pro- 
 perties. The highest oxides of this group belong to the form 
 RX 5 (see p. 240) ; the stable haloid and oxyhaloid salts of 
 phosphorus, vanadium, niobium (PF 5 , VOC1 3 , NbCl 5 ), belong 
 to the same form, but the bismuth haloid and oxyhaloid salts 
 
 1 Some chemists class all the members of Series i and 3 (Li to Cl inclusive) 
 as 'typical' elements,
 
 CH. III. 112,113] FORMS OF SALTS. 239 
 
 are BiCl s , BiBr s , BiOCl, BiOBr, &c., which belong to the 
 form RX 3 corresponding to that of the lower oxide Bi 2 O 3 . 
 
 The first and last members of a series, and more especially 
 of a ' long period,' present marked differences in their general 
 chemical behaviour ; thus lithium, potassium, and rubidium, 
 the first members of the long periods i, 2, and 3, are strongly 
 positive, whereas the last members of the same periods, 
 viz. chlorine, bromine, and iodine, are typically negative 
 elements. 
 
 Each group may be divided into two sub-groups, one 
 comprising the elements belonging to even series, the other 
 those belonging to odd series. Calling these sub-groups 
 families, we may say that the family-character is more 
 marked than the group-character in Groups I. and VII., but 
 that in Groups III., IV., and V. the group-character prepon- 
 derates, and that both the general group-character and the 
 special family-character are well seen in Groups II. and VI. 
 
 The compositions of the highest oxides, and of some of 113 
 the other salts, appear to be periodic functions of the atomic 
 weights of the elements. In dealing with this question it 
 will be well to use the term ' formula weight ' rather than 
 molecular weight, as the molecular weights of very few oxides 
 have been determined. 
 
 If R be used to represent the mass of an element ex- 
 pressed by its atomic weight ; and if X represent the masses 
 of F, Cl, Br, I, expressed by the respective atomic weights of 
 these elements, or the masses of the groups (OH), (NO 8 ), 
 (C1O 3 ), &c., expressed by these formulae, or the masses of 
 the elements or groups of elements expressed by halves of 
 the formulae, O, S, (SOJ, (CrOJ, &c. ; then we may say that 
 the oxides 
 
 R 2 0, RO, R 2 3 , R0 2 , R 2 S , 
 belong respectively to the forms 
 
 RX, RX 2 , RX S , RX 4 , RX 5 : 
 also that the salts 
 
 R 9 S0 4 ; R.2NO 3 ; R-3NO 8 , ROC1, R 2> 3SO 4 , RO.NO S ; ROC1 8 , 
 belong respectively to the forms 
 
 RX; RX t ; RX 8 , RX 8 , RX,, RX 8 ; RX 6 .
 
 240 THE PERIODIC LAW. [BOOK I. 
 
 In this way it becomes possible to give general expressions 
 for the forms of the highest stable oxides characteristic of 
 each group ; thus, 
 Group i ii in iv v vi vii vin 
 
 R 2 R 2 2 R 2 3 R 2 4 R 2 5 R 2 O 6 (R 2 O 7 ) (R 2 O 8 ) 
 or RX RX 2 RX 3 RX 4 RX 5 RX 6 (RX r ) (RX 8 ) 
 
 This statement may be put thus ; the number of oxygen 
 atoms in the general expression for the composition of the 
 highest stable oxide characteristic of each member of a series 
 increases as the atomic weights of the members of the series 
 increase. 
 
 Most of the stable salts (haloid salts, oxyhaloid salts, 
 nitrates, sulphates, chromates, phosphates, &c.) characteristic 
 of the members of each group belong to the same general 
 form (RX, RX 2 , &c.) as the oxides. But in every group 
 well-marked salts are known which belong to higher forms 
 than the oxide form : thus, some of the members of Group I. 
 form peroxides (K 2 O 2 , K 2 O 4 , &c.) ; some of the elements in 
 Group ii. form salts (such as K 2 BeF 4 , K 2 ZnCl 4 , &c.) of the 
 form RX 6 ; salts, such as BOC1 3 , KBF 4 , KAlBr 4 , &c., be- 
 longing to the form RX 5 , are found in Group III. The forms 
 of the highest salts belonging to each group, and also the 
 oxide forms, are given by Brauner 1 ; thus, 
 
 Group i ii in iv v vi vn vin 
 
 Salt forms RX T RX 6 RX 5 RX 4 RX 3 RX 2 RX /R 2 X \ 
 
 Oxide forms R 2 O R 2 O 2 R 2 O 3 R 2 O 4 R 2 O 5 R 2 O 6 (R 2 O 7 ) \R Z O J 
 or thus, 
 
 Salt forms RX 7 RX 6 RX 5 RX 4 RX 3 RX 2 RX /R 2 X \ 
 
 Oxide forms RX RX 2 RX 3 RX 4 RX 5 RX 6 (RX r ) \RXj 
 
 The statements generalised in these expressions can be 
 accepted only as rough approximations to general truths. 
 Oxides of the forms given in the table are sometimes less 
 stable than oxides of other forms; e.g. Cu 2 O is less stable 
 than CuO, PbO 8 than PbO, &c. : the form chosen for the 
 highest oxides is sometimes represented by very few if any 
 actually occurring compounds ; thus the form R 2 O 7 , charac- 
 teristic of Group VII., finds its only representative in I 2 O 7 , 
 
 1 Sitzberichte der K. Akad. zu Wien, (math-naturwiss, classe) 84. 116-;.
 
 CH. III. H3,H4] VALENCY. 24! 
 
 and the existence of this oxide cannot be regarded as proved. 
 Again, salts belonging to the general expressions given as 
 representing the highest forms are sometimes fairly character- 
 istic of the group, in other cases it is only by a dexterous 
 manipulation of formulae that the existence of such salts can 
 be discovered ; thus a great many well-marked salts of the 
 members of Group V. undoubtedly belong to the form RX 3 , 
 but it is only by having recourse to such a substance as 
 NaOH . 3H 2 O [Na(OH)(OH) 3 H s ] that a salt of the form RX 7 
 can be found belonging to Group I. 
 
 Relations can be traced between the general forms of 
 hydrogen and hydroxyl compounds, especially in Groups IV., 
 v., vi., and vu. ; thus, 
 
 Group 
 Hydrogen compounds 
 
 e.g. 
 
 IV 
 
 RH 4 
 
 SiH 4 
 
 V 
 
 RH 3 
 
 PH 3 
 
 VI 
 
 RH 2 
 SH 2 
 
 VII 
 
 RH 
 C1H 
 
 Hydroxyl compounds 
 e.g. 
 
 RH 4 O 4 
 
 Si(OH) 4 
 
 RH 3 4 
 PO(OH) 3 
 
 RH 2 O 4 
 
 S0 2 (OH) 2 
 
 RHO 4 
 
 C1O,(OH) 
 
 Dalton, and after him Berzelius, sought to elucidate the 
 laws of atomic synthesis ; they strove to find forms capable 
 of expressing the maximum number of atoms of this or that 
 element which could combine to form salts. But much had 
 to be done before these limiting forms could be found : a firm 
 standing ground appears to be now gained in the periodic 
 law ; to build a structure worthy of the foundation must be 
 the work of the future. 
 14 The valency of the elementary atoms probably varies 
 periodically with the relative weights of these atoms. Thus 
 taking Series 2, and assuming that the atom of lithium is 
 monovalent, it is seen that in this series the valency of the 
 elementary atoms increases from one to four, and again di- 
 minishes from four to one : 
 
 Li Be B C N O F 
 
 Valency I 234321. 
 
 If the evidence were sufficient to warrant the assumption 
 that the valency varies in every series in the same way as in 
 Series 2, we should have in the periodic law a most important 
 aid towards determining the valencies of all the elementary 
 M.C. 1 6
 
 242 THE PERIODIC LAW. [BOOK I. 
 
 atoms. But the evidence at present available concerning 
 valency does not permit us to make this assumption. A pro- 
 bable value for the valency of an elementary atom may be 
 deduced from the position of the element in the periodic 
 arrangement, but this value must not be considered as final. 
 It has indeed been sought to fix the valencies of elementary 
 atoms from considerations drawn from the positions of these 
 elements in the periodic classification ; but this has been 
 done only by attaching to the term 'valency' a much looser 
 meaning than that which I have attempted to shew must be 
 given if an accurate working hypothesis is to be developed. 
 In applying the periodic law to determine the valencies of 
 elementary atoms, the formulae of oxides and of solid salts 
 generally have been employed as data from which con- 
 clusions might be drawn. But if we define the valency of 
 an atom as the maximum number of other atoms with which 
 the given atom can directly interact in any molecule, then, to 
 deduce valencies from a study of solid salts, we must assume, 
 (i) that the formula of a solid salt certainly represents at 
 least the proportion between the numbers of atoms of each 
 element in the molecule ; (2) that the atom, the valency ot 
 which is to be determined, acts on, and is acted on by, certain 
 other atoms in the molecule in some cases it may be action 
 is assumed between all the atoms, in other cases only between 
 some of the atoms, in the molecule ; and (3) we must assume 
 a value for the valency of each atom, other than the given 
 atom, in the molecule. Thus to take an extreme case, 
 hydrated chloroplatinic acid H PtCl 6 . 6H..O has been re- 
 presented in this way 
 
 VIII III IV 
 
 H 2 Pt(-Cl = O = H 2 ) fi ; 
 
 and the conclusion has been drawn that the platinum atom 
 is octovalent. 
 
 I have already 1 discussed assumptions (2) and (3^1, and 
 have, I hope, shewn how unsatisfactory any conception of 
 valency must be which in the present state of knowledge is 
 based on the study of other than gaseous compounds. A solid 
 
 1 See chapter n, section 3, par. 63.
 
 CH. III. I 14, I 1 5] VALENCY. 243 
 
 compound is prepared with definite properties; analysis serves 
 to fix the composition ; the atomic weights of the elements in 
 the compound being known, a formula is found : but to 
 assume that this formula necessarily represents the ratio 
 between the numbers of different elementary atoms in the 
 molecule of this compound, is I think more than a fair in- 
 ference from the facts. For is not this to assume that the 
 ' chemical unit ' of the solid compound is a molecule, whereas 
 it may very probably be a group of molecules ? The defini- 
 tion of ' molecule ' is a physical definition, and is strictly 
 applicable only to gaseous bodies. The properties of a solid 
 may be the properties of a number of little definite parts, 
 each of which decomposes into two or more simpler groups 
 (molecules) when the solid is gasified ; the ratio between the 
 numbers of atoms in the true molecules may be different 
 from the ratio between the numbers of atoms in those groups 
 of molecules, which form the building-stones of the solid 
 compound 1 . 
 
 But it may be urged that a much wider meaning ought 
 to be given to the term valency. Better, I would reply, 
 employ another term or other terms. Let us make as much 
 use of valency as we can ; so far as it goes it is definite, with- 
 out it the chemistry of carbon compounds especially could 
 not have made the advances which it has made. But it is 
 not all. 
 
 A suggestion, which seems fairly probable, has been made 
 to the effect that the maximum valencies of the atoms increase 
 from the members of Group I. to those of Group VII., but that 
 the valency actually exhibited in the majority of gaseous 
 compounds varies from a minimum in Group I. to a maximum 
 in Group IV., and then decreases to a minimum in Group VII. 
 .15 In applying the periodic law to the case of an individual 
 element, it is necessary in the first place to consider the 
 properties both of the group and the series to which the 
 element belongs ; then the position of the element in the 
 group and series must be considered ; the relations of other 
 
 1 The experiments of Hittorf on the electrolysis of aqueous solutions of cadmium 
 iodide are very suggestive (see ante, p. 215). 
 
 1 6 2
 
 244 THE PERIODIC LAW. [BOOK I. 
 
 elements, situated similarly to the specified element, to the 
 other members of their groups and series must also be con- 
 sidered, and these relations must be compared with those of 
 the special element under consideration ; and finally the re- 
 lations of group to group and of series to series in the entire 
 scheme must be looked to. The method is strictly com- 
 parative. It is necessary to study classes of elements and 
 compounds, and to compare class with class and individual 
 with individual, before just conclusions can be drawn 1 . 
 
 The periodic law emphasises the existence of typical forms 
 for the compounds of elements ; it points to limiting values 
 for the numbers of atoms which can be associated together 
 in groups. It teaches the importance, in the chemistry of 
 solid and liquid compounds, of the law of multiple proportions. 
 It reminds us that at present we must study the properties of 
 groups of compounds, that we must sum up these properties 
 in the simplest possible formulae, and that the whole chemical 
 history of each compound must determine the form to be 
 given to the symbol by which we express that history. It 
 tells us that although we do not know whether such formulae 
 do or do not represent the relative weights of the molecules 
 of the bodies formulated, nevertheless these formulae can be 
 classified under a few types ; and that thus a certain amount 
 of order can be introduced into the classification of solid and 
 liquid compounds, general conclusions can be drawn, and pre- 
 dictions can be made which may be submitted to the test of 
 experiment. And while doing this, the periodic law keeps 
 before us the necessity of from time to time modifying our 
 scheme of classification ; it reminds us that a typical classifi- 
 cation is of necessity temporary, but that just by reason of its 
 elasticity it is suited to the present needs of the chemistry of 
 solid and liquid substances 2 . 
 
 1 The student should work out some cases in detail ; say lead in Group iv., 
 antimony in Group v., and cadmium in Group n. 
 
 2 It is interesting to observe in the applications of the periodic law the survival, 
 in modified and more precise form, of the old conception of the element as an 
 essence or principle, capable of impressing on all substances into which it entered 
 properties sufficiently definite to mark off these substances from all others which 
 did not contain this principle.
 
 CHAP. III. 115] SUMMARY. 245 
 
 An interesting paper on the periodic law, especially as applied to the clas- 
 sification cf elements and compounds, by T. Bayley, will be found in Phil. 
 Mag. (5) 13. 26. Other important papers on the same subject, by Carnelley, 
 are published in Phil. Mag. (5). 18. i et seq.\ do. do. (5). 20. 259. In these 
 papers the periodic law is illustrated by considering the melting and boiling 
 points, and to some extent also the heats of formation, of the halogen compounds 
 of the elements, and also the compounds of elements with organic radicles, and 
 also the occurrence in nature of the elements, and the relations between the 
 colours of compounds and the atomic weights of their constituent elements; and 
 the facts thus obtained are applied to determine the values to be assigned to the 
 atomic weights of various elements, and also the positions of these elements in 
 the general scheme of classification based on the law in question.
 
 [BOOK i. 
 
 CHAPTER IV. 
 
 APPLICATIONS OF PHYSICAL METHODS TO QUESTIONS OF 
 CHEMICAL STATICS. 
 
 116 CHEMISTRY being a more concrete science than physics 
 must of necessity derive help in solving its problems from 
 the use of physical methods of investigation ; but while 
 using such methods the chemist ought not to forget that his 
 aim is to find answers to chemical, not to physical, questions. 
 
 Minute descriptions of physical processes and details of 
 physical experiments are not demanded in a treatise on 
 physical chemistry; much less is there required elaborate 
 enunciations of the methods of calculation employed in 
 physical researches. Such things give, it is true, an appear- 
 ance of great accuracy and profound knowledge ; but the ap- 
 parently accurate knowledge and full discussion of physical 
 details too frequently serves as an excuse for loose state- 
 ments and superficial generalisations regarding those vital 
 chemical questions for answering which so vast a collection of 
 'precautionary and vehiculatory gear' has been provided. In 
 attempting to give an outline of the more important appli- 
 cations of physical methods to chemistry one is also liable 
 to err in the other direction : vague statements to the effect 
 that the boiling points of homologous hydrocarbons exhibit 
 constant differences, or that the chemical constitution of 
 carbon compounds is intimately connected with their optical 
 activity, or that chemical actions which involve a degradation 
 of energy in the reacting systems frequently occur, state- 
 ments such as these are utterly inadequate.
 
 CH. IV. 1 1 6, 1 1/] APPLICATIONS OF PHYSICAL METHODS. 247 
 
 I cannot hope to avoid both dangers : but I may venture 
 to believe that the contents of the present chapter will be 
 of some assistance to those who attempt to gain clear con- 
 ceptions of some of the important phenomena forming the 
 subject-matter of physical chemistry. 
 
 Some of the physical methods employed by the chemist 
 as aids in attempts to solve the questions of chemical statics 
 have been considered in the foregoing chapters of this book ; 
 in addition to these I shall consider the following; (i) ther- 
 mal methods, (2) optical methods, (3) methods which in- 
 volve measurements of the volumes of reacting substances, 
 (4) methods based on determinations of 'etherification-values', 
 and (5) a few miscellaneous methods. 
 
 SECTION I. T formal Methods*. 
 
 117 The principle of the conservation of energy lies at the 
 root of all thermo-chemical investigation. When two or 
 more chemical substances react so as to produce a new 
 system, or new systems, of substances, mechanical work may 
 be done by expansion, electrical currents may be produced, 
 heat may be generated, and energy may be lost to the 
 system in the forms of sound or radiant heat. The sum of 
 these various kinds of energy, together with the energy re- 
 maining in the final system, must be equal to the energy 
 which was present in the original system. A very large part 
 of the energy set free during chemical changes generally 
 leaves the changing systems in the form of heat; hence, 
 measurements of the quantities of heat produced during 
 definite chemical processes afford valuable information with 
 
 1 The principal text-books on the subject are NAUMANN'S Lehr- und Hand- 
 bitch tier Thermochemie (1882). THOMSEN'S l^hermochemische Untersuchungen, 
 containing in a systematic form the work of many years which has hitherto been 
 scattered through various memoirs, 4 vols. (1882-86). BERTHELOT'S Essai de 
 Mi'caniqne Chimiqite fondcc snr la Thennochiinit:, i vols. (1879) with supple- 
 ment. JAHN'S Die Grundsdtze der Thermochemie (1882). PATTISON MUIR'S 
 The Elements of Thermal Chemistry (1885). 
 
 The first book of the second volume of OSTWALD'S Lehrbuch der Allgentfiiun 
 Choiric is devoted to thermal chemistry (1887).
 
 248 THERMAL METHODS. [BOOK I. 
 
 respect to the differences between the amounts of energy 
 possessed by the systems in their original and final states. 
 To measure such differences of energy is the primary aim of 
 thermal chemistry. 
 
 We are accustomed to conceive of most chemical changes 
 as divisible broadly into two parts, (i) separation of molecules 
 into atoms, (2) re-arrangement of atoms to form new mole- 
 cules. We picture to ourselves the final arrangement of the 
 atoms as 'dependent on the nature of these atoms, and on 
 their relative positions in the molecules which composed the 
 original system, that is to say, we picture the progress of 
 mutual actions and reactions among the separated atoms. 
 We know little, or nothing, of the causes of this re-arrange- 
 ment ; but we are accustomed to say that the atoms interact 
 because of their mutual affinities. 
 
 A consideration of the circumstances under which chemical 
 changes proceed and of the connexions between these and the 
 thermal changes which accompany them will, I think, make 
 it evident that measurements of the quantities of heat pro- 
 duced during chemical occurrences do not represent measure- 
 ments of the 'chemical affinities !1 of the reacting atoms ; but 
 these measurements do enable us to draw conclusions as to 
 the constitution of chemical substances, and the general laws 
 of chemical change. 
 
 The bearing of thermochemical measurements on the 
 subjects of affinity and chemical equilibrium in general will be 
 considered in the second book : in the present section I pro- 
 pose to give a very brief sketch of the methods of thermal 
 chemistry, and an outline of the more important results ob- 
 tained relating to allotropy, isomerism, nascent state, and 
 other phenomena of chemical statics, referring the student 
 for more detailed information and discussion to my Elements 
 of Thermal Chemistry. 
 
 118 The notation of thermal chemistry used by Thomsen is 
 very simple: the formulae of the reacting substances are 
 enclosed in a square bracket, and each formula is separated 
 from the other by a comma. The formulae are always taken 
 
 1 See post, Book n.
 
 CHAP. IV. 1 1 8] NOTATION OF THERMAL CHEMISTRY. 249 
 
 to represent so many grams of the substances. The unit of 
 heat adopted is that quantity which raises the temperature of 
 i gram of water at about 18 C. through i C. The signs 
 + and are used to express quantities of heat produced or 
 which disappear. Thomsen writes the figure expressing the 
 number of atoms of each element above the symbol of that 
 element 1 . 
 
 Thus, the formula [H 2 , Cl 2 ] =44,000 + , means that a 
 quantity of heat, sufficient to raise the temperature of 4/1,000 
 grams of water at about 18 through i, is produced during 
 the chemical process represented in ordinary notation by 
 H 2 +C1 2 =2HC1, the quantities of hydrogen and chlorine 
 being taken in grams. The symbol Aq, separated by a 
 comma from another symbol, means that a large excess of 
 water is present and that its effect in the total thermal 
 change is taken into account; thus, [HC1, Aq] = 17,320 + , 
 means that 17,320 gram-units of heat are produced during 
 the solution of 36*5 grams of hydrochloric acid in a quantity 
 of water so large that addition of more water would not affect 
 the thermal value of the reaction. [H 2 , Cl 2 , Aq] = 61,320+, 
 means that the combination of 2 grams of hydrogen with 71 
 grams of chlorine in the presence of an unlimited amount 
 of water is attended with the production of 61,320 gram-units 
 of heat. [HClAq, KOHAq]= 13,750 + , means that when 
 36*5 grams of HC1 dissolved in a large excess of water react 
 with 56 grams of KOH, also dissolved in a large excess of 
 water, 13,750 gram-units of heat are produced. 
 
 The symbol H 2 O is used as in ordinary notation to repre- 
 sent 1 8 grams of water ; thus 
 
 (1) [Mn, O 2 , SO 2 , 4H 2 O] = 190,810+; 
 
 (2) [MnSO 4 4H 2 O, Aq]= 1770+; 
 
 mean, (i) that in the formation of the amount, in grams, 
 of crystallised manganous sulphate expressed by the formula 
 MnSO 4 4H 2 O, from the amounts, in grams, of manganese, 
 
 1 Thomsen appears to be the only chemist who systematically writes the indices 
 above the symbols of elements in the formulas of thermal chemistry. Thomsen 
 also sometimes uses the colon in place of the comma to express chemical reaction 
 between the substances whose formulae are separated by this symbol.
 
 250 THERMAL METHODS. [BOOK I. 
 
 oxygen, sulphur dioxide, and water, expressed by the respec- 
 tive formulae Mn, O 2 , SO 2 , and 4H 2 O, 190,810 gram-units 
 of heat are produced: (2) that 1770 gram-units of heat are 
 produced in the solution of the foregoing number of grams of 
 crystallised manganous sulphate in an unlimited quantity 
 of water. 
 
 Generally then 1 , let r=the thermal value of a chemical 
 change : let the change be the formation of a definite amount 
 of a compound 2 viz. (X a Y 6 Z c ), consisting of a parts by 
 weight of the element X, b parts by weight of the element Y, 
 and c parts by weight of the element Z; then 
 
 r=[X", Y", Z'-} (i). 
 
 Let the compound X a Y b Z c be produced as before, but in 
 presence of a large excess of water which holds it in solution ; 
 
 then 
 
 r=[X*, Y", Z<, Aq] (2). 
 
 Let the substance X a Y b Z c already existing be dissolved in 
 an unlimited amount of water; then 
 
 r=[*-I"Z<, Aq] (3). 
 
 Let the compound XYbe decomposed by the element Z 
 with formation of XZ and Y ; we get the expression 
 
 r=[XY,Z] = [X,Z]-[X, Y] (4), 
 
 that is, the total thermal change consists of two parts, (a) 
 the heat used in separating XY into X + Y, and (b) the heat 
 produced in the union of X and Z to form XZ. 
 
 Finally let the compound XY react with the compound 
 VZ to produce XZ and VY; the value of r is found by 
 
 the formula 
 
 r=[X,Z} + [V, Y]-[X, Y]-[V,Z] (5). 
 
 Equations (i) to (3) have already been illustrated. As an 
 example of the use of (4) we may take the reaction of zinc 
 with hydrochloric acid whereby zinc chloride and hydrogen 
 are produced ; 
 
 [Zn, 2HClAq] = [Zn, CPAq]-2[H, ClAq]; 
 
 1 Thomsen, Thermochemische Untersuc/iungen, 1. 5 et seq. 
 
 2 In many cases we may use the term ' molecule ' in place of ' definite amount ', 
 and 'atom' in place of 'parts by weight': but as we shall frequently deal with 
 solids and liquids it is better at present not to speak of atoms and molecules.
 
 CH. IV. I 1 8] NOTATION OF THERMAL CHEMISTRY. 25 I 
 
 or that of iron with a solution of copper sulphate to produce 
 ferrous sulphate and copper ; 
 
 [CuSO 4 Aq, Fe] = [Fe, SO 4 Aq]-[Cu, SO 4 Aq]. 
 
 As an illustration of (5) the decomposition of PbO by H 2 S 
 resulting in the production of PbS and H 2 O, may be used ; 
 [PbO, H^S] = [Pb, S] + [H 2 , O]-[Pb, O]-[H 2 , S]. 
 
 Ostwald (Lehrbuch) uses a system of notation which 
 expresses more facts about each reaction than that em- 
 ployed by Thomsen. The latter does not indicate the pro- 
 ducts of the chemical change the thermal value of which 
 is stated. Ostwald employs the ordinary notation, but sup- 
 plements each equation by a statement of the quantity of 
 heat which is produced or disappears in the reaction : he also 
 uses three kinds of type to express the state of aggregation 
 of the various bodies. A symbol printed in thick type 
 indicates a solid, ordinary type indicates a liquid, and italics 
 shew a gas. The following examples illustrate Ostwald's 
 system. 
 
 (1) H 2 +Cl.i=2JfCl+ 44,000. 
 
 (2) 2fftS+ 2l 2 = 4 //7+ 28 - 34,000. 
 
 (3) 2H 2 SAq + 2l2Aq = 4HIAq + 2S + 34,ooo. 
 
 These equations tell (i) that the sum of the internal 
 energies of 2 grams of gaseous hydrogen and 71 grams of 
 gaseous chlorine exceeds the internal energy of 73 grams 
 of gaseous hydrochloric acid by a quantity equal to 44,000 
 gram-units of heat, and (2) and (3) that the sum of the 
 internal energies of 68 grams of gaseous sulphuretted 
 hydrogen and 508 grams of solid iodine is equal to that 
 of 512 grams of gaseous hydriodic acid and 64 grams of 
 solid sulphur diminished by 34,400 gram-units of heat, but 
 that the sum of the energies of the same masses of hydrogen 
 sulphide and iodine in dilute aqueous solution exceeds the 
 sum of the energies of the same mass as before of hydriodic 
 acid in dilute aqueous solution and the same mass as before 
 of solid sulphur by 34,400 gram-units of heat. If it is 
 required to indicate a particular temperature at which one 
 or other of the reacting bodies is caused to take part in
 
 2$2 THERMAL METHODS. [BOOK I. 
 
 the reaction, this is done by Ostwald by putting the number 
 indicating the temperature in small figures in a bracket below 
 the symbol of the body; thus S (2 o) means 3 2 grams of solid sulphur 
 at 20; 2S (m) means 64 grams of gaseous sulphur at 600. The 
 value of the thermal change accompanying a change of state, or 
 a change of the same body from one temperature to another, 
 may be very easily indicated by using Ostwald's system of 
 notation. Thus H 2 O (0) = H 2 + 1440, or wnat is tne same 
 thing H 2 O (0) H 2 0(o) = 1 44> tells that the change from 
 1 8 grams of liquid water at o to the same mass of solid 
 water at the same temperature is accompanied by the pro- 
 duction of 1440 gram-units of heat. Again Cu a oo) = Cu (U ) + 600 
 tells that 6y5 grams of solid copper at 100 contain energy 
 equal to 600 gram-units of heat more than 63-5 grams of 
 solid copper at o. 
 
 Both Thomsen's and Ostwald's system of notation will 
 be used in this book ; the latter especially when it is desired 
 to indicate, shortly and clearly, differences in the states of 
 aggregation of the reacting bodies. 
 
 119 A distinction has been drawn between so-called exothermic 
 and endothennic changes ; the former are accompanied by 
 production, the latter by disappearance, of heat. 
 
 Let (P a Q b ] represent the energy in a compound formed of 
 a parts of element P and b parts of element Q: let (/**) and 
 (<2*) represent the energy in a parts of P, and in b parts of 
 Q, respectively; then, inasmuch as the energy in any system 
 resulting from a definite chemical change is equal to the 
 difference between the energy in the original system from 
 which it was produced and that lost to the system during the 
 process, it follows that 
 
 assuming that the heat produced in the formation of P a Q" 
 measures the total loss of energy ; 
 
 and therefore (P") + (Q*) > (/>*). 
 
 This equation represents an exothermic change. 
 
 But in some cases a chemical change occurs only when heat 
 is added to the changing system from without ; in such a case
 
 CHAP. IV. IIQ] EXOTHERMIC AND ENDOTHERMIC. 253 
 
 and therefore (P a ] + (Q*) < (P"Q?}- 
 
 This equation represents an endothermic change. 
 
 In some cases, a chemical reaction which seems to be 
 accompanied by disappearance of heat is found, on more 
 careful study, to form one member of a series of changes the 
 thermal sum of which is represented by a positive quantity. 
 Indeed any chemical reaction is a most complex phenome- 
 non when regarded from the thermal point of view; physical 
 changes (expansion or contraction, passage from solid to 
 liquid or gas, or vice versa, &c., &c.) form part of the total 
 change the thermal value of which is set down in a lump 
 sum. The purely chemical part of the change may be ac- 
 companied by disappearance of heat, while the complete 
 occurrence may involve the production of heat. 
 
 The following example will serve to illustrate the use of 
 the terms endothermic and exothermic. 
 
 Naumann l shewed that no action occurs when dry sul- 
 phuretted hydrogen is passed into a solution of iodine in dry 
 carbon disulphide, but that as soon as water is added, hy- 
 driodic acid and sulphur are produced. The reaction 
 2H 2 S + 2l 2 = 4HI + S 2 
 
 (gaseous) (solid) (gaseous) (solid) 
 
 would be thermally represented as 
 
 [2ff*S, 2l 2 ] = 4 \ff, /] - 2 [H\ 8] 
 
 = 24800 - 9200 
 = - 34,000. 
 
 When water is present, the reaction 
 
 2H 2 S + 2l 2 = 4HI + S 2 
 
 (in solution) (in solution) (in solution) (solid) 
 
 would be thermally represented as 2 
 
 [2H*SAq, 2l 2 Aq] = 4 \H, I, Aq] - 2 [// 2 , S, Aq] 
 = 52,800- 18400 
 = 34,400 + . 
 
 The reaction of dry sulphuretted hydrogen with dry iodine 
 would be markedly endothermic ; but when this change is made 
 
 1 Her. 2. 177; and Annalen 181. 145. 
 
 - No notice is taken in these thermal expressions of the change, if any, which 
 accompanies the decomposition of 2!, and the production of S 2 . See post, pars. 
 122, 132.
 
 254 THERMAL METHODS. [BOOK I. 
 
 one of a series the thermal value of which, taken as a whole, 
 is positive, then the complete cycle of change proceeds rapidly. 
 But the more concentrated an aqueous solution of hydri- 
 odic acid becomes the less heat is there produced on each 
 addition of the acid, until the specific gravity of the liquid 
 is i'56, after which no more heat is produced 1 ; the liquid is 
 saturated. If therefore the hydriodic acid formed in the 
 foregoing reaction is allowed to accumulate in the liquid, no 
 more water being added, a point will be reached at which the 
 sum of the thermal changes is equal to zero ; at this point 
 the chemical change stops, but proceeds again on the addi- 
 tion of a little water. It is possible to obtain an aqueous 
 solution of hydriodic acid of specific gravity r6/ ; if sulphur 
 is shaken with this liquid a little sulphuretted hydrogen and 
 iodine are produced, i.e. the change 
 
 S 2 + 4HI = 2H 2 S + I 2 
 
 (solid) (concentrated) (solution) (solution) 
 
 proceeds until the hydriodic acid becomes reduced to specific 
 gravity 1-56, when equilibrium is again established. 
 
 Portions of this cycle of change are exothermic, other 
 portions are endothermic. Variation of the mass of one of 
 the members of the changing system determines whether 
 the thermal value of the complete change shall be positive 
 or negative, and also determines the direction in which the 
 change shall proceed. This reaction may be taken as typical 
 of most if not all chemical processes. Such processes consist 
 of portions having positive thermal values and portions having 
 negative values ; small variations in the conditions may 
 determine whether the process as a whole shall belong to the 
 class of exothermic or to that of endothermic changes. 
 
 Too much stress has been laid by one school of chemists on 
 the differences between exothermic and endothermic changes. 
 120 Direct measurements of the thermal changes which ac- 
 company chemical changes can only be made in a few 
 simple cases ; it is generally necessary to have recourse to 
 indirect methods. 
 
 1 This liquid contains about 25 per cent, of HI.
 
 CHAP. IV. 120] CALCULATIONS. 255 
 
 All the calculations rest on the following deduction from 
 the theory of energy. 
 
 The total change of energy which accompanies the passage 
 of a chemical system from a definite initial to a definite final 
 state is independent of the intermediate states. 
 
 The total change of energy is of course measured by the 
 heat which is produced or disappears, and the work done by, 
 or on, the system in its passage from one state to the other. 
 But for our purpose the energy given out in forms other than 
 that of heat may be overlooked, and we may put the statement 
 in this form ; the total thermal change during a chemical 
 process is dependent only on the initial and final states of the 
 chemical system 1 . 
 
 In applying this statement, it is necessary to arrange 
 series of reactions each beginning with the same materials in 
 the same conditions and ending with the same products under 
 the same conditions ; all the processes which form one of the 
 cycles of change must be capable of calorimetrical measure- 
 ment, and all the processes in the other cycle, except that one 
 the thermal value of which is to be determined, must also be 
 capable of measurement by the calorimeter : if this be done, 
 it follows from the principle just stated that the difference 
 between the total thermal values of the two cycles of changes 
 represents the thermal value of that special portion of one of 
 the cycles which it is wished to determine. Each cycle may 
 however consist of various parts, so that it is sometimes a 
 little difficult to unravel all the changes, and to find that 
 portion of one cycle the thermal value of which has to be 
 determined by calculation. 
 
 I shall now give some examples to shew how the thermal 
 values of various chemical changes are deduced from the 
 results of experiments. 
 
 A. It is required to determine the thermal value of the 
 synthesis of CH 2 O 2 from C, H a , and O 2 . 
 
 We start with 12 grams of carbon, 2 of hydrogen, and 
 48 of oxygen; these combine to form 18 grams of water, 
 
 1 The truth of this generalisation was first proved experimentally by Hess in 
 \%V>(Pogg. 50. 38 si).
 
 256 THERMAL METHODS. [BOOK I. 
 
 and 44 grams of carbon dioxide (C + H 2 + O 3 = CO 2 + H 2 O). 
 But the same quantities of carbon, hydrogen, and oxygen 
 might be (theoretically) combined to form 46 grams of 
 formic acid and 16 grams of oxygen, and the formic acid 
 could then be oxidised, by the oxygen, to form 18 grams of 
 water and 44 grams of carbon dioxide. Stated in formulae 
 these changes are 
 
 (i) C + H 2 + 2 =CH 2 O 2 ; (2) CH 2 O 2 + O = CO 2 + H 2 0. 
 
 The following are the thermal values of the different 
 portions of these changes : 
 
 [C, 02] = 96,960+ : [H*, 0] = 68,360+ : [CH 2 O 2 , 0]= 65,900 + 
 
 but [0, 2 ] + [// 2 , 0] = [0, H\ 2 ] + [CH 2 2 , 0]= 165,320+ 
 
 .-. [0, H*, 02]=[C, 2 ] + [// 2 , 0]-[CH 2 2 , 0]= 99,420 + . 
 
 B. A rather more complicated example is furnished by 
 the determination of the thermal values of the actions (i) 
 [H, Br], (2) [H, I] ; i.e. of the reactions whereby HBr and 
 HI are conceived to be formed from their elements. 
 
 (i) [H, Br]. The data are 
 
 [If, C/, Aq] = 39,300; [HBr, Aq]= 19,900*: 
 therefore assuming that 
 
 [If, Br, Aq] = [//, C/, Aq] 
 it follows that 
 
 [H, Br] = 39,300- 19,900=19,400. 
 
 But is the formation of an aqueous solution of HBr from 
 H, Br, and water, attended with the same thermal change 
 as accompanies the formation of an aqueous solution of HC1 
 from H, Cl, and water? Or, if this assumption is not 
 justified by facts, what is the difference between the thermal 
 values of the two changes ? 
 
 Now, in the first place, the thermal values of the formation 
 of KC1 and KBr in aqueous solution are equal, i.e. 
 
 [KOHAq, HClAq] = [KOHAq, HBrAq]. 
 1 When no + or sign is given it is to be understood that heat is evolved.
 
 CH. IV. 120] CALCULATIONS. 257 
 
 But the replacement of Br by Cl is attended with production 
 of a considerable quantity of heat ; the data here are 
 
 [KBrAq, Cf]= 11,500. 
 
 Now if we analyse this change we find that the thermal 
 expression when expanded becomes 
 
 [K, Cl, Aq] + [5r, Aq] - [K, Br, Aq]= 1 1,500 : 
 but [Br, Aq] = 50o: 
 
 .'. [K, Cl, Aq] - [K, Br, Aq]= 1 1,500 - 500= 1 1,000. 
 That is to say, the replacement of Br by Cl in aqueous solu- 
 tion is represented by the thermal value 1 1 ,000 units, and as 
 the heat of neutralisation, in aqueous solution, of KOH by 
 HC1 is equal to that of KOH by HBr, it follows that 
 
 [H, Br, Aq] = [#, Cl, Aq]- 11,000=28,300 : 
 and as {HBr, Aq] = 19,900, it follows that [H, Br] = 8,400. 
 
 (2) [H, I]. The data are 
 
 [H, Cl, Aq] = 39,300 ; [HI, Aq]= 19,200. 
 
 Now 
 
 [KOHAq, HIAq] = [KOHAq, HClAqj-yo: 
 also 
 
 [KIAq, C/] = 26,2oo (iodine separating as solid): 
 
 .'. replacement of I by Cl is accompanied by production 
 of 26,200 70 = 26,130 units : 
 
 .'. [H, I, Aq] = [H, Cl, Aq] - 26,130= 13,170 : 
 and as [HI, Aq] = 1 9,200 
 
 it follows that [H, I]= 13,170- 19,200 
 
 = - 6030. 
 
 The calculations of the tieats of formation of compounds 
 are all based on the principle we are now discussing. 
 
 C. Thus, required the heat of formation of methane 
 (CH 4 ). We start with the two systems (i) C + 4#, (2) // 4 . 
 Each is completely oxidised to the same final products, viz. 
 CV9 8 + 2H S O; the difference between the quantities of heat 
 produced in these two changes is called the heat of formation 
 of CH 4 . Thus, 
 
 [0, 2 ] = 96,900 : 2 [H 2 , 0} = 1 36,800 : sum = 233,700 
 but [CH*, Q 4 ] = 213,500 
 /. [0, H*]= 20,200. 
 M.C. 17
 
 258 THERMAL METHODS. [BOOK I. 
 
 As it is important that a definite meaning should be 
 attached to the expression 'heat of formation,' a few more 
 examples are given. 
 
 D. Required the thermal value of the reaction \H, C, N\ 
 that is, of the reaction whereby HCN may be conceived to be 
 formed from its elements. 
 
 Data; [C, <9 2 ] = 96,900: $[f? 2 , 0] = 34,200: sum= 131,100 (N is 
 incombustible] but [CNH, |O]= 159,500 
 
 .-. [G,N,HY=- 28,400. 
 
 E. Required the thermal value of the reaction [TV 2 , O\. 
 Data ; the reaction 
 
 G + 2N Z O=2N Z + CO 2 when expanded thermally is 
 [0, 2N*0]=[C, 0*\-2[N\ 0]= 1 33,900: 
 but G + 2Nz+O 2 =COz+'2N. t 
 i.e. [0, iN\ O 2 ]=[C, O 2 
 .-. 2[N*, O]=- 37,000 
 
 F. Required the thermal value of the reaction [N, O~\. 
 Data; CN+2NO=CO 2 + ^N, or in thermal notation 
 
 [CN, 2NO] = [C, O 2 ] - [C, N]-2 [N, O] = 1 74,600 : 
 but CN+O 2 =CO 2 + N, or in thermal notation 
 
 [CN, 0*] = [C, 0*]-[C, ^=130,900 
 .-. 2[N, O]=- 43,7oo: 
 .-. [IV, 0]= -21,850. 
 
 The heat of formation of a substance will of course vary 
 according as the substance is formed in the gaseous, liquid, 
 or solid, state, and also according to the temperature of 
 formation. The following examples will illustrate this. 
 
 G. Required the thermal value of the formation of 
 aldehyde from its elements, i.e. of the reaction [C 2 , //*, O], 
 when the aldehyde is (a) liquid, (b] gaseous. 
 
 (a) Liquid: data, 
 
 but 2[C, C> 2 ] + 2[/^ 2 , O] =330,600 
 
 = 55,100 
 1 The transference of N from the molecule N 2 to the molecule HCN is assumed 
 
 to be accompanied by no thermal change. See post par. 132. 
 
 3 The CO 2 produced is gaseous; the heat of formation of liquid CO 2 is un- 
 
 known,
 
 CH. IV. I2O, I2l] CALCULATIONS. 259 
 
 (b) Gaseous: data, 
 
 [C 2 tf*O, 6> 5 ] = 266,000; and 2 [H-, O}= 117,400: 
 .-. [C a + # 4 + = C 2 /f 4 0] = 45,200. 
 H. If the products of a reaction are gaseous and are 
 
 maintained at a high temperature, it becomes necessary to 
 
 introduce corrections for the specific heats, and heats of 
 
 vaporisation, of these products, into the calculation of the 
 
 thermal value of the reaction. 
 
 Thus, required the thermal value of the reaction [C* 2 // 2 , O 6 ] 
 
 at 150. 
 
 Data, C 2 //2 + 
 
 at ordinary temperatures (20) 
 \C*H\ O 5 ]=2[C, 
 
 but thermal capacity of 2 gram-molecules of CO 2 for tem- 
 perature-interval 20 150 = 2482 units. 
 
 /() imol.liquidH 2 O20 ioo=i8x8o= 1440 
 thermal capacity of (b) heat of vaporisation of do. at 100 
 
 i gram-molecule -< = 18x536-5 = 9657 
 
 of H 2 O \(c) thermal capacity of i mol. steam 
 
 \ 100 150 = i8x 50x0-4805 = 432 
 
 total= 1401 1 units.
 
 260 THERMAL METHODS. [BOOK I. 
 
 !X= Cl = 30,000 units. 
 X=Br= 4,800 . 
 X=I =-18,000 . 
 
 The reverse action in the case of iodine, viz. 
 
 C 2 H 3 I O 2 + HI= C 2 H 4 O 2 + 1 2 
 is represented thermally thus, 
 
 [C 2 H 3 IO 2 , /T/] = i8,ooo. 
 
 This action occurs provided a concentrated aqueous solu- 
 tion of hydriodic acid is employed. 
 Now 2# 
 
 = 12,400. 
 But [2///, Aq] = 38,000 : 
 
 hence it follows that in the decomposition of 2//7 into H^+ 1 2 
 in dilute solution 38,000 12,400 = 25,600 units of heat would 
 disappear. 
 
 These thermal numbers shew that the process which 
 is accompanied by a large loss of energy occurs, whereas 
 that which would involve gain of energy to the system does 
 not occur. 
 
 But why does a concentrated aqueous solution of hydriodic 
 acid act as an energetic reducing agent ? We have already 
 learned (p. 254) that little or no heat is produced during 
 the absorption and solution of gaseous hydriodic acid by a 
 solution of that gas containing about 20 25 per cent, of HI ; 
 hence a concentrated solution of this compound contains 
 a considerable quantity of HI, as distinguished from HIAq. 
 But the numbers given above shew that HI contains much 
 more energy than HIAq ; hence a concentrated aqueous 
 solution of hydriodic acid is much more energetic than a 
 dilute solution of the same compound 1 . 
 
 The following tables 2 contain thermal data for discussing 
 the action of sulphuretted hydrogen as a reagent for precipi- 
 tating certain metals from acid solutions, and other metals 
 only from neutral or alkaline solutions. 
 
 1 See Naumann, Thermochemie, 495 and 501. 
 
 2 See Naumann, loc. cit. 505 510.
 
 CH. IV. I2l] CLASSIFICATION. 261 
 
 TABLE I. 
 
 Base 
 
 Reaction CdO PbO CuO HgO T1 2 O Cu 2 O Ag 2 O 
 [Base 2HClAq, ) , 
 
 H 2 SAq] J (l) 27 ' 3 29)2 3I ' 7 45 ' 3 38}5 38 ' 5 58 ' 5 
 
 ^ 2 ' 3 I5 ' 4 IS ' 3 I9 ' 27)5 I4>7 42 ' 6 
 
 (i)-(2)= + 7,000 13,800 16,400 26,300 11,000 23,800 15,900 
 
 TABLE II. 
 
 Base 
 
 Reaction Cdo" PbO CuO HgO T1 2 O Cu 2 O Ag,6 
 
 [Base, tf 2 S] (1)32,100 34,000 36,500 50,000 43,300 43,300 63,300 
 [Base, zHCl\ (2) 55,000 50,000 50,000 53,500 62,200 49,300 77,200 
 
 (i)- (2)= -22,900 16,000 13,500 3,500 18,900 6,000 13,900 
 
 TABLE III. 
 
 Base 
 
 Reaction MnO.H 2 O FeO.H 2 O NiO.H 2 O CoO.H 2 O ZnO.H 2 O 
 
 a2 t 1 ) 10 >7 I ^ 6o l8 ' 6o I 74QO 18,600 
 
 [Base Aq, ) . 
 
 2HClAq] J (2) 23 ' 00 2I ' 4 22 ' 6 
 
 (l) - (2)= - 12,300 6,800 4,000 3,700 1,700 
 
 To illustrate the application of these data, take the case 
 of cadmium. 
 
 (1) [CdO2HClAq, H 2 SAq] = 27,300: 
 
 i.e. the thermal change which occurs when aqueous H S S reacts 
 on a dilute solution of CdO in HC1 is represented by the 
 production of 27,300 units. 
 
 (2) [CdO Aq, 2HClAq] = 20,300: 
 
 i.e. the thermal change which would occur if CdO in aqueous 
 solution were neutralised by a dilute solution of HC1 would 
 be represented by the production of 20,300 units. The former 
 number exceeds the latter by 7,000, .'. the action of H 2 S, in 
 solution, on CdO, in dilute HC1 solution, is accompanied by 
 the production of 7,000 units of heat; this action readily 
 occurs. But 
 
 [CdO, H*S] = 32,100 ; and [CdO, 2/TC7] = 55,000: 
 i.e. the formation of CdS, by the action of gaseous H 2 S on solid 
 CdO, is accompanied by the production of 22,900 units of
 
 262 THERMAL METHODS. [BOOK I. 
 
 heat less than attends the action of gaseous HC1 on CdO ; 
 now solid CdS is decomposed by gaseous HC1 with formation 
 of CdCl 2 . 
 
 Moreover the numbers 
 
 [2HCt, Aq] = 34,600; whereas [H 2 S, Aq] = 4,800 
 
 shew, that gaseous hydrochloric acid possesses an excess of 
 energy measured by about 34,000 thermal units above what 
 it possesses when in dilute solution, whereas the excess of 
 energy of an equivalent mass of gaseous H 2 S above that 
 possessed by H 2 SAq is measured by about 5000 thermal 
 units. But the more concentrated an aqueous solution of 
 hydrochloric acid, the less is the quantity of heat produced 
 by adding hydrochloric acid gas to that solution ; in other 
 words, a concentrated aqueous solution of this acid is nearly 
 as energetic a reagent, provided it is used in sufficient 
 quantity, as gaseous hydrochloric acid. Hence we should 
 conclude, and our conclusion is verified by experiment, 
 that cadmium sulphide will be decomposed by concentrated 
 aqueous hydrochloric acid. 
 
 The case of antimony is especially interesting. 
 
 Antimony sulphide is decomposed by aqueous hydrochlo- 
 ric acid of greater concentration than HC1.6H 2 O; but if more 
 water than this is present, antimony chloride is decomposed 
 by sulphuretted hydrogen. Hence the two reactions 
 
 may occur until a state of equilibrium is established, which 
 is conditioned by the relative energies of the components, 
 and this again is conditioned by the relative masses of these 
 components, temperature being constant throughout. 
 122 We have been accustomed to regard most processes of 
 chemical change as consisting of two parts, (i) decomposition 
 of the molecules forming the initial system, (2) rearrangement 
 of the atoms thus produced to form the new molecules which 
 compose the final system. The first part of a change, as 
 thus regarded, must be accompanied by gain of energy to 
 the entire system, and the latter part by loss of energy. The 
 gain may exceed the loss, or vice versa ; the process as a
 
 CH. IV. 122, 123] ATOMS AND MOLECULES. 263 
 
 whole may be endothermic or exothermic. In the preceding 
 paragraphs of this section no attempt has been made to 
 separate the thermal values of these two parts of any change ; 
 the numbers given in these paragraphs represent the algebraic 
 sums of two or more quantities. In some cases the chemical 
 changes are represented in formulae which are undoubtedly 
 molecular, but in most cases we have dealt with solid or 
 liquid substances, and the thermal values assigned to the 
 various changes must therefore generally be regarded as only 
 measuring the quantities of heat produced or used during 
 the reactions, as defined in the equations, between those 
 masses of the various chemical substances which are ex- 
 pressed by their formulae when read in grams. 
 
 But if relative measurements of the gains of energy which 
 accompany the formation of atomic, from molecular, systems, 
 could be obtained, much light would certainly be thrown on 
 many questions which have been discussed or alluded to in 
 preceding chapters. 
 123 Thomsen 1 has attempted to calculate the quantity of heat 
 required to separate the molecule of carbon, assumed to be di- 
 atomic, into atoms ; his results and methods cannot be accepted 
 as conclusive 2 . The 'heat of dissociation ' of a carbon atom is 
 supposed by Thomsen to be equal to about 37,000 gram-units. 
 
 E. Wiedemann 3 has measured the heat required to change 
 the 'band spectrum' of hydrogen into the 'line spectrum'; 
 and, on the assumption that the ' line spectrum ' is associated 
 with vibrations of atoms and the ' band spectrum ' with 
 vibrations of molecules, he has calculated that about 128,000 
 gram-units of heat are required in order to separate I gram- 
 molecule of hydrogen into its constituent atoms ; and that 
 a greater quantity of heat than this is required in the case of 
 the molecule of nitrogen. 
 
 Thomsen and Wiedemann have shewn that more energy 
 is almost certainly associated with a mass of hydrogen, 
 
 1 Ber. 13. 1321 and 1388. Do. 15. 328. See also Thermochemische Untersuch- 
 ungen, 2. 101 et seq. 
 
 2 See The Elements of Thermal Chemistry > pars. 73 75: see also post par. 134. 
 
 3 Wied. Ann. C. 500, and do. 18. 509.
 
 264 THERMAL METHODS. [BOOK I. 
 
 nitrogen, or gaseous carbon, when the greater part of the 
 matter is in the state of atoms than when in the state of 
 molecules ; in other words, their investigations furnish physi- 
 cal evidence in favour of the generally adopted explanation 
 of nascent actions. 
 
 124 Some of the reactions of metals with acids were considered 
 in Chap. II. pars. 42 to 44. Thermal measurements help to 
 elucidate these actions. 
 
 If the heats of formation in aqueous solution of the sul- 
 phates of silver, thallium, copper, cadmium, mercury, nickel, 
 cobalt, iron, manganese, and zinc, are compared with the 
 heat of formation of sulphuric acid in aqueous solution, it is 
 found that the former values are greater than the latter except 
 in the cases of copper and silver : i.e. for the heavy metals 
 
 [M(or M 2 ), 0\ S0\ Aq] > \H\ O\ SO 2 , Aq], 
 
 except when M = Cu or M 2 = Ag 2 ; hence we might expect 
 the heavy metals, except copper and silver, to decompose 
 dilute sulphuric acid with evolution of hydrogen. 
 
 When M 2 = T1 2 .the positive value of the difference in 
 question is not large (1,900 units); the action between this 
 metal and dilute sulphuric acid does not proceed rapidly. 
 But when the acid is concentrated action is more energetic ; 
 now inasmuch as the heat of solution of H 2 SO 4 is large 
 
 [H 2 SO 4 , Aq]=i7,ooo 
 
 it follows that a given mass of concentrated sulphuric 
 acid contains considerably more energy than the same 
 mass of dilute acid, and hence the concentrated acid will 
 probably be less chemically stable than the dilute. The 
 reaction of thallium with the concentrated acid results in 
 the production of some sulphur dioxide. Now the change 
 H 8 SO 4 + H 2 = SO 2 +2H 2 O (assuming that this expresses the 
 origin of the sulphur dioxide) is accompanied by the pro- 
 duction of 14,900 units of heat. This change is represented 
 thermally thus, 
 
 [H 2 S0 4 , ^ = [ 
 
 If the temperature is raised the acid becomes more con- 
 centrated, and at a certain stage sulphuretted hydrogen is
 
 CH. IV. 1 24] ACTION OF ACIDS ON METALS. 265 
 
 evolved. This action is thermally probable, because 
 
 H 2 S0 4 +H 2 = i 
 when expanded thermally, is 
 
 = 23,700 units. 
 
 A similar treatment of the action of copper on sulphuric 
 acid shews that this metal would probably not decompose 
 the acid when dilute, but that the metal might be expected 
 to react slowly with concentrated acid, provided one of the 
 products were sulphur dioxide ; because 
 
 when expanded thermally, is 
 
 [Cu, 2H 2 S0 4 ]=[Cu, S0\ 0*} + 2[ff*, O\-2\H\ O\ SO 2 ] 
 = 4,500 units. 
 
 The quantity of heat set free in this action will in reality 
 considerably exceed 5000 units, because heat will be produced 
 by the action between the sulphuric acid and the water formed 
 in the change ; the amount of heat thus liberated may amount 
 to as much as 8,000 or 9,000 units per gram-molecule of water. 
 
 The fact that the mutual action of sulphuric acid and 
 water is accompanied by the production of much heat compli- 
 cates such calculations as those given above. The relations 
 between the masses of H 2 SO 4 and H 8 O employed will cer- 
 tainly condition the direction and progress of the change. 
 Starting with the system H s SO 4 + cH 2 O + #H 2 , for a certain 
 concentration of acid the final configuration will be SO 2 and 
 H 2 O, for another concentration of acid it will rather be H 2 S 
 and H 2 O, or SO 2 , H 2 S, and H 2 O. The action will also of 
 course be conditioned by temperature. 
 
 If the foregoing considerations are correct, it follows that 
 any metal which reacts with dilute sulphuric acid with evolu- 
 tion of hydrogen, might fairly be expected to react with the 
 same acid to produce sulphuretted hydrogen or sulphur 
 dioxide under certain conditions of temperature and con- 
 centration ; zinc and tin certainly do produce both of these 
 gases by their action on hot concentrated sulphuric acid 1 . 
 
 1 See p. 103. The subject of the reactions of metals with acids is treated from 
 the thermal standpoint in pars. 120 122 of The Elements of Thermal Chemistry.
 
 266 THERMAL METHODS. [BOOK I. 
 
 125 From what we have learned regarding atomic and mole- 
 cular systems, and from a consideration of the preceding 
 paragraphs of this section, it follows almost necessarily that 
 the change from one allotropic modification of an element to 
 another must be attended by production or disappearance of 
 heat. A few thermal measurements are given here to shew 
 that this conclusion is fully justified by facts. 
 
 A. [P 2 , <9 5 ] = 369,ioo units when P 2 is 62 grams of ordinary 
 
 phosphorus (P a ); 
 [P 2 , 0*] = 326,800 units when P 2 is 62 grams of amorphous 
 
 phosphorus (P/s); 
 
 /, the change of P a to P^ = 21,150 units of heat. 
 
 In the oxidation of 31 grams P a to H 3 PO 4 in aqueous solution by hypo- 
 chlorous acid, 209,500 thermal units are produced ; 
 
 in the oxidation of 31 grams PB to H 3 PO 4 in aqueous solution by hypo- 
 chlorous acid, 181,200 thermal units are produced ; 
 
 /. the change of P a to P^ = 28,300 units of heat. 
 Hence mean value of this change = 24,725 gram-units. 
 
 B. [2(?^=36> 2 ] = 59,20o units of heat; that is to say 
 
 the separation of 2 gram-molecules of ozone (O 3 ) into 3 gram-molecules 
 of oxygen (O 2 ) is attended by the production of 59,200 units of heat. 
 
 The comparative thermal instability of the molecule O 8 
 helps us to understand why ozone is so much more active as 
 an oxidising agent than ordinary oxygen 1 . 
 
 126 Too little has as yet been done to allow of the application 
 of thermal measurements to the classification of the elements 
 in any but a very general way. 
 
 The relations existing between the members of a group of 
 elements are sometimes summarised in the thermal values of 
 comparable reactions undergone by these elements. Thus, 
 (see table p. 225) taking MendelejefFs Group II. we have, 
 
 Series. 
 
 468 3 5 7 9 ii 
 
 Ca Sr Ba Mg Zn Cd - Hg 
 
 atomic weights 40 87 137 24 65 112 200 
 
 1 According to van der Meulen (Ber. 16. 1853) the thermal value of the 
 change in question, 2O 3 =3O 2 , is about 68,000 units.
 
 CH.IV. 125 127] CLASSIFICATION OF ELEMENTS. 267 
 
 The heats of formation in aqueous solution of the haloid 
 salts of these metals are arranged in the following table (data 
 from Naumann's book) : 
 
 [M, Cl\ Aq] [M, Br\ Aq] [M, F, Aq] 
 
 Ca 187,600 165,800 I353o 
 
 Sr i95)7oo 173,800 H3.4OO 
 
 Ba 196,300 174,400 144,000 
 
 Mg 186,900 165,000 134,600 
 
 Zn 112,800 90,900 60,500 
 
 Cd 9 6 ,3oo 74,400 44,000 
 
 Hg 
 
 Hence we conclude that in each case the value for 
 Ba > Sr > Ca > Mg, and for Mg > Zn > Cd > Hg. In other 
 words, the thermal value of the change [M, X *, Aq] increases 
 as the atomic weight of M increases, when M is a member of 
 an even series belonging to Group II. but decreases as the 
 atomic weight of M increases, when M is a member of an odd 
 series of the same group. The difference between the values 
 of [M, X*, Aq] for each pair of elements is nearly constant. 
 
 Thus 
 
 X=Cl X=Br X=I 
 
 Ba - Sr = 600 600 600 
 
 Sr -Ca= 8,100 8,000 8,100 
 
 Ca - Mg = 700 800 700 
 
 Mg-Zn =74,100 74,ioo 74,ioo 
 
 Zn -Cd = 16,500 16,500 16,500 
 
 Cd-Hg= 36,400 ? ? 
 
 The close relationship of magnesium to calcium, and also 
 its relations to barium and strontium, and the comparatively 
 feebly marked relations existing between magnesium, zinc, 
 cadmium, and mercury, are brought into forcible relief by 
 these numbers 1 . 
 
 127 The comparative study of classes of compounds, no less 
 than that of classes of elements, has already been considerably 
 
 1 Attention has already been drawn to the fact that there exists a well-marked 
 connexion of a periodic character between the atomic weights of the elements 
 and their heats of combination with chlorine, bromine, and iodine. (See ante, 
 par. 109.)
 
 268 THERMAL METHODS. [BOOK I. 
 
 advanced by the application of thermal methods. Thus, a 
 study of some of the thermal relations of the hydracids and 
 oxyacids of the halogens helps towards a classification of the 
 latter group of acids. 
 
 The close thermal analogy between the hydracids in 
 question is exhibited by these, among other, numbers ; 
 
 \HX, Aq] [HXAq, NaOHAq] 
 
 X=Cl = 17,400 X = 0=13,700 
 
 X= 7=19,900 X = Br= 13,700 
 
 X=I =19,200 X=I =13,700. 
 
 When we compare the heats of formation of these acids 
 in aqueous solution, we find that the value of this constant 
 for each acid decreases as the atomic weight of the halogen 
 
 increases : thus 
 
 [H, X, Aq] 
 X=Cl= 39,300 
 X= r= 28,400 
 X=I =13,200. 
 
 The three oxyacids which correspond in composition to the 
 three hydracids are HC1O 3 , HBrO 8 , and HIO 3 . The following 
 numbers shew that, in some respects at any rate, the thermal 
 relations between HC1O 3 and HBrO s are analogous to those 
 between HC1 and HBr : 
 
 [H, X, O 3 , Aq] 
 
 x= a = 2 3)9 oo 
 
 X=ffr= 12,400 
 
 hence the difference, [H, Cl, Aq] - [H, Br, Aq] is approxi- 
 mately equal to the difference [H, Cl, s , Aq] -[H, Br, O\ Aq,] 
 We might provisionally conclude from these data that the 
 difference between the heats of formation, in aqueous solu- 
 tions, of chloric and iodic acids, would probably be nearly the 
 same as the difference between the heats of formation, under 
 the same conditions, of hydrochloric and hydriodic acids. 
 The value of the second difference is 26,100; hence, on this 
 supposition, the first difference should be about 26,000. Now, 
 
 [//, CY, 03, Aq] = 2 3 , 9 oo; 
 .-.[#,!, s , Aq]=- 2,100. 
 But experiment shews that 
 
 [If, I, O 3 ,Aq]= + 55,700.
 
 CH. IV. 127, 128] CLASSIFICATION OF ACIDS. 269 
 
 Hence it is evident that iodic acid differs in the most 
 marked manner from bromic and chloric acids. This difference 
 is accentuated in the numbers expressing the heats of forma- 
 tion of these three acids from the three hydracids : thus, 
 
 [HXAq, 0*} 
 X = C1= -15,400. 
 X = Br= -15,900. 
 X=I =+42,600. 
 
 But it is to be remembered that gaseous chlorine and 
 bromine and solid iodine are employed in the calculations 1 . 
 128 A comparison of the mutual thermal actions of acids and 
 bases throws considerable light on the classification of the 
 substances which are included under these terms. The first 
 volume of Thomsen's Untersuchungen is devoted to a con- 
 sideration of this subject. 
 
 ' Heat of neutralisation of an acid by a base ' is defined as, 
 the quantity of heat produced on mixing equivalent quantities, 
 in grams, of the acid and base, in dilute aqueous solutions, 
 the products of the action being also soluble in water. 
 
 Thomsen employs a solution of 2NaOH in about 200 H 2 O 
 (grams), and adds the acid solution diluted to a similar degree, 
 temperature being 18 19; in other words he determines the 
 thermal value of the change 
 
 [2NaOHAq, 2 HXAq] in the case of a monobasic acid, 
 [2NaOHAq, H 2 XAq] dibasic 
 
 [2NaOHAq, |H 3 XAq] tribasic 
 
 [2NaOHAq, H 4 XAq] tetrabasic 
 
 (X = acid radicle) 
 
 Most of the general conclusions drawn by Thomsen, and 
 others, belong more to chemical kinetics than to statics, but 
 some of the generalisations may fitly be introduced here 2 . 
 
 The commoner acids may be broadly divided into four 
 groups according to the values of their heats of neutralisation, 
 as thus defined. 
 
 1 The application of thermal data to the classification of elements and com- 
 pounds is considered more fully in section 4 of Chap. in. of The Elements of 
 Thermal Chemistry. 
 
 2 See especially for more details Thomsen, he. dt. 1. 293 309, and 422 449.
 
 2/O THERMAL METHODS. [BOOK I. 
 
 I. Those acids which have a heat of neutralisation 
 approximately equal to 20,000 gram-units : 
 
 HN0 2 , HC10, H 2 B 2 4 , H 2 CO 3 &c. 
 
 II. Those acids which have a heat of neutralisation 
 approximately equal to 25,000 gram-units : 
 
 H 2 CrO 4 , C 2 H 4 (C0 2 H) 2 , CH,CHOH(CO 2 H) 2 &c. 
 
 III. Acids the heat of neutralisation of which is equal 
 to about 27,000 gram-units : 
 
 HC1, HBr, HI, HC1O 3 , HBrO 3 , HIO 3 , HNO 3 , H 2 S 2 O 3 , 
 H 2 SiF 6 , H.C0 2 H, CH 3 .CO 2 H &c. 
 
 Most of the acids belong to this class. 
 
 IV. Acids having a heat of neutralisation greater than 
 27,000 units, and varying from 28,000 to 32,500 units ; 
 
 CH 2 C1.CO 2 H, CHC1 2 .CO 2 H, CC1 3 .CO 2 H, H 2 C 2 O 4 , H 3 PO 3 , H 2 SO 3 , 
 H 2 SO 4 , H 2 Se0 4 , HF, HPO 3 &c. 
 
 A few acids have heats of neutralisation less than 20,000 
 units. 
 
 The basicity of an acid may be determined by thermal 
 methods. One gram-molecule of the acid in dilute aqueous 
 solution is mixed with \, , |, I, 2, &c. gram-molecules of 
 caustic soda also in dilute solution, and the heat produced in 
 the reactions is measured. (The ordinary formulae NaOH, 
 H 2 SO 4 , &c. are here assumed, for the sake of convenience of 
 nomenclature, to be molecular.) Comparing in this way HC1, 
 H 2 SO 4 , and C B H 8 O 7 (citric acid), we have this result ; 
 
 [HClAq, NaOHAq] = about 6,000 [H 2 SO 4 Aq, NaOHAq] = about 7,000 
 [HClAq, NaOHAq]= 13,500 [H 2 SO 4 Aq, NaOHAq]= 14,500 
 [HClAq, 2NaOHAq] = 13,500 [H 2 SO 4 Aq, 2NaOHAq]=: 31,000 
 
 [H 2 S0 4 Aq, 3NaOHAq] = 31,000 
 
 [C 6 H 8 O 7 Aq, NaOHAq]= 12,400 
 
 [C 6 H 8 O 7 Aq, 2NaOHAq] = 24,800 
 
 [C 6 H 8 O 7 Aq, 3NaOHAq] = 38,000 
 
 [C 6 H 8 O 7 Aq, 4NaOHAq] = 38,000. 
 
 Hence we conclude that HC1 is a monobasic, H 2 SO 4 a 
 dibasic, and C 6 H 8 O 7 a tribasic, acid. 
 
 The polybasic acids may also be classified in accordance 
 with the thermal value of the action of each gram-molecule
 
 CH. IV. 128] CLASSIFICATION OF ACIDS. 2/1 
 
 of soda with one gram-molecule of acid. Thus, comparing 
 oxalic with sulphurous acid, we find the difference between 
 the quantities of heat produced during the action of the first 
 and second molecules of soda, in the case of oxalic acid to 
 be 600, and in that of sulphurous acid to be 2750: the data 
 are, 
 
 Difference. 
 
 [H 2 C 2 4 Aq, NaOHAq]=i 3 ,840\ /[H 2 SO 3 Aq, NaOHAq]= 15,850 
 
 [HNaC 2 4 Aq, NaOHAq]= 14,440^ ' \[HNaSO 3 Aq, NaOHAq]= 13,100. 
 
 Thomsen 1 divides the dibasic acids which he has examined 
 into three groups: 
 
 I. Those in the neutralisation of which each molecule 
 of soda has the same thermal value: this group is at present 
 represented by H 2 SiF 6> and H 2 PtCl 6 2 . 
 
 II. Those in the neutralisation of which the first mole- 
 cule of soda has a smaller thermal value than the second, 
 the difference between the two values varying from 450 to 
 1900 units : this group contains the acids H 2 SO 4 , H 2 SeO 4 , 
 H 2 C 2 4 , and H r C 4 H 4 O r 
 
 III. Those in the neutralisation of which the first mole- 
 cule of soda has a larger thermal value than the second, the 
 difference between the two values varying from 1850 to 2750 
 units: the acids in this group are H 2 SO 3 , H 2 SeO 8 , H 2 CO 3 , and 
 H 2 B 2 O 4 ; H 2 CrO 4 , H 2 PHO 3 , and C 2 H 4 (CO 2 H) 2 also probably 
 belong to this group, although the differences between the 
 thermal values of the first and second molecule of soda are 
 smaller in the case of these acids than of those already 
 mentioned. 
 
 Thomsen suggests (I. pp. 304-5) that the foregoing classi- 
 fication of dibasic and tribasic acids may be summarised in 
 these typical formulae: 
 
 Dibasic Acids. 
 
 Acid of Group I. Typical formula RH 2 e.g. SiF 6 . H 2 ; 
 II. R(OH) 2 e.g. S0 2 (OH) 2 ; 
 
 III. R(OH)H e.g. SO 2 (OH)H. 
 
 1 loc. cit. 1. 302 306. 
 
 2 But it seems doubtful whether the numbers obtained by Thomsen really 
 represent the neutralisation of this acid. See Thermochtmische Untersuchnngen, 
 I. 229.
 
 2/2 THERMAL METHODS. [BOOK I. 
 
 Tribasic Acids. 
 
 Acid of Group II. Typical formula R(OH) 3 e.g. C 4 H 5 O 4 (OH) 3 ; 
 III. HR(OH)H e.g. HPO 3 (OH)H. 
 
 The ' heat of neutralisation of a base ' is defined by 
 Thomsen 1 to be the thermal value of the change which occurs 
 when equivalent quantities of base and acid react in dilute 
 aqueous solution, the products of the action being also soluble 
 in water. A dilute solution of one gram-molecule of sulphuric 
 acid (i.e. the amount of acid, in grams, expressed by the 
 formula H 2 SO 4 ) is employed; temperature being 18 19. 
 
 In other words, Thomsen measures the thermal values of 
 the following reactions: 
 
 [H 2 SO 4 Aq, 2MOHAq or 2NX 3 Aq] in the case of a mono-acid base, 
 [H 2 SO 4 Aq, M(OH) 2 Aq or N 2 X 6 Aq] di-acid 
 
 [H 2 SO 4 Aq, f M(OH) 3 Aq or N 3 X 9 Aq] tri-acid 
 
 [H 2 SO 4 Aq, JM(OH) 4 Aq or iN*X 12 Aq] tetracid 
 
 (X = H, or a radicle C M H 2n+1 ) 
 
 The bases which are soluble in water may be divided into 
 two thermal groups : 
 
 I. The group of the hydrates or hydroxides, represented 
 by NaOH and KOH. 
 
 II. The group of the anhydrous bases, represented by 
 NH 3 . 
 
 The first group comprises LiOH, NaOH, KOH, and 
 T1OH; Ca(OH) 2 , Sr(OH) 2 , and Ba(OH) 2 ; N(CH 3 ) 4 OH, 
 (C 2 H 5 ) 3 S.OH, and Pt (NH 8 ) 4 (OH) 2 : the mean value of the 
 change [H 2 SO 4 Aq, 2MOHAq (or M(OH) 2 Aq)] is equal to 
 31,350 units, when M(OH) or M(OH) 2 is one of the bases of 
 this group. 
 
 The second group comprises NH 3 and the amines of the 
 form NH 2 (C B H 2n+1 ) and NH(C n H 2n+] ) 2 : the mean value of 
 the change [H 2 SO 4 Aq, 2NX 3 Aq] is equal to 28,200, when 
 NX 3 is one of the bases of this group. 
 
 Substitution of negative radicles for H in NH 3 causes a con- 
 siderable decrease in the heat of neutralisation of the base ; thus, 
 [2NH 2 (C 6 H 6 )Aq, H 2 SO 4 Aq]=i5,5oo, 
 [2NH 2 (C 7 H 7 )Aq, H 2 SO 4 Aq]= 15,200 ; 
 [2NH 2 OHAq, H 2 SO 4 Aq] =21,600. 
 1 See especially loc, cit. 1. 422 449.
 
 CH.IV. 128] CLASSIFICATION OF BASES. 273 
 
 When CO is substituted for H 2 in 2NH 8 , the heat of 
 neutralisation of the product [(NH 2 ) 2 CO] is almost nil. 
 
 Measurements of the quantities of heat produced during 
 the reactions of acids with those bases which are insoluble in 
 water shew great irregularities. The true heats of neutrali- 
 sation of these bases cannot be determined. But from the 
 analogies between the hydrates of barium, strontium, and 
 calcium, and those of magnesium, zinc, and manganese 1 , 
 Thomsen concludes that the heats of neutralisation of the 
 bases of the magnesian class are equal to those of the bases 
 of the akaline earth metals; but as the heats of neutralisation 
 of the latter and of the alkalis are equal, Thomsen argues 
 that the mean value of the heat of neutralisation of M(OH) 2 , 
 when M = Mg, Mn, Ni, Co, Fe, Cd, Zn, or Cu, is 31,350 units. 
 
 From what has been said regarding the classification of 
 acids in accordance with their heats of neutralisation 2 , it 
 will be apparent that if 2HClAq is substituted for H 2 SO 4 Aq 
 in the preceding reactions, the mean heats of neutralisation of 
 the two groups of bases will be represented by numbers 
 smaller than 31,350 and 28,200 respectively. 
 
 The identity of the numbers expressing the heats of 
 neutralisation of bases of such different composition as KOH 
 and Pt(NH 3 ) 4 (OH) 2 points to the possibility of connecting 
 similar changes of energy with similarity of chemical type, 
 maintained through series of more or less unlike individuals. 
 The heats of neutralisation of the bases MX 3 also point 
 to the existence of a relation between change of energy and 
 composition ; but the influence of the structure of the indi- 
 vidual substance is shewn in the small values obtained for 
 NH 2 (C 6 H 5 ) and NH 2 (C 7 H 7 ), in which, although the chemical 
 type is maintained, the typical thermal value is widely de- 
 parted from. 
 
 The quantity of heat produced in the reaction [2MOHAq, 
 HXAq] when M = K, Na, &c. is nearly constant, whether 
 X = C1, Br, or I; but the value of the reaction [PbO.H 2 O, 
 HXAq], or [T1 2 O.H 8 O, HXAq] &c. differs very considerably 
 
 1 See Thomsen, loc. cit. 1. 435 440. 
 
 2 See ante, p. 270. 
 
 M.C. 1 8
 
 2/4 THERMAL METHODS. [BOOK I. 
 
 according as X = Cl, Br, or I. In the reaction with PbO.H 2 O, 
 the thermal value is greatest for HIAq, and least for HClAq. 
 Now in the reactions just mentioned, haloid salts are produced 
 which are only slightly soluble : if the heats of solution of 
 these salts are added to the values of the apparent heats of 
 neutralisation of the bases, it is found that the true heats of 
 neutralisation of PbO.H 2 O, T1 2 O.H 2 O &c. are represented by 
 the same number, whether HClAq, HBrAq, or HIAq is the 
 acid employed. If it is granted that the true heats of 
 neutralisation of these acids are the same for other bases 
 which form insoluble haloid salts, it becomes possible to 
 calculate the heats of solution of these salts. Thomsen 
 has done this for PbCl 2 , PbBr^, PbI 2 , AgCl, &c., and, carrying 
 out the same method, he has even given a value for the heat 
 of solution of barium sulphate. 
 
 Thomsen's investigation of the heats of neutralisation of 
 acids and bases serves to shew the complexity of many of 
 the reactions to which thermal values are assigned, and also 
 the necessity of making all the conditions of the changes we 
 wish to study as exactly comparable as possible. At the 
 same time it illustrates one of the dangers which beset the 
 employment of thermal methods in chemistry, the danger 
 namely of theorising regarding chemical changes which do not 
 occur, and of speculating about chemical compounds which 
 have no existence 1 . 
 
 129 The primary aim of thermal chemistry was stated in 
 par. 117 to be the measurement of the differences between 
 the quantities of energy possessed by chemical systems when 
 in certain definite initial and final states; the basis of these 
 measurements being the deduction from the general theory 
 of energy which states, that the total loss of energy during 
 the passage of a chemical system from a definite initial to 
 a definite final state is independent of the intermediate 
 states. 
 
 The application of this generalisation was illustrated in 
 par. 1 20; but we may now examine a little more closely the 
 
 1 Section 2, of Chap. III. of The Elements of Thermal Chemistry is devoted to 
 the consideration of neutralisation-phenomena.
 
 CH. IV. 129, 130] THERMAL AND CHEMICAL CHANGES. 2/5 
 
 connexion between thermal and material changes occurring 
 in the same chemical system. 
 
 30 When heat is imparted to a gaseous system of chemical 
 substances, a portion may be employed in increasing the 
 kinetic energy of the molecules, i.e. in raising the temperature 
 of the system ; another portion may be employed in doing 
 work against external forces, e.g. in causing expansion of the 
 system ; and another portion may do work against molecular 
 and atomic forces, and so produce a rearrangement of mole- 
 cules, or atoms, i.e. may cause chemical changes to proceed 
 within the system. The exact manner of the distribution of 
 the energy imparted in the form of heat will vary in each case. 
 If the purely chemical part were separated from the other parts 
 of the complete change, it is evident that the thermal value 
 of this part would be a constant quantity only under constant 
 physical conditions. Thus the difference between the energy 
 of the system 2H 2 + O 2 and that of the system 2H 2 O (both in 
 grams) at ordinary temperatures, say at 15, is measured by 
 136,800 thermal units; but if the initial system is at 200 
 and the final system is at 15 the difference will be only 
 116,500 units 1 ; assuming that the total loss of energy to the 
 system during the change is measured in each case by the 
 quantity of heat produced. Indeed in some cases change 
 of temperature may reverse a process both chemically and 
 thermally without altering the nature or the masses of the 
 reacting substances; thus 
 
 at ordinary temperatures 2H 2 O + 2C1 2 = 4HC1 + O 2 (0 
 
 but at about 200 4HC1 + O 2 = 2H 2 O + 2C1 2 (2) ; 
 
 if reaction (i) is expanded thermally it becomes 
 
 [2H 2 OAq, 2CPAq] = 4|y/, Cl, Aq] - 2 [H\ Q, Aq] = 20,400 units : 
 if reaction (2) is treated in the same way we have 
 
 foffCt, 2 ] = 2[# 2 , 0]-4[ff t C/] = 28,500 units (at 200). 
 If the reaction occurs between bodies in solution, the 
 quantity of heat which is produced or disappears will be 
 dependent on the temperature, and in determining the thermal 
 value of the chemical change it will be necessary to determine 
 
 1 For the method of calculation, see The Elements of Thermal Chemistry, par. 57. 
 
 1 8 2
 
 2/6 THERMAL METHODS. [BOOK I. 
 
 the specific heat of a solution of each of the reacting bodies 
 and of each of the products of the reaction 1 . Heat may also 
 be produced or disappear in changes of volume, or changes in 
 the states of aggregation, of the reacting bodies; thus any 
 comparisons or contrasts instituted between hydrochloric, 
 hydrobromic, and hydriodic, acid from a consideration of 
 these numbers, 
 
 [//, C7] = 22,000; [//, Br]= 8,440; [//, I]= -6,050 
 must be accepted with great reserve, because at ordinary tem- 
 peratures chlorine is a gas, bromine a liquid, and iodine a 
 solid ; the reactions formulated are not, therefore, strictly 
 comparable. 
 
 131 There is another point to be noticed in analysing the 
 thermal changes which accompany chemical processes, viz., 
 that the ordinary notation usually represents a chemical 
 change as a much simpler phenomenon than it really is. Most 
 chemical reactions are accomplished only by employing 'an 
 excess,' sometimes a large excess, of one or more of the react- 
 ing substances: thus the equation 
 
 AgCl + HI (grams) = AgI + HCl 
 
 would more nearly express the distribution of the masses of 
 the reacting bodies if it were written 
 
 Potilitzin has investigated this subject of the relations be- 
 
 tween the thermal value of a change and the masses of the 
 
 changing substances 2 . The heat of formation of a metallic chlo- 
 
 ride is greater as a rule than that of the corresponding bromide, 
 
 [MBr, C/] = [M, C/] - [M, Sr] >o. 
 
 Again it is generally true that 
 
 [MBr, HCl] = [M, Cl} + [H, Br\ - [M, Br\ - [H, Cl~\<o; 
 e.g.[AgBr,//C/]= -6,900: [KBr,^C/]= -3,250; [NaBr, HCl}= - 1,600. 
 Therefore, it would appear probable that chlorine should 
 decompose metallic bromides, but that hydrochloric acid 
 should not react with these salts. 
 
 But Potilitzin's experiments shew that the reaction 
 
 See The Elements of Thermal Chemistry, par. 55. 
 
 See abstract in Ber. 14. 2044; and 15. 918; also 16. 3051
 
 CH. IV. 1 3 I , I 32] THERMAL AND CHEMICAL CHANGES. 277 
 
 proceeds at 275 300 when MCI and Br are employed in 
 equivalent quantities, (M = K, Na, or Ag), and also that when 
 MBr and Cl react in equivalent quantities the whole of the 
 bromine is not replaced by the chlorine. 
 
 By increasing the amount of bromine, relatively to MCI, 
 in the reaction above formulated, more MBr is produced until 
 a limit is reached whereat equilibrium is established. This 
 equilibrium is not overthrown even by increasing the mass of 
 bromine, raising the temperature, and prolonging the time of 
 action. 
 
 132 I think the position has now been clearly established that 
 the thermal value of a chemical change, even of a simple 
 reaction between gaseous substances, really represents the 
 sum of various changes some of which have a positive and 
 others a negative value. Assuming that in any case it is 
 possible to separate the gain or loss of energy, measured 
 thermally, during a definite chemical reaction, into a portion 
 representing physical changes and another portion repre- 
 senting purely chemical changes, it is nevertheless generally 
 the case that the latter portion of the total energy-change 
 must itself be analysed before an accurate and precise appli- 
 cation of the thermal value can be made ; that is if the appli- 
 cation is to proceed on the lines of the molecular and atomic 
 theory. For, assuming that we have made due allowance for 
 the influence of the masses of the reacting substances and 
 for the possible formation and decomposition of molecular 
 groups during the reaction, there yet remains the important 
 consideration that heat is produced or disappears not only 
 in the formation or the decomposition of compounds, but also 
 in reactions of decomposition or formation of elements, which 
 take part in the chemical process. 
 
 Let us analyse a comparatively simple reaction ; 
 
 When this is expanded thermally we have 
 
 [2H 2 O, 2C/ 2 ]=4[#, Cl~\+[O, O]-2 [H 2 , O]- 2 [C/, Ct\. 
 That is to say, heat is used in separating each chlorine mole- 
 cule into atoms, and heat is produced in the union of each 
 pair of oxygen atoms to form a molecule.
 
 2/8 THERMAL METHODS. [BOOK I. 
 
 Let us take an apparently more simple instance 
 [H*, C1 2 ] = 44,000 units. 
 
 Remembering the fundamental distinction between atoms 
 and molecules, and moreover bearing in mind the fact that 
 the molecules of hydrogen and chlorine are both diatomic, we 
 may expand this equation thus 
 
 [H 2 , Cl z ] = 2 [H, CI] - [H, H] - [Cl, a] = 44,000. 
 
 But we do not know the true thermal value of any one of 
 the three parts of this reaction ; when therefore we write 
 [H 2 , Cl 2 ] = 44,000, we use a short way of expressing the 
 fact that when 2 grams of gaseous hydrogen combine with 
 71 grams of gaseous chlorine to produce 73 grams of gaseous 
 hydrochloric acid, at ordinary temperatures, 44,000 gram-units 
 of heat are produced. 
 
 As long as thermal measurements are regarded in this 
 way they convey precise and important information. But we 
 want something more than this; we desire to have some light 
 thrown on the rationale of chemical changes. Now our most 
 far-reaching conceptions in chemistry are based on the dis- 
 tinction implied in the terms atom and molecule ; until then 
 this distinction is practically recognised in thermal chemistry, 
 we cannot expect great advances to be made in applying 
 the mass of data already accumulated to questions of the 
 mechanism of chemical change. 
 
 133 In the Introduction to volume I. of his Essai de mecanique 
 chimique, Berthelot lays down three fundamental principles of 
 thermal chemistry [p. xxviii xxix]. 
 
 (1) The quantity of heat produced in a reaction measures 
 the sum of the physical and chemical changes which occur in 
 that reaction. 
 
 (2) The total thermal value of a reaction is dependent only 
 on the initial and final states of the changing system. 
 
 (3) Every chemical change accomplished without addition 
 of energy from without tends to the formation of that body 
 or system of bodies the production of which is accompanied 
 by the development of the maximum quantity of heat. 
 
 The first and second principles have already been illus- 
 trated and discussed. The third, under the name of the " law
 
 CH. IV. 133] LAW OF MAXIMUM WORK. 279 
 
 of maximum work " forms the basis of all Berthelot's thermo- 
 chemical generalisations. It is stated in an even more rigid 
 form as the theorem of the necessity of reactions*, " Every 
 chemical change which can be accomplished without the aid 
 of a preliminary action or the addition of energy from with- 
 out the system necessarily occurs if it is accompanied by 
 disengagement of heat." 
 
 This so-called law of maximum work may be shewn 
 theoretically to be untrue 2 ; but even supposing it were true, 
 I think that if the fundamental distinction between atom and 
 molecule is clearly grasped it will be seen that Berthelot's 
 statement is too general to throw much light on chemical 
 changes. 
 
 Berthelot's law is simply a crude application of the prin- 
 ciple of the degradation of energy; the principle, namely, that 
 energy always tends to run down from a more available to a 
 less available form. Inasmuch as the formation of a chemical 
 compound, with production of heat, is an instance of such 
 running down of energy, from the form of chemical affinity 
 to that of heat, it follows that the reversal of this process will 
 require the expenditure of work. But the law of maximum 
 work does not attempt to analyse the expression chemical 
 affinity. Under this term Berthelot includes actions and 
 reactions of different kinds. This is at once apparent from 
 the statement in the Essai* that the first fundamental principle 
 of thermal chemistry, viz. " the quantity of heat produced in 
 a reaction measures the sum of the physical and chemical 
 changes which occur in that reaction " furnishes the measure 
 of chemical affinities 4 . 
 
 Berthelot's work is saturated with the conceptions of the 
 molecular theory : but, by some fatal perverseness, he refuses 
 to apply this theory to chemical phenomena. While recog- 
 nising the existence of molecules and building his generalisa- 
 tions on a molecular foundation, he refuses to accept the 
 
 1 loc. dt.; Introduction, p. xxix., also 2. 422. 
 
 2 See Book n. Chap. n. par. 191. 
 
 3 Introduction, p. xxviii. 
 
 4 ' Ce principe fournit la mesnre dcs ajfinites chimiqucs.''
 
 280 THERMAL METHODS. [BOOK I. 
 
 conception of atom, or rather he hopelessly confuses it with 
 that of equivalent. The molecule is for him a definite and 
 definable portion of matter, the parts of the molecule are only 
 numbers. 
 
 If by chemical affinity is meant an action and reaction 
 between atoms, then the principle already quoted certainly 
 does not afford a measure of this affinity. 
 
 Berthelot's law, then, assuming its truth appears to be 
 a definite statement applicable to chemical reactions; but 
 more precise investigation shews that the application is only 
 possible when ' chemical ' is used in a vague way as including 
 much that is usually called ' physical.' 
 
 The principle of the degradation of energy is a highly 
 generalised statement applicable to certain cycles of change; 
 Berthelot attempts to apply it to parts of such cycles, forget- 
 ting that what is true of the whole is not necessarily true of 
 the parts. 
 
 Thirty years ago Thomsen 1 generalised the relations be- 
 tween chemical action and thermal change in the statement, 
 "Every simple or complex reaction of a purely chemical kind 
 is accompanied by production of heat." 
 
 If by a reaction 'of a purely chemical kind' is meant the 
 combination of atoms to form molecules, no objection can be 
 made to this statement ; we recognise its importance and 
 universality, as we recognise the same qualities in such state- 
 ments as ' all men are mortal,' or ' no white men are black.' 
 But we may doubt its utility. Thomsen explains 2 that 
 'reactions of a purely chemical kind' are those which proceed 
 without addition of energy from sources external to the 
 system, and consist only of the strivings of atoms towards 
 more stable equilibrium 3 . On the other hand a chemical 
 system may be raised to a temperature such that its consti- 
 tuents are no longer stable, and reactions may then occur 
 with expenditure of external energy ; but these changes 
 
 1 See Thermochemische Unterstichungen, 1. 12 16. 
 
 2 loc. cit. 1. 1 6. 
 
 3 "Der chemische Process ist rein chemischer Natur, wenn er ohne Aufwand 
 fremder Energie verlauft, und nur durch das Streben der Atome nach mehr 
 stabilen Gleichgewichtslagen zu Stande kommt."
 
 CH. IV. 133] LAW OF MAXIMUM WORK. 28l 
 
 do not depend solely on mutual atomic attractions. But 
 actions ' of a purely chemical kind ' never occur except as 
 parts of cycles of reactions which include changes that do not 
 consist 'solely of the strivings of atoms towards more stable 
 equilibrium.' Hydrogen and oxygen do not combine to form 
 water, neither do chlorine and hydrogen combine to form 
 hydrochloric acid, without the addition of energy from ex- 
 ternal sources. 
 
 If the statements quoted from Thomsen or Berthelot are 
 ever true, they are true only when an arbitrary separation is 
 made of chemical changes into two parts, and one of these 
 parts is alone called chemical. Every chemical change, how- 
 ever simple, consists of at least two parts, the first of which is 
 the necessary antecedent of the second ; the law of maximum 
 work ignores this duality, or, it might be more accurate to 
 say, the law assumes that the second part of a chemical pro- 
 cess can occur without the first. Every process of chemical 
 change may be compared to the flight of a stone from, and 
 its return to, the surface of the earth. During the first part of 
 this process there is a continual transference of kinetic energy 
 from the moving stone to the surrounding medium, and 
 during the second part there is a continual transference from 
 the medium to the stone, until the stone comes to rest when 
 its energy becomes a part of the total energy of the system, 
 earth + stone. If the final resting-place of the stone is nearer 
 the centre of the earth than the spot from which it was pro- 
 jected on its upward flight, then the stone contains less energy, 
 relatively to surrounding systems, at the close of the trans- 
 action than at the beginning. On the other hand, if the 
 starting-point is nearer the earth's centre than the final point 
 of rest, then the transaction has resulted in gain of energy to 
 the stone. In both cases the second part of the transaction, 
 that which occurs between the turning-point and the final 
 resting-point of the stone, is attended with loss of energy to 
 the stone; but this second part does not represent the com- 
 plete transaction. The law of maximum work if applicable 
 at all is applicable only to the second part. And moreover 
 this law ignores the fact that the stone (or chemical system)
 
 282 THERMAL METHODS. [BOOK I. 
 
 does not leave its initial point of rest of its own accord; the 
 law assumes that no work need be done, no energy expended, 
 in the passage of the stone (or system) from its original posi- 
 tion to that at which the energy-relations between it and 
 surrounding systems come within the cognisance of the 
 law. 
 
 134 An attempt has been made by Thomsen to measure the 
 thermal values of the first parts, i.e. separation of molecules 
 into atoms, of certain changes which result in the production 
 of hydrocarbons. Attention has been already 1 drawn to this 
 investigation. An account of Thomsen's argument by which 
 he arrives at a certain thermal value for each of the four 
 'bonds' of the atom of carbon is given in The Elements of 
 Thermal Oumistry (pars. 73 75). I will not reproduce that 
 account here, but rather give a brief statement of another and 
 later argument by which Thomsen has arrived at certain 
 conclusions regarding the thermal values of the ' bonds ' of 
 the atom of carbon. 
 
 Thomsen 2 assumes (i) that the four 'bonds' or 'affinities' 
 of an atom of carbon are of equal value, at least as regards 
 combination with atoms of hydrogen, (2) that all the hydrogen 
 atoms in the molecule of a hydrocarbon are bound to the 
 carbon atom with equal vigour, and (3) that carbon atoms may 
 be united together in three different ways, viz. by single, 
 double, or treble, linkings. 
 
 The heat of combustion of a gaseous hydrocarbon mole- 
 cule is theoretically divisible into two parts, (i) the heat used 
 in separating the molecule into atoms of carbon and hydrogen, 
 and (2) the heat produced in the combination of these atoms 
 with oxygen to form carbon dioxide and water. 
 
 The formula C a H w expresses the composition of paraffins. 
 As each atom of carbon has four bonds, a atoms of carbon 
 have 4a bonds ; as each atom of hydrogen has one bond 2b 
 atoms have 2b bonds ; but every carbon atom must be united 
 to another carbon atom by at least one bond, hence the total 
 number of single linkings between the carbon atoms in a 
 
 1 Seeawfc, chapter II. section IV. par. 85. 
 a Zeitschr.fiir physikal. Chemie, I. 369.
 
 CH. IV. 134] THERMAL VALUE OF CARBON BONDS. 283 
 
 paraffin molecule C a H 2A is 
 
 2 
 
 Let v be the work required to tear asunder two singly 
 linked carbon atoms, then the work required to tear asunder 
 all the singly linked carbon atoms in a paraffin molecule C a H 2A 
 is 
 
 (2a-b}v (2). 
 
 Let r be the work required to tear asunder an atom of 
 hydrogen from an atom of carbon to which it is linked in the 
 molecule C a H u , then the work required to tear asunder all 
 the hydrogen atoms in the molecule is 
 
 2*>- (3). 
 
 Hence the work required to isolate all the atoms com- 
 posing the molecule C a H 2i is 
 
 (2a-b)v + 2br (4). 
 
 Let/ be the heat of combustion of an isolated gaseous 
 carbon atom, and let fh z be the heat of combustion of two 
 isolated gaseous hydrogen atoms, then the heat of combustion 
 of the isolated atoms obtained by tearing asunder the mole- 
 cule C a U nb will be 
 
 afc+bfh, (5). 
 
 And the difference between (4) and (5) will express the 
 heat of combustion at constant volume of the gaseous mole- 
 cule C a H w ; 
 
 The heat of combustion of the gaseous molecule C H W at 
 constant pressure is found by taking into account the thermal 
 change accompanying the change of volume from C,,H M to 
 CO 2 + H 2 O; the expression is 
 
 f. C a H 2 j (const, press.) = a (fc 2v) + b (fh% 2r+v + 290) + 580. . . (7). 
 
 As this equation holds good for all paraffins, and as the 
 expressions in brackets are the same for all, fc 2v may be 
 put as=;r, and fh^ 2r + v + 290 as=j; thus we get the 
 simpler form 
 
 /.QjHjA (const, press. ) = <w+4y + 580 (8).
 
 284 THERMAL METHODS. [BOOK I. 
 
 Thomsen then finds probable values for x and y from the 
 following heats of combustion at constant pressure of five 
 paraffins : 
 
 [ = C 4 H lrt ] = 687,i9o C(CH 3 ) 4 [ = C 5 H 12 ] = 8 47 ,iio. 
 From these data, ten values tor x andy are found, and from 
 these the following most probable values are deduced by the 
 method of least squares: 
 
 x= 106,170 7 = 52,530. 
 
 The heats of combustion of the five paraffins given above 
 calculated with these values of x and y closely agree with the 
 observed values; the largest difference is 720 units in the case 
 ofC 4 H 10 . 
 
 But when the observed heats of combustion of four defines 
 (C a H w where a = b} are compared with the values calculated 
 by the use of the above values for x and y, it is found that the 
 observed are always much greater than the calculated num- 
 bers. The following data give the differences in question: 
 
 C 2 H 4 ... 15,370 C 4 H 8 ... 15,240 C 6 H 12 ... 32,570. 
 C 3 H 6 ... 16,060 C 5 H 10 ...i 5 ,5 5 o. 
 
 In the molecule C 6 H 12 there are two double linkings 
 between carbon atoms, and in each of the other molecules 
 there is one double linking; therefore the mean increase of 
 the observed over the calculated heat of combustion is 15,465 
 units for each double linking. 
 
 Thomsen then develops a formula for calculating the heat 
 of combustion of a gaseous olefine in a way similar to that 
 already sketched, but taking account of the existence of 
 ' double linkings ' in the olefine molecules : applying this 
 formula he arrives at the conclusion that 
 
 2v-u 2 = 15,465 ................................. (9), 
 
 where v means, as before, the work required to tear asunder 
 two singly linked gaseous carbon atoms, and u = the work 
 required to tear asunder two doubly linked carbon atoms. 
 
 Thomsen then turns to the acetylenes (C tt H w where 
 & = ai), and by similar reasoning to that applied to the
 
 CH. IV. 134] THERMAL VALUE OF CARBON BONDS. 285 
 
 paraffins and defines he concludes that 
 
 (10), 
 
 where v has the same meaning as before, and w represents the 
 work required to tear asunder two trebly linked carbon atoms. 
 These results may be stated in various ways. If we 
 regard a double link between carbon atoms as two several 
 linkings, and a treble as three several linkings, then 
 
 u + 7732 = v, and w + 1 4640 = v. 
 
 Thomsen's results are thus equivalent to asserting that the 
 quantity of heat produced in forming the hypothetical group 
 = C C = from gaseous isolated carbon atoms is 7732 units 
 greater than half the quantity of heat produced in forming the 
 hypothetical group = C = C = from carbon atoms, and is 14640 
 units greater than one-third of the quantity of heat produced 
 in forming the hypothetical group C = C from atoms of 
 carbon. Or, let the heat produced in forming = C = C = from 
 
 I I 
 
 C and C be x units, then the heat produced in 
 
 I i 
 
 forming = C C= from the same carbon atoms is - + 7732 
 
 units ; and let the heat produced in forming - C = C - from 
 
 I I 
 
 - C and C be y units, then the heat produced in form- 
 
 I | 
 
 ing = C C = from the same materials is - + 14640 units. 
 
 Thomsen's values represent differences; in this paper he 
 does not attempt to find the actual thermal value of either a 
 single, a double, or a treble, linking between carbon atoms. 
 
 If the combination of a pair of carbon atoms by a double 
 link is regarded as occurring in two parts each bond having 
 its own thermal value, then Thomsen's numbers assert that 
 each half of this process is accompanied by the production of 
 rather less heat than half of that produced when two carbon 
 atoms combine by a single bond. 
 
 If we admit the justness of Thomsen's conclusions we shall 
 be forced to acknowledge that the bonds of the carbon atom 
 are of unequal value; but one of the assumptions on which
 
 286 THERMAL METHODS. [BOOK I. 
 
 Thomsen has based his argument is that the bonds in question 
 are equal in value. In one case however value here means 
 chemical value and in the other it means thermal value. Both 
 terms, value and bond, are misleading. Instead of the fre- 
 quently used expression, ' in the molecule CH 4 all the bonds 
 of the carbon atom are of equal value/ it would be much 
 better to say, 'in the molecule CH 4 each hydrogen atom is 
 related to the carbon atom and to the rest of the molecule in 
 the same way as every other hydrogen atom.' 
 
 It should be noted that the conclusions arrived at by 
 Thomsen are applicable only to hydrocarbons, and that they 
 are based on but scanty data. 
 
 If, as Thomsen's results assert, the thermal value of a 
 carbon bond depends on whether that bond is satisfied by the 
 bond of another carbon atom or by that of a hydrogen atom, 
 it is almost certain that the thermal value of the carbon bond 
 will vary according as it is satisfied by the bond of an oxygen, 
 a sulphur, or a chlorine, &c. atom ; and if this is so, then in 
 all probability the thermal value of each bond of the atom of 
 oxygen, sulphur, &c., will vary with the nature of the other 
 atoms with which the atom of oxygen or sulphur is combined. 
 The affinity of atoms for atoms cannot be measured by the 
 thermal values of the atomic bonds. Indeed these bonds are 
 wholly imaginary existences ; they are protean and for ever 
 escape one's grasp ; whether the conception we try to form 
 of them be purely chemical or partly chemical and partly 
 thermal, it is at the best but a blurred and wavering image 
 which comes between us and reality. 
 
 135 A few generalisations have been established regarding 
 the connexion between the structure and the boiling points 
 of carbon compounds. Thus the difference between the 
 boiling points of two consecutive members of an homologous 
 series of carbon compounds is frequently about 19 : but the 
 numbers actually obtained shew that variations in the boiling 
 points are connected with variations other than those of mole- 
 cular weight. Goldstein 1 attempts to shew that the proportion 
 
 1 Ber. 12. 689: also abstract of paper in Russian, C. S. Journal Abstracts 
 for 1882, 374.
 
 CH. IV. 135] BOILING POINTS. 287 
 
 between the numbers of hydrogen and carbon atoms, besides 
 the total number of these atoms, influences the boiling points 
 of the members of an homologous series. Hydrocarbons of 
 analogous constitution must be compared, i.e. normal hydro- 
 carbons must be compared with normal, 
 
 e.g. CH 3 -CH 2 -CH 2 -CH 3 with CH 3 -CH 2 -CH 2 -CH 2 -CH 3 ; 
 or iso-hydrocarbons must be compared with iso-, e. g. 
 CH(CH 3 ) 2 -CH 2 -CH 3 with CH(CH 3 ) 2 -CH 2 -CH 2 -CH 3 ; 
 
 nor can the differences between the boiling points of normal 
 hydrocarbons be compared with the differences between the 
 boiling points of iso-compounds. 
 
 Goldstein investigates the change of boiling point in the 
 series of normal paraffins, i.e. hydrocarbons of the form 
 CH 3 -(CH 2 ),-CH 3 [orCH 3 -CHR'-CHJ. He gives the 
 formula 
 
 B.P. = b.p. + (i9 + ^<L 
 
 where B. P. = boiling point required, b. p. = boiling point of 
 the paraffin containing CH 2 less than that whose B. P. is re- 
 quired, and n = number of atoms of carbon in the molecule of 
 the paraffin whose b. p. is known. Thus, the boiling point of 
 C 5 H 12 (i.e. CH 3 (CH 2 ) 3 CH 3 ) is 39'O; required the boiling point 
 ofC 6 H 14 (i-e.CH 3 (CH 2 ) 4 CH 3 ). 
 
 = 39+19+12-66 
 
 = 7o-66 B. P. observed = 7o-6. 
 
 Goldstein calculated the B.P. of normal heptane (C 7 H 16 ) 
 to be 98'65 ; shortly after this, the paraffin was obtained in 
 quantity by Thorpe, and the boiling point was found to be 
 
 98 '5- 
 
 The same formula appears to hold good for determining 
 the difference between the boiling points of any two consecutive 
 iso-paraffins belonging to the form CH (CH 3 ) 8 (CH 8 ) X CH 3 .
 
 288 THERMAL METHODS. [BOOK I. 
 
 Thus, 
 
 B.P. Difference. 
 
 If this is so, it follows that the difference between the 
 boiling point of a normal paraffin and its corresponding iso- 
 paraffin (of this form) must be the same whatever be the 
 molecular weight of the two isomerides. Experiment, so far 
 as it has gone, seems to confirm this result ; thus, 
 
 TJ. , Difference between B.P. of normal 
 
 and iso-paraffin. 
 
 C 5 H 12 8"- S 
 
 C 6 H 14 8-6 
 
 C 7 H 16 8- 5 
 
 ."'* v ; We have very little precise knowledge regarding the 
 T-i bpiling points of isomeric hydrocarbons. From the data 
 ~ w ~* accumulated it has been concluded, that, of two or more 
 
 isfpmeric hydrocarbons, that one has the lowest boiling point 
 -. tibfe molecule of which is characterised by containing the 
 
 greatest number of ' side chains n . Thus 
 
 Pentane (C B H 12 ). B.P. 
 
 ;... ./<) normal: CH 3 (CH 2 ) 3 -CH 3 39 
 
 "*- "1 isopropyl-methylmethane : CH 2 - CH(CH 3 ) 2 - CH 3 3O'5 
 
 (c) tetramethylmethane : C(CH 3 ) 4 9'5 
 
 Hexane (C 6 H 14 ). 
 
 (a) normal : CH 3 (CH 2 ) 4 CH 3 70-$ 
 
 () isopropyl-ethylmethane : CH 2 - CH(CH 3 ) 2 - C 2 H 5 62 
 
 (c) di-isopropyl : CH(CH 3 ) 2 -CH(CH 3 ) 2 58 
 
 (d) trimethyl-ethylmethane : C(CH 3 ) 3 (C 2 H 5 ) 43 48 
 
 The replacement of one or more atoms in a molecule by 
 another atom or other atoms is attended with a change of 
 boiling point. The data accumulated point to the existence 
 of definite relations between the boiling points of the com- 
 pounds and the nature and relative positions in the molecules 
 of the substituted and substituting atoms. Thus the change 
 from a hydrocarbon to an alcohol by substitution of OH for 
 H is accompanied in many cases by a rise of about 100 in 
 the boiling point ; the change from a monohydric to a dihydric 
 1 For data see Naumann, loc. dt. pp. 168 172.
 
 CH.IV. 135 138] SUMMARY. 289 
 
 alcohol is also attended by a rise of B. P. amounting to about 
 100 ; the substitution of a bromine atom for an atom of 
 chlorine in chloroderivatives of hydrocarbons is accompanied 
 by a rise of B. P. equal to about 23, and the value of the 
 increase is nearly constant in very many cases 1 . 
 
 36 In this section I have tried to trace some of the connexions 
 between the results of thermal measurements of chemical 
 phenomena and certain statical aspects of these phenomena. 
 We have found that every chemical phenomenon is a complex 
 occurrence, and that it is almost impossible fully to dis-r 
 tinguish those portions which would more appropriately be 
 called physical from those which are undoubtedly chemical. 
 We have also found that thermal measurements, being essen- 
 tially measurements of changes of energy, are intimately coQr 
 nected with problems belonging to chemical kinetics, and 
 that until we know something of chemical affinity we are nat 
 in a position fully to discuss the data of thermal chemistry. 
 
 5 
 SECTION II. Optical Methods. 
 
 37 In this section I wish to give some account of the attempts 
 which have been made to elucidate the relations existing b 
 tween the composition of chemical compounds and (i) th'e 
 refractive powers, (2) the power of rotating a ray of polarised 
 light, and (3) the absorption-spectra, of these compounds. 
 The subject is more limited than that considered in the first 
 section of the present chapter ; it belongs more completely 
 than thermal chemistry to the domain of chemical statics, 
 although like other questions in chemical science it presents 
 aspects which are essentially kinetical. 
 
 38 Let a ray of light pass from air into a liquid medium 
 denser than air ; let the angle of incidence = i, and the angle 
 
 of refraction = r ; then . = 11 = refractive index of the 
 sin r 
 
 medium. 
 
 1 An account of the present state of knowledge regarding the connexions 
 between the B.P. and constitution of carbon compounds will be found in a 
 pamphlet by W. Marckwald, Uber die Bez^ehiingen zwischen dem Siedepunkte 
 mill tier Zusammcnsetzitng chcmischer Verbindungcn. (Friedlander, Berlin, 1888). 
 
 M.C. 19
 
 290 OPTICAL METHODS. [BOOK I. 
 
 Let the light employed consist only of light of one 
 wave-length, and let the liquid medium consist of a single 
 
 definite chemical compound, then the quantity f -j-J was 
 
 called by Gladstone and Dale 1 the specific refractive energy of 
 the liquid examined (^=spec. grav. of the liquid referred to 
 water as unity). Landolt 2 called the product obtained by 
 
 multiplying r-J into the molecular weight of the liquid, 
 
 i.e. \ i ) M, the refraction-equivalent of the liquid compound 
 in question. 
 
 The quantity ( ^ ) was said by Gladstone and Dale to 
 
 be independent of temperature 3 . 
 
 Objection has been taken to the use of this purely em- 
 pirical formula in attempts to trace connexions between the 
 constitution and refractive powers of compounds 4 . The formula 
 
 f ^ - J . j for finding the refraction-equivalent of a compound 
 
 was deduced from the general principles of Clerk Maxwell's 
 electro-magnetic theory of light by A. Lorenz, and also in- 
 
 dependently by H. Lorenz 5 . The formula f-^- - \~j , 
 
 where Ap = refractive index of the theoretical ray of infinite 
 wave-length, was deduced by the use of a method given by 
 Cauchy, and was supposed to give results practically inde- 
 pendent of dispersion. Other formulae have been proposed 
 by different physicists. Briihl 6 has recently examined all the 
 formulas hitherto proposed for calculating the refraction- 
 equivalents of compounds ; he concludes that no formula 
 gives the true laws of dispersion, and that none of them 
 enables us to determine whether a limiting value independent 
 
 Proc. R. S. 12. 448, and Phil. Trans. 153. 317. 
 
 Pogg. Ann. 122. 545 ; and 123. 595. 
 
 See Proc. R. S. 18. 49 ; and also Phil. Trans. 160. 9. 
 
 See especially Wiedemann, Ber. 15. 467. . 
 
 Wied. Ann. 9. 641 ; 11. 70. 
 
 Ber. 19. 2821 (references are here given to many other memoirs).
 
 CH. IV. 138 140] MOLECULAR REFRACTION. 2QI 
 
 of dispersion does or does not exist for the quotient ^~ . 
 
 Bruhl states that the influence of the dispersion of different 
 bodies on their refractive powers has not been satisfactorily 
 deduced from any optical theory; and that in investigations 
 into the connexions between the refractive powers and the 
 chemical constitution of compounds the influence of disper- 
 sion must be neglected if it cannot be eliminated by purely 
 empirical methods. 
 
 Of the different formulae proposed, Bruhl prefers 
 
 _ 
 
 + 2 
 
 because it gives results which are more consistent and less 
 influenced by changes of temperature than those obtained by 
 any of the other formulae. 
 
 139 In 1863 Gladstone and Dale 1 concluded that 'every 
 liquid has a specific refractive energy composed of the 
 specific refractive energies of its component elements, modi- 
 fied by the manner of combination.' Many and lengthy 
 memoirs have been published on this subject since 1863 > 
 the general result has been to confirm the statement of 
 Gladstone and Dale, and at the same time to trace a more 
 precise connexion between the refraction-equivalent of a 
 compound and the manner in which the elements of that com- 
 pound are combined. One of the fullest and most important 
 memoirs is that published in 1887 by BriihP. As this 
 investigation includes many of the results formerly obtained 
 I propose to confine myself in the main to giving an account 
 of this work. Investigations have been confined hitherto 
 chiefly to liquid compounds of carbon. 
 
 140 Let us follow Bruhl in calling the product of the specific 
 refractive energy and the molecular weight of a compound 
 the molecular refraction (R), and the product of the specific 
 refractive energy and the atomic weight of an element 
 
 1 See Phil. Trans. 160. 9. 
 
 2 Annaltii, 235. i ; or Ber. 19. 2746; or Zeitschr. fiir physikal. Chemie, 
 1. 307. 
 
 I 9 2
 
 2Q2 OPTICAL METHODS. [BOOK I. 
 
 the atomic refraction (r). And, as Briihl does, let us use 
 the following formulae for determining these constants : 
 - A M y - \ A 
 
 where M= molecular weight, and A = atomic weight 1 . 
 
 Assuming that the molecular refraction of a compound is 
 the sum of the atomic refractions of its constituent elements, 
 and that the refraction of each atom has a constant value in 
 all its compounds, we may express the molecular refraction (R) 
 of a compound of carbon hydrogen and oxygen, C B H 2m O p , as 
 
 where (r)C, (r)H, and (r)O represent the atomic refractions of 
 carbon, hydrogen, and oxygen, respectively. 
 
 By determining the differences between the molecular 
 refractions of members of an homologous series of carbon 
 compounds, values are obtained for what may be called the 
 molecular refraction of the group CH 2 ; by determining the 
 differences between the molecular refractions of a series of 
 compounds, differing by 2H, values are obtained for the 
 atomic refraction of hydrogen ; and by deducting the value 
 for 2H from that for CH 2 , a number is obtained which is 
 taken as the atomic refraction of carbon. By similar methods 
 a value can be found for the atomic refraction of oxygen. 
 The molecular refraction of any compound of carbon hydrogen 
 and oxygen can then be calculated, on the assumption that 
 the value is equal to the sum of the atomic refractions of the 
 constituent elements, and compared with the observed value. 
 141 The calculated values for (R) do not agree in every case 
 with the observed values. Hence the molecular refraction of 
 a compound is probably connected with the arrangement, 
 as well as with the nature and number, of the atoms which 
 compose the molecule of the compound. What then is the 
 nature of the connexion between the arrangement of the 
 atoms forming a molecule and the refraction of that molecule ? 
 Bruhl thinks that the present data warrant general con- 
 
 1 Briihl uses light with the wave-length of the ray C ; many observers determine 
 /a for the red hydrogen line H.
 
 CH. IV. 141] MOLECULAR REFRACTION. 2Q3 
 
 elusions only regarding compounds of carbon, hydrogen, and 
 oxygen. 
 
 The paragraphs devoted to isomerism (par. 69 et seg.} con- 
 tain data which shew that isomerism may be connected either 
 with changes in the actual valencies of the atoms forming a 
 molecule, or with changes in the distribution of the interatomic 
 reactions. Thus, the formula C 3 H 8 O expresses the composition 
 of (i) propylic aldehyde, (2) acetone, and (3) allylic alcohol; 
 assuming the correctness of the structural formulae of these 
 three compounds, viz. 
 mur PH r/ (2) H 3 C-C-CH 3 , (3) H 2 C-CH-CH 2 OH, 
 
 (I) ttgLx - C tt 2 l-N^TT 
 
 o 
 
 (i) and (2) contain each a trivalent carbon atom and a 
 monovalent oxygen atom in direct union, and also a pair 
 of tetravalent carbon atoms, and (3) contains two trivalent 
 carbon atoms neither of which is in direct union with oxygen, 
 and also a tetravalent carbon atom in direct union with 
 an atom of oxygen which is divalent. The actual valencies 
 of the atoms are the same in (i) as in (2), but are not the same 
 in (3) as in (i) or (2); the distribution of some of the inter- 
 atomic reactions varies in (i), (2) and (3). In none of these 
 cases is the molecule saturated, i.e. in no case does each 
 polyvalent atom directly interact with its maximum number of 
 monovalent atoms (see ante, par. 70). These examples shew 
 that isomerism occurring in unsaturated molecules may be 
 connected either with changes in the actual valencies of 
 some of the atoms or with changes in the distribution of the 
 interatomic reactions. But when isomerism occurs in saturated 
 molecules it must be connected with changes in the distri- 
 bution of the interatomic reactions and not with changes 
 in the actual valencies of the atoms, because saturated mole- 
 cules are, by definition, those in which each polyvalent atom 
 directly interacts with its maximum number of monovalent 
 atoms. The following structural formulae for different propylic 
 alcohols (C 4 H B OH) illustrate this kind of isomerism: 
 
 X CH 3 /CH 3 
 
 H 3 C-CH s -CH 2 -CHoOH, CH-CH a OH, HO-C-CH 3 . 
 
 \CH 3 \CH 3
 
 294 OPTICAL METHODS. [BOOK I. 
 
 That kind of isomerism which is exhibited only by 
 unsaturated molecules and is connected with changes in the 
 actual valencies of the atoms is called by Briihl saturation- 
 isomerism, while that kind of isomerism which is exhibited 
 both by saturated and unsaturated molecules and is connected 
 with changes in the distribution of the interatomic reactions 
 unaccompanied by changes of valencies is called by Briihl 
 position-isomerism. 
 
 Briihl's data shew that different saturation-isomerides of 
 the general form C^H^O^ have different molecular refractions, 
 but that the molecular refraction of a series of position- 
 isomerides of the general form C x H y Oz is nearly a constant 
 quantity. 
 
 In order to find the exact influence on the molecular 
 refraction of a compound C x H y O z of changes in the valencies 
 of the carbon and oxygen atoms, Briihl first finds values for 
 the atomic refraction of the tetravalent carbon atom and the 
 divalent oxygen atom in saturated molecules. The difference 
 between (R) for each pair in the homologous series CH 2>(+2 
 gives a value for (R) CH 2 ; as the formula C M H 2K+2 can be 
 expressed as #CH 2 +H 2 , the same data allow a value for 
 (R)H 2 to be found; the difference between (R)CH 2 and 
 (R)H 2 gives (r)C. By similar methods (r) O is found. 
 
 Taking C IV and O" to represent a tetravalent atom of 
 carbon and a divalent atom of oxygen, respectively, then 
 Briihl's data lead to the values * 
 
 (r) C IV = 2-48 ; (r) O" = I -58 ; (r) H = i "04. 
 
 Values of (R) are then calculated for unsaturated com- 
 pounds containing a pair of directly interacting trivalent 
 carbon atoms, using the above values for (r) C &c., and 
 the calculated values are compared with those obtained by 
 experiment. 
 
 The influence on (R) of the change from a pair of directly 
 interacting tetravalent carbon atoms to a pair of directly inter- 
 acting trivalent carbon atoms is then determined ; Briihl's data, 
 given for about 20 compounds of the general form C^H^, C^H^O,, 
 
 1 The formula ( -^ j . -r is used, and /u is determined for the line C.
 
 CM. IV. 141, 142] MOLECULAR REFRACTION. 295 
 
 and Q-HyCl^XX, shew that this change is accompanied by an 
 increase in (R) amounting to about 1 1*85. Determinations 
 of (R) for seven compounds 2 each containing two pairs of 
 directly interacting trivalent carbon atoms, shew a mean 
 increase in (R) of 2 x 175. 
 
 Bruhl states these results by saying that the mean partial 
 value of an etJiylene grouping of a pair of carbon atoms in the 
 molecular refraction of a compound of the form C. tr H > O r is 
 175. The phrase ethylene grouping of two carbon atoms is 
 used because ethylene, H 2 C CH 2 , is the simplest compound 
 containing a pair of directly interacting trivalent carbon 
 atoms. 
 
 Bruhl then determines (R) for various ketones, aldehydes, 
 and other compounds CH 2W O containing a monovalent 
 oxygen atom in direct union with an atom of carbon, or it 
 may be said containing a carbonyl group, C O, and by 
 subtracting (R) CH 2M (= #CH 2 ), he obtains the mean partial 
 value of a carbonyl grouping of an oxygen and a carbon atom 
 in the molecular refraction of a compound C^H^O, ; this value 
 is found to be 76. 
 
 These conclusions may be stated thus : 
 
 /C C^, and 76 added for each carbonyl grouping, 
 
 (R) C x H y 2 =^ (r) C+y (r) H + z (r) O, 
 
 where (r) C = 2*48, (r)O=rs8, and (r) H = 1-04, with 175 
 
 added for each pair of carbon atoms grouped as in ethylene, 
 \ 
 
 <C-0. 
 
 142 Let us now consider one or two of the applications which 
 Briihl makes of these conclusions. 
 
 Acetic aldehyde CH 8 CHO is easily polymerised to par- 
 aldehyde C 6 H 12 O 8 . The change is probably represented by 
 the equation 
 
 3H 3 C - CHO = H 3 C . HC - O - CH . CH 3 . 
 
 0-C-O 
 
 /\ 
 HCH 3 
 
 1 The maximum is 2-29, and the minimum i'59; difference = 7. 
 
 2 Two compounds CjjH.jn-a and five diallyl compounds.
 
 296 OPTICAL METHODS. [BOOK 1. 
 
 If this is correct, we have three carbonyl groupings in 
 3CH 3 . CHO, and no carbonyl groupings in C 6 H 12 O 3 ] therefore 
 (R)C 6 H 12 O 3 ought to be equal to three times (R)CH 8 . CHO di- 
 minished by 3 x 76 = 2-28. The observed value of (R)CH 3 . CHO 
 is 11-5, and (i 1-5 x 3) - 2-28 = 32*22 ; the observed value of 
 (R)C fi H 12 3 is 32-4- 
 
 Amylene C 5 H 10 is easily polymerised to diamylene C 10 H 20 ; 
 the molecules of both compounds probably contain one pair 
 of directly interacting trivalent carbon atoms, or one ethylene 
 grouping ; if this is so, the molecular refraction of diamylene 
 ought to be equal to twice that of amylene diminished by 
 the value for one ethylene grouping, which is 175. The ob- 
 served values of (R) are these; C 5 H 10 = 24-64, C 10 H 20 = 47'i2 ; 
 now 24-64 x 2 = 49*28, and 49*28 47'I2 = 2'i6 which is slightly 
 greater than 175. Two isomerides of diamylene are known, 
 tetrahydroterpene obtained by the reaction of phosphonium 
 iodide with turpentine, and cymhydrene obtained from 
 camphor by reaction with iodine. The observed molecular 
 refractions of the three isomerides (C 10 H 20 ) are these : 
 
 diamylene 47'i2 . 
 
 tetrahydroterpene 46-02 '" jlj"" 1 
 
 ...dlff. = '22. 
 
 cymhydrene 45 '80 
 
 The calculated value of (R)C 10 H 20 is 45-6, if (r)C = 2-48 
 and (r)H= ro4 ; as (R) observed is nearly equal to (R) cal- 
 culated in the cases of tetrahydroterpene and cymhydrene, 
 and is greater by 1-52 than (R) calculated for diamylene, we 
 should conclude that diamylene contains one ethylene group- 
 ing, and that the other isomerides contain only tetravalent 
 carbon atoms. The study of the three hydrocarbons so far 
 as it has gone confirms this conclusion. 
 
 Both the isomerides pentene and isoprene, C 5 H 8 , probably 
 contain a pair of ethylene groupings ; pinene, C 10 H 16> probably 
 contains one ethylene grouping, and each of its isomerides 
 diisoprene and limonene probably contains a pair of ethylene 
 groupings. Assuming these statements to be correct, and 
 comparing the observed with the calculated values of (R) for 
 these five hydrocarbons, we have these results :
 
 C1I. IV. 142] MOLECULAR REFRACTION. 297 
 
 (R) 
 calcd. observd. diff. 
 
 f pentene, two ethylene groupings 24*22 24-60 +-38 
 6 8 1 isoprene, two 24*22 24-62 +-40 
 
 fpinene, one 43'i9 43'66 +-47 
 
 Ci H ](i < diisoprene, two 44'94 45'4 +'io 
 
 (limonene, two 44'94 45'o6 +-12 
 
 The structural formulae of the different hydrocarbons C 6 H 10 , 
 C^H^, C 5 H 8 , and C 10 H 16 , are not yet fully ascertained, but it 
 is very probable that the statements made by Bru'hl con- 
 cerning the number of ethylene groupings in each are correct ; 
 some of these hydrocarbons belong to the class of open chain 
 compounds and others to the closed ring group ; hence, if we 
 may judge from these data, the closing of a chain of carbon 
 atoms, or the opening of a ring of the same atoms, does not 
 affect the molecular refraction provided there is no change in 
 the saturation-isomerism of the molecules. In confirmation 
 of the conclusion that molecular refraction is not directly 
 connected with the existence of closed rings, Briihl tabulates 
 the molecular refractions of 24 benzene compounds, belonging 
 to many different classes but each containing a single benzene 
 nucleus, and shews that the mean difference between the ob- 
 served and the calculated values of (R) is +3 x r8i (max. 
 diff. = 3 x 2-17, min. diff. = 3 x 1-58), the calculated values 
 being arrived at by using (r)C = 2-48, (r)O = 1*58, (r)H = 1-04. 
 Hence it appears that the six-carbon benzene nucleus con- 
 tains three ethylene groupings 1 . 
 
 A considerable amount of evidence is certainly brought 
 forward by BrUhl in support of the statement that " position- 
 isomerides have nearly identical molecular refractions, but 
 saturation-isomerides have different molecular refractions... 
 the increase in molecular refraction being nearly propor- 
 tional to the number of ethylene, acetylene 4 , and carbonyl, 
 groupings, and this proportionality being more exact the 
 smaller is the dispersion of the compounds." 
 
 1 For an example of the application of Briihl's method to the terpenes, see 
 Ber. 21. 145. 
 
 - A pair of directly interacting divalent carbon atoms is called by Briihl an 
 acetylene grouping of two carbon atoms ; acetylene (IIC-CH) being the simplest 
 compound in which such a grouping occurs.
 
 298 OPTICAL METHODS. [llOOK I. 
 
 Briihl then formulates the fundamental refraction-law as 
 follows : 
 
 "The atomic refraction of carbon and oxygen is not in- 
 variable, but depends upon the [actual valencies of those 
 atoms in different molecules] 1 . The atomic refraction of these 
 elements is however nearly constant provided saturation is 
 unchanged, and in such cases is only very slightly dependent 
 on the configurations of the atoms. The monovalent elements 
 exhibit nearly invariable atomic refractions." 
 
 In support of the last part of this statement Bruhl shews 
 that the atomic refractions of hydrogen and chlorine calculated 
 from direct observations very closely agree with the values 
 calculated from observations made on compounds of these 
 elements; that (R) HC1 gas = (r) H + (r) Cl (from direct ob- 
 servations of (r) H and (r) Cl); and lastly that (r) H and (r) Cl 
 deduced from observations on liquid carbon compounds are 
 the same as (r) H and (r) Cl deduced from observations on 
 gaseous carbon compounds. 
 
 Nasini 2 has made determinations of (R) for various carbon 
 compounds containing sulphur, and has deduced two values 
 for the atomic refraction of sulphur according as the atom 
 directly interacts with two other atoms or with only one. 
 Wiedemann 3 has arrived at similar results. The atomic re- 
 fraction of sulphur appears to vary largely in compounds 
 containing both oxygen and sulphur. 
 
 143 It should be noticed that the conclusions arrived at by 
 Briihl can be applied at present only to such compounds of 
 the forms C, H, and C x H, O, as do not exhibit large dis- 
 persion. Nasini's observations 4 on naphthalene derivatives 
 and other compounds with large dispersive power, and some 
 of the experiments of Gladstone 5 on compounds containing 
 relatively very much carbon, shew that the nature of the 
 connexion between the refractive powers and the compositions 
 of compounds has not yet been fully elucidated 6 . 
 
 1 Briihl uses the expression 'satisfaction of the affinity' (Befriedigung der 
 Affinitdt). 2 Ber, 15. 2878. 3 Wied. Ann. 17. 577. 
 
 4 Gaz. 14. 150; 15. 59; 17. 72. 
 
 5 C. S. Journal Trans, for 1884, 241. 
 
 6 Kanonnikow (original paper in Russian; see abstract in Ber. 16. 3047) has
 
 CH. IV. 143, 144] POLARISATION. 299 
 
 144 If a ray of plane polarised light is passed through a plate 
 of quartz cut at right angles to its optical axis, the position of 
 the plane of polarisation of the emergent ray does not coincide 
 with that of the incident ray ; the plane has been rotated 
 through a certain angle, called the angle of rotation. If the 
 rotation takes place in the same direction as that in which 
 the hands of a watch appear to move as we look at the face, 
 the quartz is said to exhibit dextrorotatory power ; this is 
 expressed by prefixing -f to the value of the angle of rotation. 
 If the rotation takes place in the direction opposite to that in 
 which the hands of a watch appear to move as we look at the 
 face, the quartz is said to exhibit laevorotatory power ; this is 
 expressed by prefixing to the value of the angle of rotation. 
 
 Optically active transparent media are those which rotate 
 the plane of polarisation of a ray of light passed through 
 them; they are divided into dextrorotatory substances, e.g. 
 some specimens of quartz, sugar in aqueous solution, &c., and 
 laevorotatory substances, e.g. other specimens of quartz, tur- 
 pentine, quinine in alcoholic solution 1 , &c. 
 
 To determine the amount of rotation caused by any sub- 
 stance, it is necessary to have an instrument wherein a ray of 
 light may be polarised, and the position of the plane deter- 
 
 found the molecular refractions of a number of solid carbon compounds, by 
 dissolving them in chemically inactive solvents and measuring the refractive 
 indices of the solutions, the values of the indices of the solvent being known. 
 Kanonnikow concludes that neither the degree of concentration of the solution, 
 nor the physical condition of the solid, exerts any marked effect on the refractive 
 power of the dissolved substance. Conclusions are drawn as to the structural 
 formulae of various carbon compounds ; Bruhl's generalisations, on the whole, are 
 confirmed. 
 
 The same chemist (see abstract in er. 17. ref. 157; the abstracts, referate, in 
 the Berichte beginning with vol. 1 7 are paged separately from the original papers) 
 has attempted to determine (r) for various metals, by finding (R) for various salts 
 of carbon acids and deducting (R) for the acids. His numbers point to the 
 conclusion that in a 'group' of metals (as 'group' is used in the classification 
 based on the periodic law) (r) increases as the atomic weights of the metals 
 increase. Kanonnikow also tries to deduce values for (R) for the groups NO 3 , 
 SO 4 , &c. , and so to find the distribution of the interatomic actions in sulphates, 
 nitrates, &c. (See also Bull. Soc. Chim. 41. 548.) 
 
 1 For details concerning polarised light, and circular polarisation considered 
 from the physical stand-point, see Glazebrook's Physical Optics, chaps, xi. 
 and xiv.
 
 300 OPTICAL METHODS. [BOOK I. 
 
 mined ; the polarised ray may be passed through a known 
 quantity of the medium under examination ; and finally the 
 position of the plane of the emergent ray may be deter- 
 mined. Such instruments, known as polarimeters or polaristro- 
 bometers, are described in detail in various text-books 1 . 
 
 Let us consider a liquid carbon compound, say C 10 H 16 . 
 The angle of rotation, a, depends on (i) the thickness of the 
 layer of liquid through which the light passes, (2) the wave- 
 length of the ray of light employed, and in most cases 
 (3) the temperature at which the observation is made. The 
 first of these conditions will be determined if we know the 
 length of the column of liquid employed, and the second 
 is rendered definite by making use of monochromatic light. 
 
 Let /= length of column of liquid in decimetres, ^=spec. 
 grav. of liquid referred to water at 4, and a = angle of rotation 
 of plane of polarisation of light of given wave-length 2 ; then 
 
 [a]= specific rotatory power of the liquid, for the given ray,= j j. 
 
 That is to say, the specific rotatory power of an optically 
 active substance is the angle through which the plane of 
 polarisation of a given ray is rotated by passing through a 
 column i decimetre long of a liquid containing I gram of the 
 substance in I cubic centimetre. 
 
 For chemical purposes it is sometimes better to adopt 
 the definition of molecular rotatory power \iri\ suggested by 
 
 Krecke 3 , viz. 
 
 m a 
 100' l.d* 
 
 where m = molecular weight: m is divided by 100 to obviate 
 the use of inconveniently large numbers. 
 We have then 
 
 r n m a 
 
 and M= -7^. 
 
 1 See especially Armstrong and Groves, Organic Chemistry, 569 et scq. ; 
 and also Watts's Dictionary, 3rd Supplt. 11981207. 
 
 2 It is customary to indicate the light employed by placing a letter below the 
 bracket ; thus [a] D means spec, rotatory power for light of wave-length D. 
 
 3 J.fiir prakt. Chemie (2). .5. 12.
 
 CH. IV. 144] SPECIFIC ROTATORY POWER. 3O1 
 
 If the substance to be examined is a solid, it must be 
 dissolved in an optically inactive menstruum. In such a case, 
 /= length in decimetres of column of solution employed, p = 
 grams of optically active substance in 100 grams of solution 
 (i.e. gram-percentage composition), and f=spec. grav. of 
 solution referred to water at 4; then/. d=c = concentration, 
 i.e. grams of active substance in 100 c.c. of solution; and, 
 assuming that the solvent has no influence on the rotatory 
 power of the dissolved substance, 
 
 As the value of [2] generally rises as temperature rises 1 , 
 thermometric observations must be made. The value of [3] 
 also varies with variations in (i) the nature, and (2) the 
 quantity, of the inactive solvent employed ; the preceding 
 formula therefore gives only the apparent specific rotatory 
 power of the solid substance. 
 
 That [a] varies according to the nature of the solvent is 
 shewn by Hesse's observations on turpentine oil 2 ; 
 
 pure turpentine oil+alcohol oil + benzene oil + acetic acid 
 
 (C IO H, e ) (amount of solvent varied in each case from 10 per cent, to 90 per cent.) 
 
 [a] B 37'oi ; 37'035 to 38'486 ; 37'i94 to 39'449 > 37'i48 to 4o'222. 
 The following numbers 3 illustrate the dependence of [x] 
 on the amount of solvent employed; 
 Value of [a] 
 
 Aqueous solution of maximum. minimum. Difference. 
 
 Tartaric acid + I4'i8 + 3'2o io -98 
 
 Codeine - 1 3775 -iii 0> 5o 26'25 
 
 Quinine - i6g-2$ -ii6-o 53'25 
 
 Landolt (loc. cit.} has shewn that the true value of [a] 
 for a solid or liquid may be found in many cases from a num- 
 ber of observations made with solutions of varying concen- 
 tration; the more concentrated the solution the more nearly 
 
 1 For numbers illustrative of this in the case of aqueous solutions of tartaric 
 acid see Diet. 3rd Supplt. 1 209. 
 
 2 Hesse, Annalen 176. 89 and 189 : see also Landolt's Handbook of the Polari- 
 scope (English translation), 54 94. This book presents a view of the whole subject 
 of circular polarisation, chemically considered. See also Landolt, Ber. 21. 191. 
 
 8 Landolt, loc. cit,
 
 3O2 OPTICAL METHODS. [BOOK I. 
 
 does the value found for [a] approach the true value, i.e. the 
 more nearly does the observed, agree with the true, specific 
 rotatory power. It is better to use several solvents and make 
 a series of observations with each; the value deduced for [a] 
 is generally the same for each solvent. 
 
 The nature and extent of the variations in [a] caused by 
 varying the quantity of solvent appear to differ for each 
 optically active solid substance 1 ; in some cases the relation is 
 very complicated, in others it may be expressed by a com- 
 paratively simple formula 2 . 
 
 That the observed and calculated values of [a] agree 
 closely, provided a sufficient number of observations is made, 
 is evident from these results (Landolt) : 
 
 [a]/> calculated from observations on mixtures with 
 
 Active substance. [ a ]o observ 
 
 ed (i) (2) 
 
 (3) 
 
 (4) (5) max.diff. 
 
 
 C 2 H 5 OH CH 3 OH 
 
 H 2 
 
 C 6 H 6 CH 3 CO 2 H 
 
 
 Dextrorotatory "1 
 ethyl tartrate J 
 
 8-27 8'42 
 
 8 -09 
 
 - - 
 
 -'22 
 
 Dextrorotatory } 0- 
 
 1 4 -87 
 
 
 
 + 72 
 
 turpentine J 
 
 
 
 
 
 Lsevorotatory | 
 turpentine J 
 
 3 6- 9 7 
 
 - 
 
 36'97 36-89 
 
 -'12 
 
 Laevorotatory ) , 
 
 _.--_.:__ f l61 '55 
 
 i6o-8 3 
 
 i6i-2 9 
 
 
 
 -72 
 
 nicotine 
 
 The true specific rotatory powers of camphor, cane sugar, 
 
 Active substance. 
 
 Solvent. 
 
 [a] D for 
 pure substance. 
 
 [a] for 
 dilution. 
 
 Difference. 
 
 Isevorotatory turpentine 
 
 alcohol 
 
 36"97 
 
 3879 
 
 + I'82 
 
 dextrorotatory ,, 
 
 PJ 
 
 I 4' I 7 
 
 i5'35 
 
 + i'i8 
 
 lae vorotatory nicotine 
 
 falcohol 
 (water 
 
 i6o-8 3 
 
 74'i3 
 
 -22'2 4 
 
 -87-i6 
 
 
 [alcohol 
 
 8-2 7 
 
 io-i9 
 
 + I'92 
 
 (water 8'O9 28-i2 +2o-o 3 
 
 2 Thus, for solutions of turpentine in alcohol, Landolt gets the formula 
 
 [a] D =36 '974 + -004816417 + ooo [331^ 
 
 where q percentage of inactive solvent. (For more details see Landolt, loc. 
 c it, 81 94.) For dry inverted sugar Grubbe (Ber. 18. 2207) finds the following 
 formula when f varies from o to 30; 
 
 [>]= ~ 2 3'35 + '30406 (/- 20) + -001654 (/ - 2o) 2 . 
 
 For a fuller treatment of the methods employed for finding the true value of 
 [a] from observations on solutions, see Diet. 3rd Supplt. 1 2 1 2 1213; also Landolt , 
 Per. 21. 191.
 
 CH. IV. 144, 145] SPECIFIC ROTATORY POWER. 303 
 
 and dextroglucose, have been determined by Landolt, Tollens, 
 and Schmitz 1 . But I think it should be noted that the obser- 
 vations on which is based the method for determining [a] 
 were necessarily made with solutions of liquid compounds in 
 inactive solvents, whereas in the cases of camphor and sugar 
 we have to deal with solutions of solid substances ; it is 
 possible that the value of [a] for liquid camphor may be diffe- 
 rent from that for solid camphor 2 . It should also be observed 
 that any deductions concerning the relations between specific 
 rotatory power and molecular structure, drawn from a study 
 of liquid compounds, could not be applied in a precise manner 
 to solid compounds, assuming the true value of [a] for these 
 compounds to be known. 
 145 In attempting to trace relations between the specific rota- 
 tory power and the composition of compounds, we must dis- 
 tinguish relationships between [a] and the composition of 
 molecules whose empirical formulae at least are known, from 
 those between the same constant and such mixtures of mole- 
 cules in varying proportions as are presented by solutions of 
 varying concentration. 
 
 For although in the latter cases no precise conclusions can 
 be drawn regarding the relative arrangements of the atoms in 
 the molecules, yet the study of specific rotatory power may 
 help to throw light on such general questions as the action of 
 solvents, the distinction between chemical and physical change, 
 and so forth. 
 
 Pribram 3 has determined [a] for aqueous solutions of cane 
 sugar, tartaric acid, and nicotine, with the result that [a] does 
 not become constant even in very dilute solutions 4 . Pribram 
 thinks that this result is more in keeping with the hypothesis 
 
 1 See Landolt, loc. cit. 8492: Tollens, and Schmitz in Ber. 9. 1531: 
 10. 1403 : and do. 1414. 
 
 2 Biot states that fused liquid tartaric acid is markedly dextrorotatory, but the 
 solidified acid is feebly Isevorotary (Diet. 3rd Supplt. 1209). Landolt's value of 
 [a] for solid camphor is 55'6 (see Diet., loc. V. -374): while Gernez obtained 
 the value 7O'33 for fused camphor (do. do. p. 1209). 
 
 3 Ber. 20. 1840. 
 
 4 The most dilute solutions used were, '222 p.ct. for cane sugar, '3471 p.ct. 
 for tartaric acid, and '8826 p.ct. for nicotine.
 
 304 OPTICAL METHODS. [BOOK I. 
 
 that the solvent brings about some gradual change in the 
 configuration of the atoms forming the molecule of the dis- 
 solved compound, than with either of the other hypotheses 1 
 that have been suggested, one of which asserts that the mole- 
 cules of the solid consist of aggregates of true molecules, and 
 that these are separated by the solvent, and the other supposes 
 that the solvent forms a series of compounds with the dissolved 
 substance, which compounds are of different rotatory powers 
 and vary in quantity with variations in the relative amounts 
 of the solvent and the dissolved substance. 
 
 146 All known compounds which possess the power of ro- 
 tating the plane of polarisation of a ray of light when in 
 the liquid state or in solution are compounds of carbon : 
 van't Hoff 2 , following in the steps of Le Bel 3 , has endeavoured 
 to trace a precise connexion between the molecular structure 
 of these compounds and their rotatory power. The hypo- 
 thesis of Le Bel and van't Hoff connects optical activity with 
 the presence of one or more asymmetric carbon atoms in the 
 molecule of the optically active body. The definition of 
 an asymmetric carbon atom implies the conception of the 
 arrangement of atoms in three dimensions in space. An 
 atom of carbon is supposed to be situated at the centre of 
 a regular tetrahedron, and to be in direct union with four 
 atoms or radicles situated at the four summits of the tetra- 
 hedron ; when these four atoms or radicles are all different, 
 two geometrically different forms of the configuration may 
 
 Fig. 46. Fig. 47. 
 
 1 References to memoirs in which these hypotheses are discussed will be found 
 in Pribram's paper. 
 
 2 La Chimie dans FEspace; and more particularly in a pamphlet published in 
 1887, entitled Dix Annees dans fhistoire d'une Theorie. 
 
 ' Bull. Soc. Chim. 22. 337; 23. 295.
 
 CH. IV. 146] ASYMMETRIC CARBON ATOMS. 305 
 
 exist. These two forms bear to each other the relation of an 
 object to its image ; neither is superposable on the other 
 (s. figs. 46 and 47). An atom of carbon related in this way 
 to four different radicles is said to be asymmetric, because 
 there is no symmetry in the configuration, while at the same 
 time a plane of symmetry arises so soon as two of the four 
 radicles are the same. 
 
 Any compound containing an asymmetric carbon atom 
 may exhibit geometrical isomerism : each isomeride will differ 
 from the other in rotatory power, and if the isomerides are 
 crystallisable they will assume enantiomorphous (non-super- 
 posable) forms. Ammonium malate, for instance, crystallises 
 in two enantiomorphous forms, as represented in figs. 48 and 
 49; these crystals differ exactly in the same way as the 
 
 Fig. 48. 
 
 Fig. 49- 
 
 molecules of the two isomerides are supposed to differ. Many 
 other optically active compounds shew differences in rotatory 
 power accompanied by the power of crystallising in enantio- 
 morphous forms 1 . 
 
 We should expect then to find all those compounds opti- 
 cally active the molecules of which contain one or more 
 asymmetric carbon atoms, and also to find that all optically 
 active compounds contain asymmetric carbon atoms. 
 
 So far as investigation has gone, the molecule of every 
 compound which exhibits rotatory power contains at least 
 one carbon atom in direct union with four different radicles 2 . 
 The following formulae, in which the asymmetric carbon 
 
 1 Van't Hoffs Dix Anntes... p. 30. 
 
 2 For details of individual compounds s. van't Hoff, /. c. pp. 31 48. 
 
 M. C, 20
 
 306 OPTICAL METHODS. [BOOK I. 
 
 atoms are indicated by italics, shew the composition of some 
 commonly occurring optically active compounds ; 
 
 OH OH 
 I I 
 
 Tartaricacid CO 2 H C C CO 2 H ; 
 
 i i 
 H H 
 H 
 I 
 
 Lactic acid CH 3 C CO 2 H; 
 
 I 
 
 OH 
 H 
 I 
 Secondary amylic iodide CH 3 C C 3 H 7 . 
 
 I 
 
 Investigation has also shewn that those derivatives of 
 optically active compounds which do not themselves contain 
 asymmetric carbon atoms do not possess rotatory power; in 
 other words, a change of structure resulting in the removal 
 of the asymmetric atoms is always accompanied by loss of 
 optical activity. But compounds do exist which certainly 
 contain asymmetric carbon atoms and yet do not rotate the 
 plane of polarisation of a ray of light. Some of these may 
 be resolved into two isomerides of equal and opposite rotatory 
 powers, e.g. racemic acid ; others cannot be resolved into 
 active isomerides, e.g. mesotartaric acid. 
 
 Consider the formulae 
 
 (RaRaRO C . C(R 1 R 2 R 3 ) and (R 6 R 5 R 4 ) C . C(R 1 R 2 R 3 ), 
 where R^ &c. represent different radicles ; the first formula 
 shews each of the two asymmetric carbon atoms in direct 
 combination with the same radicles [R^R^R,,, and (CR^R,,)], 
 the second formula shews one asymmetric carbon atom di- 
 rectly combined with the radicles R I} R 2 , R 3 , and (CR 4 R 5 R 6 ), 
 and the other asymmetric carbon atom in direct union with 
 the radicles R 4 , R 6 , R 6 and (CR^RJ. The first formula 
 represents a symmetrical molecule, the second an tmsymme- 
 trical molecule. 
 
 Let us now advance a step farther and compare the 
 structures represented by the formulae 
 
 (R 3 R 2 R 1 )C.C(R 1 R 2 R 3 ) and (R 2 R 3 R t ) C. CC
 
 CH. IV. 146] HYPOTHESIS OF VAN'T HOFF. 307 
 
 Both formulae are symmetrical, but the structure repre- 
 sented by one is the reflection or image of that represented 
 by the other. The isomeride represented by one of these 
 formulae ought to rotate the plane of polarisation to the right, 
 and the other isomeride ought to rotate the plane an equal 
 amount to the left. A mixture or compound of these isome- 
 rides in equal molecular proportions would be optically in- 
 active, because every dextrorotatory molecule would be 
 opposed by a laevorotatory molecule. But such a mixture 
 or compound would be resolvable into a dextrorotatory and 
 a laevorotatory isomeride. 
 
 Unsymmetrical compounds containing asymmetric carbon 
 atoms must be active, or if inactive they must be resolvable 
 each into two isomerides of opposite rotatory powers. 
 
 Inactive compounds which are resolvable into two isome- 
 rides of equal and opposite activities are said in the language of 
 van't Hoff's hypothesis to be inactive by external compensation. 
 
 Now let the structure represented by the formula 
 
 be considered 1 . Each half of this molecule is the complement 
 or reflected image of the other ; one half will neutralise the 
 optical activity of the other half; the whole will be inactive 
 by internal compensation. 
 
 A compound which is inactive by internal compensation 
 must contain at least two asymmetric carbon atoms, and the 
 formula must be symmetrical. The hypothesis asserts the 
 existence of such inactive compounds, and declares that they 
 cannot be resolved into active isomerides because their in- 
 activity is the result of the atomic configuration of their 
 molecules, and is not produced by the opposition of molecules 
 of dextrorotatory power to an equal number of isomeric 
 molecules of laevorotatory power. 
 
 The hypothesis of van't Hoff divides compounds containing 
 asymmetric carbon atoms into three classes : 
 
 (i) Those which are optically active: such compounds 
 are produced in pairs consisting of a dextrorotatory 
 
 1 Models of the different structures made in pasteboard are helpful. 
 
 2O 2
 
 308 OPTICAL METHODS. [BOOK I. 
 
 and a laevorotatory isomeride ; they are either sym- 
 metrical or unsymmetrical. 
 
 (2) Those which are inactive but may be resolved into 
 two isomerides of equal and opposite rotatory powers ; 
 they are inactive by external compensation. 
 
 (3) Those which are inactive and non-resolvable; they 
 are inactive by internal compensation. 
 
 Van't Hoff (I.e. pp. 54 55) shews that an unsymmetrical 
 compound containing n asymmetric carbon atoms may exist 
 in 2" optically different modifications, and that a symmetrical 
 compound containing 11 asymmetric carbon atoms may have 
 
 |2* active isomerides, and |2 2 inactive non-resolvable isome- 
 rides 1 . 
 
 There are three general methods for separating inactive 
 resolvable bodies into their dextrorotatory and laevorotatory 
 isomerides. 
 
 In the first method advantage is taken of the differences 
 between the actions of some minute organisms on the two 
 active isomerides. For instance, when penicillium is allowed 
 to act on a dilute solution of ammonium racemate, Isevorota- 
 tory tartrate of ammonium is found in the liquid after a time, 
 the isomeric dextrorotatory tartrate being destroyed by the 
 action of the organism. 
 
 The second method proceeds by treating the inactive com- 
 pound with an active body with which one of the isomeric 
 constituents of the inactive compound combines more readily 
 than the other. For instance, crystals of laevorotatory tartrate 
 of cinchonine, and a solution of dextrorotatory tartaric acid, 
 may be obtained by adding the proper quantity of active 
 cinchonine to a solution of racemic acid, and crystallising. 
 
 The third method consists in separating the inactive body 
 into two active isomerides by crystallisation at a definite 
 temperature. For instance, when a solution of racemic acid 
 is neutralised by soda and another equal quantity by ammonia, 
 and the solutions are mixed and evaporated at a temperature 
 a little below 28, crystals both of dextrorotatory and laevoro- 
 
 1 Many applications are given in pp. 55 62 of van't Hoff's Dix Annces, &c.
 
 CH. IV. 146, 147] HYPOTHESIS OF VAN'T HOFF. 309 
 
 tatory sodium-ammonium tartrate are obtained 1 . Van't Hoff 2 
 has shewn that the change from sodium-ammonium racemate 
 to the two tartrates is accomplished by heating the dry salt 
 with water in the ratio NaNH 4 . H 4 C 4 O 6 . H 2 O: sH 2 O to a little 
 under 27; and that the change from the two tartrates to 
 the racemate (and water) is effected by heating the dry 
 mixture to a little above 27. The changes may be repre- 
 sented thus (the racemate crystallises with H 2 O and the tar- 
 trates with 4H 2 O) : 
 
 2(NaNH 4 .H 4 C 4 O 6 .4H 2 O)^2(NaNH 4 .H 4 C 4 O 6 .H 2 O) + 6H 2 O. 
 
 Slight variations of temperature above or below 27 deter- 
 mine the direction in which the change occurs. Some other 
 racemates appear to undergo change to tartrates at a definite 
 temperature 2 . 
 
 The change of inactive racemates to the active tartrates 
 and vice versa is closely analogous to some changes which 
 occur among inorganic compounds ; for instance, when a 
 mixture of the sulphates of magnesium and sodium in mole- 
 cular proportion is heated a little above 21 it is changed to 
 a double sulphate and water, and at a little under 21 the 
 double sulphate is resolved into the two single sulphates : 
 MgS0 4 . 7H 2 O + Na 8 SO 4 . ioH 2 O ^ MgNa 2 (SO 4 ) 2 . 4H 2 O + I3H 2 O. 
 
 The process of resolution by heat of the inactive racemate 
 is also very analogous to the physical process of fusion ; and 
 as one speaks of the fusion-point, so van't Hoff uses the 
 expression transition-point to indicate the temperature at 
 which the chemico-physical change in question occurs 8 . 
 47 The hypothesis of van't Hoff and Le Bel connects the 
 power of rotating the plane of polarisation of a ray of light 
 primarily with the configuration of the parts of molecules, but 
 it points to the formation of molecular aggregates without 
 change of molecular structure as a cause of the removal, or 
 rather disappearance, of optical activity. Optical activity 
 appears to be independent of the nature and number of the 
 
 1 For examples of the application of the three methods, see van't Hoff, /. c. 
 pp. 64-69. 
 
 3 See van't Hoff, /. c. p. 69. 
 
 3 For details, see van't Hoff, Journal fiir physikal. Chemie, 1. 165, 227.
 
 3IO OPTICAL METHODS. [BOOK 
 
 atoms which form the molecule of a carbon compound, and to 
 be connected only with the configuration of these atoms. We 
 cannot assign a definite part of the total rotatory power of a 
 compound molecule to each of the atoms or even groups of 
 atoms which form the molecule ; nor can we connect the 
 rotatory power with changes of valency or with changes in 
 the distribution of the atomic interactions, except in so far as 
 these are concerned in changes from a configuration contain- 
 ing asymmetric carbon atoms to another configuration which 
 does not contain such atoms. 
 
 The specific rotatory powers of many compounds readily 
 undergo change when small changes occur in certain physical 
 conditions. Some active bodies become inactive by heating, 
 and at another temperature the change is sometimes reversed. 
 The value of [a] of a solution of an active body in an inactive 
 solvent is dependent on the nature and the quantity of the 
 solvent. The addition of one inactive solvent to the solu- 
 tion of an active body in another solvent is sometimes 
 accompanied by a great change in the rotatory power of the 
 liquid ; thus about one half of the alcohol in an alcoholic 
 solution of cinchonine may be replaced by chloroform without 
 much change of rotatory power, but if as much as ^th f 
 the chloroform in a solution of the same alkaloid in this 
 solvent is replaced by alcohol a marked change in rotatory 
 power occurs 1 . Again, the rotatory power of a body in solu- 
 tion sometimes changes on keeping until a constant value is 
 attained; thus the value of [a] for a freshly prepared aqueous 
 solution of milk sugar or certain glucoses decreases on keep- 
 ing, and the final value is more quickly attained by boiling 
 the liquid 2 . 
 
 This readiness to change shewn by the rotatory powers of 
 carbon compounds finds some explanation in van't Hoff's 
 hypothesis, especially in the development of it made by 
 Wislicenus. For Wislicenus shews 3 that besides those con- 
 figurations which are conditioned by the affinities of the 
 
 1 Watts's Diet. 3rd Supplt. 1210. 
 
 2 Land oil's Handbook of the Polariscope, p. 62. 
 
 3 See ante, par. 94. 

 
 CH. IV. 147, 148] MAGNETIC ROTATORY POWER. 3!! 
 
 atoms of a molecule containing asymmetric carbon atoms, other 
 configurations will probably exist which will be relatively 
 unstable, and that the existence and number of these will be 
 conditioned by the action of heat and by collisions with mole- 
 cules of other kinds ; as these unstable forms are only geome- 
 trically different from the stable configurations they will be 
 optically active, but their rotatory power will not probably be 
 the same as that of the stable form. 
 
 Krecke 1 has endeavoured to generalise the relations be- 
 tween the molecular rotatory powers* [m] of certain compounds 
 and of their active derivatives ; but the data are insufficient. 
 148 A large number of measurements of the rotatory power 
 of compounds when under magnetic influence has been made 
 by Perkin 3 . The liquid compound to be examined was placed 
 in a glass tube the ends of which were let into the poles of a 
 large electromagnet; the tube formed part of a polariscope. 
 Sodium light was employed. 
 
 A great many compounds exhibit optical activity under 
 these conditions. 
 
 Perkin measures the rotations of liquid compounds and 
 refers the results to lengths of liquids related to each other in 
 the same proportion as the molecular weights of the gases 
 obtained by vapourising these liquids. 
 
 The molecular rotation of water is taken as unity. Let r = 
 observed rotation of a specified compound and r = rotation 
 of water; let Mw = molecular weight of the compound and 
 Mw = molecular weight of water; and let a?=spec. grav. of 
 the compound and ^' = spec. grav. of water [= i]; then mole- 
 
 _, . r . Mw r . Mw 
 cular rotatory power (Mol. R) = 
 
 r' . Mw' .d' 
 
 1 J- JUr prakt. Chemie, (2). 5. 6. See also Flavitsky, Ber. 15. 5 ; Th. Thomsen, 
 Ber. 13. 2168, 2264, 2269; 14. 29, 134, 203, 807, 1647; and against him, 
 Landolt, Ber. 14. 296, 1048. 
 
 2 See ante, p. 300. 
 
 3 C. S. Journal, Trans. 1884. 421 ; 1886. 777; 1887. 808.
 
 312 OPTICAL METHODS. [BOOK I. 
 
 About 150 compounds were examined, the observation of 
 r being repeated five to ten times for each compound, and the 
 spec. grav. of each being carefully determined. 
 
 In strictly homologous normal carbon compounds each 
 increment of CH 2 produces a constant increment (i'O23) in 
 molecular rotatory power. But when the addition of CH 2 is 
 accompanied by a change in the distribution of the atomic 
 interactions the change of Mol. R. is not constant ; for in- 
 stance, the change from a normal paraffin CH s .?zCH 2 . CH 3 to 
 the next higher isoparaffin CH(CH 3 ) 2 . CH 2 . CH 3 produces 
 an increase in Mol. R. equal to 1-023 + '105; in the change 
 from a normal acid to the next higher iso-acid of the same 
 series, CH. 2 has a different value; and so on. When chlorine is 
 substituted for hydrogen in a hydrocarbon the molecular 
 rotatory power is increased, but each chlorine atom has a 
 different value from the others. 
 
 These results indicate that the molecular rotatory power 
 of a compound is not the sum of certain constant values 
 assignable to each atom or atomic group, but that it depends 
 on the arrangement of the atoms which form the molecule. 
 This result is confirmed by the outcome of attempts to assign 
 values to the atomic rotatory powers of oxygen and carbon. 
 The atomic rotatory power of hydrogen may be deduced 
 thus: 
 
 (1) Mol. R. of C H 2n + 2 =Mol. R. 
 
 but Mol. R. of #CH 2 = 1-023. 
 
 The value thus deduced for At. R. of H is -254. 
 
 (2) Mol. R. of QH^ = Mol< R Qf CmH2m + i . 
 
 then 'Mol. R. of C n H 2n + 2 - Mol. R. of C m H ta + 1 
 
 = At. R. of H, if n = m; 
 [e g Mol. R. ofC 6 H 14 _ 3 - 323=Mol R of C3H7 . 
 
 but Mol. R. of C 3 H 8 = 3-577, .'. At. R. of H = "254]. 
 
 The value thus deduced for At. R. of H is "254. 
 
 The difference between -508 (At. R. of H = -254) and 1-023 
 (Mol. R for CH a in normal homologous series) gives the num-
 
 CH. IV. 148] MAGNETIC ROTATORY POWER. 313 
 
 her '515 as the atomic rotatory power of carbon in normal 
 homologous series. Similar methods are applied to the data 
 for oxygen compounds, and the results are these; 
 
 Oxygen in alcoholic OH At. R. = 'i94, 
 
 Oxygen in carboxylic OH =-137, 
 
 Oxygen in carboxylic CO ='261. 
 
 When these values are applied to calculate Mol. R. for series 
 different from those which furnished the data, numbers are 
 obtained which do not agree with the observed numbers. 
 
 Nor can a constant value be found for the atomic rotatory 
 power of chlorine; the value varies according to the series of 
 compounds considered, according as one or two hydrogen 
 atoms are replaced by one or two chlorine atoms, according 
 as the hydrogen replaced is in one part of the molecule or 
 in another part, and so on. 
 
 The general conclusion is that change of molecular rota- 
 tory power of carbon compounds under magnetic influence is 
 intimately connected with changes in molecular structure, so 
 that any cause which alters this structure also alters the 
 rotatory power. 
 
 Perkin attempts to use determinations of Mol. R. for various 
 compounds formed by the action of water on other compounds 
 for throwing light on the question whether these compounds 
 are hydrates, i.e. compounds of water, or compounds of oxygen 
 and hydrogen with other elements. 
 
 In all measurements of Mol. R. the molecular rotatory 
 power of water under the magnetic influence is taken as 
 unity; if therefore a compound is formed by addition of water 
 to another, Mol. R. for the new compound might be expected 
 to be equal to that for the original compound plus one for 
 each molecule of water added ; if the observed Mol. R. is less 
 than Mol. R. thus calculated, the difference may be explained 
 by supposing that the formation of the new compound has 
 involved a rearrangement of the atoms of the reacting mole- 
 cules. Here are a few examples of the application of this 
 method :
 
 314 OPTICAL METHODS. [BOOK I. 
 
 HCO 2 H . H 2 O Mol. R. observed = 2 '666 Mol. R. HCO 2 H + i 
 
 " =2-671 
 CH 3 C0 2 H.H 2 3-554 CH 3 C0 2 H + i 
 
 CH 3 CH 2 CO 2 H . H 2 O 4-512 CH 3 CH 2 CO 2 H 
 
 + 1=4-462. 
 
 H 2 S0 4 2-315 
 
 H 2 S0 4 . H 2 O 3-188 = Mol. R. H 2 SO 4 + -873 
 
 H 2 SO 4 .2H 2 4-113= H 2 SO 4 .H,0 
 
 + 925 
 
 H 2 SO 4 .3H 2 O 5-064= H 2 SO 4 .2H 2 O 
 
 + 951- 
 
 Perkin considers that the bodies formed by adding 
 water to formic acetic and propionic acids are either hydrates 
 of these acids, or only mixtures; but that a compound of sul- 
 phur oxygen and hydrogen [perhaps SO(OH)J, and not a 
 hydrate of sulphuric acid, is produced when sulphuric acid 
 and water react in the ratio H 2 SO 4 : H 2 O. The difference 
 between Mol. R. for some organic anhydrides and Mol. R. for 
 the corresponding acids averages about 74; in other words, 
 the combination of a molecule of water with an anhydride to 
 form an acid raises Mol. R. by about 74; hence, Perkin 
 argues, when H 2 O is added to H 2 SO 4 the change which occurs 
 is so far analogous to that of the conversion of an anhydride 
 into an acid that it cannot be regarded as a simple hydration 
 of sulphuric acid. 
 
 The following data lead to the conclusion that chloral 
 hydrate is not a compound of chloral and water, but that the 
 reaction between these compounds involves a rearrangement 
 of some of the atoms of the reacting bodies: 
 
 Mol. R. of CC1 3 . CHO liquid = 6'59i 
 
 Mean Mol. R. of liquid CC1 3 . CHO . H 2 O = 7-037 
 
 Increase in Mol. R. for combination of H 2 O = '446. 
 
 149 Researches on the relations between the composition and 
 the absorption-spectra of carbon compounds have been con- 
 ducted by Hartley 1 . From the results thus obtained, Hartley 
 concludes, that the normal alcohols C n H 2n+1 . OH are remark - 
 
 1 Phil. Trans. 170. 257. See also C. S. Journal's., for 1881. 153 et seq. 
 See also report of the B.A. committee ^gn Spectrum Analysis; Brit. Ass. Reports 
 for 1880. 258 et seq.
 
 CH. IV. 149] ABSORPTION-SPECTRA. 315 
 
 ably transparent to the ultra-violet rays methylic alcohol 
 transmits all rays up to wave-length 2000, but octylic alcohol 
 transmits nothing beyond 3464; that a normal acid of the 
 C n H 2im CO 2 H series always exhibits a greater absorption of 
 the more refrangible rays of the ultra-violet spectrum than the 
 normal alcohol with the same number of carbon atoms; 
 and that in both alcohols and acids addition of CH 2 is accom- 
 panied by increased absorption. 
 
 From an examination of the absorption-spectra of very 
 many carbon compounds, Hartley concludes, that absorption- 
 bands are never present in the ultra-violet part of the spec- 
 trum obtained by passing light through a compound in the 
 molecule of which the carbon atoms are arranged in an 'open 
 chain', but that such bands are present in the absorption- 
 spectra of all benzene derivatives. Inasmuch, however, as 
 benzene hexachloride C 6 H 6 C1 6 is very transparent, and exhi- 
 bits no bands, it would appear that the mere closing of the 
 chain of carbon atoms is not the sole condition necessary for 
 the production of absorption-bands. Hartley thinks that each 
 carbon atom must be in direct union with at least three other 
 carbon atoms. 
 
 This supposition is in accordance with the observation 
 that solutions of naphthalene, anthracene, and phenanthrene, 
 in transparent media, shew absorption-bands, similar to, but 
 lower in refrangibility than, the benzene bands ; and that 
 these solutions likewise exhibit much more intense absorption 
 than benzene. 
 
 Terpenes (C 10 H 16 ) and camphor (C ]0 H J6 O) exhibit more 
 intense absorption than compounds of the paraffinoid group, 
 but no bands appear in the spectra of the light transmitted 
 by these compounds ; hence their molecular structure appears 
 to be related on the one hand to the paraffinoid and on the 
 other hand to the benzenoid group of compounds. 
 
 By taking advantage of the differences in the character 
 of the absorption exhibited by different compounds e.g. the 
 character of the absorption-spectrum of cymene is very dif- 
 ferent from that of the terpenes it is possible to detect 
 minute quantities of certain compounds in presence of large
 
 316 OPTICAL METHODS. [BOOK I. 
 
 quantities of others, and also broadly to classify carbon 
 compounds into groups. Further, by taking advantage of 
 the differences in the positions of the bands in the spectra of 
 the light transmitted by isomeric compounds, it will be 
 possible, when sufficient data have been obtained, to de- 
 termine the class to which this or that isomeride belongs. 
 Moreover, the gathering together of this data will doubtless 
 be the means of gaining much precise knowledge regarding 
 the relations between the molecular structure and the actinic 
 properties of compounds 1 . For the experiments of Hartley * 
 tend to the conclusion that although greater or less absorp- 
 tion is connected with molecular vibrations, yet the special 
 selective absorption characteristic of benzenoid compounds is 
 rather to be connected with atomic vibrations. These ex- 
 periments also shew that the mean rate of vibration of the 
 rays absorbed by molecules of naphthalene and anthracene 
 is less than that of the rays absorbed by benzene molecules, 
 and hence, remembering the similarity of the character of the 
 absorptions in these three cases, it is concluded that the 
 amplitudes of the vibrations of the naphthalene and anthra- 
 cene molecules are greater, and the rates of vibration are 
 slower, than those of the benzene molecules. Hence it would 
 follow that the atomic vibrations which probably give rise to 
 the observed selective absorption are closely dependent on 
 the vibrations of the molecules as wholes. 
 
 Now if a connexion between the vibrations of molecules 
 and the vibrations of parts of these molecules is established, 
 and if this connexion is elucidated by precise data, we shall 
 certainly have made an important advance in solving the fun- 
 damental problem of chemistry, which is to trace the relations 
 between the composition and the properties of bodies. 
 
 A further step in this direction has been made by Abney 
 and Festing 3 , who have mapped the absorption which occurs 
 in the infra-red region of the spectrum, and have thus been 
 
 1 For the application of his general conclusions to essential oils, quinoline, 
 hydrocyanic and cyanuric acids, &c., see Hartley, C. S. Journal Trans, for 1880. 
 676 ; do. for 1882. 45 ; and Chem. News, 40. 269. 
 
 5 C. S. Journal Trans, for 1881. 165167. 
 
 3 Proc. R. S. 31. 416, and Phil. Trans, for 1881. 887.
 
 CH.IV. 149, 150] MOLECULAR VOLUMES. 317 
 
 able to shew that there is a definite connexion between the 
 nature of the atomic groups in the molecules of many carbon- 
 compounds, and the vibrations of the rays stopped by these 
 compounds 1 . 
 
 SECTION III. Methods based on determinations of the molecular 
 volumes of compounds' 2 . 
 
 150 The quotient obtained by dividing the formula-weight by 
 the specific gravity of a compound (referred to water at 4) is 
 generally called the specific volume of that compound. The 
 term specific volume, however, evidently expresses the relative 
 volume of unit weight of the substance. The quotient in 
 question is sometimes called the molecular volume of the com- 
 pound formulated. This expression strictly interpreted im- 
 plies that the formula-weight is identical with the molecular 
 weight, and that the specific gravity and formula-weight are 
 
 1 Kriiss and Oeconomides (Ber. 16. 2051), and Kriiss (Ber. 18. 1426, 2586), 
 have traced some connexion between the shifting of absorption towards or away 
 from the less refrangible part of the spectrum and the substitution of hydrogen in 
 benzenoid compounds by CH 3 , Br, NH 2 , NO 2 , &c. Reference may here be made 
 to a paper by G. Kriiss [Ber. 15. 1243, and 16. 2051] on an optical method for 
 determining whether or not chemical action has occurred between two substances 
 in solution, all the possible products of the reaction being also soluble under the 
 experimental conditions. The method consists, essentially, in comparing the 
 sums of the absorption-spectra of the original liquids with the absorption-spectrum 
 of a mixture of these liquids. 
 
 2 It may be well to gather together here references to the most important 
 articles and papers on the subject of this section: KOPP, Annalen 96. 153, 303; 
 100. 19, &c. BUFF, Annalen Supplbd. 4. 129, and Ber. 4. 647. THORPE, 
 C. S. Journal, Trans, for 1880. 141, 327. L. MEYER, Annalen Supplbd. 5. 129; 
 also Die modernen Theorien (4th Ed.), 284 292 ; English Ed. pp. 259-267. 
 ELSASSER, Annalen 218 302. STAEDEL, Ber. 15. 2559. WEGER, Annalen 221. 
 61. RAMSAY, C. S. Journal, Trans, for 1879. 463 ; do. for 1881. 49. 66. 
 LOSSEN, Annalen 214. 81. Compare also SCHIFF, Ber. 14. 2761; 15. 1270; 19. 
 560; Annalen 220. 71, 278; 223. 247. SCHALFEJEW, Ber. 15. 2209; 16. 1853. 
 ZANDER, Annalen, 224. 56. LOSSEN and ZANDER, Annalen, 225. rog. LOSSEN, 
 Annalen, 243. 64. GARTENMEISTER, Annalen, 233. 249. HORSTMANN, Ber. 19.* 
 1591; 20. 766. ISCHERMAK, Annalen, 112. 129; 114. 25. SCHRODER, Wied. 
 Ann. 11. 997; 14. 656; KRAFFT, Ber. 15. 1687. VOLLMAR, Ber. 15. 2560. 
 WILSON, Proc. R. S. 32. 457. NEUBECK, Zeitschr.fiir physikal. Chemie, 1. 649. 
 See also O. E. Meyer's Die Kinetische Theorie der Case, 216 221 : and WATTS' 
 Diet.; 1. 440 el seq. and (more especially) 3rd Supplt. 2117 et seq.
 
 3l8 PHYSICAL METHODS. [BOOK I. 
 
 expressed in terms of the same standard. The value of 
 
 formula-weight . . 
 
 r^ is equal to the product of specific volume 
 spec, gravity 
 
 multiplied into molecular weight, assuming the latter to be 
 the same as the formula-weight; or we may say that, if the 
 weight expressed by the formula is taken in grams, the quo- 
 formula-weight ,, r ,. 
 tient - jS represents the number of cubic centi- 
 spec. gravity 
 
 metres occupied by an amount of the substance in grams 
 proportional to its molecular weight. Now we can deter- 
 mine the molecular weights of gaseous compounds only : 
 if the specific gravities of compounds are referred to hydro- 
 molecular weight 
 
 gen as unity, then, - r~ = const. = 2. Never- 
 
 spec. gravity 
 
 r 1 ^- i. formula-weight . . . . ... 
 
 theless, if the quotient ^ is obtained for a 
 
 spec, gravity 
 
 number of liquid compounds, we shall have a series of com- 
 parable values, which if formula-weight of liquid is a simple 
 multiple of molecular weight of gas represent the volumes 
 occupied by quantities of various liquid compounds pro- 
 portional to the molecular weights of the same compounds 
 in the state of gases. 
 
 The meaning to be attached to the expression 'volume 
 occupied by a quantity proportional to molecular weight ' 
 will be discussed in paragraph 156. 
 
 The name atomic volume is generally applied to the quo- 
 atomic weight 
 
 tient r- ? ~n = (water = i). 
 
 spec, gravity of solid element 
 
 The determinations of the specific gravities of liquids 
 necessary for finding values for the quotient we are discussing, 
 should be made under comparable conditions ; this is roughly 
 fulfilled by determining the specific gravities at the boiling 
 points of the liquids 1 . 
 
 1 It would be advisable to compare those volumes of liquids for which 
 temperature and pressure are equal fractions of their critical values. (See 
 Ostwald's Lehrbttch, 1. 336.) Full details regarding the methods used for de- 
 termining the spec. grav. of liquids at their boiling points will be found in Thorpe's 
 paper, loc, cit.; see also Ramsay (loc. cit.) ; Schiff (loc. cit.); and Neubeck (loc. cit.).
 
 CH. IV. 150, 151] MOLECULAR VOLUMES. 319 
 
 Let the molecular volume, i.e. the quotient 
 
 formula-weight of liquid compound 
 spec, gravity referred to water 
 
 be expressed by the symbol ( V}. Then the value of ( F) for 
 a compound is in some cases equal to the sum of the values 
 of ( V) for the elementary atoms which form the molecule of 
 that compound. But is (F) always the sum of the atomic 
 volumes of the constituent elements, and has each elementary 
 atom a constant value ? 
 
 For many carbon compounds Kopp has shewn that 
 
 But in some cases the observed value of ( V) does not agree 
 with that calculated by this formula; thus 
 
 Aldehyde C 2 H 4 O : calculated (V) = (2 . ii) + (4- 
 
 observed (V) =S^'5- +47 
 
 Acetic acid C 2 H 4 O 2 : calculated (F) = ( 2 !!) + (4- 5'5) + ( 2 -7'8) = 59'6 
 
 observed (F) =63-5. +3-9 
 
 The value of ( V] for a compound C x H v O t is conditioned, 
 according to Kopp, by the value of ( F) for the oxygen atom, 
 or atoms, in the molecule. Kopp gives the following two 
 values, according as the oxygen atom acts as a monovalent or 
 divalent atom in the given molecule 1 ; 
 
 Applying these values to the case of aldehyde, we have 
 
 ( 2 .ii) + (4. 5-5)+ 12-2-56-2; 
 
 a result which agrees very closely with the observed value, 
 viz. 56-5. For acetic acid we have 
 
 I2'2 = 64'o: observed = 63-5. 
 ^OH 
 
 1 Kopp used the expression 'oxygen within the radicle' as synonymous with 
 what is now called divalent (singly-linked) oxygen atoms; and 'oxygen without 
 the radicle' as synonymous with monovalent (doubly-linked) oxygen atoms.
 
 32O PHYSICAL METHODS. [BOOK I. 
 
 Or again, for ethylic acetate, 
 O 
 
 O C 2 H 5 
 
 observed == 107*8. 
 
 Or, once more, for acetone and its isomeride allylic alcohol, 
 
 (i) (F)H 3 C C -CH, = (3.n) + (6. 5-5)+ 12-2 = 78-2: observed = 78-0; 
 I 
 O 
 
 (2) 
 
 H H 2 
 
 Instead of assigning two values to the oxygen atoms in 
 compounds of the form Q-H^O.,, it would probably be better to 
 employ the value ( V] = 23-2 (i.e. 11 + 12-2), which attri- 
 butes the influence on the total value of ( F) due to the 
 presence of the group CO to both the atoms which com- 
 prise this group. 
 
 Schiff (loc. cit.} concludes that the value of (F) O" varies 
 according to the nature and arrangement of all the con- 
 stituents of the molecule ; and also, that the value of 
 ( F) X - C - O is always greater than that of ( F) C - O - X, 
 where X represents a radicle. 
 
 Kopp 1 deduced two values for (F)S; thus (F)S I = 28'6, 
 (F)S n = 22'6: but only one value for ( F)C, and one for 
 (F)H and (F)C1. Many and very varying values have 
 been found by different observers for ( F)N : thus Kopp 
 assigns the value 2-3 to ( F)N when N occurs in amines, and 17 
 when N occurs in CN and in some nitro-compounds; Ramsay 
 gives (F)N = 3'6 in amines, = 9-0 in pyridine, lutidine, &c., 
 and = 7 in aniline, toluidine, and dimethylaniline. 
 152 If the influence exerted by the oxygen in a carbon com- 
 pound on the value of ( V) for that compound varies accord- 
 ing to the actual valencies of the oxygen atoms in the mole- 
 cule, it appears probable that the total value of ( V] will also 
 depend on the actual valencies of the carbon atoms in the 
 molecule. Buff 2 thought that his determinations shewed that 
 the value of ( F) for compounds containing trivalent (doubly- 
 
 1 See also Ramsay, C. S. Journal Trans, for 1879. 471 i. 
 
 2 Annalen, Supplbd. 4. 143 et seq.
 
 CH.1V. 152, 153] MOLECULAR VOLUMES. 321 
 
 linked) carbon atoms is greater than the value calculated on 
 the assumption that ( V}C ni = ( F)C IV = 1 1. Thus, 
 
 (1) DichlorethyleneCUzzC 1 " C UI -H 2 , (^ = 79-9: 
 
 (F) calculated = 78-6; diff.= + i'3. 
 
 (2) Carbon dichloride CL C" 1 C" 1 C1 2 , ( V) = 1 1 5-4 : 
 
 (V) calculated=H3'2; diff.= + 2'2. 
 H 3 C IV 
 
 (3) Amylene ^ >C ni C'" - C IV H 3 , ( F) = 1 1 2 : 
 
 H 3 C IV H 
 
 " ( V) calculated = 1 10 ; diff.= +2*0. 
 
 (4) Valerylene H 3 C C IU C" C m C IV H, , ( V) = 104-0 : 
 
 H H 
 
 (V) calculated = 99; diff.
 
 322 PHYSICAL METHODS. [BOOK I. 
 
 also vary, apparently, in accordance with the distribution of 
 the interatomic reactions in molecules wherein all the carbon 
 atoms are tetravalent, and all the oxygen atoms are divalent. 
 Thorpe (loc. cit.} has given some examples of such variations; 
 but Zander 1 has extended the number of examples con- 
 siderably. Thus a comparison of ( V) for propyl and isopropyl 
 compounds shews that the normal compounds always exhibit 
 a smaller value than the iso-compounds : 
 
 C 3 H 7 OH C 3 H 7 I C 3 H 7 Br C 3 H 7 C1 
 
 highest value of ( V) obtained for normal \ 
 
 /H.C C C X\ \ 81-4 108-2 97-5 917 
 compound^ 3 H 2 H 2 ) ) 
 
 lowest value of ( F) obtained for iso- 
 
 compound X-CH 3 ] f 82> 3 ^S 99'o 
 
 But the molecules of both classes of compounds contain only 
 tetravalent carbon atoms 2 . 
 
 Lossen 3 has collected the most trustworthy data bearing 
 on the question as to whether or not a constant value can be 
 assigned to (F)CH 2 . Kopp gave 22 as the mean value for 
 this group. Lossen shews that the differences between the 
 values of (F) for successive homologues of the acid series 
 C n H 2n+1 CO 2 H nearly agree with the differences calculated on 
 the basis of (F)CH 2 =22; but that in the series of alcohols 
 C n H wl CH 2 OH the value of (F)CH 2 varies from 187 to 21, 
 assuming that the other atoms exert a constant influence on 
 the total value of ( V). Apparently then a variable value 
 must be assigned to (F)C IV , or to ( F)H, or to both of these 
 quantities. 
 
 Some light is thrown on this point by Zander's comparison 
 (loc. cit^) of ( F) for propyl, isopropyl, and allyl, compounds, 
 which leads to the conclusion that the difference between ( F) 
 for a normal propyl and the corresponding allyl compound, 
 i.e. between two compounds differing in composition by H 8 , 
 varies from 57 to 8'9 (having a mean value of 7'i): hence, if 
 
 1 Annalen 'OA. 138: 224. 56. 
 
 2 See also Brown Proc. R. S. 26. 238. Also Elsasser, Annalen 218. 302. 
 8 Annalen 214. 8r et seq.
 
 CH. IV. 153] MOLECULAR VOLUMES. 323 
 
 we assume that the difference in question is wholly due to the 
 difference in empirical composition, we appear forced to con- 
 clude that the value of the influence exerted on ( V) by the 
 monovalent atom H is variable 1 . 
 
 Thorpe (loc. cit.} got these results for compounds containing 
 only tetravalent carbon atoms in their molecules: 
 H 2 CC1 2 (F)= 65-12; hence (F)Cl = 2i-6; (assuming (F)C=u, 
 
 HCC1 3 (F)= 84-53; 
 CC1 4 (^) = 103-68; 
 Taking the mean value for(F)Cl, viz. 22-5, and applying this 
 to calculate the values of ( V] for each of the preceding com- 
 pounds, we have 
 
 (F)H 2 CClo= 67-0 observed= 65-12 diff.= -r88 
 
 (F)HCCl^ 84-0 = 84-53 =+ -53 
 
 (V) CCl 4 =ioro =103-68 =+2-68 
 
 Hence the value of ( F)C1 appears to be variable. This is more 
 
 strikingly illustrated by Staedel's comparison 2 of the differences 
 
 in the values of ( F), and also the differences in the boiling 
 
 points, at various pressures, of chlorine compounds derived 
 
 from C 2 H 4 . 
 
 The differences in (F), and also in B.P., between the 
 following pairs of compounds, viz. 
 
 C1H 2 C CH 2 C1 and H 3 C-CH 2 C1, 
 C1H 2 C CHC1 2 and H 3 C CHC1 2 , 
 C1H 2 C CC1 8 and H 3 C CC1 3 , 
 
 1 Besides the empirical difference of H 2 , there is a difference in the actual 
 valencies of some of the carbon atoms in propyl and allyl compounds ; 
 thus, normal propylic alcohol is H 3 C C C OH, and allylic alcohol is 
 
 H 2 H 2 
 H 2 C ni C 1 " C OH. See also Weger, Annalen 221. 61, who gets different 
 
 H H 2 
 
 values for ( V) CH 2 in different series of compounds. See Ber. 16. 2458, where 
 Kopp reminds us that this number was given by him as a mean value, and 
 nothing more. Schiff (Annalen 220. 286, and 291) concludes that (F)C almost 
 certainly varies according to the nature and the arrangement of the constituents of 
 the molecule in which C occurs. Horstmann (Ber. 20. 766) collects many data 
 which lead him to the conclusion that ' unsaturated compounds with closed chain 
 formulae have considerably smaller molecular volumes than those with open chain 
 formulae and multiple linkings of atoms '. Neubeck (Zeitschr. fur physikal. Chemit, 
 1. 649) shews that (V] for benzene derivatives is modified according to the 
 position [ortho, meta, or para] of the replacing groups. 
 
 2 Ber. 15. 2559. 
 
 21 2
 
 324 PHYSICAL METHODS. [BOOK I. 
 
 express differences corresponding with change of CH 3 into 
 CH 2 C1, i.e. with the introduction of the first chlorine atom in 
 place of an atom of hydrogen into the hydrocarbon residue 
 CH, 
 
 The differences in the values of the same quantities be- 
 tween the following pairs of compounds, viz. 
 
 CLjHC CH, and H 2 C1C CH 3 , 
 C1 2 HC CH 2 C1 and H 2 C1C-CH 2 C1, 
 C1 2 HC CHC1 2 and H 2 C1C CHC1 2 , 
 C1 2 HC CC1 3 and H 2 C1C CC1 3 , 
 
 express differences corresponding with the introduction of the 
 second chlorine atom (in place of an atom of hydrogen) into 
 the residue CH 8 . 
 
 And lastly, by comparing ( V) and B.P. for the following 
 pairs of compounds, viz.: 
 
 C1 3 C CH 3 and C1 2 HC-CH 3 , 
 C1 3 C CH 2 C1 and C1 2 HC-CH 2 C1, 
 C1 3 C CHC1 2 and C1 2 HC CHC1 2 , 
 C1 3 C CC1 3 and C1 2 HC CC1 3 , 
 
 the differences corresponding with the introduction of the 
 third chlorine atom into the group CH 8 are determined. 
 Now the differences in question are: 
 
 for the first chlorine atom (V}= 14-20: B.P. 
 
 second (F)= 16-37: B.P. = 3i'3o; 
 
 third ( V}=-- 19-16: B.P. = i6-o4. 
 
 Hence each chlorine atom has a different 'volume-value' 
 and a different 'boiling-point-value'. If we choose to at- 
 tribute the observed differences to the carbonaceous parts of 
 the molecules, i.e. to C 2 H 4 in C 2 H 4 G1 2 , to C 2 H 3 in C 2 H 3 C1 3> &c., 
 we seem still obliged to admit that carbon and hydrogen 
 atoms have varying 'volume-values', and varying 'boiling- 
 point-values ', in the molecules formulated. 
 
 154 The remark made in paragraph 1 5 1 that the value of ( F) 
 for a compound is equal to the sum of the values of ( V] for 
 each of the elementary atoms in the molecule of that com- 
 pound, must evidently be supplemented by the statement, 
 that in the case of carbon compounds, at any rate, the value 
 of ( V} is not constant for C or O, and probably not for H or
 
 CH.IV. 154, 155] MOLECULAR VOLUMES. 325 
 
 Cl, but varies in accordance with (i) the actual valencies of 
 the atoms of carbon and oxygen, and (2) the distribution of all 
 the atomic interactions in the molecule. The precise character 
 of the connexion between the values of ( V) for C, O, H, and 
 Cl, and the valencies on the one hand, and the nature 
 of the atoms (or atomic groups) in direct union within any 
 molecule on the other hand, cannot be ascertained until 
 much more experimental data has been accumulated 1 . The 
 known data regarding the values of ( V) cannot therefore be 
 applied in other than a very tentative way to the selection of 
 one from among several possible structural formulae 2 . 
 55 The values of ( V) for many solid compounds have been 
 compared, and attempts have been made to generalise the 
 relations between these values; but, as might be expected 
 from considering how little comparable are the conditions 
 under which the relative densities of solids have been deter- 
 mined, the conclusions are either vague and difficult of precise 
 application, or represent only interesting relations between 
 certain numbers, without much, if any, connexion with 
 chemical facts. 
 
 By considering the difference between (F)MO and ( F)M, 
 a fairly constant value for ( F)O in the oxides is sometimes 
 obtained: thus for PbO and Fe 2 O 8 , the difference in question 
 is about 5-5. But in other oxides the value of ( F)O appears 
 to be very variable ; thus, 
 
 (F)CuO-(F)Cu = 5'i; but (F) CuoO-(F) Cu 2 = 10-5. 
 Brauner and Watts 3 have drawn the following conclusions 
 
 1 It is pointed out by Lossen (loc. cit.) that careful determination of ( V) for 
 many series of carbon compounds and for many individuals in each series, are 
 now required. 
 
 2 An illustration of the difficulties which are 'met with, and of the uncertain 
 nature of the results obtained, is furnished by the contradictory conclusions of 
 Thorpe (see Watts's Diet, 3rd Supplt. 2117 18) and of Masson and Ramsay (see 
 C. S. Journal Trans, for 1881, 51 et sey.) regarding the structural formula of POC1 :) . 
 Thorpe concludes that the formula ought to be written C1 2 =P O Cl, Masson 
 and Ramsay think that C1 3 ~ P O more nearly represents the facts. In connexion 
 with the formula of this compound see the experiments of Michaelis and La Coste 
 (Ber. 18. 2118). 
 
 3 Phil. Mag. [5] 11. 60.
 
 326 PHYSICAL METHODS. [BOOK I. 
 
 from comparisons of (F)MO and (F)M for different series 
 of oxides. 
 
 (1) In strongly basic oxides the value of ( F)O is nega- 
 tive ; the more basic the oxide, and the greater the value of 
 ( F)M in the oxide, the more negative is the value of ( F)O. 
 
 (2) In oxides of heavy metals and non-metals the value 
 of ( F)O is positive. 
 
 (3) In oxides of the earth metals the value of (V)O 
 is nil. 
 
 The values of ( F) for isomorphous compounds generally 
 vary little; thus, 
 
 (F)MgO.Al 2 O 3 = 4i'4 (V) ZnO .Fe 2 O 3 = 47'o 
 
 ( V} ZnO . Al 2 O 3 = 4o-2 (F) MnO . Cr 2 O 3 =46'4. 
 
 The greater the agreement between the angles of crystals 
 belonging to the same class, the less do the values of ( V} 
 differ, e.g. 
 
 ( (V\ ptc3=4r2 } Crystals are alm St identical 
 
 (V) BaCO 3 =45'S crystals exhibit differences 1 from those of SrCO 3 and 
 PbC0 3 . 
 
 Kopp 2 has concluded that if D, the difference between 
 what he calls the ' molecular volumes ' of two isomorphous 
 
 (V} (V} 
 
 compounds, is represented as D = YJTJ/\ J7\~\ then the 
 
 " 
 
 value of D may attain a maximum, equal to 0*328, without 
 isomorphism being impossible. 
 
 Determinations of ( V} for anhydrous and hydrated salts 
 promise to throw some light on various questions implied in 
 the commonly used expressions 'water of crystallisation' and 
 ' water of constitution '. 
 
 Graham distinguished ' saline ' water from ' basic ' water in 
 salts and acids ; the replacement of the former by another salt, 
 or by an oxide, produced a double salt, or in the case of acids 
 
 1 For more details see Naumann's Handbuch der Allgeineinen und Physikal- 
 ischen Chetnie, 360 362. 
 
 2 Annalen 36. r. Fogg. Ann. 52. 262; 53. 446; 56. 371. See also article 
 " Isomorphie ", in the News Handworterbiuh der Chetnie.
 
 CH.IV. 155] MOLECULAR VOLUMES. 327 
 
 a normal salt; the replacement of the 'basic' water in an acid 
 produced a basic salt. Thus, 
 
 MgSO 4 H 2 O 6H 2 O gave MgSO 4 K 2 SO 4 6H 2 O; 
 
 saline basic 
 
 N 2 O 5 H 2 O 3H 2 O gave f N 2 O 5 CuO 3H 2 O normal nitrate of copper. 
 
 CuO 3CuO bas j c 
 
 3H 2 O gave f N 2 
 
 basic j j 
 
 Graham further distinguished basic water from water of 
 constitu tion ; e.g . 
 
 H 2 SO 4 .H 2 O, from C 2 O 3 .H 2 O. 
 
 basic constitutional 
 
 Thorpe and Watts 1 have determined (F) for the salts 
 MSO 4 , when M = Mg, Zn, Cu, Mn, Fe, Co ; and for the hy- 
 drated salts MSO^H 2 O when M = Mg, Zn, &c. and x varies 
 from i to 7. 
 
 The value of ( F)MSO 4 was found to be independent of 
 the nature of M for the dehydrated salts. The difference 
 ( F)MSO 4 .;trH 2 O-( F)MSO 4 gave the increase in ( V] for;trH 2 O 
 added to the salts. The following results were obtained. 
 
 Mean difference between values of 
 
 and (F)S.H 2 O =107 
 (F)S.H 2 (F)S.2H 2 0=i3' 3 
 (F)S.2H 2 (J/)S. 3 H 2 0=i 4 -5 
 (F)S. 3 H 2 
 (F)S.6H 2 O 
 
 Hence the value of (F)MSO 4 .^H 2 O is changed to a 
 different amount by each of the molecules of water which 
 combines with the salt; or, it may be said, that the water 
 molecules contribute in unequal degrees towards the total 
 value of ( F). 
 
 Clarke 2 has compared the differences between (F) for 
 hydrated and ( V} for dehydrated salts, belonging to two 
 classes of compounds. 
 
 In the first class, when M = Ca, Sr, Ba, Mg, Cu, Fe, or Co, 
 and x varies from 2 to 6, the mean value of 
 
 1 C, S. Journal Trans, for 1880. 102. 
 
 * Amer, Journal of Sci. and Arts, (3). 8. 428.
 
 328 PHYSICAL METHODS. [BOOK I. 
 
 was found to be= 1376 (with a maximum value of 15-0, and 
 a minimum of 12-5). 
 
 The second class comprised various hydrated oxides and 
 hydroxides, viz. 
 
 B 2 O 3 3H 2 O, I 2 O 6 H 2 O, K 2 OH 2 O, CuOH 2 O, SrOH 2 O, BaOH 2 O, 
 A1 2 3 H 2 O, Mn 2 3 H 2 O, Fe 2 O 3 H 2 O. 
 
 In this class the value of the difference 
 
 ( V) oxide *H 2 O - ( V) oxide 
 
 x 
 varied from 7*4 to IQ'4. 
 
 If S represent one of the chlorides belonging to the first 
 class, or one of the oxides belonging to the second class, then, 
 for class I, the formula (F)S ^H 2 O = ( F)S + (x . 1376) gives 
 numbers which agree fairly well with the observed results; but 
 no such simple relation between ( F)S ^H 2 O and ( F)S can be 
 traced among the results obtained for compounds belonging 
 to class II. 
 
 But the hydrates of class I belong to the group of com- 
 pounds containing 'water of crystallisation', whereas those 
 of class II, or most of them at any rate, belong to the group 
 containing 'water of constitution'; hence, although the results 
 obtained by Thorpe and Watts (loc. cit.} lead to the conclusion 
 that the value of (F)H 2 O in the salts MC1^H 2 O is probably 
 different for each addition of H 2 O, nevertheless Clarke's num- 
 bers, taken as a whole, emphasise the difference between 
 'water of crystallisation' and 'water of constitution', and shew 
 that the chemical difference implied in these expressions is 
 connected with the relative magnitudes of the spaces occupied 
 by chemically comparable quantities of the hydrated salts 
 belonging to each class of compounds. 
 
 formula-weight , , 
 
 156 The quotient r^ ., has been treated as an empi- 
 
 specmc gravity 
 
 rically determined quantity; incidentally it has been regarded 
 as expressing the volume occupied by a quantity of the com- 
 pound formulated proportional to the mass of the molecules 
 which form the vapour of that compound. The question is 
 often propounded in papers on 'Specific volumes', whether the
 
 CH. IV. 156] MOLECULAR VOLUMES. 329 
 
 volume of an element in the free state is, or is not, identical 
 with the volume of the same element in combination. This 
 question, it seems to me, may be better put in another form. 
 What is the connexion between the value of ( V) for a given 
 compound, and the nature and arrangement of the atoms 
 which constitute the molecule of that compound ? It has been 
 shewn (pars. 152, 153) that the partial value to be assigned to 
 each atom is not a constant quantity; in other words tha.t(V) 
 varies with variations in the arrangement, no less than in the 
 nature, of the atoms which form the molecule of the com- 
 pound for which ( V) has been determined. But is there any 
 connexion between the variations of ( V), the valencies of the 
 atoms on the one hand, and the distribution of the interatomic 
 reactions on the other ? From the data concerning isomeric 
 carbon compounds, firstly, containing only saturated poly- 
 valent atoms, and secondly, containing also unsaturated poly- 
 valent atoms, we may conclude, I think, that both connexions 
 exist. It seems probable that a decrease in the actual valency 
 of an atom, other things remaining the same, is attended by 
 an increase in the value of ( V). But Staedel's investigation 
 (par. 153) shew r s that the latter value is also modified by the 
 nature of all the atoms in the molecule. If these connexions 
 can be made precise, and their nature ascertained by careful 
 investigation, it may become possible to trace relations be- 
 tween the volumes occupied by molecules of defined structure 
 and the energy-differences of these molecules, and perhaps to 
 connect with these the differences in the values of the refrac- 
 tive, and the rotatory, powers^of the same molecules 1 . 
 
 If the value of (V) for a compound is regarded from the 
 point of view of the molecular theory, a connexion may be 
 traced between this value and the partial value of ( V] for each 
 atom in the molecule of the compound. For it has been shewn 
 
 1 We should thus gain clearer conceptions of the properties of atoms as these 
 are exhibited in atomic interactions, and also be able to connect these interactions, 
 in a more precise manner than is yet possible, with the properties of the systems 
 thereby formed. If this view is accepted it is evident that the results obtained by 
 the various physical methods discussed in this and the preceding section must 
 have kinetical as well as statical aspects (see Book H.).
 
 330 PHYSICAL METHODS. [BOOK I. 
 
 by L. Meyer 1 , and by Loschmidt 2 , that the spaces occupied 
 by gaseous molecules (calculated from data based on the 
 transpiration-coefficients of the substances) are connected with 
 the atomic structure of these molecules, in the same general 
 way as has been shewn by Kopp and others to hold in the 
 case of liquid compounds 3 . The Clausian sphere-of-action 
 (ivirkungsspliare) of a molecule is the smallest space which the 
 molecule can occupy under given conditions. Changes in 
 these conditions (e.g. change of temperature), changes in the 
 form of the molecule, or changes in the arrangement of the 
 atoms in the molecule, will be accompanied by changes in the 
 space occupied by the molecule. The relations between the 
 values of these smallest spaces (spheres-of-action) occupied by 
 the molecules of two gases can be calculated, by means of a 
 formula deduced from the general principles of the molecular 
 theory, from observations of the transpiration-coefficients of 
 the gases. Putting the experimentally determined value of 
 ( F) as the value of the molecular sphere-of-action of one of 
 the gases, the values of the molecular spheres-of-action of other 
 gases can be found, and compared with those calculated from 
 
 T ;r > T./T i , T i i r atomic weight 
 
 Kopp s, Meyer s. and Loschmidt s, values for ^ ^ 
 
 specific gravity 
 
 of nitrogen, oxygen, hydrogen 4 , &c., and from the partial values 
 assigned, by different chemists, to various atoms in determining 
 the total value of ( V) for molecules containing these atoms. 
 This is done by O. E. Meyer (loc. cit. pp. 219 221). The 
 observed and calculated values of (V) agree as closely as 
 could be expected, considering that regard has been paid in the 
 calculations solely to volume, whereas the molecular spheres- 
 of-action must be conditioned by the form, the diameter, and 
 the length, of the molecular systems. Hence there is a well- 
 established probability in favour of the conclusion that the 
 partial values assigned to the different atoms, in determining 
 
 1 Annalen, Supplbd. 5. 129. 
 
 2 Sitzberichte der K. Akad. zu Wien (mat/i.-naturwiss. dasse). 52. (2nd part) 395. 
 8 See O. E. Meyer's Die Kinetische Theorie der Case, 216 221. 
 
 4 For a description of the determination of this constant for oxygen and other 
 gases from measurements of the transpiration-coefficients of these gases, see 
 L. Meyer, Annalen, Supplbd. 5. 129.
 
 CH. IV. 156, 157] ETHERIFICATION. 33! 
 
 the total value of ( V} for a liquid compound, are proportional 
 to the volumes occupied by these atoms in the gaseous state. 
 But this is just the conclusion drawn from an empirical study 
 of the values of ( V) determined for series of liquid compounds. 
 Much work must however be done before precise connexions 
 can be traced between the total value of ( V} and the partial 
 values assigned to the various atoms in any molecule. 
 
 It has generally been assumed that the volumes of differ- 
 ent liquids are under comparable conditions at the boiling 
 points of the liquids; but van der Waal's investigations 1 have 
 shewn that those volumes of liquids are comparable for which 
 temperature and pressure are equal fractions of their critical 
 values. In order therefore to compare molecular volumes 
 i.e. to compare values of ( V] it would be advantageous to 
 determine by experiment the critical temperature and pres- 
 sure of the liquid compounds examined. This has been done 
 in very few cases; but until it is done, considerable doubt 
 must be thrown on the value of the elaborate deductions 
 which have been drawn from the data regarding molecular 
 volumes 8 . 
 
 SECTION IV. Method based on the determination of 
 ' Etherification-values!* 
 
 157 The rate of formation of ethereal salts by the mutual 
 actions of alcohols and carbon-containing acids has been 
 
 1 Die Continuitiit des gasformigen und fliissigm Zustandes. (Leipzig, 1881). 
 Comp. Ostwald's Lehrbuch, 1. 336 339. 
 
 2 Neubeck's results (Zeitschr. fur physikal. Chemie, 1. 649) shew that the 
 relations which exist between the molecular volumes of various benzene deriva- 
 tives at ordinary pressures also hold good at pressures of 450 and 200 mm. 
 
 3 The papers by Menschutkin, of which this section is a very condensed 
 summary, will be found in J. fiir prakt. Chemie, (2) 24. 49: do. 25. 193, and 203 
 (abstracts in C. S. Journal for 1881. 1117; 1882. 384, 485, and 595). Abstracts 
 will also be found in Ber. 14. 2630, 2819: 15. 162, 248, and 721. A paper con- 
 taining a summary of Menschutkin's results will be found in Ann. Chitn. Phys. 
 (5). 30. 81. (Abstract in C. S. Journal for 1884. 726.) See also Zeitschr. fiir 
 physikal. Chemie, 1. 611.
 
 332 PHYSICAL METHODS. [BOOK I. 
 
 studied by Menschutkin : many of his results have a more 
 direct bearing on the questions of chemical kinetics, some of 
 them however may find a place here. The standard reac- 
 tions in terms of which determinations are stated are these : 
 
 (i) HCH 2 OH + CH 3 C0 2 H = CH 3 CO 2 (CH 3 ) + HOH ; 
 
 CH 
 
 (2) HC 
 
 X3 
 
 By varying the alcohol in (i) and the acid in (2), comparable 
 series of values are obtained for (i) alcohol-acetic system, and 
 (2) acid-isobutylic system. The number of molecules of 
 HCH 2 OH decomposed in reaction (i), and the number of 
 molecules of HCO 2 H decomposed in reaction (2), when 
 equilibrium is established, are taken as 100, and the results with 
 other alcohols and acetic acid, or with other acids and iso- 
 butylic alcohol, are stated in terms of this unit. 
 
 The expression 'etherification-velocity' is used to denote 
 the amount of action during one hour; the expression 'etheri- 
 fication-limit' is used to denote the amount of action when 
 equilibrium is established. Thus the statement ' the etherifica- 
 tion-velocity of CH 8 CH 2 OH is 67'3, and the etherification- 
 limit is 95'6' means, that when equal numbers of molecules 
 of CH 8 CH 2 OH and CH 8 CO 2 H react, 67-3 molecules of 
 CH 8 CH 2 OH are decomposed during the first hour, and 95^6 
 when the action ceases, the number of molecules of HCH 2 OH 
 decomposed under similar conditions (at the close of the 
 reaction) being taken as loo 1 . 
 
 The following, among many other numbers, were obtained 
 by Menschutkin. 
 
 Alcohol-acetic system. 
 
 Formula of Alcohol. Velocity. Limit. 
 
 HCH 2 OH 80-0 100-0 
 
 CH 3 .CH 2 OH 67-3 95-6 
 
 C 2 H 5 .GH 2 OH 66-9 96-0 
 
 1 The process is conducted at 153 154; the residual acid is determined by 
 titration. Two to five grams of alcohol are sufficient, and the process is always 
 applicable except the ethereal salt produced should be unstable at the temperature 
 of experiment.
 
 CH. IV. 157] ETHERIFICATION. 333 
 
 Hence, the substitution of CH 3 for H in the primary alcohol 
 H.CH^OH appears to be accompanied by a decrease in the 
 etherification-velocity of about I2'5, and in the limit of about 
 
 4'5- 
 
 The following conclusions are drawn by Menschutkin from 
 his determinations of the reaction-values of the system 
 R.CH 2 OH + CH 3 CO 2 H. 
 
 (1) The reaction-values (i.e. velocity and limit) of the 
 normal group C n H 2n41 in the alcohols C n H g , m CH 9 OH are 
 practically the same. 
 
 (2) Isomerism in the C B H 2n+1 radicles of primary alcohols 
 influences only the velocity-value, not the limiting value. 
 
 (3) Unsaturated alcohols (R . CH 2 OH) exhibit lower re- 
 action-values than saturated alcohols ; e.g. the values for 
 C 2 H 8 -CH 8 OH are smaller than those for C 2 H S -CH 2 OH. 
 
 From his study of the etherification of secondary alcohols 
 R 2 CHOH, the same chemist concludes that these alcohols 
 exhibit lower values than primary alcohols ; and that the 
 same radicle has smaller values in a secondary than in a 
 primary alcohol. The limiting value for tertiary alcohols 
 cannot be determined on account of the occurrence of 
 secondary changes; the velocities shew great irregularities. 
 
 Further results obtained by Menschutkin shew that definite 
 connexions, the precise nature of which cannot yet be traced, 
 exist between the actual valencies of the atoms, and also the 
 distributions of the interatomic reactions, in the molecules of 
 alcohols, and the etherification-values of these alcohols 1 . 
 
 By multiplying the limiting value of each compound by 
 the molecular weight of that compound (and dividing by 100), 
 numbers are obtained which exhibit the influence, on the 
 etherification-limit, of the molecular weights of the members of 
 the system studied. Menschutkin gives the following numbers 
 as representing molecular limits. In a later paper he calls 
 these numbers simply weight-limits, in distinction to the per- 
 centage limits already explained. 
 
 1 For a more precise statement of Menschutkin's conclusions on this point see 
 abstract in Ber. 14. ?8i8.
 
 334 PHYSICAL METHODS. [BOOK I. 
 
 Acid-isobi4tylic system. 
 
 Molecular Difference for 
 
 Acid. 
 
 limit. 
 
 each CH 2 . 
 
 CH 3 CO 2 H 
 
 40-42 v 
 
 
 C 2 H 5 C0 2 H 
 
 5o'83\ 
 
 10*41 
 
 (C 3 H 7 )C0 2 H 
 
 6i-i7 x 
 
 I0< 34 I9 . 8l 
 
 (C 6 H U )C0 2 H 
 
 80-98 / 
 
 9'9= ~^ 
 
 (C 7 H 15 )C0 2 H 
 
 102-05^ 
 
 21-07 
 
 Tr^'C'3 
 
 Mean difference for each increment of CH 2 = 10-29. 
 
 The value of the molecular, or weight, limit for any mem- 
 ber of this series of acids (the alcohol being isobutylic) may 
 be found by the formula, 
 
 molecular limit = 40-42 + (n- 2) 10-29; 
 
 when n = number of carbon atoms in the molecule of the 
 acid. 
 
 Thus, in the acid (C 3 H 7 ") CO 2 H 72 = 4, hence 
 
 molecular limit = 40-42 + (2 . io'29) = 6ro; observed value = 6i'i7. 
 
 Menschutkin gives the expression a + (n 2}d for finding 
 the molecular etherification-limit for an acid in any system of 
 alcohol arid acids, when a = molecular limit for the first acid 
 of the series, and d- mean increase, for each increment of 
 CH 2 , in the molecular limit of the acids of the series. 
 
 The rule is, to the value of the limit for the given alcohol 
 with the first acid of the series, add (n 2) d, that is, add (;/ - 2) 
 times the mean homologous difference (i.e. the mean differ- 
 ence for each increment of CH 2 ) between the weight-limits of 
 the given acid and the first acid of the series, when n = num- 
 ber of carbon atoms in the molecule of the given acid. 
 
 Thus, required the weight-limit for the caproic-butylic 
 system. For the acetic-butylic system a = 40*52, and d= io - 29 ; 
 caproic acid is C 8 H n .CO 2 H; therefore the weight-limit re- 
 quired is 40-52 + (4. 10-29) = 8r68. 
 
 It is evident that the percentage limit can easily be found 
 when the values of a and d are given. In the case in question 
 we have, 
 
 percentage limit = ' IOO = 70-41. [C 6 H U . CO,H = n6].
 
 CH. IV. 157, 158] CAPILLARY-CONSTANTS. 335 
 
 Menschutkin gives the following values for a and d in 
 various systems of alcohols and acids of the acetic series : 
 
 acid-ethylic system 
 
 acid-propylic 
 
 acid-butylic 
 
 acid-amylic 
 
 acid-hexylic 
 
 acid-heptylic 
 
 acid-caproic 
 
 a = 39-94 
 a = 40-23 
 a= 40*42 
 = 40-55 
 = 40-64 
 0=4071 
 a =40-77 
 
 = 10-29. 
 
 It is also possible to vary the alcohol, the acid remaining 
 constant, and from the data obtained to calculate the weight- 
 limit for any given system 1 . 
 
 From a comparison of the etherification-values for primary 
 secondary and tertiary acids, and also of the same values for 
 hydroxy- and chloro-acids &c., Menschutkin draws certain 
 conclusions regarding the connexions between the variations 
 in these values and the molecular structures of the various 
 acids. For instance, the velocity of etherification of the 
 primary acids is much greater than that of the secondary 
 acids, but the limiting values are nearly identical in both 
 series. 
 
 A study of these conclusions shews that much is to be 
 hoped for from the application of Menschutkin's method, but 
 that more data must be obtained before we have precise 
 knowledge concerning the connexions between the rate of 
 formation of ethereal salts and the chemical constitutions of 
 the interacting alcohols and acids 2 . 
 
 SECTION V. Miscellaneous methods. 
 
 158 That the ' capillarity '-constants' of liquid carbon compounds 
 are connected with the chemical constitutions of these 
 compounds is apparent from researches by Mendelejeff 3 , 
 
 1 See details in C. S. Journal, Abstracts for 1882. 387. 
 
 2 See some of Menschutkin's generalisations in C. S. Journal, Abstracts for 
 1882. 485, 598: and an application to the formula of maleic and fumaric acids 
 in do. do. 1882. 383. 
 
 8 Compt. rend. 80. 52; 51. 97.
 
 336 PHYSICAL METHODS. [BOOK I. 
 
 Wilhelmy 1 , and especially Schiff 2 . The capillarity-constants 
 are calculated from experimental data by methods which need 
 not be discussed here (see abstracts of Scruffs papers in C. S. 
 Journal, or see Ostwald's Lehrbuch, I. 479). SchifFs results 
 lead to capillarity-equivalents for certain atoms, e.g. C = 2H, 
 O = 3H, Cl = 7H, &c., that is, they tend to shew that n atoms 
 of one element have the same partial value in the capillarity- 
 constant of a series of compounds as m atoms of another 
 element. The capillarity-equivalent of the same elementary 
 atom seems to vary with variations in the actual valency of 
 that atom, and also with variations in the chemical type of 
 the compounds examined. 
 
 159 The rates of flow through capillary tubes of liquid com- 
 pounds have been measured by several observers, especially by 
 Graham 3 and by Pribram and Handl 4 . The results obtained 
 are sufficient to establish the fact of a connexion between the 
 transpiration-rates and the chemical constitution of liquid 
 carbon compounds. But they do not elucidate the exact 
 nature of this connexion. Ostwald 5 suggests that measure- 
 ments should be made at the boiling points of various liquids, 
 as some of the results obtained by Pribram and Handl sug- 
 gest that the transpiration-rates of equal weights of analo- 
 gous compounds under these conditions would be found to be 
 nearly proportional to the molecular weights of the com- 
 pounds. 
 
 160 The facts of electrolysis have been used as arguments in 
 discussing the constitution of chemical compounds ; but 
 the questions on which electrolytic data throw light rather 
 belong to the domain of chemical kinetics than to that of 
 statics 6 . 
 
 . l Pogg. Ann. 121. 55. 
 
 a Aririalen,Z2Z. 47 ; Gazetta, 14. 368 (abstracts in C- S. Journal, Abstracts for 
 1884. 808, and 1885. 717.) 
 
 3 Phil. Trans. 1861. 373. 
 
 4 Sitzungsberichte der K. K, Acad. zu Wien, 1878 (June part); 1879 (June 
 part). 
 
 6 Lehrbuch, 1. 507. 
 
 8 See Book n. chap. in.
 
 CH. IV. 159, 1 60] ELECTROLYSIS. 337 
 
 Faraday's laws of electrolysis, translated into modern 
 chemical language, assert that the parts or ions into which a 
 compound is separated by electrolysis are chemically equi- 
 valent and carry with them equal quantities of electricity. 
 
 Electrolytes belong to the type of salts, using the term 
 in its widest meaning. Metallic salts are generally good con- 
 ductors when molten, and they readily undergo electrolysis. 
 But most, if not all, single liquid compounds, e.g. water, 
 alcohol, ether, are nearly dielectrics. Aqueous solutions of 
 most salts are electrolytes ; and the nature of the electrolytic 
 decomposition is clearly connected with the quantity of the 
 solvent. Hence it is probable that a chemical action of some 
 kind occurs between the salt and the water; and the true 
 electrolyte may be a molecular aggregate, or aggregates, 
 formed by the union of the two kinds of molecules. This 
 view is confirmed, on the whole, by the electrolytic behaviour 
 of many double salts, some of which are decomposed by the 
 current in the same way as a mixture of their constituents, 
 while others give distinctive products. The behaviour of con- 
 centrated aqueous solutions of cadmium iodide and chloride 
 points to the existence and electrolytic decomposition of 
 aggregates, probably Cd 3 X 6 , in these solutions, while the be- 
 haviour of dilute solutions of the same salts is explained by 
 supposing that the body undergoing electrolysis is the ordi- 
 nary molecule CdX 2 . Whatever be the exact nature of the 
 connexion between the passage of the current through a 
 solution of a salt and the electrolysis of the salt, there can be 
 little doubt that the process is intimately conditioned by the 
 nature and amount of the solvent; and the most probable 
 explanation of this conditioning effect is that which assumes 
 the formation of more or less unstable compounds of the 
 solvent with the dissolved body. 
 
 But considerations such as these are evidently better dis- 
 cussed when we are treating the subject of chemical change, 
 than when we are dealing with chemical composition 1 . 
 
 1 See Book 11. chap. III. The student would do well to read the chapter on 
 Electrolysis in Ostwald's Lehrbuch 1. 533 568. 
 
 M. C. 22
 
 338 PHYSICAL METHODS. 
 
 Concluding Remarks on Part I. 
 
 161 The general aim of the first part of this book has been to 
 give a fairly complete account of the present state of know- 
 ledge regarding the questions of chemical statics, indicating 
 where such knowledge requires to be chiefly supplemented, 
 or rendered more precise, by new experimental researches. 
 
 I have regarded those questions which are concerned with 
 substances, or systems of substances, in equilibrium as broadly 
 belonging to chemical statics ; but I have been obliged to 
 pay more or less attention to the kinetical aspects presented 
 by all such questions. 
 
 It may be said that the fundamental conception of atom 
 and molecule, stated and illustrated in chapter I., has been 
 regarded in its applications to explain resemblances and 
 differences between physical and chemical phenomena, nascent 
 actions, allotropy, isomerism, and the classification of elements 
 and compounds; and that the principal methods, both purely 
 chemical and chemico-physical, which are employed in ex- 
 amining these problems, have been sketched, and their appli- 
 cations illustrated. 
 
 A way has thus been cleared by which we may hope to 
 approach the more difficult problems of chemical kinetics.
 
 BK.II. CH.I. 162] 
 
 BOOK II. 
 CHEMICAL KINETICS. 
 
 CHAPTER I. 
 
 THE LAW OF MASS-ACTION.
 
 34O THE LAW OF MASS-ACTION. [BOOK II. 
 
 regarded now from the statical and now from the kinetical 
 point of view. 
 
 A complete account of any chemical change must include 
 the statement of the relations between the reacting bodies, 
 and also of the relations between the forces concerned in the 
 change. 
 
 163 The question of chemical kinetics is : what is the cause of 
 chemical change ? The answer to this question has always 
 been the same : the cause of chemical change is chemical 
 affinity 1 . 
 
 To trace the history of the term cliemical affinity, and to 
 find a definite and quantitative meaning for this term, is to 
 give a complete account of chemical kinetics. 
 
 The word affinity suggests the notion of kinship or 
 relationship ; it embodies the conception of the earliest 
 chemists that those bodies which are ready to enter into 
 union are akin to one another. In the sixteenth and seven- 
 teenth centuries the notion of kinship was so far modified 
 that chemical processes were regarded as caused by the 
 mutual attractions of bodies. After Newton had demon- 
 strated the law of gravitation, the conception of one body 
 attracting another with a force varying according to the 
 masses of the bodies and their distances apart was adopted 
 in chemistry, and was developed until it culminated in the 
 tables of affinity drawn up by Bergmann in the latter part of 
 the eighteenth century. 
 
 164 Bergmann thought that the cause of chemical combina- 
 tion was identical with the cause of gravitative attraction ; 
 but he said that the results differed according as the at- 
 traction was manifested between masses or between minute 
 particles of bodies. In the latter cases the attraction was the 
 greater the nearer were the particles ; hence, said Bergmann, 
 chemical action occurs more readily between liquids or gases 
 than between solids. 
 
 1 I have closely followed Ostwald (Lehrbuch der Allgemeinen Chemie] in 
 dealing with the subject of chemical affinity. The second volume of Ostwald's 
 Lehrbuch is devoted to this subject. Without the help of this book I could not 
 have given a clear account of affinity.
 
 CH. i. 163, 164] BERGMANN'S TABLES OF AFFINITIES. 341 
 
 Bergmann taught that the result of the chemical at- 
 traction, or affinity, between two bodies is to cause a change 
 wholly in the direction of the stronger attraction, unless this 
 should be reversed by the more powerful attractive force of 
 heat. Thus, suppose that two bodies, A and BC, are brought 
 into conditions such that chemical action is possible; if the 
 attraction, or affinity, of A for B is greater than that of B for 
 C, then BC will be decomposed and the only products of the 
 change will be the new bodies AB and C ; but if the at- 
 traction, or affinity, of B for C is greater than that of B for A, 
 no chemical change will occur. 
 
 By applying this conception experimentally Bergmann 
 was able to determine the order of the affinities of series of 
 bodies. Thus, it was required to determine the order of the 
 affinities of three bodies, A, B and C, towards the body D. 
 A compound AD was formed and this was caused to interact 
 with B and C, respectively ; if AD was decomposed by B 
 forming BD and A, then the affinity of B for D was said to 
 be greater than that of A for D ; if AD was decomposed by 
 C forming CD and A, and if BD was also decomposed by C 
 forming CD and B, then C was said to have a greater affinity 
 for D than either A or B. These results were then tabulated 
 in a table of affinity as follows : 
 
 Order of affinities towards D. 
 
 C 
 
 B 
 
 A. 
 
 But it was frequently found that a body which had no action 
 on another when the two were mixed in solution at the 
 ordinary temperature would decompose that other when the 
 two were fused together at a high temperature. Hence 
 Bergmann found it necessary to perform a vast number of 
 experiments, and to draw up at. least two tables of affinity for 
 each substance, one shewing its affinities at ordinary tem- 
 peratures in solution, and the other shewing its affinities 
 at high temperatures when fused with other substances. 
 Bergman n's table for potash, for instance, was constructed 
 thus :
 
 342 THE LAW OF MASS-ACTION. [BOOK II. 
 
 ORDER OF AFFINITIES FOR POTASH. 
 
 Wet way (ord. temp.). Dry way (high temp.). 
 Sulphuric acid Phosphoric acid. 
 
 Nitric Boric 
 
 Hydrochloric Arsenic 
 
 Phosphoric Sulphui'ic 
 
 Arsenic Nitric 
 
 Acetic Hydrochloric 
 
 &c. &c. &c. 
 
 This table conveyed the information that a solution of 
 a compound of potash with any acid in the left-hand 
 column would be decomposed by a solution of any acid 
 placed in the same column above the acid which was com- 
 bined with potash ; and that a solid composed of potash with 
 any acid in the right-hand column would be decomposed by 
 heating with any acid placed in the same column above the 
 acid which was combined with potash. 
 
 In Bergmann's view, affinity acted in one direction only. 
 165 The publication by Berthollet in 1803 of the Essai de 
 Statique Chitnique marked the next great step in advance in 
 the study of affinity. 
 
 Berthollet, like Bergmann, regarded chemical action as 
 the result of attractions between the small particles of bodies. 
 When conditions are favourable, this attraction results, ac- 
 cording to Berthollet, first in cohesion and then in combina- 
 tion. But other forces may come into play which are opposed 
 to the attraction called affinity; heat may cause the ex- 
 pansion of substances which would otherwise combine ; 
 solution may weaken, or destroy, the cohesion of the 
 . particles of a solid. Whether combination occur or not, and 
 if it occur, whether the products remain unchanged or not, 
 depends, on Berthollet's view, upon the relative magnitudes of 
 the opposing forces. If the attraction between the particles 
 of different kinds of matter is greater than the action of the 
 forces which tend to separate these particles, then a new 
 compound or compounds will be formed. Should these 
 compounds be solids under the experimental conditions, the 
 cohesion of their particles will act in the same direction as 
 the attraction of affinity which is the immediate agent in
 
 CH. i. 165] BERTHOLLET'S WORK ON AFFINITY. 343 
 
 their production. The final arrangement of the particles of 
 two kinds of matter depends, according to Berthollet, not 
 only on the relative magnitudes of the different attractions 
 between them, but also on the relative masses of the re- 
 acting bodies ; thus, a relatively small attraction may be made 
 to overcome a greater, by largely increasing the mass of one 
 of the two kinds of matter. 
 
 Berthollet regarded a liquid holding a solid in solution as 
 a system in a state of more or less unstable equilibrium ; by 
 removing some of the liquid by evaporation, or by lowering 
 the temperature, or in other ways, this equilibrium might be 
 overthrown, and crystals might separate containing particles 
 both of the solid previously in solution and also of water 
 changed from the liquid to the solid state. Such a system, 
 said Berthollet, will present two extreme cases ; in one case 
 all the solid is held in solution by the liquid, and in the other 
 all the liquid is changed to the state of solid. Between these 
 extremes there may be many states each marked by a certain 
 definite relation between the amounts of solid and liquid 
 compounds ; for Berthollet regarded the solution, no less than 
 the crystals which separated, as a compound, or a series of 
 compounds, of water and salt. 
 
 Combination and solution were looked on by Berthollet 
 as analogous actions. He said 
 
 " In solution, one pays attention chiefly to the liquidity acquired by 
 the solid by combining [with the solvent], and especially to the uniformity 
 of the parts of the liquid compound.... In a combination one principally 
 considers the other properties of the compound which is produced, 
 comparing therewith the properties of the substances which produced it. 
 In most cases solution is due to a combination so feeble that the 
 properties of the dissolved substance do not disappear". 1 
 
 Again ; 
 
 " Chemical action is reciprocal ; its effect is the result of a mutual 
 tendency to combination. One ought not, strictly speaking, to say that 
 a liquid acts upon a solid, rather than that the solid acts upon the liquid ; 
 it is more convenient however to ascribe the whole of the action to one 
 of the substances, when one wishes to examine the products of the action, 
 rather than the action itself." * 
 
 1 Essai, 1. 5960. a Essai, 1. 3637.
 
 344 THE LAW OF MASS-ACTION. [BOOK II. 
 
 When lime is placed in water, mutual action, said Berthollet, 
 begins at once, but the cohesion of the particles of the solid 
 is so great that the dissolving action of the water does not 
 produce any marked effect for some time ; but water is being 
 absorbed by the lime, and thus the effect of the cohesion of 
 the particles of the lime is slowly overcome by that of the 
 solvent action of the water, until finally the lime dissolves. 
 During this process two combinations of lime and water are 
 formed, one solid, the other liquid ; the effect of one force, 
 cohesion, is to increase the amount of the former ; the effect 
 of another force, solution, is to increase the amount of the 
 latter combination. A state of equilibrium is established, 
 and continues so long as the conditions are unchanged ; 
 but alteration of temperature, or changes in the relative 
 masses of water and lime, suffice to overthrow this equilibrium 
 and to establish another 1 . 
 
 Berthollet not only formed a clear mental image of a 
 system as held in equilibrium by the actions and reactions of 
 its various constituents, but he had also what I think must be 
 regarded as a very clear conception of the chief forces con- 
 cerned in maintaining this equilibrium. In the summary to 
 Part I. of the Essai, he says : 
 
 "The chemical qualities of different substances depend (i) on their 
 tendencies to combine, whereby they mutually saturate each other, and 
 which tendencies remain more or less dominant in the compounds 
 produced ; (2) on their relations to heat, which modify their combining 
 powers, by causing variations in the quantities of the substances coming 
 within the spheres of mutual action, and also by opposing elasticity 
 (elasticite'*'} to condensation, the latter of which is one of the effects of 
 combination ; (3) on the mutual actions of their small particles (molecules*), 
 acting in the same direction as the affinity which has produced com- 
 bination, but opposed to actions and reactions between these particles 
 and those of other substances ; (4) on their relations to other substances, 
 which combine with them, but not so as to produce a mutual saturation 
 
 1 Essai, 1. 37. 
 
 3 Elasticity Berthollet uses this word as meaning nearly the same as dilata- 
 tion, or perhaps we might now say disgregation. 
 
 3 Molecules. This word as employed by Berthollet means only a small particle ; 
 I have thought it better not to use the term molecule, as this is now employed with 
 a more definite meaning than small particle.
 
 CH. I.l66] BERTHOLLET AND BERGMANN. 345 
 
 (saturation^}, but rather a division and varying distribution of properties, 
 and chiefly of those properties which depend on the constitution (con- 
 stitution}?* 
 
 L66 Berthollet's conception of affinity as an attractive force 
 acting between the minute particles of bodies, and modified 
 in its results by the action of other forces, led him to pay 
 great attention to the influence of the masses of the bodies 
 taking part in any chemical change. Just as the cohesion, 
 and elasticity, &c., of the members of a system of bodies are 
 dependent, among other conditions, on the masses of the 
 bodies, so, in Berthollet's view, is affinity dependent on mass : 
 
 " Every substance," said Berthollet, " which enters into combination 
 reacts by its affinity and its mass." 3 
 
 The conception which the great French chemist formed of a 
 chemical reaction was radically opposed to that upheld by 
 his illustrious Swedish predecessor. 
 
 Let two acids interact with a base in aqueous solution. 
 Bergmann asserted that the acid with the stronger affinity 
 combined with the whole of the base, and the other acid 
 remained uncombined. Berthollet declared that both acids 
 interacted with the base, and that the mass of the base which 
 remained combined with either acid when equilibrium was 
 established depended partly on the intensity of the attraction 
 between the particles of the base and of the acids, and partly 
 on the relative masses of the three bodies present in the 
 reacting system. 
 
 Bergmann taught that a chemical change proceeds in one 
 direction only, and that the direction is entirely dependent on 
 the relative affinities of the interacting bodies; but he was 
 obliged to acknowledge that the affinities of some bodies for 
 
 1 Saturation. By saturation of properties Berthollet means that merging of 
 the properties of the constituents in those of the new compound which is so 
 characteristic of chemical change. 
 
 2 Constitution. The constitution of a substance is conditioned according to 
 Berthollet by its condensation and dilatation : ' the properties which depend on 
 the constitution' of a substance may be taken as meaning, broadly, the physical 
 properties of the substance. 
 
 3 ssai, 1. 2.
 
 346 THE LAW OF MASS-ACTION. [BOOK II. 
 
 another are sometimes so nearly balanced that a compound 
 of all the reacting bodies is produced ; and he was also forced 
 to admit that the order of the affinities of a series of bodies 
 for one and the same body may be changed or even reversed 
 by changing the physical conditions under which the chemical 
 reaction proceeds. 
 
 Berthollet, on the other hand, taught that a chemical 
 change may, and often does, proceed in two directions ; that 
 is to say, that certain bodies may react to produce others 
 which may then by their interactions reproduce the original 
 bodies ; that the equilibrium which is finally attained by a 
 system of interacting bodies is the result of the action and 
 reaction of all the members of the system; and that the 
 conditions which chiefly affect this equilibrium are the affinity 
 and the mass of each body, and also the physical conditions 
 under which the change proceeds and the physical properties 
 of the different possible products of the change. 
 
 Berthollet's researches established three points of funda- 
 mental importance : chemical action is conditioned not only 
 by the intensities of the affinities, but also by the relative 
 masses, of the reacting bodies ; a chemical change is gene- 
 rally more or less reversible by changing the masses of the 
 reacting bodies, it is only, in extreme cases that a chemical 
 change proceeds wholly in one direction ; the forces which 
 come into play in chemical occurrences are of the same kind 
 as those which we call physical. 
 
 167 The period of sixty years following the publication of 
 Berthollet's Essai is not marked by any great advance in the 
 study of chemical affinity ; nevertheless various important 
 researches were conducted in this period the results of which 
 served to emphasize the importance of Berthollet's funda- 
 mental conception of the influence of the relative masses of 
 chemically reacting bodies on the course of a chemical 
 change and on the equilibrium finally attained by the system. 
 
 In 1853 Bunsen 1 examined the change which occurs when 
 a mixture of carbon monoxide and hydrogen is exploded 
 with a quantity of oxygen less than sufficient for the com- 
 
 1 Annalen, 85. 131 ; see also Horstmann, Amialen, 190. 238.
 
 CH. I. 167, 1 68] WORK OF GULDBERG AND WAAGE. 347 
 
 plete combustion of both gases. Bunsen shewed that some of 
 the oxygen enters into combination with the carbon mo- 
 noxide and some with the hydrogen, and that the quantity of 
 each of these gases burnt depends on the relative masses of 
 the combustible gas and the oxygen. 
 
 In 1855, Gladstone 1 , by studying the amount of change 
 which occurs when potassium sulphocyanide and ferric 
 chloride react in aqueous solution, exhibited very clearly the 
 influence of mass on chemical change. Gladstone shewed 
 that when ferric chloride and potassium sulphocyanide react, 
 only a portion of each salt is changed unless the mass of one 
 is made 600 or 700 times as great as that of the other ; he 
 also shewed that the quantity of ferric sulphocyanide formed 
 increases continuously with an increase in the quantity of 
 potassium sulphocyanide used. 
 
 It is important to note that Gladstone used determina- 
 tions of physical properties, such as depth of colour, as in- 
 dications and measurements of the chemical change which 
 occurred. 
 
 Berthollet and P. de Saint Gilles 2 in 186263 made a 
 large number of measurements of the amount of change 
 which occurs when an alcohol and an acid react to form an 
 ethereal salt and water, and established the influence of the 
 masses of the reacting bodies on the change in question. 
 168 The year 1867 is marked in the history of chemistry by 
 the publication of a most important memoir on affinity by 
 Guldberg and Waage entitled Etudes sur les Affinitts Chimi- 
 
 Guldberg and Waage restate Berthollet^ law of mass- 
 action in a form in which it is capable of quantitative ap- 
 plication ; they assert that 
 
 1 Phil. Trans. 1855. 179; and C. S. Journal, 9. 54. 
 
 2 Ann. Chim. Phys. (3). 65. 385; 66. 5; 68. 225. Among other memoirs on 
 the influence of mass may be mentioned Margueritte Compt. rend. 38. 304 ; Tissier, 
 Cotnpt. rend. 41. 312; Dulong, Ann. Chim. Phys. 82. 275; Rose, Pogg. Ann. 
 94. 481; 95. 96, 284, 426; Malaguti, Ann. Chim. Phys. (3). 37. 198; Chic- 
 zynski, Annalen, Supplbd. 4. 226; Morris, Annalen, 213. 253. 
 
 3 Published by the University of Christiania ; continuation in J. fiir praki. 
 Chemie (2). 19. 69.
 
 34$ THE LAW OF MASS-ACTION. [BOOK II. 
 
 Chemical action is proportional to the active mass of each of 
 the bodies taking part in the reaction. 
 
 The active mass of a specified body taking part in a 
 reaction is the mass of that body stated in equivalent 
 weights, present in unit volume of the chemical system. Thus 
 if solutions of hydrochloric acid, sulphuric acid, and caustic 
 soda are mixed in the ratio 2HC1: H 2 SO 4 : 2NaOH, the 
 active masses of the hydrochloric acid, sulphuric acid, and 
 soda are I, I, and I, respectively, H 2 SO 4 being taken as one 
 equivalent of sulphuric acid. 
 
 Guldberg and Waage's law of mass-action states that the 
 action of each substance in a system of interacting bodies is 
 proportional to the active mass of that substance, and that 
 the total action is proportional to the product of all the active 
 masses. 
 
 But the amount of chemical change which occurs when 
 two or more substances react is not dependent solely on the 
 active masses of the substances, it is also conditioned by the 
 chemical nature, and the state of aggregation, of the sub- 
 stances, the temperature, and other variables. Guldberg and 
 Waage group together these variables and express them by 
 a coefficient called by them the coefficient of affinity, and 
 represented by the symbol k. 
 
 Let two substances P and Q react, and let the active 
 masses of these be represented by the symbols / and q ; 
 further let the coefficient of affinity for the reaction between 
 P and Q be represented by k ; then the amount of chemical 
 change which occurs will be proportional to the product 
 k. p. q. Let the products of the interaction of P and Q be 
 two new bodies P' and Q, and let the active masses of these 
 bodies be represented by the symbols /' and q, and the 
 coefficient of affinity for the reaction between P' and Q' be 
 represented by k', then the amount of chemical change which 
 occurs between P' and Q' will be proportional to the product 
 k'. /'. q'. Now when P and Q interact certain quantities of 
 P' and Q' will be formed, and these will at once interact to 
 re-form P and Q ; this will proceed until equilibrium is 
 established, after which no further change will occur in the
 
 CH. I.l68] WORK OF GULDBERG AND WAAGE. 349 
 
 active masses of the various bodies nor in the values of the 
 coefficients of affinity of either the direct or the reverse 
 change. When equilibrium is attained the product k. p. q, 
 will be equal to the product k'.p'. q . Hence the conditions of 
 equilibrium are expressed by the equation 
 
 k.p.q. = k'.p'.q. 
 
 But as the reaction between P and Q proceeds the active 
 masses of these bodies will be decreased, and the active 
 masses of the products of the change, P and Q', will be in- 
 creased. Let P, Q, P', and Q represent the masses of the 
 four bodies present in the chemical system at the beginning 
 of the change, these masses being stated in equivalent 
 weights ; when equilibrium is established x equivalents of 
 P and x of Q will disappear and x equivalents of P and 
 x equivalents of Q' will simultaneously be formed ; let /, q, 
 /', and q' represent the active masses of the four bodies 
 present when equilibrium results, then the values of these 
 active masses will be as follows : 
 
 P-x Q-x , P + x , Q'+x 
 
 p = , q = , P > Q 
 
 v V f V v 
 
 where v = the total volume of the system, taken as unity. 
 
 By substituting the values for/, q,p', and q' in the equation 
 of equilibrium we have 
 
 (P-x}(Q-x}=^ (P* + *)?+*). 
 
 This equation holds good for all values of P, Q, P', and Q. 
 
 k' 
 
 The ratio -r can be calculated from a determination of x for 
 k 
 
 one special case, and from the value of this ratio values can 
 be found for x, and therefore for the distribution of the four 
 reacting bodies when equilibrium results, starting with any 
 specified quantities of P, Q, P / , and Q'. 
 
 Guldberg and Waage thus put Berthollet's conception of 
 the influence of mass into an exact form. They consider the 
 masses of the several bodies comprising a chemical system 
 present at the moment when equilibrium is established. The
 
 350 THE LAW OF MASS- ACTION. [BOOK II. 
 
 attempts made to formulate the influence of mass on chemical 
 change previous to the work of the Norwegian naturalists 
 had been implicitly based on measurements of the masses of 
 the reacting bodies present when the reaction began. 
 169 In their first memoir (Etudes &c.) Guldberg and Waage 
 regard the occurrence of a chemical change as caused by 
 ' chemical force ' ; they say that when equilibrium results in a 
 system of four bodies, P, Q, P', and Q', the force bringing 
 about the formation of P' and Q' is held in equilibrium by 
 the force which causes the re-formation of P and Q. They 
 also attempt to take into account the possibility of secondary 
 changes among the reacting bodies and to express these in 
 equations. But the formulae thus arrived at are too com- 
 plicated for practical application ; and moreover the con- 
 ception of chemical force is vague and unsatisfactory. 
 
 In their second memoir 1 Guldberg and Waage follow the 
 example of van't Hoff 8 , and, abandoning the notion of 
 chemical force, attempt to find formulas which may be 
 applied in practice by starting with the clear conception of 
 chemical equilibrium being dependent on the equality of the 
 rates of the direct and reverse chemical changes ; i. e. they 
 consider that equilibrium results in a chemical system when 
 the quantity of substance changed in one direction is equal to 
 that formed in the other direction in a given time. Many 
 measurements had been made of the rates of chemical actions, 
 but Guldberg and Waage were the first to establish clearly 
 the connexion between the velocity of a chemical change and 
 the attainment of equilibrium by the system. This was done 
 in their memoir of 1867, but the formulae given in that 
 memoir are complicated and scarcely suited for accurate 
 application. The equation arrived at in the second memoir 
 as representing the connexion between reaction-velocity and 
 equilibrium is identical with that we have already considered ; 
 viz. k.p.q = k'.p '. q'. 
 
 Let there then be a chemical system of four bodies, P, Q, 
 P", and Q'; let P and Q react to produce P and Q', and 
 P' and Q' react to re-produce P and Q ; equilibrium results 
 
 1 J.furprakt. Chemie, (2). 19. 69. 2 Ber. 10. 669.
 
 CH. I. 169, I/O] WORK OF GULDBERG AND WAAGE. 351 
 
 when the velocity of the direct change (i.e. the production of 
 F and Q'} is equal to that of the reverse change (i.e. the 
 production of P and Q). The conditions of equilibrium are 
 expressed by the equation 
 
 k.p.q. = k'.p'.q', 
 or, as before, 
 
 k' 
 It is important to note here that the ratio -r is not analysed ; 
 
 it is simply the ratio of the affinity of P and Q to that of the 
 affinity of F and Q ; and the term affinity is used as a short 
 expression for the unknown cause of the chemical reaction 
 between the reacting bodies. 
 
 170 Guldberg and Waage tested their equation of equilibrium 
 both by using the results obtained by other chemists and 
 also by experiments which they themselves conducted. 
 
 Thus the results of Berthollet and P. de Saint Gilles 1 on 
 the etherification of alcohols by reacting with organic acids 
 were used by Guldberg and Waage. The members of the 
 reacting system are alcohol, acid, ethereal salt, and water ; 
 the direct change results in the production of ethereal salt 
 and water, and the reverse change produces alcohol and acid. 
 The following numbers shew the close agreement between 
 the observed and calculated values of x t i.e. the number of 
 equivalents of acid or alcohol transformed into ethereal salt 
 and water when equilibrium is established. 
 
 SERIES I. 
 
 Q 
 
 Observed. 
 
 Calculated. 
 
 One equivalent acid + 
 
 i 
 
 665 
 
 668 
 
 Q equivalents alcohol. 
 
 i '5 
 
 779 
 
 772 
 
 
 2 
 
 828 
 
 827 
 
 
 2-8 
 
 856 
 
 870 
 
 
 3 
 
 882 
 
 878 
 
 
 12 
 
 932 
 
 930 
 
 
 500 
 
 I'OOO 
 
 I '000 
 
 SERIES II. 
 
 P 
 
 
 
 One equivalent alcohol + 
 
 I 
 
 665 
 
 668 
 
 P equivalents acid. 
 
 2 
 
 858 
 
 856 
 
 
 5 
 
 966 
 
 972 
 
 1 Ann. Chim. 
 
 Phys. (3). 
 
 68. 385. 

 
 352 THE LAW OF MASS-ACTION. [BOOK II. 
 
 SERIES III. P Observed. Calculated. 
 
 One equiv. acid + o '665 '668 
 
 one equiv. alcohol + 0*13 '626 '648 
 
 P equivs. ethyl acetate. 0-85 '563 '550 
 
 i'6 -521 -487 
 
 SERIES IV. Q 
 
 One equiv. acid+ o '882 '871 
 
 three equivs. alcohol + i '809 '803 
 
 Q equivs. water. 2 739 744 
 
 8 -468 -512 
 
 Guldberg and Waage themselves examined the reaction 
 which occurs between barium sulphate and potassium carbo- 
 nate in presence of water. In this case two of the four 
 members of the system are insoluble, viz. barium sulphate 
 and barium carbonate. Guldberg and Waage shewed that if 
 the absolute masses of the insoluble members of a reacting 
 system are fairly large, and the volume of the liquid is kept 
 constant, the changes in the absolute masses of the insoluble 
 bodies do not appreciably affect the active masses of these 
 bodies 1 ; and this result was fully confirmed by Ostwald 2 . 
 
 In the reaction between potassium carbonate (P} and 
 barium sulphate (Q) producing potassium sulphate (P'} and 
 barium carbonate (Q'), let the active mass of the potassium 
 carbonate be /, that of the barium sulphate q, that of the 
 potassium sulphate p\ and that of the barium carbonate q ', 
 then, as q and q' are constant, the equation of equilibrium 
 becomes 
 
 The following numbers shew how closely the values of 
 x calculated for the condition that equilibrium is attained 
 agree with the observed values : 
 
 SERIES I. Q Observed. Calculated. 
 
 I equiv. barium sulphate+ 3'5 719 715 
 
 500 equivs. water (at 1 00) + 2^5 "500 '500 
 
 Q equivs. potassium carbonate 2 "395 '391 
 
 i -176 -178 
 
 1 J.fiir prakt. Chemie, (2). 19. 469. '* J.fiir prakt. Chemie, (2). 22. 256.
 
 CH. I. 170,171] WORK OF GULDBERG AND WAAGE. 353 
 
 SERIES II. Q Q Observed. Calculated. 
 
 i equiv. barium sulphate 4- 2 '25 -20 -198 
 
 500 equivs. water (at ioo)+ 3 "25 '408 '409 
 
 <2 equivs. potassium carbonate + 2 -50 trace -coo 
 Q equivs. potassium sulphate. 
 
 171 Experimental evidence in favour of Guldberg and Waage's 
 law of mass-action has been obtained by various observers 
 using different methods. One of the great difficulties consists 
 in finding suitable methods for measuring the distribution of 
 the members of a reacting system all of which remain in 
 solution when equilibrium is established. Very many of the 
 methods which have been found to give trustworthy results 
 are based on the same principle, which is that the amount of 
 chemical change in a homogeneous system is deducible from 
 measurements of some definite physical property of the 
 system and determinations of the changes in the value of 
 this property. 
 
 Thomsen 1 , in 1869 and subsequent years, shewed that 
 when two acids and a base react in aqueous solution, the 
 distribution of the base between the acids can be determined 
 by thermo-chemical methods. Let the heat of neutralisation 
 of the acid A by the given base be x gram-units, and let the 
 heat of neutralisation of the other acid B by the same base be 
 y gram-units ; then if both acids simultaneously react with 
 the base the quantity of heat produced may be x units, in 
 which case the whole of the base has combined with the 
 acid A, or y units, in which case the whole of the base has 
 combined with the acid B, or a number between x and y t in 
 which case the base has divided itself between the two acids ; 
 in the last case the proportion of base which has combined 
 with each acid may be calculated from the observed thermal 
 value of the reaction 2 . 
 
 In 1876 Ostwald 3 shewed that the distribution of a base 
 between two acids can be determined from measurements of 
 the specific volume of a solution of each acid, of the base, of 
 the liquid formed by mixing each acid separately with the 
 base, and of the liquid formed by mixing both acids simul- 
 
 1 Pogg. Ann. 138. 65. 2 See post par. 183. 
 
 3 PSS- Ann. Ergzbd. 8. 154. 
 M. C. 23
 
 354 THE LAW OF MASS-ACTION. [BOOK II. 
 
 taneously with the base 1 . The results 'obtained by Thomsen 
 and by Ostwald have fully confirmed the law of mass-action 
 enunciated by Guldberg and Waage ; and this law has also 
 been upheld by other series of experiments conducted by 
 various chemists 2 . 
 
 The law of mass-action may then be regarded as well- 
 established ; this law asserts that the amount of chemical 
 change which occurs when a system of interacting bodies 
 attains equilibrium is proportional to the product of the 
 active masses of all the bodies taking part in the change and 
 the coefficient of affinity of the change. 
 
 1 See post par. 184. 
 
 2 These experiments will be described in some detail later; see pars. 185, 186.
 
 CHAPTER II. 
 
 CHEMICAL DYNAMICS. 
 
 72 A DETAILED examination of the applications of the law 
 of mass-action, which was stated and briefly illustrated in 
 Chap. I., leads to the consideration of the forces which come 
 into play in chemical changes 1 . 
 
 As forces are measured in dynamics either by measuring 
 the velocity produced in a specified mass in unit of time, or 
 by opposing the unknown force by another of known amount 
 until equilibrium is attained, so may measurements of chemical 
 forces be obtained by determining the amount of change 
 which occurs in unit of time, or by opposing the direct change 
 by another in the opposite direction and determining the 
 conditions of equilibrium. 
 
 It is important to notice that when we speak of chemical 
 force the term force is used with a meaning different from 
 that in which it is employed in dynamics : by chemical force 
 we mean the product of the active masses of the various bodies 
 comprising the changing system and the constant of velocity of 
 the change. And by velocity we mean, not the ratio of space 
 traversed to time used as in dynamics, but the ratio of 
 material chemically changed to time used in the change. 
 
 Using the term chemical force with this meaning, we 
 shall find that a chemical change is conditioned by changes 
 in the chemical force in much the same way as an electric 
 current is conditioned by changes of potential. 
 
 1 In this Chapter I have again closely followed Ostwald's Lehrbuch der 
 Allgemeinen Chemie, Bd. II. The present chapter is a condensed account of 
 the greater part of the second book of Ostwald's Verwandtschaftslehre. 
 
 232
 
 356 VELOCITY OF CHEMICAL CHANGE. [BOOK II. 
 
 Those methods of measuring what we have called chemical 
 forces which are based on determinations of the velocities of 
 chemical changes may be called kinetical methods, while the 
 term statical methods may be applied to those which are 
 founded on determinations of the conditions of equilibrium. 
 
 The methods whereby measurements have been made of 
 the velocities of chemical changes, with the view of de- 
 termining the intensities of the chemical forces, have usually 
 been chemical ; whereas both physical and chemical methods 
 have been used for determining the conditions of equilibrium 
 of chemical systems. 
 
 I shall begin by considering some of the kinetical 
 methods. 
 
 SECTION I. Velocity of Chemical CJiange. 
 
 173 Wenzel 1 , in 17/7, measured the times required by different 
 acids to dissolve equal quantities of the same metal, and he 
 attempted to draw inferences from the results as to the 
 relative affinities of the acids. Thus, he says : 
 
 " If an acid dissolves one drachma of copper or zinc in an hour, then 
 an acid of half the strength requires two hours to dissolve the same 
 amount of copper or zinc, the surfaces exposed and the temperature being 
 constant." 
 
 Berthollet 2 made observations somewhat similar to those 
 of Wenzel. He said that the velocity of a chemical change 
 is greater the greater is the chemical force ; but he noticed 
 that the velocity diminishes as the change approaches com- 
 pletion, and that reactions which begin rapidly often finish 
 very slowly. 
 
 174 Wilhelmy 8 , in 1850, gave a mathematical form for the 
 fundamental connexion between the quantity of material 
 changed and the time required in a chemical reaction. 
 
 Wilhelmy examined the inversion of cane sugar in aqueous 
 solution in the presence of acids; C lz H^O n + H 2 O = 2C 6 H 12 O 6 . 
 The amount of change at any moment can be determined by 
 measuring the specific rotatory power of the liquid. 
 
 1 Lehrevon der Verwandshaft [Dresden, 1777], 28. 
 
 a Essai, 1. 409. 3 Pogg. Ann. 81. 413, 499.
 
 CH. II. 173-175] SIMPLEST CASES. 357 
 
 The assumption made by Wilhelmy was that the mass of 
 sugar changed in unit-time is proportional to the mass of 
 sugar remaining unchanged in the reacting system. 
 
 Let A = mass of sugar originally present; let x= mass ot 
 sugar changed in time 6 ; then the ratio of the amount 
 changed, dx, to the time, dO, is given by the equation 
 
 where Axh the amount of unchanged sugar and c is 
 a constant. 
 
 The ratio - expresses the velocity of the chemical change, 
 
 or, in shorter words, the reaction-velocity. 
 
 Ostwald 1 integrates the above equation to get it into a 
 form in which it may be applied ; he counts the time from 
 the moment when the sugar solution is brought into contact 
 with the acid, i.e. when = o and x = o. The final form in 
 which the value of the constant appears is 
 
 i A 
 
 The numbers shew that ^ log -= - is nearly constant for 
 u A x 
 
 values of varying from 15 to 630 minutes. 
 
 Later experiments conducted by Ostwald 2 on the in- 
 version of cane sugar have confirmed the result of Wilhelmy, 
 that the reaction-velocity at each moment is proportional to 
 the mass of sugar capable of undergoing change. 
 75 Experiments conducted by different chemists with dif- 
 ferent changing systems have shewn that the result obtained 
 by Wilhelmy holds good in very many and very different 
 cases. This result may be stated in these words : 
 
 TJie amount of chemical change at any moment is pro- 
 portional to the mass of the changing body in the system. 
 
 Among the more important researches which have es- 
 tablished the accuracy of this statement may be mentioned, 
 Harcourt and Esson's examination of the reaction between 
 
 1 Lehrbuch, 2. 617? 2 J.fiirprakt. Chemie (2). 29. 385.
 
 358 VELOCITY OF CHEMICAL CHANGE. [BOOK II. 
 
 potassium permanganate and a large excess of oxalic acid l , 
 and the reaction between peroxide of hydrogen and hydriodic 
 acid 2 ; Ostwald's examination of the catalytic change of 
 methylic acetate to methylic alcohol and acetic acid in 
 presence of different acids 8 ; van't Hoff's examination of the 
 change of dibromosuccinic acid (from fumaric acid) to bromo- 
 malei'c acid and hydrobromic acid by boiling with water, and 
 of monochloracetic acid to glycollic acid and hydrochloric 
 acid in presence of water 4 . 
 
 T A 
 
 In all these cases the value of the expression ^ log is 
 
 v jci X 
 
 nearly constant 8 . The fact, that the velocity of the early stages 
 of a chemical change is often different from the velocity when 
 the change has proceeded for a little time, introduces a possible 
 source of error into the observations on which the statement 
 concerning the proportionality between the rate of change and 
 the mass of the changing body is based. But this error may 
 be obviated by counting the time from the moment when the 
 velocity of the change becomes regular, or by determining 
 the reaction-velocity for definite intervals while the change 
 proceeds 6 . 
 
 The outcome of these experiments then is to establish 
 a simple relation between the quantity of a body undergoing 
 chemical change and the time occupied in accomplishing the 
 change. In all cases only one body was undergoing change, 
 or if more than one actually underwent change then the 
 masses of all except one were made so large that changes 
 in these masses could practically be neglected. It is also 
 to be noted that all the changing systems examined were 
 homogeneous; no separation of gases or solids occurred 
 during the various processes. With these limitations, it 
 appears that chemical change obeys the same law as gravi- 
 
 1 Phil. Trans, for 1866. 193. 2 Phil. Trans, for 1867. 117. 
 
 3 J-furprakt. Chemie (2). 28. 449. 
 
 4 Etudes de dynamique chitnique [Amsterdam, 1884], 14. 
 
 5 For details of the methods used for measuring the velocities of these changes, 
 and for tables shewing the actual and observed values of the constant, see 
 Ostwald's Lehrbuch, 2. 616624. 
 
 6 See Ostwald, loc. cit. 624.
 
 CH. II. 175, 176] MORE COMPLEX CASES. 359 
 
 tative, electrostatic, electrodynamic, electromagnetic, and 
 other physical changes. 
 .76 But we must now proceed to cases where more than one 
 body undergoes chemical change at the same time. 
 
 If we assume that the amount of 'change which each 
 member of the system undergoes is proportional to the active 
 mass of that body, then the product of the active masses of 
 all the changing bodies gives the function which expresses 
 the velocity of the complete reaction. 
 
 In order to find whether this assumption is justified by 
 facts, Ostwald 1 begins by finding an expression for the 
 reaction-velocity when two bodies only are concerned. Let 
 A and B represent the masses of the bodies originally 
 present, and let x = the portion of each changed in the time 
 0, these masses being measured in equivalents; then the 
 reaction-velocity is 
 
 ~ Q =(A-x}(B-x}c, 
 
 where c is a constant. 
 
 If equal numbers of equivalents of the two bodies are 
 concerned in the change then A = B, and 
 
 dx . . 
 
 -^(A-^c. 
 
 By integration, taking x and 6 simultaneously equal to 
 zero, the equation 
 
 - 
 A x 
 
 is obtained. 
 
 If the fundamental assumption is correct, the product Ac 
 
 must remain constant when x varies : Ac= -*. . - . 
 
 (J /i X 
 
 The experiments made by Hood 2 on the change of 
 potassium chlorate and ferrous sulphate in acid solution to 
 potassium chloride and ferric sulphate, are used to test the 
 accuracy of the equation. In these experiments 9 varied 
 from 20 to 520 minutes, and Ac was almost constant, ranging 
 from '00737 to -00760; when 6 became 628 and 639 mins. 
 
 1 Lehrbuch, 2. 626634. ! PkU. Mag, (5). 6. 371.
 
 360 VELOCITY OF CHEMICAL CHANGE. [BOOK II. 
 
 Ac became -00726 and -00725, but in these cases A x was so 
 small that the calculation of Ac is uncertain. 
 
 Among other determinations whereby values are found 
 
 for the function ^.-j -- are (i) Warder's measurements of 
 tj A. x 
 
 the rate of saponification of ethylic acetate by caustic 
 soda 1 ; (2) Ostwald's determination of the rate of change of 
 acetamide in presence of an acid into acetic acid and the 
 ammonium salt of the acid used 2 ; and (3) van't Hoff's 
 experiments on the velocity of the reaction wherein sodium 
 monochloracetate and soda are changed to sodium glycollate 
 and sodium chloride 3 . In the first set of experiments the 
 rate of change was determined by titrating from time to time 
 with a standard acid ; in Ostwald's experiments the rate of 
 change was determined by decomposing the unchanged 
 acetamide by sodium hypochlorite and measuring the nitrogen 
 evolved ; and in the third case van't Hoff measured the 
 amount of change in specified times by titrating the residual 
 soda by means of a standard acid. 
 
 In each set of experiments Ac has a nearly constant 
 value; the value varies from "106 to "113 in Warder's ex- 
 periments where 6 varies from 5 to 120 minutes ; in Ostwald's 
 experiments Ac varies from -0087 to -0092, 6 varying from 
 15 to 240 minutes; and in van't Hoff's experiments, where 6 
 varies from 9 to 374 minutes, Ac varies from '00551 to -00633. 
 
 The expression already given for the reaction-velocity 
 when the two bodies undergoing change are present in equal 
 numbers of equivalents is applicable with some modification 
 when an excess of one of the reacting bodies is employed 4 . 
 In this case A is not equal to B and on integrating the 
 
 equation - = (A x} (B x) c, we obtain the expression 
 
 Hood 5 determined the rate of the change occurring 
 
 1 Amer. C. Journal for 1882. No. 5. 2 J. fur prakt. Chemie (2). 27. i. 
 3 Etudes de dynamique chimique, 20. 4 See Ostwald, loc. cit. 631. 
 6 Phil. Mag. (5). 6. 378.
 
 CH. II. 176,177] CO-EXISTENCE OF REACTIONS. 361 
 
 between ferrous sulphate and potassium chlorate when an 
 excess of one of the salts was used: In one case there was 
 twice as much chlorate employed as was required for the 
 reaction ; and in the other case four times as much ferrous 
 sulphate as was required. If A FeSO 4 and =KC\O 3 , 
 then in the first case A = 2B, and 
 
 A- X - 
 
 and in the second case B = ^A, and 
 A-*- 
 
 The actual value found for Ac in the first set of experi- 
 ments varied from '001965 to '00202, varying from 30*5 
 to 360 minutes ; and the actual value found for Ac in the 
 second case varied from -00411 to '00431, varying from 
 24 to 231 minutes. 
 
 There is then ample experimental evidence in support of 
 the assertion that when more than one body is simultaneously 
 undergoing chemical change the rate of the change is pro- 
 portional to the product of the active masses of all the bodies 
 in the changing system 1 . 
 
 177 The foregoing treatment of the relation between the rate 
 of a chemical change and the amount of the changing bodies 
 implies, that if more than one substance is undergoing change, 
 each obeys the law of mass-action, and each change proceeds 
 as if it were independent of the others. The truth of this 
 proposition is rendered apparent by the close agreement 
 between the observed rates of many different chemical 
 reactions and the values calculated on the assumption that 
 the amount of change at any moment of any one member of 
 the system is proportional to the active mass of this body, 
 and the total change at any moment is proportional to the 
 product of the active masses of all the changing bodies. 
 
 1 Ostwald, loc. cit. 632 634, develops the necessary equations for more 
 complex reactions than those we have considered, but these equations cannot yet 
 be applied for lack of experimental data.
 
 362 VELOCITY OF CHEMICAL CHANGE. [BOOK II. 
 
 This proposition is called by Ostwald the principle of the 
 co-existence of reactions. 
 
 Many of the reactions considered in the previous para- 
 graphs have been regarded as more simple than they really 
 are ; small secondary changes have been overlooked. For 
 instance, when methylic acetate reacts with water in the 
 presence of an acid to produce acetic acid and methylic 
 alcohol, the rate of change is influenced by the acetic acid 
 produced. If these secondary changes are taken into account 
 in the calculation of the theoretical constant of each reaction, 
 the total change being treated as made up of the primary 
 change and one or more small secondary changes, the values 
 obtained for the constant shew smaller variations than if the 
 small secondary changes are overlooked. But this is exactly 
 what ought to be if the principle of the co-existence of re- 
 actions is true 1 . 
 
 178 When a solid and a liquid interact we have a heterogeneous 
 system. The amount of change in a given time is here also 
 proportional to the product of the active masses of the changing 
 bodies. But the active mass of the solid is proportional to 
 the surface exposed, and not to the total mass of the solid. 
 The equation by which the reaction-velocity can be calculated 
 must therefore be modified. If w = the surface of the solid 
 the equation becomes 
 
 - = (A-x\cw 
 and by integration 
 
 log =cwd. 
 & A x 
 
 It is difficult to apply this equation ; the results of ex- 
 periments shew a certain amount of variation in the value of 
 what ought to be a constant. But it is almost impossible 
 to get a constant surface of a solid ; the solution of the solid 
 in the liquid causes the action to slacken ; gases are some- 
 times formed on the surface and the surface is diminished, 
 and so on 2 . 
 
 1 Ostwald, loc. cit. 2. 636, puts the principle of the co-existence of reactions 
 into a mathematical form. 2 See Ostwald, loc. cit. 2. 638640.
 
 CH. II. 178-180] METHODS FOR MEASURING CHANGE. 363 
 
 SECTION II. Chemical Equilibrium. 
 
 179 We must now glance at the statical methods whereby it 
 has been attempted to measure chemical forces. In these 
 methods a chemical system is brought into equilibrium by 
 opposing a change in one direction by a change in the 
 opposite direction, and the distribution of the various 
 members of the system is determined when equilibrium 
 results. 
 
 The methods which are applicable here are either chemical 
 or physical. Chemical methods may be used in cases where 
 the system is heterogeneous and one or more of the members 
 of the system can be measured by some ordinary analytical 
 process without disturbing the equilibrium which the system 
 has attained ; for instance, an acid reacts with an insoluble 
 salt of another acid forming a soluble salt and a new acid 
 e.g. calcium oxalate and hydrochloric acid produce calcium 
 chloride and oxalic acid the soluble acid or salt may be 
 determined in a portion of the system when equilibrium has 
 been reached. Physical methods may be used in cases where 
 the system is homogeneous and where the removal of any 
 portion of a member of the system would disturb the equi- 
 librium of the system : in these methods either a physical 
 change which accompanies and forms the measure of the 
 chemical change is measured ; or a physical property is 
 measured the value of which is dependent on the distribution 
 of the chemically reacting bodies \ 
 
 180 If a body A is changed to A', and if A' is changed to A, 
 the system will attain equilibrium when the velocity of the 
 primary change is equal to that of the reverse. Let / be the 
 active mass of A, and/' the active mass of- A'', let x be the 
 number of equivalents of A changed to A', and let x be the 
 number of equivalents of A' changed to A, at any moment; 
 
 1 Steinheil (Annalen, 48. 153 [1843]) was tne fi fst to &i ve a general statement 
 of the theory shewing the dependence of physical properties of a chemical system 
 on changes in the arrangement of the members of the system. The theory is 
 given in detail in Ostwald's Lehrbuch, 2. 753 759.
 
 364 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 then the velocity of the direct change f J is 
 
 and the velocity of the reverse change \jn \ 1S 
 
 -</---v : 
 
 But x must equal x and dx= dx'\ so that 
 
 And therefore the reaction-velocity of the whole change, 
 
 dx . 
 
 JQ, is expressed as 
 
 The condition of equilibrium is ,. = o ; therefore, if is 
 the value obtained by x when equilibrium results 
 
 
 Now as p % is the mass (in equivalents) of the body A, 
 and /' + is the mass of A', present in the system when 
 equilibrium results, and as these masses are independent of 
 the original values of p and /', the equation shews equi- 
 librium to result in a system of two chemically interacting 
 bodies when the active masses of the bodies are in the 
 same ratio as the velocity-constants of the primary and 
 reverse changes. 
 
 The value of can be determined experimentally, and 
 from this the ratio of the velocity-constants of the two parts 
 of the change can be calculated. 
 
 If one of the two bodies is in a different state of aggregation 
 from the other, then the active mass of one is constant ; thus 
 if the system is composed of a solid and a liquid or a gas, 
 the active mass of the solid is constant towards the liquid or 
 gas; hence, in such a case the active mass of the other
 
 CH.II.l8o] SYSTEMS OF TWO BODIES. 365 
 
 constituent must also be constant in order that equilibrium 
 may result. Such cases are comparatively simple ; and they 
 comprise by far the greater number of cases in which the 
 equation of equilibrium for a system composed of two 
 changing bodies can at present be applied. 
 
 The case of water in contact with ice at o is a typical 
 one. Equilibrium is independent of the mass of the ice ; and 
 as the mass of water in unit volume of the system is inde- 
 pendent of the absolute mass, it follows that a mixture of 
 ice and water, in any proportion, remains in equilibrium at o. 
 But if the system is compressed the active mass of the water 
 is increased, and therefore equilibrium is upset, and is restored 
 again only at a temperature lower than o. If a solid ex- 
 pands on melting, then equilibrium between this solid and 
 its own liquid is attained under pressure only at tempera- 
 tures higher than that of the normal melting point of the 
 solid. 
 
 So also in cases of evaporation of liquids, equilibrium 
 results at a definite temperature when the active mass of the 
 vapour bears a certain constant ratio to that of the liquid ; 
 to maintain the constancy of this ratio the active mass of the 
 vapour must remain constant, but this is done by keeping the 
 pressure constant. The constancy of the pressure of a vapour 
 over a liquid is therefore a function of the temperature, and 
 not of the relative quantities of vapour and liquid. 
 
 Cases of solution belong to the category we are now 
 discussing. When a salt dissolves in water the active mass 
 of the solid is constant, and therefore equilibrium must result 
 when a definite mass of the solid has dissolved, and must be 
 independent of the relative masses of dissolved and undis- 
 solved salt but dependent on the temperature. 
 
 The attainment of equilibrium in many cases of allotropic 
 change is also conditioned by the constancy of the ratio 
 of the active masses of the changing bodies. For instance, 
 in the change of paracyanogen (CN) n to gaseous cyanogen 
 (CN) 2 equilibrium results when the gas attains a certain 
 pressure which is independent of the mass of paracyanogen 
 present but varies as the temperature varies.
 
 366 CHEMICAL. EQUILIBRIUM. [BOOK II. 
 
 So also with red and yellow phosphorus 1 . If red 
 phosphorus is heated to 440 the pressure of the vapour 
 increases up to a limit which is independent of the mass of 
 solid phosphorus present ; but on continued heating the 
 pressure falls until it again attains a constant value. If yellow 
 phosphorus is heated to 440 the pressure of the vapour is 
 much greater than that from red phosphorus at the same 
 temperature; but the pressure falls until it attains the same 
 value as that which marks the final equilibrium between red 
 phosphorus and its vapour at the same temperature. The 
 results are represented graphically in the accompanying 
 curve. 
 
 Troost and Hautefeuille have shewn that red phosphorus 
 exhibits different properties according to the temperature at 
 
 Yellow 
 
 Red 
 
 which it is prepared. Red phosphorus at 440 gives a certain 
 vapour-pressure ; equilibrium results when the active mass of 
 the gas has attained a certain value, and this value depends 
 on the pressure ; but on continued heating another variety of 
 red phosphorus is produced, and therefore the active mass 
 changes, and therefore the pressure changes until equilibrium 
 again results. Yellow phosphorus at 440 gives a certain 
 vapour-pressure; but the composition of the vapour is 
 changing, and therefore the pressure changes until the 
 vapour attains a definite composition, when its active mass 
 becomes constant and equilibrium results 2 . 
 
 1 Hittorf, Pogg. Ann. 126. 193 ; Troost and Hautefeuille, Ann. Chim. Phys. 
 (5). 2. 153; Lemoine, Ann. Chim. Phys. (4). 24. 129. 
 
 2 For a more detailed discussion of these and other cases of equilibrium in 
 heterogeneous systems composed of two constituents, see Ostwald's Lehrbtich, 2. 
 643650.
 
 CH. II. 1 80, l8l] SYSTEMS OF FOUR BODIES. 367 
 
 181 Let us now briefly consider the equilibrium of a system 
 comprising four changing bodies. 
 
 Let the two bodies A and B be changed to A' and B'\ 
 let the active masses (in equivalents) of the four bodies 
 originally present be /, g, p', and q ', respectively; and let 
 x be the number of equivalents of A and B changed to 
 A' and B', and x' the number of equivalents of A' and B 
 changed to A and B, at any moment ; then the velocity of 
 the direct change is expressed by the equation 
 
 and the velocity of the reverse change by the equation 
 
 and therefore the velocity of the complete change is 
 
 and the condition of equilibrium, i.e. the condition under 
 which -JQ =o and x=% (s. par. 180) is given by the 
 equation 1 
 
 The simplest case in which to apply this equation is 
 obtained by using equivalent quantities of A and B and 
 allowing these to react without the addition of either A' 
 or B' ; in this case p = q= i and /' = q = o, and therefore 
 (i _)V=f </,hence 
 
 The value of i.e. amount of A and B changed, and that 
 of i i.e. amount of A and B remaining unchanged, is 
 determined experimentally, and from these values the ratio 
 of the velocity-constants is calculated. 
 
 1 This equation is identical with that obtained by Guldberg and Waage for the 
 equilibrium of a system of four bodies, but the constants c and c' appear here as 
 reaction-velocities, not as ' forces.'
 
 368 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 / fc \2 
 Ostwald calls the ratio [3^] the partition -coefficient of 
 
 the reaction ; the ratio of the velocity-constants in this case is 
 equal to the square root of the partition-coefficient 
 182 Three important series of experiments with homogeneous 
 systems have given results to which the equation 
 
 can be applied: these are Thomsen's measurements of the 
 quantities of heat produced by the interaction between an 
 acid and the neutral salt of another acid ; Ostwald's measure- 
 ments of the specific volumes of the solutions obtained by 
 mixing an acid with the neutral salt of another acid ; and 
 Berthelot and P. de Saint Gilles' determinations of the amount 
 of ethereal salt formed when equilibrium results between an 
 acid and an alcohol. 
 
 183 Thomsen's experiments are based on the proposition that 
 if the heat of neutralisation of an acid by a base is x units, 
 and the heat of neutralisation of another acid by the same 
 base is y units, the heat produced on mixing equivalent 
 masses of the two acids with the base will be z units, and 
 z will be equal to x, or equal to y t or will be a number 
 between x and y, and that from observations of x, y, and z 
 just conclusions can be drawn as to the partition of the base 
 between the acids. 
 
 The acids chosen to begin with were nitric and sulphuric, 
 and the base was soda. Whether nitric acid is added to 
 an equivalent quantity of sodium sulphate, or sulphuric acid 
 to an equivalent quantity of sodium nitrate, or equivalent 
 quantities of soda, nitric acid, and sulphuric acid are mixed, 
 the distribution of the reacting bodies when equilibrium 
 results will be the same, and the thermal value of the 
 change will be the same 1 . 
 
 Sulphuric acid and soda were mixed in equivalent 
 quantities in dilute aqueous solution (SO 3 + 2OoH 2 O and 
 
 1 This proposition may be deduced from the principles of thermal chemistry ; 
 it has also been experimentally proved by Thomsen; see Pogg. Ann. 138. 65 ; or 
 Thermochemische Untersnchungen, 1. 98.
 
 CH. II. 182,183] THERMAL METHODS. 369 
 
 Na 2 O + 2OOH 2 O), the quantity of heat produced was 31,380 
 gram-units. The quantity of heat which disappeared when 
 sulphuric acid was added to sodium sulphate in dilute aqueous 
 solution was determined for different proportions of the acid 
 and salt ; the result can be expressed by the equation 
 
 [>H 2 SO 4 Aq, Na 2 SO 4 Aq] = - -^ 3300 gram-units. 
 
 If therefore I + n equivalents of sulphuric acid react with 
 an equivalent of soda the thermal value of the change may be 
 expressed thus 
 
 [i + ;*H 2 S0 4 Aq, Na f OAq] = 31,380-^3,300. 
 
 Nitric acid and soda were then mixed in dilute solution 
 (N 2 O e + 2OoH 2 O and Na 2 O + 2OoH 2 O); the quantity of heat 
 produced was 27,230 gram-units. The quantity of heat 
 which disappeared when nitric acid was added to sodium 
 nitrate in dilute solution was 80 gram-units ; this is so small 
 that it may be neglected, and the reaction between equiva- 
 lent quantities of nitric acid and soda may be expressed 
 thermally as 
 
 [H'N 2 6 Aq, Na'OAq] = 27,230. 
 
 Equivalent quantities of nitric acid and sodium sulphate 
 in dilute solution were then mixed ; the quantity of heat 
 which disappeared was 3,500 units. Now if the sole products 
 of the reaction between equivalent quantities of nitric acid 
 and sodium sulphate in dilute solution were sulphuric acid 
 and sodium nitrate, the quantity of heat which would dis- 
 appear in this reaction would be equal to the difference 
 between the heat of neutralisation of nitric acid and that 
 of sulphuric acid by soda l ; this quantity is 
 
 27,230-31,380- -4,150. 
 
 But the quantity of heat which was actually used was 
 3,500 ; therefore the whole of the sodium sulphate had not' 
 been changed to sodium nitrate, and therefore the system 
 when in equilibrium contained sodium nitrate and sulphate 
 and also nitric acid and sulphuric acid. And moreover, if the 
 
 1 [Na 2 S0 4 Aq, N 2 O 5 Aq] = [Na 2 OAq, N 2 O 5 Aq]-[Na 2 OAq, SO 3 Aq]. 
 M. C. 24
 
 3/0 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 only reaction which occurred between sodium sulphate and 
 nitric acid were formation of sodium nitrate and sulphuric 
 
 acid, we might conclude that (= '84) parts of the sulphate 
 
 had been changed. 
 
 But we know that the sulphuric acid produced in the 
 change would react with the unchanged sodium sulphate 
 with disappearance of heat ; this must be taken into account 
 in the calculation. 
 
 Let | be the number of equivalents of sodium sulphate which 
 have been decomposed by the nitric acid, then will also be the 
 number of equivalents of sodium nitrate formed, and also the 
 number of equivalents of sulphuric acid formed, and I will 
 be the number of equivalents of sodium sulphate remaining; the 
 total thermal change will therefore consist of three parts; 
 
 (1) decomposition of Na 2 SO 4 = -3i,38o, 
 
 (2) formation of Na 2 N 2 O 6 = + f 27,230, 
 
 (3) reaction between H 2 SO 4 and i -Na 2 SO 4 . 
 
 The thermal value of (3) will be found by using the equation 
 already given ; this equation will now assume the form 
 
 3>300. 
 
 As the observed thermal value of the complete reaction 
 was 3,500 we have the equation 
 [Na 2 SO 4 Aq, H 2 N 2 O 6 Aq] 
 
 = -3,500 = (27230- 31380)- (i -)--- 3,300. 
 
 rV 8 
 
 Thomsen found that if is taken as f, the calculated value 
 of the equation is 3550, which is almost identical with the 
 observed value. 
 
 Applying the equation of equilibrium given in par. 182 
 to the reaction between sodium sulphate and nitric acid, the
 
 CH. II. 183] THERMAL METHODS. 371 
 
 value of is found to be f ; hence, as 
 
 c ( % 
 
 it follows that -, 4 ; i.e. the ratio of the velocity-constants of 
 the direct and reverse changes is 4. 
 
 By substituting these values for -, and in the equation of 
 equilibrium given in par. 181, viz. 
 
 equations are obtained which can be applied to find the 
 thermal values of the change occurring between different 
 quantities of nitric acid and sodium sulphate in presence 
 of varying masses of sulphuric acid or sodium nitrate. Thus, 
 to take one case, let p, q, p', and q' represent the masses 
 (in equivalents) of nitric acid, sodium sulphate, sulphuric 
 acid, and sodium nitrate, respectively; let qi^p' = q' = o, 
 and let p be variable ; we have 
 
 Thomsen measured the thermal change when / varied ; 
 the following table presents the observed and calculated 
 values : 
 
 Gram-units of heat disappeared. 
 
 p . Calculated. Observed. 
 
 \ '121 920 900 
 
 \ -232 l66o 1620 
 
 \ -423 2660 2580 
 
 1 "667 3550 3500 
 
 2 '849 3950 4050 
 
 3 -903 4040 4100 
 
 The differences are within the limits of the experimental 
 errors. 
 
 Other series of experiments were conducted, (i) in which 
 / = 2, g=i, q' = o, and ff varied from o to 3 ; (2) in which 
 q = q I, /' = o, and / varied from \ to I ; and (3) in which 
 p = q = o, q = i , and p' varied from I to 2 ; in all these ex- 
 
 242
 
 372 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 periments the observed values agreed well with the calculated 
 values. 
 
 Thomsen also conducted experiments with sodium sulphate 
 and hydrochloric acid ; here also it was found that f of the 
 sodium sulphate was decomposed, and therefore in this reaction 
 
 also = 4. The proportions of the reacting bodies were then 
 
 varied and numbers were obtained which agreed well with 
 those calculated by the use of the equation of equilibrium. 
 
 Thomsen's thermochemical investigation of the partition 
 of a base between two acids fully confirms the accuracy of the 
 equation 
 
 184 Ostwald's experiments are based on measurements of the 
 specific gravities of solutions of equivalent quantities of acids 
 and bases and of the salts obtained by the reactions of these 
 acids and bases, and also of the liquids formed when two of 
 the acids are mixed with an equivalent quantity of one of 
 the bases. The following example illustrates Ostwald's 
 method : 
 
 (i) Sp. gr. of solution of caustic soda (approx. normal) [i vol.] 
 (ii) Sp. gr. of an equivalent solution of sulphuric acid [i vol.] 
 (iii) Sp. gr. of solution of sodium sulphate [2 vols.] 
 
 (i) 1-04051 1-04051 
 
 (ii) 1*02970 Nitric acid [i vol.] 1-03083 
 
 Sum 2-07021 Sum 2-07134 
 
 (iii) 2-05918 Sodium nitrate [2 vols.] 2-05266 
 
 Diff. -0-01103 Diff. -0-01868 
 
 The increase in spec. grav. accompanying the neutralisation 
 of soda by nitric acid is greater by '00765 than the increase 
 which accompanies the neutralisation by sulphuric acid. 
 
 Now if sodium sulphate and nitric acid do not react when 
 mixed, the spec, gravity of the mixed solution would be 
 Sodium sulphate [2 vols.] 2*05918 
 Nitric acid [i vol.] 1*03083 
 
 Sum 3*09001 
 But the observed spec. grav. was [3 vols.] 3*08343 
 
 Diff. -0-0065 8
 
 CH.II.l84] VOLUMETRIC METHODS. 373 
 
 If the nitric acid and sodium sulphate had been completely 
 changed to sodium nitrate and sulphuric acid, the change in 
 spec, gravity would have been -0076$ ; thus 
 
 Sodium nitrate [2 vols.] 2-05266 
 Sulphuric acid [r vol.] 1*02970 
 
 Sum 3*08236 
 Sod. sulphate [2 vols.] + nitric acid [i vol.] 3-09001 
 
 Diff. - 0*00765 
 
 Therefore when sodium sulphate and nitric acid react 
 in equivalent quantities the greater part, but not the whole, 
 of the soda goes into combination with the nitric acid. 
 
 Before the exact distribution of the soda between the two 
 acids can be determined, it is necessary to measure the changes 
 in spec, gravity which may accompany secondary reactions. 
 Ostwald's measurements shewed that the observed spec. 
 gravity agreed with the calculated, within the limits of ex- 
 perimental error, (i) when solutions of nitric and sulphuric 
 acids were mixed, (2) when sodium nitrate was mixed with 
 sodium sulphate, (3) when sodium nitrate was mixed with 
 nitric acid. But when sodium sulphate was mixed with 
 sulphuric acid the observed spec, gravity was greater than 
 that calculated on the assumption that no chemical change 
 occurred; the increase in spec, gravity was found to agree 
 very closely with that calculated by the interpolation-for- 
 
 Ostwald then applied this correction, and arrived at the 
 result that when sodium nitrate and sulphuric acid interact in 
 equivalent quantities in dilute aqueous solution, two-thirds 
 of the soda remains combined with the nitric acid, and one- 
 third enters into combination with the sulphuric acid. This 
 result is identical with that obtained by Thomsen. A similar 
 examination of the reaction between sodium chloride and 
 sulphuric acid gave a result the same as that which Thomsen 
 obtained. 
 
 Hence Ostwald's volumetrical investigation of the partition 
 of a base between two acids fully confirm the accuracy of the 
 
 equation (/-)(?-*)* = (/ + ) (tf + c '-
 
 374 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 185 Van't Hoff 1 , in 1877, use ^ tne results of the experiments 
 of Berthelot and P. de Saint Gilles on the etherification of 
 alcohols, in order to test the accuracy of the equation of 
 equilibrium which he had deduced independently of Guldberg 
 and Waage. The experiments shewed that equilibrium was 
 established in a mixture of equivalent quantities of alcohol 
 and acetic acid when two-thirds of the alcohol and the acid 
 were transformed into ethereal salt and water ; therefore here 
 
 also -7 = 4; and the equation for calculating when/ varies is 
 
 
 where/ = active mass of alcohol, q = active mass of acetic acid, 
 /' = active mass of ethereal salt, q = active mass of water ; 
 initial conditions being q = I and />' = q = o. 
 
 The following table gives some of the results : 
 
 P __ j ___ 
 
 Calculated. Observed. 
 
 05 -049 -05 
 
 08 -078 -078 
 
 18 '171 '171 
 
 28 -232 '226 
 
 '33 "3" >2 93 
 
 50 -423 -414 
 
 67 -528 -519 
 
 ro -667 -673 
 
 1-5 -785 -816 
 
 2 -845 -87 
 2-80 -895 -892 
 
 3 -902 -90 
 945 -97 
 
 In another set of experiments p = q=\,p' = o > and q' 
 was variable; the calculated values of agreed well with 
 the observed values. 
 
 By these experiments the equation of equilibrium is again 
 verified. 
 186 The equation of equilibrium 
 
 Ber. 10. 669.
 
 CH. !!.! 85, 1 86] VARIOUS CASES. 375 
 
 may be applied to heterogeneous systems. For dealing with 
 systems composed of solids and liquids or gases, we must 
 distinguish cases in which one, two, or three, of the inter- 
 acting bodies are solids \ 
 
 When one of the four bodies is a solid, the equation 
 becomes 
 
 where h = active mass of the solid. 
 
 If the initial conditions are such that/ = ^= I and /' 
 we have the equation 
 
 by means of which the ratio of the reaction-velocities can be 
 calculated from observations of h, or h can be calculated if 
 
 - is known. 
 c 
 
 The simplest case is that in which one body reacts with 
 the solid, the other two bodies being absent at the beginning 
 of the reaction ; we have/ = ^ = o, and 
 
 - F 
 
 This last case is considered by Ostwald (he. cit.} in detail, 
 the reacting bodies being hydrochloric acid and solid calcium 
 
 oxalate ; the values obtained for - h are not constant. This 
 
 c 
 
 reaction therefore shews divergences from the results which 
 ought to follow if the law of mass-action held good. But it is 
 possible to reconcile the results to some extent with deductions 
 from this law ; at any rate the experiments of Ostwald do 
 not require us to reject the law of mass-action, but they 
 rather open a path which will probably lead to fresh dis- 
 coveries concerning chemical equilibrium. (See Ostwald, 
 he. cit.} 
 
 When two of the interacting bodies in a system of four 
 bodies are solids, the other two being liquids or gases, the 
 active masses of the solids may be put as h and //, re- 
 
 1 Ostwald, Lehrbuch, 2. 658670.
 
 37" CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 spectively, and the equation of equilibrium then assumes the 
 following form ; 
 
 and therefore j- = -, 1 = constant; 
 
 or in words, equilibrium is attained when the active masses of 
 the two liquid or gaseous constituents of the system are in a 
 fixed ratio which is independent of the absolute or relative 
 masses of the two solid constituents. 
 
 In 1871, Deville conducted a series of experiments on the 
 reaction between iron, iron oxide, water-gas, and hydrogen \ 
 In these experiments water was heated in a retort connected 
 with a tube containing iron, the other end of the tube being 
 in connexion with a mercury-pump and a manometer. A 
 vacuum having been obtained, the contents of the retort, as 
 also those of the tube, were raised to a constant temperature, 
 and the pressure was measured by the manometer ; the 
 pressure was composed of the partial pressures of the water- 
 gas and the hydrogen formed by the reaction between the 
 iron and the steam. As the reaction consisted of a direct 
 change of steam + iron to hydrogen + iron oxide, and a 
 reverse change of hydrogen + iron oxide to steam + iron, 
 equilibrium ought to have been attained when the active 
 masses of the steam and hydrogen bore a constant ratio 
 to each other at a specified temperature. As the active mass 
 of a gaseous constituent of a system is conditioned by the 
 pressure, it follows that if p v = the partial pressure of the 
 hydrogen and p z = the partial pressure of the water-gas, the 
 
 ratio y ought to have been constant at each temperature. 
 
 The temperature of the water in the retort was kept at o in 
 one series of experiments, and at 10 in the other series ; the 
 temperature of the tube varied from 200 to 1600. Small 
 errors might readily be made in the measurements of the 
 pressures, especially at the higher temperatures, and at these 
 temperatures small errors would considerably affect the 
 
 1 Compt. rend. 70. 1105; 71. 30.
 
 CH. ii. 1 86] VARIOUS CASES. 377 
 
 values of . The following table shews that Deville's results 
 confirm the equation of equilibrium. 
 
 / 
 
 A 
 
 A 
 
 a 
 
 A 
 
 A 
 
 A 
 
 A 
 A 
 
 200 
 
 4 6 
 
 9'59 
 
 048 
 
 '97 
 
 i9'53 
 
 os 
 
 265 
 
 46 
 
 6-42 
 
 072 
 
 i'57 
 
 23 '5 1 
 
 067 
 
 360 
 
 46 
 
 4-04 
 
 114 
 
 95 
 
 7-63 
 
 124 
 
 440 
 
 46 
 
 2-58 
 
 178 
 
 I -01 
 
 579 
 
 174 
 
 860 
 
 4 6 
 
 1-28 
 
 3 6 
 
 1-30 
 
 2-39 
 
 54 
 
 1040 
 
 46 
 
 92 
 
 50 
 
 1-27 
 
 1-91 
 
 66 
 
 1600 
 
 4 6 
 
 'Si 
 
 90 
 
 1-63 
 
 1-17 
 
 1-40 
 
 The experiments of Guldberg and Waage on the reaction 
 between a solution of potassium carbonate and solid barium 
 sulphate (referred to in par. 170) present the conditions of 
 equilibrium of a system composed of two solid and two liquid 
 constituents. Expressing the active masses of the soluble 
 bodies, potassium carbonate and sulphate, by p and p', the 
 
 equation of equilibrium asserts that the ratio , -.. should 
 
 remain constant independently of the masses of the barium 
 carbonate and sulphate. The following numbers exhibit the 
 values actually obtained for this ratio ; 
 
 f 
 
 200 o 39*5 4*06 
 
 250 o 50-0 4-0 
 
 350 o 71-9 3-87 
 
 250 25 30-0 4-0 
 
 300 25 40-8 3-94 
 
 200 50 '5 3'95 
 
 There are as yet but few data by which may be tested 
 the correctness of the deduction from the equation of equi- 
 librium, that when three of the four bodies constituting a re- 
 acting system are solids, the equilibrium must be conditioned 
 by the active mass of the liquid or gaseous constituent and 
 must be independent of the masses of the three solid bodies. 
 
 Isambert 1 has examined the equilibrium of the system 
 obtained by heating together solid ammonium chloride and 
 
 1 Cornet, rend. 102. 1313.
 
 378 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 lead oxide; his results shew that when equilibrium is 
 attained for a specified temperature, the pressure of the 
 ammonia gas produced in the reaction is constant and is 
 independent of the masses of the solid ammonium chloride, 
 lead oxide, and lead chloride (or oxychloride). 
 187 We have now passed in review a large amount of varied 
 experimental evidence which establishes on a firm basis the 
 law of mass-action, and the principle of the co-existence of 
 reactions. These two generalisations assert that the amount 
 of change undergone by a chemically reacting system is pro- 
 portional to the product of the active masses of the constituents 
 of the system and the coefficient of affinity of the change, and 
 that when several changes take place simultaneously the total 
 change is equal to the sum of the particular changes. We 
 have found that in place of the phrase coefficient of affinity 
 we may use the expression reaction-velocity ; but we have not 
 attempted as yet to analyse the conception underlying these 
 expressions. 
 
 The law of mass-action and its applications to different 
 cases of chemical change have been treated so far in a purely 
 empirical manner. The law was gained by determining the 
 distribution of the reacting bodies in certain systems which 
 had attained equilibrium, and it was applied to determine the 
 conditions of equilibrium in other systems and the velocities 
 of the reactions which occurred before equilibrium was at- 
 tained. 
 
 Besides the particular methods considered in the preceding 
 paragraphs of this chapter, there are two general methods which 
 may be used in attempts to solve the problems of chemical 
 dynamics ; one of these is thermodynamical, and the other is 
 molecular.
 
 
 CH. II. 187, 1 88] THERMODYNAMICAL METHODS. 379 
 
 SECTION III. Thermodynamical methods applied 
 to chemical equilibrium*. 
 
 188 Horstmann 2 , in 1873, propounded a thermodynamical 
 theory of dissociation which is also generally applicable 
 to other cases of chemical equilibrium, inasmuch as the 
 processes which occur in a system before it attains chemical 
 equilibrium are generally reversible processes. Horstmann's 
 method consisted in applying the second law of thermo- 
 dynamics to the phenomena of dissociation; he concluded 
 that these processes, like all other reversible processes, tend 
 to bring the system to that condition wherein the entropy of 
 the system has attained its maximum value under the given 
 conditions. To determine the conditions under which the 
 entropy of a specified system undergoing a reversible change 
 becomes a maximum is therefore to determine the conditions 
 of equilibrium of that system. 
 
 Let Q = quantity of heat added to a body at constant 
 
 temperature T, then ^.= gain of entropy to the body; let 
 
 Q l = quantity of heat lost by a body at constant temperature 
 T v then -^ = loss of entropy to the body. All chemical 
 
 and physical changes occurring spontaneously are accom- 
 panied by an increase in the entropy of the system. This 
 statement holds good for non-reversible changes; but as 
 no actually occurring change is completely reversible the 
 statement holds for all changes. 
 
 Suppose that one of two bodies is hotter than another 
 and loses heat to the colder ; the hotter body at temperature 
 
 7^ loses heat Q, therefore its entropy is decreased by -^ ; the 
 colder body at temperature T 9 gains heat Q, therefore its 
 
 1 In this section I have again followed Ostwald ; but the methods discussed 
 in this section are so largely physico-mathematical that I have attempted only the 
 briefest outline, referring the student to Ostwald's Lehrbuch, 2. 702 728, and to 
 the original memoirs. 
 
 ' Annalen, 170. 192.
 
 380 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 entropy is increased by -^ ; but as 7\ > T y it follows that 
 1 2 
 
 ^ < ; in other words the entropy of the system is in- 
 
 *l -* 2 
 
 creased by the passage of heat from the hotter to the colder 
 body. 
 
 Changes of state involving changes of pressure and volume 
 are also accompanied by changes of entropy; if the tempera- 
 ture is constant the entropy-change is easily found ; if volume 
 and temperature change simultaneously with pressure the total 
 change may be regarded as partly adiabatic until the final 
 temperature is reached, and then isothermal until the system 
 attains equilibrium ; the latter part of the change is alone 
 accompanied by a change of entropy. As it is possible to 
 pass from any given state of a system to any other by a 
 path which is partly adiabatic and partly isothermal, it is 
 possible to lay down the principles on which the entropy- 
 change accompanying any material change may be de- 
 termined. 
 
 189 The application of thermodynamical methods to the study 
 of chemical equilibrium has been much developed by Willard 
 Gibbs 1 . 
 
 Gibbs shews that the criterion of the equilibrium of a 
 system is contained in the following statement ; 
 
 For the equilibrium of any isolated system it is 
 necessary and sufficient that in all possible variations 
 of the state of the system which do not alter its entropy, 
 the variation of its energy shall either vanish or be 
 positive ; or, in other words, in all possible variations 
 of the state of the system which do not alter its energy, 
 the variation of its entropy shall either vanish or be 
 negative. 
 
 As the masses of the constituents of a system undergoing 
 chemical change do not remain constant, an equation which is 
 to express the conditions of equilibrium of such a system must 
 take into account the changes of energy produced by changes 
 
 1 Amer. Journ. of Sci. and Arts, (3). 16. 441 ; 18, 277. See also Clerk 
 Maxwell, South Kensington Science Conferences [1876].
 
 CH. II. 189] THERMODYNAMICAL METHODS. 3$I 
 
 in the masses of the constituents. This is done by Gibbs by 
 introducing into his equations a term which represents the 
 potential of each constituent. If an infinitesimal mass of a 
 body is introduced into a homogeneous system without 
 disturbance of the homogeneity and without change in the 
 entropy and volume of the system, then the increase in the 
 energy of the system divided by the infinitesimal mass of the 
 substance added is the potential of that substance in the 
 system. 
 
 The energy of the entire system is a function of the 
 entropy and the volume of the system, and the masses of 
 its constituents ; if the energy is known in terms of these 
 variables, then the absolute temperature and the pressure of 
 -the system, and the potentials of its constituents, can be 
 calculated in terms of the same variables. In this way all 
 the independent relations between the seven variables, energy, 
 entropy, volume, masses of constituents, temperature, pressure, 
 and potentials of constituents, can be found ; and on these 
 relations depend most of the properties of the system, in- 
 cluding its chemical properties. A single equation from 
 which all these relations are deducible is called by Gibbs 
 a fundamental equation. 
 
 Gibbs shews how such fundamental equations are found. 
 He then applies these equations to ideal gases, and then to 
 ideal gas-mixtures, i.e. mixtures of ideal gases which obey 
 the law of Dalton 1 , and so he deduces the conditions of 
 equilibrium of such mixtures of gases. Assuming that the 
 laws of ideal gas-mixtures apply to cases in which chemical 
 change occurs in the mixtures themselves, at certain tem- 
 peratures, resulting in the formation of one kind of com- 
 ponents from another kind, Gibbs deduces a formula for find- 
 ing the specific gravity of a gas-mixture from its temperature 
 and pressure 2 . He applies this formula to the gas-mixtures 
 obtained by heating nitrogen peroxide (N 2 OJ, phosphorus 
 
 1 For convenience' sake, Gibbs states this law in these terms; " The pressure 
 in a mixture of different gases is equal to the sum of the pressures of the different 
 gases as existing each by itself at the same temperature and with the same value 
 of its potential." 
 
 2 See/tarf, par. 205.
 
 382 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 pentachloride, formic acid, and acetic acid, and finds that 
 the calculated results agree on the whole very well with the 
 observed values for the specific gravities of these gases. Hence 
 it is probable that the fundamental equations obtained by 
 purely thermodynamical reasoning are applicable to all cases 
 of gaseous dissociation. But dissociation-processes are in- 
 stances of chemical equilibrium ; hence it is to be expected 
 that each of the classes into which the problems of chemical 
 equilibrium may be divided has its appropriate fundamental 
 equation by the use of which a full thermodynamical expla- 
 nation can be given of this class of cases of equilibrium. 
 190 One of the forms in which the criterion of stability is 
 stated by Gibbs involves the use of a certain function, i|r, 
 which is defined by the equation 
 
 t = e-fy, 
 
 where e = energy of the system, tj = entropy of the system, 
 and t absolute temperature; then equilibrium results when 
 in all possible variations of the state of the system which do 
 not alter its temperature, the variation of ^ either vanishes 
 or is positive. 
 
 This form of stating the criterion of stability is in many 
 cases more convenient than that given in par. 189 for deducing 
 the conditions of equilibrium of any system. The meaning 
 of the function -\Jr has been developed by von Helmholtz * on 
 lines different from those adopted by Gibbs. Helmholtz 
 divides the internal energy of a system into two parts ; the 
 free energy which can be completely changed into other forms 
 of energy, and the bound energy which is that portion of the 
 total energy required for establishing the state of the system 
 conditioned by the entropy of the system ; as every stable state 
 corresponds to a maximum entropy, the bound energy cannot 
 be changed to other forms within the system, nor without 
 external action on the system. The bound energy is 
 measured by the difference between the total and the free 
 energy. Helmholtz's free energy is identical with Gibbs' 
 function i/r, 
 
 1 'Die Thermodynamik Chemischer Vorgange,' Sitaber. der Wiss. Akod zu 
 Berlin, 1882, also Helmholtz's Wissenschoftliche Abhandlungen, 2. 958.
 
 CH. II. IQO, 191] THERMODYNAMICAL METHODS. 383 
 
 All the properties of a system may be represented in 
 equations as functions of the free energy of the system. 
 Such equations have been deduced for some of the chemical 
 properties of a system in equilibrium, e.g. for dissociation- 
 processes of different orders of complexity, and for reciprocal 
 actions when some members of the system are gases and some 
 solids. These equations lead to results identical with those 
 already obtained by the use of the empirical method of 
 Guldberg and Waage x . 
 
 The transformability of the chemical energy of a system 
 into other forms of energy is measured by the free energy, 
 and not by the total energy, of the system. For instance, 
 the energy obtained from a chemical reaction in the form of 
 heat does not measure the electrical energy obtainable from 
 the same system ; for the latter is obtained by the transforma- 
 tion of the free energy only and not of the total energy. So 
 also in a chemical change, the direction of the change is 
 determined by the free energy of the changing system, and 
 this is not measured by finding the quantity of the heat 
 produced in the change. 
 
 II One of the consequences of the general criterion of stability 
 deduced from the second law of thermodynamics is, that 
 Berthelot's so-called ' law of maximum work ' is inaccurate. 
 
 Berthelot's law asserts that 'every chemical change accom- 
 plished without the addition of energy from without tends to the 
 formation of that body or system of bodies the production of 
 which is accompanied by the development of the maximum 
 quantity of heat.' 2 
 
 Now a system is in equilibrium when its entropy has 
 attained the maximum value possible under the conditions. 
 But inasmuch as entropy is measured by a quantity of heat 
 divided by a temperature, it is only at the absolute zero 
 of temperature that dS = dQ (S = entropy, Q = quantity of 
 heat); hence it is only at the absolute zero that thermal 
 
 1 See Ostwald, Lekrbuch, 2. 716 724; also P. Duhem, ' Le potentiel thermo- 
 dynamique' [Paris, 1886 7]. 
 
 2 See ante, Book I., par. 133 for a discussion of the practical applications 
 of this statement.
 
 384 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 changes directly measure changes of entropy. When a 
 chemical change is accompanied by the production of much 
 heat, and the change occurs at a low temperature, the thermal 
 change will roughly measure the entropy-change ; therefore 
 if such a change be possible it will occur. But if the quantity 
 of heat produced in a chemical process is small, the entropy- 
 change which the system undergoes may be largely con- 
 ditioned by changes other than the thermal change. Indeed 
 in some cases heat may be lost to the system, and yet the 
 total change in the entropy may be positive ; in such cases 
 chemical change will occur with the disappearance of heat, 
 because the decrease in the entropy of the system caused by 
 the loss of heat will be more than balanced by the increase 
 in the entropy caused by the changes of state which the 
 system undergoes. 
 
 Such chemical changes are analogous to the physical change 
 of water in vacua into water-gas ; in this case the water loses 
 heat, but the loss of entropy thus suffered is more than 
 balanced by the gain of entropy accompanying the change 
 from liquid to gaseous water. 
 
 So far as the law of entropy has been applied to chemical 
 processes, it has led to the same conclusions regarding the 
 equilibrium of chemical systems as have been gained by the 
 application of the law of mass-action. The general con- 
 ception of chemical change which is given by both methods 
 of investigation is that of a system attaining equilibrium as 
 the result of processes occurring in opposite directions. Ac- 
 cording to van't Hoff 1 , the directions of chemical processes 
 which result in equilibrium vary with variations of tempera- 
 ture in such a way that the lower the temperature the more 
 is equilibrium established with the production of heat, but the 
 change can occur in one direction only at the absolute zero. 
 Berthelot's ' law ' would then hold good for the limiting case 
 that the change should occur at 273. As the temperature 
 at which most chemical changes occur is not very high very 
 many changes are accompanied by production of heat. 
 
 Berthelot's ' law of maximum work ' is the modern form 
 
 1 Dynanrique chimique, 153.
 
 CH. II. 191,192] MOLECULAR METHODS. 385 
 
 assumed by the old Bergmannic view of affinity. Berthelot, 
 like Bergmann, regards chemical affinity as acting in one 
 direction only. But the outcome of all recent investigation 
 is to negative this view, and to confirm the conception of 
 affinity which was first clearly introduced into chemistry by 
 the great French naturalist Berthollet. 
 
 SECTION IV. Molecular methods applied to 
 chem ical equilibrium. 
 
 192 In 185 1 Williamson 1 suggested that the amount of chemical 
 change which occurs between two interacting bodies is de- 
 pendent on the velocities of the atomic interchanges which 
 take place between the molecules of the bodies. He extended 
 this conception to molecules all of the same kind, and con- 
 cluded that " in an aggregate of molecules of any compound 
 there is an exchange continually going on between the elements 
 which are contained in it." He supposed, for instance, that 
 in a vessel filled with hydrochloric acid the molecules HC1 
 are continually exchanging hydrogen and chlorine atoms ; 
 if then a solution of copper sulphate is added to hydrochloric 
 acid " the hydrogen does not merely move from one atom of 
 chlorine to another, but in its turn also replaces one atom 
 of copper, forming chloride of copper and sulphuric acid." 
 When one product of a chemical change is insoluble it is 
 removed, and so almost the whole of one of the original 
 substances is decomposed ; but if all the products remain in 
 solution, the atomic interchanges proceed in both directions 
 and equilibrium is thus established. 
 
 In 1857 Clausius 2 developed a conception similar to 
 that put forward by Williamson, and applied it especially 
 to explain the phenomena of electrolysis. He supposed that 
 the movements of the molecules of a liquid result in the 
 production of such a condition of some of the molecules as 
 makes these molecules ready to exchange their constituent 
 parts. As increasing temperature is equivalent to increasing 
 
 1 C. S. Journal, 4. no; 229. Also Phil. Mag. (3). 37. 350. 
 
 2 Pogg- Ann. 101. 338. 
 
 M.C. 25
 
 386 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 the kinetic energy of the molecules, increase of temperature 
 will bring about further separation of molecules into parts, 
 and will therefore increase the chances of the exchange of 
 parts of molecules. 
 
 Clausius' hypothesis postulates differences in the conditions 
 of the molecules forming a liquid compound at any specified 
 temperature, and asserts that some of the molecules will 
 be more ready to exchange parts than others 1 . 
 
 Pfaundler 2 , in 1867 and 1874, developed the hypothesis of 
 Clausius and Williamson and applied it to many chemical 
 reactions, and more particularly to explain the phenomena of 
 dissociation 8 . 
 
 Pfaundler considers the motion of agitation of the molecules 
 of a gas, and also the motion of parts of the molecules ; ac- 
 cording to the kinetic theory of gases, the sum of the kinetic 
 energies due to these two motions is constant at a constant 
 temperature, and the sum of each is constant, but the two 
 motions may be very differently distributed among the indi- 
 vidual molecules. The results of collision between two 
 molecules will depend on the ratio between the energy of 
 agitation, and the energy of rotation of the parts, of the 
 molecules ; the limiting cases are when both energies are 
 at a maximum, or both are at a minimum, or either is at 
 a maximum compared with the other at a minimum. 
 193 Guldberg and Waage 4 , in 1879, brought the hypothesis of 
 chemical action being due to differences in the states of the 
 molecules of a gas or liquid into a form in which it could 
 be quantitatively applied. Let the molecules of two substances 
 which react chemically with one another be represented by 
 A and B; let these molecules be composed of the atoms 
 (or atomic groups) aa, and bb y respectively, performing certain 
 vibrations within the molecules A and B. At certain points 
 in these vibrations the atoms aa on the one hand, and the 
 
 1 For some account of the applications of the hypothesis of Clausius, see 
 post, par. 204. 
 
 2 Fogg. Ann. 131. 55 et seq. (especially, pp. 6671); do. Jubelbd. 182. 
 
 3 See Section v. of the present Chapter. 
 
 4 Journal fur prakt. CAenu'e, (2). 19. 75.
 
 CH. II. 193, 194] MOLECULAR METHODS. 387 
 
 atoms bb on the other hand, will be so far separated from one 
 another that the attraction between them will be very small ; 
 a molecule the atoms of which are in this condition will be 
 ready to undergo chemical change. Suppose that a molecule 
 A comes near to a molecule B at the moment when each is 
 ready to undergo change, chemical action will occur with the 
 production of two new molecules, C, each composed of the 
 atoms ab. If the number of molecules of A which are in this 
 condition of readiness to undergo change be a, the total 
 number of molecules of A in unit volume of the system 
 being p, and if the number of molecules of B ready to 
 undergo change be b, the total number of molecules of B 
 being g, then the frequency of collision of the molecules 
 which are ready to change will be represented by the product 
 (apbq\ and the velocity of formation of the new molecules, C, 
 will be represented by $apbq, where <j> is a velocity-coefficient 
 which depends on the temperature and the chemical nature 
 of the substances A and B. The nature of this dependence 
 must be experimentally determined. An expression, similar 
 to that given, can be found for the velocity of re-formation of 
 A and B; and hence the amounts of A, B, and C, which are 
 present when equilibrium is attained can be calculated for any 
 initial state of the system. 
 
 The equation of equilibrium thus found is 
 $apbq = tfa'b'p'q'. 
 
 If k is put as = $ab and k' as = fy'a'b', the equation becomes 
 kpq = k'p'q'. 
 
 This equation is essentially the same as that which 
 Guldberg and Waage arrived at by the use of methods 
 which did not involve any theory of the structure of matter. 
 We have already traced the development and applications 
 of this equation of equilibrium \ 
 
 194 J- J- Thomson 2 has given a general conception of chemical 
 equilibrium in terms of the vortex-atom theory of the structure 
 of matter. 
 
 1 Ante, pars. 172 186. 
 
 2 On the motion of vortex rings. The Adams Prize Essay for 1882. (See 
 also Phil. Mag. (5). 15. 427; 17. 233; 18. 233.) 
 
 252
 
 388 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 A compound molecule of a gas is regarded by this theory 
 as consisting of two, or more, vortex rings. This united vortex 
 ring will separate into its parts when subjected to a disturbing 
 influence, such as the action due to other vortex rings in the 
 neighbourhood. The theory thus leads to a conception of 
 chemical combination closely resembling that enunciated by 
 Williamson, Clausius, and Pfaundler. But for a compound 
 gas to be more than a mere mixture of elementary gases it is 
 necessary that 'the mean time during which an atom is paired 
 with another of a different kind, which we shall call the paired 
 time, should be large, compared with the time during which it 
 is alone and free from other atoms, which we shall call the 
 free time' (loc. cit. p. 115). 
 
 The ratio of paired to free time will be diminished by any 
 disturbance to which the gas is subjected; when the diminu- 
 tion is carried past a certain amount, the gas is decomposed. 
 
 Now 'the pairing of two atoms is attended by a large 
 
 increase in the translatory energy;' but as these atoms are 
 only paired for a time, ' the whole increase in the translatory 
 
 energy of a large number of molecules will depend on 
 
 the ratio of the paired to the free times' of the vortex 
 atoms which form the molecules of the substance (loc. cit. 
 p. 1 1 6). The value of this ratio in the case of an elementary 
 gas will to a great extent condition the chemical properties of 
 that gas ; it will also determine whether chemical combination 
 shall or shall not occur between two gases, and if it occurs, it 
 will fix the proportions between the amounts of the various 
 compounds produced. An elementary gas will readily enter 
 into chemical combination, only when the ratio of free to 
 paired time is larger for the molecule of the element, than for 
 that of the compound produced. The value of the ratio in 
 question may therefore afford a measure of the relative 
 affinities for each other of the atoms of various compound 
 molecules. 
 
 This conception of chemical change is applied by Thomson 
 chiefly to processes of dissociation ; the results obtained will 
 be briefly considered in the next section.
 
 CH. II. 194, 195] DISSOCIATION. 389 
 
 SECTION V. Dissociation. 
 
 195 Certain changes brought about by heat and resulting in 
 the formation of systems in equilibrium are classed together 
 under the common term dissociation. 
 
 By this term is meant a change from one chemical system 
 to another simpler system which change is caused by heat 
 and is reversible. The composition of the constituents of the 
 simpler system is less complex than that of the bodies which 
 form the original system. At least one member of the simpler 
 system is gaseous under the conditions of the experiment. The 
 resolution of the compound N 2 O 4 into 2NO 2 , or of C 6 H n Br 
 into C 5 H 10 and HBr, or of CaCO 3 into CO 2 and CaO, and the 
 subsequent re-formation of the original compound on cooling 
 the products of each action, are examples of dissociation. 
 
 In the change of N 2 O 4 into 2NO 2 , both the original body 
 and that formed by heating the original are gases ; hence the 
 change in question must be accompanied by a decrease in the 
 spec. grav. of the gas. If it has been proved that the only 
 change which occurs when N 2 O 4 is heated is the gradual dis- 
 appearance of the N 2 O 4 with the simultaneous production of 
 2NO 2 , then the amount of this change which occurs at any 
 specified temperature and pressure can be calculated from 
 observations of the spec. grav. of the gas at that temperature 
 and pressure. 
 
 There are cases where a gas becomes specifically lighter 
 as temperature increases, without our being able to demon- 
 strate by conclusive experiments that the decrease in spec, 
 grav. is accompanied by dissociation of the gas into simpler 
 components. For instance, the spec. grav. of the gas ob- 
 tained by heating ammonium chloride is considerably less 
 than the value calculated on the assumption that this gas 
 consists of the compound NH 4 C1; and the spec. grav. 
 decreases as temperature rises, until at about 350 it is very 
 nearly identical with that calculated for a mixture of equal 
 volumes of NH 3 and HC1 (calcd. = -93; observed = ro). We 
 seem justified in considering the gas obtained by heating 
 NH 4 C1 to 350 to be a mixture of equal volumes of NH 3
 
 390 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 and HC1, with perhaps a little unchanged NH 4 C1, although 
 there is no absolutely conclusive experimental demonstration 
 that this is so. In support of this conclusion may be men- 
 tioned Pebal's 1 proof that if the vapour obtained by heating 
 ammonium chloride is diffused through a porous septum the 
 diffusate contains considerable quantities of free ammonia. 
 
 Another instance of this kind is presented by acetic acid 
 vapour. Ramsay and Young 2 have shewn that this vapour 
 becomes specifically heavier by increasing pressure at any 
 temperature or by decreasing temperature at any pressure. 
 They contrast this behaviour with that of the vapour of 
 alcohol and ether, which are almost certainly non-dissociable 
 bodies; the spec, gravities of these vapours increase as tempera- 
 ture is decreased, at a fixed pressure, until a certain value is 
 reached after which decrease of temperature does not change 
 the spec, gravities. The conclusion to be drawn from these 
 observations is that acetic acid vapour at low temperatures 
 is probably composed for the most part of molecules which 
 are more complex and heavier than those which chiefly 
 compose this vapour at high temperatures, and that the 
 former are dissociated into the latter as temperature rises. 
 
 When the spec. grav. of the gas obtained by heating a 
 definite compound decreases as temperature increases, and 
 reverts to its original value when the temperature falls to 
 its initial value, and when the change of spec. grav. quanti- 
 tatively corresponds with a change of composition which can 
 be presented in a definite manner,, and which is perfectly 
 justifiable on other grounds, and is the only change of 
 composition which will explain the observed variations of 
 spec, grav., we are justified in regarding the variations of 
 spec. grav. as indications and measures of the change of 
 composition. For if we do not thus regard these variations 
 of spec, grav., then we must regard the gases in question 
 as having abnormal coefficients of expansion 3 , and coefficients 
 so abnormal as to demand a complete revision of our con- 
 
 1 Annalen. 126. 193. 
 
 2 C. S. Journal, Trans, for 1886. 790; Phil. Mag. (5). 23. 129. 
 
 3 Deville and Troost, Compt. rend. 64. 237; 91. 54; Berthelot, do. 91. 77.
 
 CH. II. 195, 196] DISSOCIATION. 39! 
 
 ceptions regarding the relations between the volumes of gases 
 and changes of temperature. For instance, we should have 
 to admit that the coefficients of expansion of such gases as 
 ammonium chloride, phosphorus pentachloride, &c., which 
 gases are generally regarded as undergoing dissociation on 
 heating, increase as temperature rises, but increase rapidly 
 until a maximum is reached and then increase slowly. But 
 there is no conclusive proof that the coefficients of expansion 
 of any gases change in this way ; and moreover it has been 
 experimentally shewn that the coefficients of expansion of 
 the following elementary and compound gases are practically 
 unchanged for a very large range of temperature ; hydrogen, 
 oxygen, nitrogen, sulphur, tellurium, mercury, carbon di- 
 oxide, hydrogen chloride, arsenious oxide l . 
 
 196 The so-called abnormal vapour-densities of various gases 
 are at once explained if we suppose that the gases in question 
 are dissociated on heating, and that therefore the observed 
 vapour-densities are the spec, gravities of mixtures and not of 
 single gases. For instance the composition of sulphuric acid 
 is undoubtedly expressed by the formula H 2 SO 4 ; if this com- 
 pound were gasified the spec. grav. of the gas must be 49 
 times that of hydrogen (H 2 SO 4 = 98); but the spec. grav. 
 of the gas obtained by vaporising sulphuric acid is con- 
 siderably less than 49, and the spec. grav. decreases as 
 temperature rises until at about 400 the value obtained is 
 24-5. These results are at once explained by supposing that 
 the compound H 2 SO 4 is dissociated into a mixture of equal 
 volumes of the two gaseous compounds SO 3 and H 2 O, as the 
 spec. grav. of such a mixture would be 24-5 times that of 
 hydrogen. As the variations in the spec. grav. of the vapour 
 obtained by heating sulphuric acid as temperature increases 
 and decreases are exactly similar to the variations observed 
 in the spec, gravities of gases which undoubtedly undergo 
 dissociation, we are justified in saying that the expression 
 abnormal vapour-density of sulphuric acid should not be used, 
 because the vapour is not sulphuric acid but is a mixture of 
 two, and probably three, gases in variable proportions. The 
 
 1 V. Meyer, Ber. 13. 2022; see also Langer and Meyer, Ber. 18. Ref. 133.
 
 392 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 other cases of so-called abnormal vapour densities cease to 
 be abnormal when we are prepared to admit the occurrence of 
 dissociation. 
 
 197 The amount of dissociation which any body undergoes 
 depends upon the temperature, and also on the pressure. 
 As the body is heated, temperature rises, and the rate of 
 dissociation increases until a maximum is reached, after which 
 the rate of dissociation decreases until the change is completed; 
 on cooling the products of dissociation in contact with each 
 other, this process is reversed. If pressure and temperature 
 are kept constant, the system composed of the original body 
 and the products of dissociation settles down into equilibrium, 
 which is disturbed either by changing the temperature or the 
 pressure, although in some cases change of pressure does not 
 affect the equilibrium nearly so much as it does in other 
 cases 1 . 
 
 The pressure at which equilibrium is attained for any 
 specified temperature is usually called the equilibrium-pressure 
 for that temperature 2 . 
 
 198 Consider the effect of heat on a quantity of ammonium 
 chloride enclosed in a vacuous vessel connected with an 
 air-pump and a manometer. As the solid is heated, vapour 
 is produced, and this vapour consists of equal volumes of 
 ammonia and hydrogen chloride possibly mixed with small 
 quantities of ammonium chloride gas. This change proceeds, 
 with constant rise of temperature, and increase of pressure in 
 the interior of the vessel. Now let the temperature be kept 
 constant, say at 350, dissociation proceeds until the pressure 
 of the gases in the vessel attains a certain amount when the 
 process of dissociation stops, and equilibrium is established 
 between the three bodies, ammonium chloride, ammonia, and 
 hydrogen chloride. Now let temperature be raised through 
 a definite interval, say to 400; dissociation proceeds, more 
 ammonia and hydrogen chloride are produced, and pressure 
 increases until it reaches a limit whereat the system again 
 attains equilibrium. Now let a portion of the gases be 
 
 1 See next page. 
 
 2 The terms equilibrium-tension, and tension of dissociation are also used.
 
 CH. II. 197, 198] DISSOCIATION. 393 
 
 pumped out of the vessel, temperature being maintained at 
 400; pressure falls, dissociation begins and proceeds until 
 the former pressure is reached. Now let temperature be 
 decreased, say to 350 ; combination of ammonia and 
 hydrogen chloride begins and pressure falls, and this pro- 
 ceeds until a new state of equilibrium is attained. 
 
 This is a typical and simple case of dissociation ; one 
 definite body is resolved into two others and these again 
 recombine to form the original body. In this instance the 
 amount of dissociation is increased either by increasing the 
 temperature at a constant pressure, or by lowering the pressure 
 at a constant temperature. 
 
 Now consider the effect of heat on a mixture of the two 
 gases hydrogen and iodine 1 . Let a mixture of equal volumes 
 of these gases be maintained at 440, and let the pressure be 
 kept at about six atmos. ; combination occurs between the 
 gases with production of hydrogen iodide, and this proceeds 
 until (after about an hour) the system attains a state of 
 equilibrium whereat 24 per cent, of the hydrogen originally 
 present remains uncombined with iodine. Now let the 
 pressure be decreased to 2 atmos., then to I atmo., and then 
 to 380 mm., temperature remaining at 440 ; the state of equi- 
 librium is practically unchanged, the amount of uncombined 
 hydrogen varying only very slightly from 24 per cent, of the 
 amount originally present. Now let the temperature be de- 
 creased to 350, the pressure remaining constant, a new state 
 of equilibrium is attained, but more slowly than at the higher 
 temperature, and this is practically unchanged if the pressure 
 is varied from 4 atmos. to 760 mm. 
 
 But although the final state of equilibrium of a mixture of 
 equal volumes of hydrogen and iodine at 350 or 440 is 
 almost independent of pressure, yet the rate at which that 
 equilibrium is attained at these temperatures varies almost 
 directly as the pressure. 
 
 In this instance we have probably a more complex oc- 
 currence than the change of ammonium chloride into ammonia 
 and hydrogen chloride. 
 
 1 Lemoine, Ami. Cliiin. Phys. (5). 12. 145; 26. 289, especially pp. 304 344.
 
 394 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 199 Now consider a case wherein a solid is dissociated into 
 another solid and a gas. Let calcium carbonate be heated in 
 a vacuous vessel connected with an air-pump and a manometer. 
 The change which occurs may be represented thus 
 
 i -;rCaCO. 
 
 Let the temperature be kept constant ; carbon dioxide 
 accumulates until the pressure becomes constant, and the 
 system remains in equilibrium. At 860 the equilibrium- 
 pressure is 8 1 mm. and at 1000 it is 520 mm. Now let 
 pressure be diminished by removing some of the carbon 
 dioxide ; the direct change proceeds until the former pressure 
 is restored when the equilibrium again results. If the tempe- 
 rature is now decreased, carbon dioxide is absorbed, the reverse 
 change occurs, and the pressure falls until a fresh equilibrium 
 is attained. The whole process follows the same course as 
 that observed in such a case as ammonium chloride. Equi- 
 librium is conditioned by temperature and pressure and is 
 independent of the masses of the solid members of the 
 system, viz. lime and calcium carbonate. 
 
 200 Let us now consider a case wherein a solid and a gas 
 react to produce more than one compound which compounds 
 are dissociated by heat into their solid and gaseous con- 
 stituents. Silver chloride and ammonia combine to form 
 two compounds, 2AgC1.3NH 3 and AgC1.3NH 3 . If silver 
 chloride is brought into contact with ammonia in an apparatus 
 wherein temperature and pressure can be regulated, the system 
 which is formed may be composed of the gas NH 3 and any 
 or all of the three solids AgCl, 2AgC1.3NH 3 , and AgC1.3NH 8 . 
 If temperature is kept constant at about 15, ammonia is 
 absorbed with decrease of pressure and the compound 
 2AgCl . 3NH 3 is produced ; if sufficient ammonia is supplied 
 the system attains equilibrium at a constant pressure, and the 
 only components of this system are 2AgC1.3NH 3 and am- 
 monia. By raising temperature equilibrium is upset, and 
 pressure increases because of the production of more ammonia; 
 but at a definite temperature equilibrium is again attained ; 
 this equilibrium is independent of the ratio between the
 
 CH. II. 199, 200] DISSOCIATION. 395 
 
 masses of the two solid members of the system, viz. AgCl 
 and 2AgCl . 3NH 3 , and is conditioned only by the temperature 
 and the pressure. 
 
 Suppose equilibrium has been attained at say 20, and 
 that the system consists of 2AgCl. 3NH 3 and ammonia; let 
 ammonia be pumped into the vessel so that the pressure is con- 
 siderably increased; formation of the compound AgCl^NH, 
 begins, and pressure falls until equilibrium is attained in the 
 system consisting of ;r(2AgC1.3NH 3 ), y (AgC1.3NH 3 ), and 
 ^rNH 3 . If the temperature is now lowered, more ammonia 
 is absorbed, more AgC1.3NH 8 is formed, and pressure con- 
 tinues to fall until a new state of equilibrium is attained. 
 For every temperature there is a certain pressure whereat 
 equilibrium is established ; this equilibrium is independent of 
 the ratio between the masses of the solid members of the 
 system, viz. 2AgCl-3NH 3 and AgC1.3NH 3 . 
 
 In this case then two processes occur ; dissociation of the 
 compound 2AgC1.3NH 3 into silver chloride and ammonia, and 
 dissociation of the compound AgC1.3NH 3 into 2AgC1.3NH 3 
 and ammonia. The compositions of the two systems may be 
 represented as 
 
 (i) 
 (2) 
 
 In each case equilibrium is independent of the ratio of 
 x to y. At any specified temperature each system attains 
 equilibrium at a definite pressure ; the differences between the 
 equilibrium-pressures of the two systems, at the same tempe- 
 rature, are so great that it is easy to study the relations 
 between temperature and pressure on the one hand and the 
 composition of each system on the other hand. The equi- 
 librium-pressures for the two systems at temperatures varying 
 from 6 to 20 are given in the following table 1 : 
 
 1 Horstmann, Ber. 9. 749. Isambert, Comp. rend. 66. 1259; 70. 456.
 
 396 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 Temp. Equilibrium-pressure in mm. 
 
 2 AgCl. 3 NH 3 AgCl. 3 NH 3 
 
 6 22 
 
 7 23-4 
 
 8 24-9 432 
 
 9 26-5 446 
 
 10 28-2 465 
 
 12 31-9 520 
 
 16 40-9 653 
 
 18 46-6 723 
 
 20 52-6 793 
 
 201 If a solid were changed by heat into a series of other 
 solids and a gas, and if the equilibrium-pressures of the dif- 
 ferent systems thus produced were nearly the same at any 
 specified temperature, it would be impossible to disentangle 
 the various processes of dissociation occurring when such a 
 solid was heated, and to establish the connexions which 
 certainly exist between temperature and pressure and the 
 composition of the various members of the complete system. 
 
 Such a case occurs when certain hydrated salts are 
 heated. For instance copper sulphate forms a series of 
 hydrates CuSO 4 .^H 2 O; if a crystal of the ordinary hy- 
 drate CuSO 4 .5H 2 O is heated in a closed vessel of such a 
 size that the water of the crystal is more than sufficient to 
 saturate the air in the vessel, water-gas is evolved, and the 
 pressure increases ; after a time the process stops. If the 
 temperature is now allowed to fall, water is re-absorbed, and 
 the pressure decreases. But the change of pressure is irre- 
 gular and a long time must elapse before equilibrium is attained. 
 At a moderate temperature the crystal is slowly dehydrated, 
 but at the same time small quantities of water are re-absorbed 
 by parts- of the crystal which had before given off water. 
 Irregularities in the form or surface of the crystal largely affect 
 the processes of dehydration and rehydration, and cause fluc- 
 tuations in one direction or the other. As these fluctuations 
 are accompanied by changes of pressure, it is almost im- 
 possible to establish equilibrium, at a specified temperature, 
 in the system consisting of ^CuSO 4 +/CuSO 4 .5H 2
 
 CH.II.2Ol] DISSOCIATION. 397 
 
 varying quantities of other hydrates of CuSO 4 . Several pro- 
 cesses of dissociation are proceeding simultaneously, and the 
 equilibrium-pressure for any one of the dissociating systems 
 at a constant temperature is so nearly the same as that for 
 the other systems that the establishment of an equilibrium- 
 pressure for the whole system is not attained *. 
 
 If hydrated sodium phosphate, Na 2 HPO 4 . 12H 2 O, is heated 
 in a closed vessel, water-gas is given off, and the pressure 
 increases. For any temperature there is an equilibrium- 
 pressure established which is independent of the relative 
 amounts of the dehydrated salt and the various hydrates 
 present. This equilibrium-pressure is the same whether the 
 salt Na 2 HPO 4 . I2H 2 O or a less hydrated salt than this is 
 used, provided the quantity of water in the salt is more than 
 that required by the formula Na 2 HPO 4 . ;H 2 O. If the salt 
 Na 2 HPO 4 -7H 2 O is heated, a series of equilibrium-pressures 
 is obtained different from those pressures which characterise 
 the process when a salt is used with any quantity of water 
 more than that required by the formula Na 2 HPO 4 . 7H 2 O but 
 not exceeding that contained in the salt Na 2 HPO 4 . I2H 2 O. 
 The following numbers represent the results obtained by 
 Debray*. 
 
 Temp. Equilibrium-pressures 
 
 Salt with 7 to 12 HO. Salt with less than 7 H 2 O. 
 
 I2'3 7-4 mm. 4-8 mm. 
 
 16-3 8-9 6-9 
 
 207 14-1 9-4 
 
 24 -9 i8'2 12-9 
 
 3i '5 30'2 21-3 
 
 36 -4 salt melted 39-5 30-5 
 
 40 - o 50*0 41*2 
 
 This process presents an example of dissociation of a 
 solid body into solid and gaseous constituents intermediate 
 in complexity between that exhibited by CuSO 4 . 5H 2 O on the 
 one hand, and the pair of salts, 2AgC1.3NH 3 and AgC1.3NH 3 , 
 on the other hand. 
 
 1 For further details see Naumann, Ber, 7. 1537; or Ibid. Thermochctiiie, 
 1 45 6. See also Lescoeur, Compt, rend. 102. 1 466. 
 
 2 Conip. rend. 66. 195.
 
 398 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 202 The relations between volume, temperature, and pressure, 
 which accompany the merely mechanical absorption of a gas 
 by a solid are different from those which mark the formation 
 of a dissociable compound of a gas and a solid. 
 
 The absorption of ammonia by charcoal may be con- 
 trasted with the combination of ammonia with silver chloride. 
 In the latter case ammonia is absorbed at 12 when the 
 pressure is equal to about 3i'9 mm., and absorption continues 
 at this temperature and pressure until the silver chloride is 
 changed into the compound 2AgC1.3NH 3 ; the process then 
 stops, and the pressure must be raised to about 520 mm. 
 before absorption of ammonia again takes place ; the result 
 of the second process is the formation of the compound 
 AgC1.3NH 3 . Charcoal on the other hand absorbs ammonia 
 at all pressures, temperature being constant, and the quantity 
 of the gas absorbed increases regularly with increase of 
 pressure. 
 
 Palladium absorbs large quantities of hydrogen. When 
 temperature is kept constant, the volume of hydrogen ab- 
 sorbed is constant although the pressure is caused to increase 
 considerably; but after the quantity of hydrogen absorbed 
 corresponds approximately to that required on the assumption 
 that the compound Pd 2 H has been formed, the volume of 
 hydrogen then absorbed increases largely as the pressure 
 increases. In this case two processes very probably occur ; 
 the first results in the formation of the dissociable compound 
 Pd 2 H, and this follows the ordinary course of such changes ; 
 the second consists in the mechanical absorption of hydrogen 
 by the compound previously formed, and this in turn follows 
 the ordinary course of such occurrences. 
 
 These instances shew how observations of the relations 
 between temperature and pressure and the process of ab- 
 absorption of a gas by a solid, or the evolution of a gas 
 from a solid, enable conclusions to be drawn regarding the 
 formation or non-formation of a compound, or compounds, of 
 the gas with the solid. 
 
 203 Processes of dissociation lead to the production of chemical 
 systems in equilibrium. The generalisations which have been
 
 CH. II. 202, 203] DISSOCIATION. 399 
 
 made regarding chemical equilibrium hold good in cases of 
 dissociation. Let us consider a few classes of dissociation- 
 processes with the view of stating the law which expresses 
 the conditions of dissociation in each class \ 
 
 The cases presented by heterogeneous systems composed of 
 solid and gaseous constituents admit of more simple treatment 
 than those presented by homogeneous systems all the members 
 of which are gases. The simplest case is that which presents 
 itself when a solid dissociates into another solid and a gas, 
 e.g. when calcium carbonate dissociates into calcium oxide 
 and carbon dioxide. 
 
 Assuming the law of mass-action, it follows that equi- 
 librium must result when the active masses of the members 
 of the system bear a certain constant ratio to each other. 
 But the active masses of the solids are constant 2 ; therefore 
 equilibrium will be conditioned by the active mass of the 
 gas ; now the active mass of the gas varies with variations of 
 pressure and temperature ; hence equilibrium will be attained 
 at any specified temperature when the pressure exerted by 
 the gas acquires a certain fixed value, and this pressure will 
 be independent of the masses of the solids. The equation 
 of equilibrium assumes the form 
 
 cu = CMM'. and therefore - u ot 
 c 1 u l 
 
 where c and c^ are the velocity-constants of the direct and 
 reverse changes, respectively, u active mass of one solid, 
 t =active mass of the other solid, and 8 = active mass of 
 the gas. 
 
 This result is in keeping with what we have already learnt 
 regarding this class of dissociation-processes. 
 
 When a solid dissociates into equal volumes of two gases, 
 e.g. NH 4 C1 to NH 3 +HC1, the equation of equilibrium is as 
 before cu 
 
 where u = active mass of original solid, and u l and ?/ 2 represent 
 
 1 Here again I merely give a condensed outline of Ostwald's treatment of this 
 subject in his LehHnich, 2. 670701. 
 
 2 Ante, par. 170.
 
 4OO CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 the active masses of the two gases when equilibrium results ; 
 hence 
 
 cu 
 
 -=>* 
 
 tt is constant, as it represents the active mass of a solid 
 present in excess. 
 
 Hence when a solid dissociates into equal volumes of two 
 gases the product of the active masses of the gases is equal to 
 a constant when equilibrium results, and is independent of 
 the mass of the solid body. 
 
 If the space in which the dissociation proceeds is vacuous, 
 or contains an indifferent gas, then w t = ;/ 2 , and 
 
 But if the space already contains one of the gaseous 
 products of dissociation, then u l has not the same value 
 as u 2 ; the greater t the smaller is # 2 , and vice versa; hence 
 the amount of dissociation may be very much lessened 
 by increasing u^ or u z ; but it cannot be wholly stopped, 
 because to make u^ = o, u z must be made = oo . 
 
 As an example of the dissociation of a solid into two 
 gases in presence of an excess of one of these gases, may be 
 taken the results obtained by Isambert on the dissociation 
 of ammonium hydrosulphide (NH 4 HS) into ammonia and 
 sulphuretted hydrogen in presence of excess first of sulphur- 
 etted hydrogen and then of ammonia 1 . 
 
 When equilibrium results, the product of the active masses 
 of the two gases must be the same in each series of experi- 
 ments at the same temperature. Hence if p l and / a are the 
 partial pressures of the two gases when neither is in excess, 
 and p[ and /,' are the partial pressures when sulphuretted 
 hydrogen is in excess, and //' and p." are the partial 
 pressures when ammonia is in excess, the equation 
 
 AA=A'A'=A"A;', 
 
 must be realised. Isambert's results shew a fair agreement 
 
 1 Comp. rend. 92. 919 ; 94. 958.
 
 CH. II. 203, 204] DISSOCIATION. 4OI 
 
 between the values which ought to be constant 1 . Ostwald 
 indicates a source of error overlooked by Isambert. Con- 
 sidering this, and also considering the difficulties in making 
 accurate measurements of the partial pressures, the observed 
 results must be regarded as agreeing very well with the 
 calculated results. 
 
 If a solid dissociates into equal volumes of three gases, or 
 into two volumes of one gas and one volume of another gas, 
 the equation of equilibrium becomes 
 
 CU = C^UfaUi, 
 
 provided some quantity of one or other of the gaseous 
 products of dissociation is present in the space in which 
 dissociation occurs; but if the space is vacuous -or contains 
 only an indifferent gas, then 
 
 cu = Cjttf, 
 for in this case u 1 = u z u s . 
 
 Experiments on the dissociation of ammonium carbamate 
 by Naumann 2 shewed that the equilibrium-pressure is inde- 
 pendent of the mass of the solid present : 
 
 CO.ONH 4 .NH 2 ^CO 2 + 2NH S . 
 
 Horstmann's experiments, wherein excess of ammonia was 
 sometimes present and sometimes excess of carbon dioxide 3 , 
 and more particularly similar experiments by Isambert 4 , 
 have shewn that the product of the partial pressures of the 
 two gases is constant at a constant temperature. 
 
 Cases of homogeneous dissociating systems are considered 
 by Ostwald (loc. cit. 693 698), and the various forms are found 
 for the equation of equilibrium, and are applied particularly to 
 the dissociation of nitrogen tetroxide. A convenient form 
 for the equation is that in which it gives a method of cal- 
 culating the spec. grav. of a dissociating gas from observations 
 of pressure and temperature. 
 
 304 As processes of dissociation are caused by heat and are 
 attended with changes of energy to the dissociating systems, 
 
 1 For actual numbers see Ostwald, loc. cit. 685. 2 Amialen, 187. 48. 
 
 3 Ber. 4. 779. 4 Compt. rend. 93. 731 ; 97. 1212. 
 
 M. C. 26
 
 402 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 it is necessary to examine briefly the thermodynamical aspects 
 of these occurrences. It will also be incumbent on us to glance 
 at the explanation of dissociation which is afforded by the 
 molecular and atomic theory. 
 
 The general conception of a dissociable gas at a specified 
 temperature which is presented by the kinetic theory of 
 gases is that of a system of molecules the kinetic energy of 
 some of .which is different from that of the mean value of the 
 kinetic energy of the whole number, and in which system the 
 distribution of the energy of rotation of parts of molecules 
 also varies. When heat is expended upon this system the 
 energy of rotation of the parts of the molecules is increased, 
 and the kinetic energy of the molecules is also increased. 
 The result is that some of the molecules are separated into 
 parts ; as temperature rises more molecules are separated ; 
 but as the number of undissociated molecules becomes smaller 
 the chances of any molecules undergoing dissociation also 
 become smaller ; hence the velocity of dissociation increases, 
 as temperature rises, to a maximum, and then diminishes to a 
 minimum when all the molecules have been separated into 
 parts. Now suppose the temperature to be kept constant 
 at a certain point in the process of dissociation ; some mole- 
 cules are being separated into parts, and this separation is 
 accompanied by disappearance of heat ; but at the same time 
 the translatory energy of some of the portions of molecules 
 has become such that re-combination occurs, and this process 
 is attended with production of heat. If then no heat is 
 allowed to enter or leave the system, the system will settle 
 down into equilibrium when the number of molecules which 
 dissociate in unit of time is equal to the number which is 
 re-formed in the same time. 
 
 205 In par. 189 was given a brief statement of Willard Gibbs' 
 thermodynamical treatment of chemical equilibrium. 
 
 A dissociable gaseous system is one some of the con- 
 stituents of which can be produced from the other con- 
 stituents ; such a system will be in stable equilibrium when 
 its energy has attained the minimum value possible for the 
 entropy and volume of the system. An equation can be
 
 CH. II. 204206] DISSOCIATION. 403 
 
 found for such a system connecting the spec. grav. with the 
 temperature, pressure, and volume. To find whether this 
 equation holds good for actual dissociable gaseous systems, 
 notwithstanding the occurrence of chemical action, Gibbs 
 compares the spec, gravities of the gases obtained by 
 heating nitrogen tetroxide (N 2 O 4 ), formic acid, acetic acid, 
 and phosphorus pentachloride, at different pressures and 
 temperatures, with the spec, gravities calculated by means of 
 the equation deduced for an ' ideal gas-mixture with con- 
 vertible components.' The equation in question is 
 
 where Z> = spec. grav. of the gaseous mixture, Z^spec. grav. 
 of the less dense component of the mixture, t = temperature, 
 / = pressure, and A, B, and C are constants to be determined 
 experimentally for each dissociable system. The observed 
 results agree very closely with the calculated numbers in most 
 cases ; but some discrepancies are observed, especially in the 
 case of phosphorus pentachloride. 
 
 Gibbs concludes his paper with these words ; 
 
 " The constants of these equations are of course subject to correction 
 by future experiments, which must also decide the more general question, 
 in what cases, and within what limits, and with what degree of approxi- 
 mation, the actual relations can be expressed by equations of such 
 form." 
 
 106 A very brief sketch was given in par. 194 of the appli- 
 cations to chemical equilibrium of the vortex-atom theory of 
 matter by J. J. Thomson. 
 
 The mean time during which an atom is paired with 
 another of a different kind is called the paired time ; and the 
 mean time during which the vortex-ring atom vibrates alone 
 and unpaired is called the free-time. The conditions which 
 determine the ratio of paired to free time in a dissociable gas 
 will determine the amount of dissociation in that gas. The 
 theory gives a means of investigating the effect of a dis- 
 turbing influence, such as the action of heat, light, or electricity, 
 or of other vortex-rings in the neighbourhood, on two vortex- 
 
 262
 
 404 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 atoms. Whether the effect shall be to separate the atoms, 
 or to make the connexion between them stronger, depends on 
 the direction in which the vortex-rings are moving. If they 
 are moving in the same direction with different velocities the 
 effect of the disturbance will be to make them hold more 
 firmly together ; but if they are moving in opposite directions 
 with different velocities the effect of the disturbance will be 
 to separate the rings. 
 
 Thomson then considers the conditions under which the 
 ratio of paired to free time is so reduced that the gas separates 
 into its constituents. He considers cases of various degrees of 
 complexity, beginning with that of an elementary gas the 
 molecules of which are diatomic. He shews how an equation 
 is arrived at for such a gas whereby the ratio of the number 
 of free atoms to the number of molecules at any time may be 
 determined. This equation may be expressed as an equation 
 giving the vapour-density of the dissociated gas; and the 
 results calculated by it can then be compared with the ex- 
 perimentally determined results. Further, this form of the 
 equation varies according as it is assumed that the dissoci- 
 ation is produced by collisions between the molecules, or by 
 some external agency such as heat, light, or electricity. In 
 the simple case of iodine vapour " if the dissociation were due 
 to the collisions of the particles, then the paired time would 
 vary inversely as the number of collisions, and... dissociation 
 would be the same at all pressures." But the dissociation- of 
 iodine vapour is dependent on the pressure, hence the dis- 
 sociation is probably not due to collisions between the mole- 
 cules, but rather to the action of some external agency. 
 In considering the change of gaseous hydriodic acid into 
 iodine and hydrogen it is shewn that the amount of the 
 change, at a given temperature, should be much less de- 
 pendent on pressure than in the case of iodine vapour. This 
 conclusion follows whether the change is regarded as the effect 
 of collisions between the molecules, or as the effect of an 
 external agency. The experimental results obtained by 
 Lemoine 1 confirm Thomson's theoretical deduction. Other 
 
 1 See The Elements of Thermal Chemistry, par. 160.
 
 CH. II. 2O6 2O8] DISSOCIATION. 405 
 
 cases are considered in the paper referred to, and equations 
 are deduced whereby the conditions which determine the 
 ratio of paired to free time, and therefore determine the 
 amount of dissociation, may be obtained. 
 07 Dissociation-processes come under the laws which express 
 the conditions of chemical equilibrium. In a chemical de- 
 composition we have doubtless collisions occurring between 
 different kinds of molecules resulting in the shattering of 
 these molecules and the formation of molecules of other 
 kinds. The theoretically simplest case of dissociation occurs 
 when the molecules of one kind of matter are separated into 
 parts by the action of heat without the occurrence of reactions 
 between the parts of the molecules; such a separation probably 
 occurs in the dissociation of the molecule I 2 into the atoms 
 I + I. In the dissociation of molecules of the composition HI 
 into the molecules H 2 and I 2 , it is probable that two actions 
 occur, one being represented by the equation 
 
 and the other by the equation
 
 406 CHEMICAL EQUILIBRIUM. [BOOK II. 
 
 Chemical change then follows the same laws as other classes 
 of physical occurrences; the differences between chemical 
 and physical occurrences are differences of degree and not of 
 kind. 
 
 It is important to notice that although the thermody- 
 namical treatment of chemical equilibrium provides for the 
 consideration of the influence of temperature, nevertheless 
 there has not as yet been any thorough examination of the 
 effect of variations of temperature on the velocities of 
 chemical changes. 
 
 Some chemical occurrences seem to be independent of 
 temperature, while others are largely conditioned by changes 
 in this variable. Various formulse have been given for shew- 
 ing the connexion between temperature and rate of change, 
 but none is altogether satisfactory 1 . 
 
 In the earlier statement of the equation of equilibrium 
 
 the constants k and k' were called the coefficients of affinity 
 of the direct and reverse parts of the complete process ; as we 
 proceeded it was found possible to substitute the more exact 
 expression reaction-velocity for the vaguer term used at first. 
 But no attempt has yet been made to analyse these coefficients, 
 or to trace connexions between their values and the composi- 
 tion and other chemical properties of the bodies which take 
 part in the various changes. It is necessary now to proceed 
 to this part of our subject. 
 
 1 See Ostwald, Lehrbuch, 2. 728740.
 
 CHAPTER III. 
 
 CHEMICAL AFFINITY. 
 
 209 IN Chapter I. of this Book I have placed before the 
 student a sketch of the views concerning chemical affinity 
 which prevailed before the publication of Berthollet's Essai 
 de Statique Chimique; I have tried to shew the importance 
 of Berthollet's assertion that every chemical change is con- 
 ditioned not only by the affinities but also by the masses 
 of the interacting bodies ; I have passed in review the work 
 of Guldberg and Waage, which led to an accurate statement 
 of the law of mass-action, by incorporating the conception 
 of equivalency with that of mass, and by considering the 
 distribution of the members of a changing system when 
 equilibrium is established ; I have given a short account of 
 those researches by Ostwald and others, which, while con- 
 firming the ideas of Guldberg and Waage by applying them 
 to different classes of chemical changes and rinding the ex- 
 pression of the fundamental law appropriate to each class, 
 have also amplified these ideas by adding to the law of 
 mass-action the principle of the coexistence of reactions; 
 I have tried to help the student to form a conception of 
 a changing chemical system as swinging in two directions 
 until equilibrium is attained, and to regard the direct and 
 reverse changes as conditioned by the active mass and the 
 coefficient of affinity of each member of the system ; I have 
 sought to give proofs of the assertion that those reactions
 
 408 CHEMICAL AFFINITY. [BOOK II. 
 
 which seem to proceed only in one direction are really 
 limiting cases of equilibrium ; and finally I have glanced 
 at the thermodynamical and the molecular methods whereby 
 the law of mass-action and the principle of the coexistence of 
 reactions have met with a general confirmation. . 
 210 The fundamental equation of equilibrium, kpq k'p'q', 
 assumes a more workable form when written 
 
 In these equations P, Q, P ', and Q' = number of equivalents 
 of each reacting body in a system of four bodies ; p, q, /, and 
 q = active mass of each body present in the system when 
 equilibrium is established ; x = number of equivalents of P 
 and Q decomposed, and number of equivalents of P' and Q' 
 formed, when equilibrium results ; and k and k' = coefficients 
 of affinity of the direct and reverse change, respectively. 
 (v. par. 169.) 
 
 In applying this equation it is necessary to determine x 
 for some special initial values of P, Q, P', and Q', hence to 
 
 find the value of the ratio y-, to use this value in order to 
 
 calculate x for various values of P, Q, P', and Q', and to 
 compare the observed values of x with those thus calculated. 
 (For examples, v. par. 170.) 
 
 The coefficients k and k' may be regarded as represent- 
 ing the chemical forces which respectively cause the formation 
 of P and Q', and the re-formation of P and Q. But the 
 notion of chemical force is at present vague and inexact : 
 we found it better to follow van't Hoff, Guldberg and Waage, 
 and others, in regarding k and k' as the velocity-constants 
 of the direct and reverse change, respectively. As thus inter- 
 preted, the equation 
 
 establishes a quantitative connexion between the equilibrium 
 of a chemical system and the velocities of the two parts into 
 which the complete change may be divided.
 
 CH. III. 2092 1 I ] AFFINITY-COEFFICIENTS. 409 
 
 But although it is advantageous, at present, to regard -p 
 
 as the ratio of the velocity-constants of the two parts of the 
 complete change, yet we cannot be satisfied with this inter- 
 pretation. For -r represents the value of the ratio of the 
 
 affinity of the two bodies P and Q to the affinity of the bodies 
 P and Q' produced by the interaction of P and Q ; and- the 
 elucidation of chemical affinity is the ultimate object of our 
 inquiry. Let us then examine the results which have been 
 obtained by applying the equation of equilibrium. 
 
 SECTION I. 
 
 Specific affinity -coefficients of acids and bases. 
 
 Ill In par. 181 the application of the equation of equilibrium 
 to a system of four bodies was considered. The bodies A 
 and B are changed to A' and B' ; the active masses of the 
 four bodies at the beginning of the process are P, Q, P', Q', 
 respectively; x represents the number of equivalents of .A 
 and B changed to A' and B at any moment, and x represents 
 the number of equivalents of A and B' changed to A and B 
 at the same moment ; c is the velocity-constant of the direct 
 change, and c is the velocity-constant of the reverse change ; 
 then the velocity of the direct change is 
 
 (/>-*) (<2-*)*; 
 
 the velocity of the reverse change is 
 
 (P'-x-](Q-x}c; 
 and the velocity of the total change is 
 
 When equilibrium results the velocity of the total change 
 must = o ; if then = value attained by x when equilibrium 
 results, we have the conditions of equilibrium expressed in 
 terms of the velocities of the two parts of the total change by 
 the equation
 
 4IO CHEMICAL AFFINITY. [BOOK II. 
 
 If the initial conditions are made such that one equivalent 
 of A and one of B are present and A' and B' are absent, we 
 have P = Q = i, and F = Q = o ; the equation then becomes 
 
 and hence 
 
 As can be determined by experiment, the ratio of the 
 velocity-constants, -, , can be calculated. 
 
 212 This form of the equation of equilibrium has been applied 
 by Thomsen to the case of the interaction between an acid 
 and the neutral salt of another acid in dilute aqueous solution. 
 When equivalent masses of hydrochloric acid and sodium 
 sulphate interact, Thomsen found that f = f ; the same value 
 was found when nitric acid was substituted for hydrochloric ; 
 these results were on the whole confirmed by Ostwald, who 
 employed a different experimental method. (For details, v. 
 pars. 183, 184.) 
 
 By repeated experiments with a neutral salt and different 
 acids it is obvious that values can be found for in each case ; 
 and from these, values are at once deduced for the ratio of 
 
 the velocity-constants, -; . This ratio, -j . is the same as the 
 
 c ' c " 
 
 / fc \2 
 
 ratio f _ J , so that to express the ratio in question we 
 
 may employ either form, -, or ( J ; the ratio ~- -.. is 
 
 identical with that formerly expressed by the symbols j-, , and 
 
 called the ratio of the affinities of the reacting bodies. Hence 
 investigations conducted on the lines just indicated will lead 
 to measurements of the relative affinities of different acids for 
 the same base. Such investigations have been conducted by 
 Thomsen, Ostwald, and others. 
 
 Suppose that equivalent masses of Na 2 SO 4 and HC1 inter- 
 act in dilute aqueous solution ; the direct change which occurs 
 will result in production of NaCl and H 2 SO 4 , but these will
 
 CH. III. 2 1 I, 212] AFFINITY-COEFFICIENTS. 4!! 
 
 react to reproduce Na 2 SO 4 and HC1 ; if measurements of 
 are made i.e. if the number of equivalents of each body 
 present when equilibrium is attained is determined we have 
 
 values for the ratio which is the same as \/ -. or T,- 
 
 I V c K 
 
 We thus determine the ratio of the affinities of the two acids, 
 sulphuric and hydrochloric, towards the base soda. If another 
 series of measurements of f is made when equivalent masses 
 of Na 2 SO 4 and HNO 3 react in dilute aqueous solution, we 
 shall determine the ratio of the affinities of the two acids 
 sulphuric and nitric towards the base soda. We can thus 
 obtain a series of ratios k : k' , k : k", k : k"', &c. which 
 express the relative affinities of various acids towards a 
 specified base in terms of some one acid chosen as a 
 standard. 
 
 There is another way of looking at the meaning of the 
 ratio we are considering. When an acid interacts with an 
 equivalent mass of the neutral salt of another acid until equi- 
 librium is attained, the number of equivalents of the salt 
 remaining unchanged is i (giving the same meaning to 
 as before), and the number of equivalents of the salt decom- 
 posed is ; but as each equivalent of salt decomposed pro- 
 duces one equivalent of base and one of acid, f is also the 
 number of equivalents of the base which has combined with 
 the added acid, and I - expresses the number of equi- 
 valents of the base which has remained in combination with 
 
 the first acid. The ratio ,, then expresses the distribution 
 
 of the base between the acids. Thus in the case of Na 2 SO 4 
 reacting with H 2 N 2 O 6 , Thomsen found = f ; that is, f of the 
 base (Na 2 O) had entered into combination with nitric acid, 
 and ^ of the base remained combined with sulphuric acid, 
 when equilibrium was attained. Hence, if the affinity of an 
 acid is measured by the quantity of a base with which it com- 
 bines when competing for the base with another acid in dilute 
 aqueous solution, the three compounds being present in equi- 
 valent quantities, it follows that the affinity of nitric acid for 
 soda is twice that of sulphuric acid for the same base.
 
 412 CHEMICAL AFFINITY. [BOOK II. 
 
 Thomsen uses the term avidity of an acid for a base, but 
 it seems better not to introduce a new term when we have 
 already employed the word affinity to express the same con- 
 ception. 
 
 The following numbers are taken from Thomsen's Unter- 
 suchungen (i. 308) : 
 
 Relative affinity. 
 
 Nitric acid ro 
 
 Hydrochloric acid i'o 
 
 Hydrobromic acid 0*89 
 
 Sulphuric acid 0*49 
 
 Dichloracetic acid 0*36 
 
 Oxalic acid 0*24 
 
 Monochloracetic acid 0*09 
 
 Acetic acid 0*03 
 
 Take the numbers for sulphuric and monochloracetic 
 acids, '49 and '09 ; these numbers tell that when one equi- 
 valent of sulphuric acid reacts with one equivalent of sodium 
 monochloracetate in dilute solution until equilibrium is estab- 
 lished, the base divides itself between the acids in the ratio 
 
 I '40 
 49 : "09; or .. = ~ ; hence ='155; in other words, 
 
 15*5 p. c. of the total soda remains combined with the 
 monochloracetic acid and 84^5 p. c. enters into combination 
 with the sulphuric acid. 
 
 113 The thermal methods employed by Thomsen, and the 
 volumetric methods used by Ostwald, for determining the 
 distribution of a base between two acids, when the three 
 bodies react in equivalent quantities in dilute solutions, have 
 already been described (pars. 183, 184). Ostwald conducted 
 a series of experiments with the special purpose of determin- 
 ing whether the relative affinity of an acid varies with varia- 
 tions in the base 1 . The acids compared were nitric and sul- 
 phuric, hydrochloric and sulphuric, and hydrochloric and 
 nitric ; the bases were potash, soda, ammonia, magnesia, zinc 
 oxide, and cupric oxide. The following table shews the ratio 
 in which an equivalent of each base divided itself between an 
 equivalent of each acid: 
 
 1 See Lehrbuch, 2. 784; or J.ftir prakt. Cliemie, (2). 16. 385.
 
 CH. III. 212, 213] AFFINITY-COEFFICIENTS. 
 
 413 
 
 Rase. 
 
 Potash 
 
 Soda 
 
 Ammonia 
 
 Magnesia 
 
 Zinc oxide 
 
 Copper oxide 
 
 RELATIVE AFFINITIES. 
 
 H 2 N 2 6 
 H 2 SO 4 ' 
 
 ^=2-00 
 o-333 
 
 0-333 
 0-652 
 
 0-638 
 
 0-617 
 ?383 
 
 = r6i 
 
 0-409 
 
 0-97 
 
 The ratio of the affinities of hydrochloric and nitric acids 
 is evidently independent of the nature of the base, whereas in 
 the case of sulphuric and hydrochloric, or sulphuric and 
 nitric, acids, the ratio varies in accordance with the nature of 
 the base. The reason for this apparent difference is to be 
 sought for in the numbers which express the volume-changes 
 attending the action of sulphuric acid on normal sulphates. 
 Ostwald shews that when sulphuric acid and normal sulphates 
 react in equivalent quantities, only a portion of the sulphate 
 is changed into the acid salt, and that the amount of this 
 change depends on the base present in the normal sulphate. 
 Hence, Ostwald concludes, that 
 
 "sulphuric acid... does not exert affinity on a base with its whole 
 mass but only with that part which is not combined to form acid 
 sulphate. The greater this part, the greater will the affinity of sulphuric 
 acid appear to be." 
 
 It is probable that the true relative affinity of sulphuric acid, 
 like that of hydrochloric and nitric acids, is independent of 
 the nature of the base with which the acid combines. 
 
 The influence of temperature on the relative affinities of 
 the three pairs of acids is then examined by Ostwald in the 
 same way as has been employed for examining the influence 
 of the nature of the base.
 
 4H CHEMICAL AFFINITY. [ROOK II. 
 
 The results are contained in the following table. 
 
 RELATIVE AFFINITIES (for Soda). 
 Temp. 
 
 H 2 N 2 O 6 
 
 H 2 C1 2 
 
 H Cl 
 
 H 2 S0 4 ' 
 
 ' H 2 S0 4 " 
 
 IIL H^07 
 
 ^55=i-90 
 
 0*659 
 
 1^=1-02 
 
 0-345 
 
 0-341 93 
 
 1-90 
 
 0-667 
 
 - = 2'OO 
 
 0-333 
 
 0*657 
 =1-92 
 0*343 
 
 1-92 , 
 ^-=0-96 
 
 2'00 V 
 
 0-669 
 
 0-666 
 
 I<99 0-Q8 
 
 o-33i - " 
 
 o-334 '" 
 
 2-02 9 
 
 40 
 
 w JJ 1 
 
 0-703 0-703 
 
 60 -J 2-^- ->*>, 
 
 Here again the relative affinities of hydrochloric and nitric 
 acids remain constant, while that of sulphuric acid varies with 
 variations of temperature. The variation in the value of the 
 relative affinity of sulphuric acid is shewn to be inversely as 
 the amount of acid which has combined with the normal 
 sulphate; this confirms the provisional conclusion that the 
 true relative affinity of sulphuric acid is in all respects 
 comparable with the relative affinities of hydrochloric and 
 nitric acids. 
 
 The final result of these experiments is, that the relative 
 affinities of the acids are expressed by constant numbers. 
 
 In another paper 1 , Ostwald extends the volumetric method 
 to a number of acids, both monobasic and dibasic, including 
 several carbon-acids. He has also determined the refractive 
 indices of many of the solutions of acids, bases, and salts, 
 already employed, and from these he has arrived at measure- 
 ments of the amounts of change ; so that most of the data on 
 which his calculations are based have been gained by two 
 independent methods. The results agree very well ; Ostwald, 
 however, thinks that the volumetric method gives more trust- 
 worthy results than the optical method. The following table 
 presents the results of the volumetric experiments. 
 
 1 J.fiirprakt. Chemie, (2). 18. 328; Lehrbuch, 2. 785.
 
 CH. III. 2 1 3,214.] AFFINITY-COEFFICIENTS. 415 
 
 PROPORTIONS IN WHICH BASES ARE SHARED AMONG MONOBASIC 
 ACIDS. 
 
 ACIDS. Potash. Soda. Ammonia. Mean. 
 
 1 Dichloracetic : nitric 77 77 75 76 
 
 2 Dichloracetic : hydrochloric 74 75 73 74 
 
 3 Dichloracetic : trichloracetic 70,73 71,71 70,72 71 
 
 4 Dichloracetic : lactic 8 9 n g 
 
 5 Monochloracetic : trichloracetic 92 92 92 92 
 
 6 Formic : trichloracetic 97 96 97 97 
 
 7 Formic : lactic 43 46 48 46 
 
 8 Formic : acetic 25 23 23 24 
 
 9 Formic : butyric 21 21 19 20 
 
 10 Formic : isobutyric 19 19 18 19 
 
 11 Butyric : acetic 54 52 53 53 
 
 12 Isobutyric : acetic 56 51 53 53 
 
 13 Propionic : formic 78 80 79 79 
 
 14 Glycollic : formic 43 44 45 44 
 
 One equivalent of the neutral salt (of potassium, sodium, 
 or ammonium) of the acid placed first in column i reacted 
 with one equivalent of the acid placed after it in the same 
 column ; the numbers in the columns of bases represent the 
 percentage amounts of base withdrawn from the first acid by 
 the action of the second. 
 
 These results confirm the conclusion that the relative 
 affinities of the acids are expressed by constant numbers. 
 214 This question of the constancy of the numbers expressing 
 the relative affinities of acids is very important. Having 
 shewn by experiment that the question, Are these numbers 
 independent of the nature of the base? must be answered in 
 the affirmative, Ostwald 1 proceeds to examine the subject 
 somewhat as follows. 
 
 The absolute affinity of an acid A for a base B is a func- 
 tion of both ; let it be represented by f(A, B}; then by putting 
 A and A' as two acids and B and B' as two bases, the state- 
 ment that the relative affinities of the acids are independent 
 of the nature of the bases, may be put in the form, 
 
 f(A,B] 
 
 f(A',B) f(A',B'Y 
 
 Lehrbwh, 2. 787; J. filr prakt. Chemic, (2). 16. 442.
 
 416 CHEMICAL AFFINITY. [BOOK II. 
 
 And by changing the means we get 
 f(A, B) _f(A', B} 
 
 But the second equation means that the relative affinities 
 of the bases are independent of the nature of the acids. 
 Hence the affinity between an acid and a base is the product 
 of two specific affinity-coefficients, one of which belongs to the 
 acid and the other to the base. 
 
 This conclusion is of very great importance; it rests on 
 the experimental evidence already sketched, but it is also 
 confirmed by a large amount of indirect evidence. An exam- 
 ination of this evidence leads us not only to place greater 
 trust in the accuracy of the conclusion already stated, but it 
 also shews how values have been found for the affinities of 
 many acids by methods other than the thermal method 
 used by Thomsen and the volumetric method employed by 
 Ostwald. 
 
 215 When acetamide is brought into contact with water 
 and an acid, it is changed to acetic acid, and ammonia, which 
 combines with the acid. 
 
 The change may be formulated thus, 
 
 CH 3 .CO.NH 2 + H S O = CH 3 .CO.OH + NH 3 . 
 
 The rate of this change varies with the nature of the acid 
 used. 
 
 If each acid possesses a specific affinity-coefficient, we 
 might expect that the reaction under consideration would be 
 quantitatively conditioned by the value of the coefficient for 
 each acid used. 
 
 Now we have already seen that the ratio of the affinities 
 
 of two acids may be expressed in the form ^, and that 
 this ratio is equal to the square root of the ratio of the 
 velocity-constants of the reaction - - = L/- f ; hence if the 
 
 velocities of the change of acetamide to acetic acid and 
 ammonia are. measured, using different acids, we shall be able
 
 CH. III. 214 2 1 6] AFFINITY COEFFICIENTS. 417 
 
 to find the affinity-constants of the acids ; and the values 
 thus obtained may be expected to be the same as those 
 deduced for the same acids by the thermal or volumetric 
 study of the reactions which occur when these acids react 
 with bases 1 . 
 
 The course of the change was observed by decomposing 
 the ammonium salt formed by sodium hypobromite, and 
 measuring the nitrogen evolved. The reaction is not free 
 from secondary changes; the ammonium salt formed causes 
 the velocity-constant of the stronger acids to be greater, and 
 the constant for weak acids to be smaller, than would be the 
 case were the ammonium salt not formed. The time was 
 determined in each case at which one-half of the total aceta- 
 mide had been changed ; the reciprocals of these times are the 
 velocity-constants ; and the square-root of the ratio of these is 
 the ratio of the affinities of the acids. The occurrence of se- 
 condary reactions makes the numbers obtained rather doubtful ; 
 nevertheless the order of the affinities of the acids examined is 
 the same as the order of the affinities determined by the more 
 accurate volumetric method, and in the cases of the stronger 
 acids the individual numbers agree very fairly, Ostwald also 
 determined the velocity-constants when the reaction had pro- 
 ceeded for a short time only; under these conditions but little 
 ammonium salt was formed, and the secondary changes were 
 eliminated to a considerable extent. When the values thus 
 obtained are compared with those formerly arrived at, the 
 influence of the secondary reaction caused by the ammonium 
 salts is very marked, especially with the weaker acids 2 . 
 J16 When methylic or ethylic acetate in aqueous solu- 
 tion is kept at a moderate temperature the acetate is very 
 slowly changed to alcohol and acid, but if an acid is added 
 the change proceeds more rapidly ; 
 
 CH S . COOCH 3 + H 2 O = CH 3 . COOH + CH 3 . OH. 
 
 1 See Ostwald, J. fur prakt. Chetnie, (2). 28. 449; or Lehrbuch, 2. 798. It 
 has already been shewn (par. 1 76) that the reactions in question follow the law of 
 mass-action and the principle of the coexistence of reactions. 
 
 - The numbers are given in the table on p. 421. 
 
 M. C. 27
 
 41 8 CHEMICAL AFFINITY. [BOOK II. 
 
 This reaction has been used by Ostwald 1 for determining the 
 affinities of many acids ; the velocity of the change was 
 measured by titrating with a standardised baryta solution, as 
 the change proceeded the amount of acid in the liquid 
 increased. 
 
 As only a limited quantity of one body is undergoing 
 change, the velocity-constant of the reaction should be found 
 by the formula deduced for such cases from the law of mass- 
 
 T A 
 
 action 2 , viz. c = ^log-, - where A = number of equivalents 
 
 v si X 
 
 of methylic acetate originally present, and x number of 
 equivalents changed in time 6. The velocity-constants of 
 about 30 acids have been determined by Ostwald, and from 
 these the affinity-constants have been calculated in terms of 
 hydrochloric acid as unity ; the results agree very fairly well 
 with those previously obtained ; in the cases of weak acids 
 the values found by the methyl acetate method are con- 
 siderably larger than those deduced from the observations 
 with acetamide. 
 
 217 The inversion of cane-sugar by means of acids in dilute 
 solution has been used by Ostwald as a third process whereby 
 values may be found for the affinities of various acids 3 ; 
 
 The velocity of the change was determined by measuring 
 the amount of inverted sugar by means of Fehling's solution. 
 The same formula was employed as was used for calculating 
 the velocity-constants of the change of methylic acetate to 
 alcohol and acid. The results are in keeping with those 
 formerly obtained ; but as the inversion-process is more free 
 from secondary reactions than either the acetamide-process or 
 the methyl acetate process, the values found for the affinities 
 of the acids by the first-named method are to be preferred to 
 those obtained by the other methods. 
 
 1 y.fur prakt. Chemie, (2). 28. 449; or Lehrlutch, 2. 803. 
 
 2 See par. 174. 
 
 3 Lehrbuch, 2. 810.
 
 CH. III. 2 1 6 219] AFFINITY COEFFICIENTS. 419 
 
 218 Some other reactions in which acids take part have been 
 examined by Ostvvald with the view of determining whether 
 the reactions are quantitatively conditioned by the affinities of 
 the acids. 
 
 Ammonia solution reacts with bromine to form nitrogen 
 and hydrobromic acid ; if an acid is present, an ammonium 
 salt is produced and the change proceeds more slowly. 
 Ostwald 1 has shewn that the stronger acids retard this 
 change more than the weaker acids, and that the times re- 
 quired for a definite amount of the change to be accomplished 
 vary approximately inversely as the affinities of the acids. 
 
 In another memoir*, Ostwald has examined various cases 
 of oxidation and reduction occurring in presence of free acids 
 and has shewn that these are retarded to an amount propor- 
 tional to the affinities of the acids. The reactions examined 
 were, firstly, that occurring between bromic and hydriodic 
 acids, HBrO 8 Aq + 6HIAq = HBrAq + 3H 8 O + 6IAq the re- 
 tarding effects of about a dozen acids being measured and, 
 secondly, that occurring between chromic acid and iodine, 
 
 2CrO 3 Aq + 6HIAq = 2CrO 3 H 3 + 61 Aq. 
 
 The change which occurs when solid calcium oxalate reacts 
 with various acids to produce a soluble calcium salt and oxalic 
 acid has also been examined by Ostwald 3 . The amount of 
 change which has occurred when equilibrium is established 
 depends on the affinities of the acids employed*. 
 
 219 A few determinations have been made of the velocity- 
 constants of reactions brought about by bases. Warder 
 measured the velocity of the saponification of ethylic acetate 
 
 1 Zeits.fiirphysikal. Chemie,1. 124. 
 
 2 Ibid. 2. 127 ; see also Burchard, Zeils. fiir physikal. Chemie, 2. 796. 
 8 Lehrbuch, 2. 793. 
 
 4 Other processes have been employed for determining the distribution of the 
 members of a system when equilibrium results, or when a certain amount of 
 change has been accomplished; among the more important of these are the 
 colorimetric method, e.g. measurements of amount of FeCl 3 changed to Fe(SCy) 8 
 by reacting with KSCyAq (Gladstone, Phil. Mag. (4). 9. 535); and optical 
 methods, especially that founded on measurements of rotatory power (v. especially 
 Jellet, Trans. Royal Irish Acad. 25. 391). 
 
 272
 
 42O CHEMICAL AFFINITY. [BOOK II. 
 
 by soda 1 . Reicher extended the method to potash, lime, and 
 a few other bases 2 . Ostwald has applied the same process to 
 ammonia, substituted ammonias, and substituted ammoniums 3 . 
 The results can be regarded only as a starting-point for further 
 investigations. But we shall see that the electrical method of 
 observation is to be preferred to that based on the saponifica- 
 tion of ethereal salts. 
 
 220 There is then a large amount of evidence in favour 
 of the statement that many different reactions of acids 
 are quantitatively conditioned by certain coefficients which 
 depend only on the constitution of the acids, and the de- 
 gree of dilution, and are independent of the nature of the 
 chemical reaction. These coefficients, or affinity-constants, 
 can be determined by different methods. Of the methods 
 which we have considered, the most trustworthy are (i) that 
 based on the inversion of cane-sugar, (2) that wherein the 
 change of methylic acetate into alcohol and acid is measured, 
 (3) that which rests on determinations of the change of aceta- 
 mide into acetic acid and ammonia, (4) that which determines 
 the division of a base between two acids either by measuring 
 the thermal change or the volume-change which accompanies 
 the chemical change. 
 
 The following table presents the numbers deduced by 
 Ostwald for the affinities of various acids by the different 
 methods. 
 
 1 Amer. Chem. Journal, 1882. No. 5. 
 
 2 Annalen, 228. 257. 
 
 3 Lehrlmch, 2. 819.
 
 CH. III. 219, 22O] AFFINITY COEFFICIENTS. 
 
 RELATIVE AFFINITIES OF ACIDS. (OSTWALD.) 
 
 421 
 
 ACID 
 
 I 
 
 sugar 
 inversion 
 
 II 
 
 methyl 
 acetate 
 
 in 
 
 acetamide 
 
 IV 
 division of 
 base 
 between 
 two acids 
 
 Hydrochloric 
 
 100 
 
 IOO 
 
 IOO 
 
 98 
 
 Hydrobromic 
 
 I0 5'5 
 
 99'I 
 
 9 8 
 
 
 Hydriodic 
 
 
 9 8-I 
 
 
 
 
 
 Nitric 
 
 100 
 
 957 
 
 9 8 
 
 IOO 
 
 Chloric 
 
 ior8 
 
 97-2 
 
 
 
 
 Sulphuric 
 
 73-2 
 
 73 % 93 
 1 [io 4 - 5 6] 
 
 65-4 
 
 66 
 
 Methane sulphonic 
 
 
 
 100-37 
 
 
 
 
 
 Ethane sulphonic 
 
 100 
 
 99-33 
 
 
 
 
 
 Propane sulphonic 
 
 
 
 98-98 
 
 
 
 
 
 Isobutane sulphonic 
 
 
 
 98-53 
 
 
 
 . 
 
 Pentane sulphonic 
 
 
 
 97-82 
 
 
 
 
 
 Hexane sulphonic 
 
 95-4 
 
 9894 
 
 
 
 
 
 Isethionic 
 
 95 '9 
 
 98-87 
 
 
 
 
 
 Benzene sulphonic 
 
 IO2'2 
 
 99-54 
 
 
 
 
 
 Formic 
 
 12-4 
 
 11-49 
 
 5 
 
 3'9 
 
 Acetic 
 
 6-32 
 
 5-87 
 
 2 '34 
 
 1-23 
 
 Propionic 
 
 
 5-5i 
 
 
 1-04 
 
 Butyric 
 
 
 
 5'47 
 
 
 
 0-98 
 
 Isobutyric 
 
 579 
 
 5-18 
 
 
 
 0*92 
 
 Monochloracetic 
 
 22 
 
 20'8 
 
 ! 3 
 
 7 
 
 Dichloracetic 
 
 52-1 
 
 48 
 
 40-8 
 
 33 
 
 Trichloracetic 
 
 86-8 
 
 82-6 
 
 80 
 
 80 
 
 Glycollic 
 
 1 1'4 
 
 
 
 
 
 
 
 Diglycollic 
 
 16-3 
 
 
 
 
 
 
 
 Lactic 
 
 10-3 
 
 9-49 
 
 5 
 
 3'3 
 
 Methoxyacetic 
 
 13-5 
 
 
 
 
 Ethoxyacetic 
 
 117 
 
 
 
 
 
 
 
 Methoxypropionic 
 
 11-8 
 
 
 
 
 
 
 
 Hydroxyisobutyric 
 
 10-3 
 
 9-60 
 
 
 
 
 
 Trichlorolactic 
 
 
 26-3 
 
 
 
 
 
 Pyruvic 
 
 25-5 
 
 25-9 
 
 
 
 
 
 Oxalic 
 
 43 
 
 43 
 
 22-6 
 
 
 
 Malonic 
 
 17-5 
 
 16*9 
 
 
 
 
 
 Glyceric 
 
 13-1 
 
 
 
 
 
 
 
 Succinic 
 
 7-38 
 
 7-04 
 
 2'5 
 
 i "45 
 
 Malic 
 
 11 '3 
 
 10-86 
 
 4'7 
 
 2-82 
 
 Tartaric 
 
 
 15-15 
 
 7'5 
 
 5 '2 
 
 Pyrotartaric 
 
 10-3 
 
 
 
 
 Racemic 
 
 
 15-15 
 
 
 
 
 
 Citric 
 
 13-1 
 
 1279 
 
 4 
 
 
 
 Phosphoric 
 
 24-9 
 
 
 
 
 
 Arsenic 
 
 21-9 
 
 
 
 
 
 
 
 1 The affinity of sulphuric acid appears less than that of its derivatives obtained 
 by replacing hydrogen by indifferent, or even basic, radicles. But it is to be noted 
 that H 2 SO 4 is compared with SO 2 . OH . OCH 8 &c. If molecular quantities are 
 to be compared, the observed numbers for sulphuric acid reactions must be 
 doubled; if this is done the affinity of sulphuric acid is 104-56.
 
 422 CHEMICAL AFFINITY. [BOOK II. 
 
 None of these numbers can be accepted as final. Some of 
 the reactions used for finding the affinity-constants are more 
 free from secondary changes than others. It has already 
 been pointed out that the presence of normal salts tends to 
 make the stronger acids appear stronger, and the weaker 
 acids appear weaker, than they really are. This influence 
 exerted by normal salts also depends on the dilution of the 
 acids and on the temperature; the subject has been examined 
 experimentally in a series of memoirs by Spohr 1 . The ex- 
 planation which Spohr gives of the phenomena is based on 
 the molecular conception of chemical action which was shortly 
 discussed in par. 193. 
 
 221 Besides the methods described in the preceding para- 
 graphs, there is another method for determining the relative 
 affinities of acids and bases, which is more widely applicable, 
 more easily applied, and more accurate, than any. This 
 method rests on the connexion which exists between the 
 affinities of acids and the electrical conductivities of their 
 aqueous solutions. 
 
 The following numbers 2 shew the existence of a definite 
 connexion between the electrical conductivities of various 
 acids in aqueous solutions and the velocity-constants of 
 chemical reactions conditioned by the same acids ; the 
 numbers are all referred to hydrochloric acid = 100. 
 
 1 J- fur prakt. Chemie, (2). 32. 32; 33. 265; Zeitschr. fur physikal. Chemie, 
 2. 194 (especially the last paper), v. also par. 237. 
 
 2 Ostwald, Lehrbuch, 2. 823. For a description of Ostwald's methrds and 
 apparatus for measuring the conductivities of electrolytes see Zeils. fiir physikal, 
 Chemie, 2. 561.
 
 CH. III. 220,221] ELECTRICAL CONDUCTIVITIES OF ACIDS. 423 
 
 ACID. 
 
 Conductivities. 
 
 Hydrochloric 
 
 100 
 
 Hydrobromic 
 
 ion 
 
 Nitric 
 
 99-6 
 
 Ethane sulphonic 
 
 79-9 
 
 Isethionic 
 
 77-8 
 
 Benzene sulphonic 
 
 74-8 
 
 Sulphuric 
 
 65-1 
 
 Formic 
 
 1-68 
 
 Acetic 
 
 1-424 
 
 Monochloracetic 
 
 4'9 
 
 Dichloracetic 
 
 25-3 
 
 Trichloracetic 
 
 62-3 
 
 Glycollic 
 
 i-34 
 
 Methyl glycollic 
 
 176 
 
 Ethyl glycollic 
 
 1-30 
 
 Diglycollic 
 
 2-58 
 
 Propionic 
 
 0-325 
 
 Lactic 
 
 1-04 
 
 Oxypropionic 
 
 0-606 
 
 Glyceric 
 
 1-57 
 
 Pyruvic 
 
 5-60 
 
 Butyric 
 
 0-316 
 
 Isobutyric 
 
 0-311 
 
 Oxyisobutyric 
 
 1-24 
 
 Oxalic 
 
 197 
 
 Malonic 
 
 3'i 
 
 Succinic 
 
 0-581 
 
 Malic 
 
 i '34 
 
 Tartaric 
 
 2-28 
 
 Racemic 
 
 2-63 
 
 Pyrotartaric 
 
 i -08 
 
 Citric 
 
 1-66 
 
 Phosphoric 
 
 7-27 
 
 Arsenic 
 
 5-38 
 
 Velocity-constants. 
 
 Methylic acetate Inversion of 
 reaction. sugar. 
 
 100 100 
 
 98 in 
 
 92 100 
 
 98 
 
 99 
 73'9 
 
 0-345 
 
 4'3 
 23-0 
 68-2 
 
 0-304 
 o'9 
 
 6-70 
 0-3 
 0-268 
 0*92 
 17-6 
 2-87 
 
 1-18 
 2-30 
 2-30 
 
 1-63 
 
 92 
 104 
 
 i'53 
 0-4 
 4-84 
 27-1 
 
 75-4 
 1-31 
 1-82 
 i-37 
 2-67 
 
 1-07 
 0-8 
 172 
 6-49 
 
 0-335 
 i -06 
 18-6 
 3-08 
 
 1-27 
 
 1-07 
 173 
 
 6-21 
 
 4-81 
 
 The agreement between the values in the three columns 
 for these acids shews that there is a close parallelism between 
 the electrical conductivities and the affinities of the acids. 
 The three sets of values were not all determined for equal 
 dilutions of the acids used ; hence the first question to be 
 considered in inquiring more closely into the connexion
 
 424 CHEMICAL AFFINITY. [BOOK II. 
 
 between the electrical conductivities and the affinities of acids 
 is ; how are the conductivities modified by dilution ? 
 
 222 In dealing with this subject, Ostwald determines the mole- 
 cular conductivities of the acids examined. 
 
 Let that number of grams of an acid which is equal to the 
 molecular weight of the acid be dissolved in water, and let this 
 solution be placed in a vessel the parallel sides of which are 
 formed of infinite electrodes placed I centim. apart ; then the 
 electrical conductivity of this system, expressed in Ohms or 
 in mercury units, is defined to be the molecular conductivity of 
 the electrolyte. The molecular conductivity expresses the 
 quantity of electricity which is conveyed across the electro- 
 lyte in I second when the difference of potential between the 
 electrodes is I volt ; inasmuch as each ion carries the same 
 quantity of electricity with it, the quantity carried across the 
 electrolyte measures the number of molecules which suffer 
 electrolysis in the process. If p molecular conductivity, 
 and X = electrical conductivity as ordinarily defined (in 
 mercury units) then p,= io 7 X, where n = number of litres to 
 which the molecular weight of the acid taken in grams is 
 diluted 1 . 
 
 223 The molecular conductivities of solutions of acids vary 
 greatly with dilution. This statement rests on the expe- 
 riments of Arrhenius, Kohlrausch, and others. Considering 
 first, the monobasic acids, Ostwald has arrived at the law of 
 dilution for monobasic acid*. This law states that the dilu- 
 tions at which the molecular conductivities of monobasic acids 
 exhibit equal -values bear a constant relation to each other. For 
 instance the molecular conductivity of monochloracetic acid 
 at any dilution is equal to that of formic acid when the latter 
 is 16 times more dilute than the former, and is equal to that 
 of butyric acid when the latter is 256 times more dilute than 
 the monochloracetic acid. 
 
 The following table exhibits some of the data on which 
 this statement rests. Dilution is stated in litres ; it is ex- 
 pressed by means of the exponent /, which is defined by the 
 
 1 Ostwald, Lehrbuch, 2. 824. 
 
 2 Lehrbuch, 2. 825838; or Phil. Mag. Aug. 1886. 104.
 
 ON r to p p ; 
 
 ^,00 oo o? 
 
 ON ON.OO >H w M .-H qO 
 
 to O N fi 7^ yn N 
 4 tn M b i^ c< vb 
 
 CO -^- "i\O SO t>. tx 
 
 - M CO ^ u^vO t^OO 
 
 1-1 H CS CS fO -^ LO 
 
 N ro Tf un^O t>-oo OA O 
 
 .-* * P r ^P P ^ P 
 
 HI n CO rf u-v\O t^OO ON O 
 
 ^ntC'o ^-> 
 
 rj- uvo f>>OO ON O
 
 426 CHEMICAL AFFINITY. [BOOK II. 
 
 relation, dilution = 2 P . The conductivities are here expressed 
 in terms of an arbitrary unit which is 4-248 times greater 
 than the mercury unit. The measurements have been ex- 
 tended to nearly 100 monobasic acids; all -obey the law. 
 
 The conductivities of the stronger monobasic acids HC1, 
 HBr, HI, HNO S , HC1O 8 , &c. nearly reach their maxima in 
 moderately dilute solutions; hence the conductivities of these 
 acids vary but little with dilution. The conductivities of the 
 weaker monobasic acids, on the other hand, increase largely 
 as dilution increases ; the rate of this increase varies ; the 
 weaker the acid, and therefore the smaller the conductivity, 
 the greater, as a rule, is the increase for a given dilution. 
 The molecular conductivities of the stronger monobasic acids 
 reach a maximum equal to about 400 in mercury units, at a 
 moderate dilution; the conductivities of the weaker acids also 
 reach a maximum in very dilute solutions, but this maximum 
 is not quite the same for all monobasic acids 1 . This fact 
 opens a new inquiry; if there is a close parallelism between 
 the chemical reaction-velocities, and therefore the affinities, of 
 acids and the electrical conductivities of these acids, does this 
 parallelism hold between the affinities and the maximum con- 
 ductivities, or between the affinities and the conductivities at 
 varying dilutions stated with reference to the maximum values? 
 For instance : the maximum conductivities of hydrochloric, 
 hydrobromic, and hydriodic, acid are practically identical, 
 viz. 400 (in mercury units); the maximum conductivities of 
 ethane sulphonic and methane sulphonic acids are identical, 
 viz. 368 ; the maximum conductivities of isobutane sul- 
 phonic and benzene sulphonic acids are identical, viz. 356; 
 moreover the rate at which the conductivities increase as 
 dilution increases, stated in terms of the maximum conduc- 
 tivities, is practically identical in these three groups of acids. 
 Now if the reaction-velocities of all the acids in any one of 
 the groups are the same, but if this number is different from 
 the value for any other of the three groups, we must conclude 
 that the parallelism between conductivity and affinity holds 
 
 1 Ostwald, Zeitschr. fur physikal. Chemie, 1. 74 and 97.
 
 CH. III. 223, 224] ELECTRICAL CONDUCTIVITIES OF ACIDS. 427 
 
 good between maximum conductivity and affinity; on the 
 other hand if the reaction-velocities of all the acids in the 
 different groups are the same, we must conclude that the 
 parallelism holds good between affinity and the relative con- 
 ductivities at varying dilutions stated with reference to the 
 maximum conductivities. Should it appear that affinity is 
 closely connected with maximum conductivity, it will only 
 be necessary to determine the conductivity of an acid in a 
 dilute solution in order to find its affinity; but should it appear 
 that affinity and rate of increase of conductivity, relatively 
 to maximum conductivity, are closely connected, it will be 
 necessary to determine the conductivity of an acid at varying 
 dilutions until the maximum conductivity is reached, before 
 an approximate value is found for its affinity. 
 
 The following numbers shew that affinity is closely 
 connected with relative conductivity and not only with maxi- 
 mum conductivity 1 : 
 
 ^ 
 
 Reaction-velocity. 
 
 ACID. Methylic acetate. Sugar-inversion. Conductivity. 
 
 Hydrochloric 24-12 21*87 4 O1 
 
 Hydrobromic 23-7 24-38 403 
 
 Hydriodic 23-33 401 
 
 Methane sulphonic 24-30 368 
 
 Ethane sulphonic 23-80 23-44 367 
 
 Isobutane sulphonic 23-41 355 , 
 
 Benzene sulphonic 23-94 22*82 358 
 
 The acids have practically identical reaction- velocities ; the 
 rate at which their conductivities increase as dilution increases 
 is practically the same, but their maximum conductivities are 
 different. 
 
 In order to arrive at exact determinations of the affinities 
 of monobasic acids by the electrical method, it is therefore 
 necessary to measure the conductivities of these acids in 
 solutions of increasing dilution until the maximum value is 
 obtained. But it is extremely difficult to do this ; indeed the 
 maximum conductivity of a weak acid cannot be directly 
 
 1 Ostwald, Zeitschr. fur physikal. Chemie, 1. 78.
 
 428 CHEMICAL AFFINITY. [BOOK II. 
 
 determined, because at great dilutions the impurities in the 
 water affect the result more than the minute trace of acid 
 present. 
 
 Ostwald 1 has examined the conductivities of weak mono- 
 basic acids in dilute solutions. The starting-point is the 
 generalisation made by Kohlrausch 2 , to the effect that the 
 electrical conductivity of a salt of a strong monobasic acid 
 is the sum of two constants, one of which depends entirely on 
 the nature of the acid, and the other entirely on the nature 
 of the base. Ostwald's researches shew that the difference 
 between the conductivity of a strong monobasic acid and 
 that of its sodium salt is approximately a constant, and 
 that this value becomes more nearly constant as the maxi- 
 mum conductivity is more nearly approached. Hence, he 
 concludes, that the difference in question has a constant value 
 when maximum conductivity is reached. Similarly the dif- 
 ference between the conductivity of a strong monobasic acid 
 and its potassium salt is expressed by a constant, while 
 another constant expresses the difference when a lithium 
 salt is used. Further, if the conductivities of solutions of a 
 series of sodium salts of strong monobasic acids are compared 
 with those of a series of potassium salts, there is found to be 
 a constant difference ; e.g. the conductivity of the lithium salt 
 is always approximately 97 units less than that of the sodium 
 salt, and that of the potassium salt is always approximately 
 2i' i units less than that of the sodium salt. The conduc- 
 tivity of an alkali salt of a strong monobasic acid is therefore 
 the sum of two constants, one of which belongs to the acid 
 and the other to the base ; Kohlrausch's generalisation is fully 
 confirmed for the alkali salts of strong monobasic acids. The 
 constant expressing the influence of the base may be found 
 by subtracting the maximum conductivity of the strong acid 
 from that of its normal salt with the base in question. 
 > In a more recent paper 3 , Ostwald develops the application 
 
 1 Zeitschr.fur physikal. Chemie, 1. 78, and 97. 
 
 2 Wied. Ann. 6. 167. 
 
 3 Ostwald, loc. cit. 2. 840.
 
 CH.III. 224,225] ELECTRICAL CONDUCTIVITIES OF ACIDS. 429 
 
 of the law of Kohlrausch. Kohlrausch's law may be put in 
 this form ; 
 
 p = k (u + v) 
 
 where /j, = conductivity, u = velocity of transference of one 
 ion, v = velocity of transference of the other ion, and k 
 fraction of the total mass of electrolyte that is dissociated in 
 the solution undergoing electrolysis. This way of stating the 
 law rests partly upon the hypothesis which Arrhenius has 
 developed from van't Hoff's law of osmotic pressure, viz. that 
 some of the molecules of an electrolyte in solution are disso- 
 ciated into their ions, and that the greater the number of 
 dissociated molecules the greater is the conductivity of the 
 electrolyte (v. post, par. 235). Electrolytic conductivity, then, 
 seems to depend upon (i) the amount of dissociation, and (2) 
 the velocities of motion of the ions into which the molecules of 
 the electrolyte are dissociated. The conductivity of a binary 
 electrolyte at infinite dilution may be stated as p = u + v. 
 Kohlrausch 1 has shewn that the conductivities of solutions of 
 sodium chloride, potassium iodide, and similar salts, prac- 
 tically reach their limiting values at a dilution of about 5000 
 litres; knowing then the maximum conductivity of one of 
 these salts in solution, the velocity of transference of each ion 
 can be found, provided we know the ratio of the velocities of 
 the two ions (for the maximum conductivity is equal to the 
 sum of the two velocities). The ratio in question can be 
 determined from observations of the variations of concentra- 
 tion of the solution during electrolysis. In the case of potas- 
 sium chloride the mean value of the ratio - is -94; the maxi- 
 mum molecular conductivity of the salt at 25 is 140-3 
 in mercury units 2 . Hence the velocities of the ions, stated in 
 corresponding values, are 
 
 K = 67-9; = 72-4. 
 Similarly, values are obtained for the velocities of the ions 
 
 1 Wied. Ann. 26. 198. 
 
 - Kohlrausch, Pogg. Ann. 103. 35.
 
 430 CHEMICAL AFFINITY. [BOOK II. 
 
 of potassium nitrate, sodium chloride, and sodium nitrate; 
 the mean values are as follows: 
 
 As a mean value for the velocity of hydrogen as an ion, 
 Ostwald takes the number 320*5 at 25; this value may require 
 to be somewhat altered. 
 
 The foregoing treatment of the law of Kohlrausch furnishes 
 Ostwald with a means for finding the maximum conductivity 
 of a monobasic acid. Let M= maximum conductivity of the 
 acid; let /A = maximum conductivity of the sodium salt of the 
 acid; then /* = 44'5 + m, where m is the velocity of transference 
 of the negative ion, 44*5 being the velocity of the positive ion, 
 viz. sodium. Then as the positive ion of the acid is hydrogen, 
 and as the velocity of this ion is 320*5, we have 
 
 M= 320*5 + m ; and therefore M = fj, + 276. 
 
 In other words; to find the maximum conductivity of a 
 monobasic acid, in mercury units at 25, add 276 to the 
 maximum conductivity of the sodium salt of the acid. 
 
 But it must be remembered that dilution affects the con- 
 ductivities of the normal salts of weak and strong mono- 
 basic acids in the same way, e.g. dilution from 32 to 1024 
 litres raises the conductivity of the sodium salts of all mono- 
 basic acids about 10 units. This fact, established by Ostwald 1 , 
 gives a means for finding the maximum conductivity of the 
 sodium salt of a monobasic acid from the observed conduc- 
 tivity at stated dilution, without introducing a serious error. 
 It is only necessary to add a certain number to the observed 
 conductivity; the value of this number is independent of the 
 nature of the acid. The following table 2 gives the data for 
 sodium chloride: 
 
 Maximum conductivity at 25 (Kohlrausch} = 119-9. 
 
 V 
 
 M 
 
 d 
 
 a 
 
 v 
 
 M 
 
 d 
 
 a 
 
 32 
 
 1 07 '6 
 
 12-3 
 
 288-3 
 
 250 
 
 113-9 
 
 6-0 
 
 282-0 
 
 64 
 
 109-9 
 
 IOO 
 
 286-0 
 
 512 
 
 115-8 
 
 4'i 
 
 280-1 
 
 128 
 
 1 1 2X> 
 
 7-9 
 
 283-9 
 
 1024 
 
 II7-S 
 
 2-4 
 
 278-4 
 
 
 
 
 
 oo 
 
 119-9 
 
 
 
 276-0 
 
 1 Zeitschr.fiirphysikal. Chemie, 1. 97. 2 Ostwald, Ibid. 2. 843.
 
 CH. III.225, 226] ELECTRICAL CONDUCTIVITIES OF ACIDS. 43 1 
 
 In this table v = dilution in litres, JJL = conductivity in mer- 
 cury units at 25, d= difference between observed and maxi- 
 mum conductivity, and a = 276 + d y in other words a = number 
 to be added to conductivity of sodium salt at stated dilution 
 to obtain the maximum conductivity of the acid. 
 
 In using this table it is assumed that the acid is mono- 
 basic. This assumption can be tested by finding whether the 
 increase in molecular conductivity is approximately 10 units, 
 when dilution is increased from 32 to 1024 litres; if the acid 
 is //-basic, the increase will be approximately n . 10 units. 
 
 The results embodied in the preceding table may be used 
 to determine the velocity of transference of the negative ions 
 of monobasic acids. The method consists in determining the 
 conductivity of the sodium salt of the given acid for a stated 
 dilution; then adding the number required to give the maxi- 
 mum conductivity of the salt (d in the table); and finally 
 deducting 44*5 (the velocity of sodium as an ion) from the 
 result. The following table gives Ostwald's results in more 
 convenient form: v = dilution in litres, and b = numbers to be 
 deducted from molecular conductivity of sodium salt at dilu- 
 tion v, in order to get the velocity of transference of the 
 negative ion: 
 
 v b 
 
 32 32-2 
 
 64 34'5 
 
 128 36-6 
 
 v b 
 
 256 38-5 
 
 512 40-4 
 
 1024 42' i 
 
 co 44-5 
 
 226 The research, of which a condensed account is given 
 in the preceding paragraph, furnishes a method for finding 
 the maximum molecular conductivity of a monobasic acid from 
 observations of the conductivity of its sodium salt at stated 
 dilutions. The further development of the method of Ostwald 
 (loc. '/.) makes it probable that the maximum conductivity 
 of some acids may be calculated from a knowledge of their 
 composition alone. Ostwald 1 calculates the velocities of the 
 negative ions of 44 monobasic acids of very different com- 
 position; from the results so obtained he draws conclusions 
 
 1 Loc. at. 847.
 
 432 CHEMICAL AFFINITY. [BOOK II. 
 
 regarding the connexions between the composition and the 
 velocities of transference of these ions. These conclusions are: 
 
 (1) isomeric ions travel with equal, or almost equal, velocities; 
 
 (2) as the number of atoms forming the negative ions increases 
 the velocity of transference of the ions decreases; (3) the 
 substitution of one atom by another influences the velocity 
 with which the ion travels, e.g. the velocity is decreased by 
 substituting chlorine, or hydroxyl, for hydrogen, but this effect 
 is marked only in the comparatively simple ions; (4) when the 
 number of atoms forming the negative ions is more than about 
 12, the velocities of these ions seem to depend almost entirely 
 on the number, and not at all, or hardly at all, on the nature, 
 of the atoms. If the number of atoms in various negative 
 ions is taken as abscissae, and the velocity of transference as 
 ordinates, an asymptotic curve is obtained running convex to 
 the abscissae-axis, from which the velocity of ions formed of 
 more than about 12 atoms can be calculated, from the com- 
 position of these ions, to within + i to 2 units, without any 
 measurements of conductivity. Hence it becomes possible 
 to find the maximum conductivity of a monobasic acid the 
 negative ion of which is composed of not less than about 12 
 atoms, from the composition of the acid alone. 
 
 227 The relations between the electrical conductivities and 
 the dilution of polybasic acids differ from those established for 
 the monobasic acids. The polybasic acids conduct as if they 
 were first of all separated into hydrogen and a radicle con- 
 taining replaceable hydrogen, then, as dilution increases, into 
 hydrogen and a radicle containing less replaceable hydrogen, 
 and finally into hydrogen and the acidic radicle containing no 
 replaceable hydrogen 1 . In other words: a dibasic acid con- 
 ducts at first as if the ions were H and HR, but on further 
 dilution the ions become H z and R\ so the stages which can 
 be distinguished in the conduction of a solution of a tribasic 
 acid as dilution increases are three, the ions being (i) //and 
 H,R, (2) H t and HR, and (3) H 3 and R. 
 
 When polybasic acids form unstable and easily decom- 
 
 1 Ostwald, Lehrbuch, 2. 831 et set/., (or Phil, Mag. August, 1886).
 
 CH. III. 226,227] ELECTRICAL CONDUCTIVITIES OF ACIDS. 433 
 
 posed normal salts, e.g. selenious acid or phosphoric acid, the 
 molecular conductivities of these acids follow nearly the same 
 course, as dilution increases, as the monobasic acids. In the 
 following table the molecular conductivities of selenious and 
 monochloracetic acids are placed side by side ; dilution is 
 stated in litres. 
 
 Dil. H 2 SeO 3 CH 2 C1.CO 2 H Dil. H 2 SeO 3 CH 2 C1.CO 2 H 
 
 2 32-5 2T2 256 igi l6l 
 
 4 41-4 297 512 231 199 
 
 8 53-5 40-5 1024 267 236 
 
 6 70-3 54-6 2048 295 270 
 
 32 92-3 73-4 4096 312 
 
 64 120 97'4 
 
 128 154 126 
 
 The relations between the dilution and the molecular con- 
 ductivities of the polybasic acids which form stable normal 
 salts with neutral reaction are different from those just de- 
 scribed. The molecular conductivities of the stronger dibasic 
 acids of this class increase until a value is reached about the 
 same as that for the stronger monobasic acids; at about this 
 point the second replaceable hydrogen atom appears to take 
 part in the conduction, the ions are now probably H z and R 
 and conductivity increases as dilution increases, until it 
 reaches a maximum. The following numbers give the mole- 
 cular conductivities of oxalic acid, sulphuric acid, and 
 methane disulphonic acid. Dilution is stated in litres. 
 
 Dil. H 2 C 2 4 H 2 S0 4 CH 2 (S0 3 H) 2 . 
 
 2 120 394 569 
 
 4 152 410 622 
 
 8 187 428 651 
 
 1 6 224 456 674 
 
 32 261 494 694 
 
 64 293 541 7ii 
 
 128 319 592 727 
 
 256 339 640 740 
 
 512 355 68 4 75i 
 
 1024 371 7^9 756 
 
 2048 391 74i /6o 
 
 4096 420 753 757 
 
 M. C. 28
 
 434 CHEMICAL AFFINITY. [BOOK II. 
 
 Oxalic acid reaches the maximum of the strong monobasic 
 acids at about the dilution of 512 litres, sulphuric acid has 
 reached this maximum at 2 litres, while the molecular con- 
 ductivity of methane sulphonic acid, which is a very strong 
 acid, is much greater even at 2 litres than the maximum 
 value for the strong monobasic acids. Of the three acids here 
 considered, the weakest is oxalic, and the strongest is methane 
 sulphonic; the changes in the conductivity of oxalic acid as 
 dilution increases follows a course somewhat similar to that 
 noticed in the case of a fairly strong monobasic acid, say 
 dichloracetic acid, until a dilution of 512 litres or so is reached, 
 after which the second replaceable atom of hydrogen probably 
 begins to be separated and the electrolysis proceeds according 
 to the scheme H 2 + R. The molecular conductivities of 
 dichloracetic acid are given in order that they may be com- 
 pared with those of oxalic acid : 
 
 Dil. CHC1 2 .CO 2 H Dil. CHC1 2 .CO 2 H Dil. CHC1 2 .CO 2 H 
 
 2 
 
 109 
 
 32 
 
 2 S 6 
 
 512 
 
 339 
 
 4 
 
 146 
 
 6 4 
 
 286 
 
 1024 
 
 342 
 
 8 
 
 i83 
 
 128 
 
 308 
 
 2048 
 
 343 
 
 16 
 
 222 
 
 2 S 6 
 
 324 
 
 
 
 The changes in the molecular conductivity of sulphuric 
 acid as dilution increases cannot be compared strictly with 
 the changes of conductivity of a monobasic acid ; some of 
 the second replaceable hydrogen atoms are probably sepa- 
 rated even in solutions so concentrated as 4 litres, and con- 
 ductivity continues to increase until a maximum is reached 
 which is approximately double that of the stronger mono- 
 basic acids; but the influence of either replaceable atom of 
 hydrogen cannot be wholly separated from the influence of 
 the other. If the equivalent conductivities of sulphuric acid 
 obtained by dividing the molecular conductivities by two, 
 are compared with those of a monobasic acid there is still 
 a marked difference in the relations between conductivity and 
 dilution in the two cases. 
 
 Methane sulphonic acid is a decidedly stronger acid than 
 sulphuric; in this case dilution influences the equivalent con- 
 ductivity (i.e. molecular conductivity divided by two) in
 
 CH . III. 227,228] ELECTRICAL CONDUCTIVITIES OF ACIDS. 43$ 
 
 much the same way as it affects the conductivity of a strong 
 monobasic acid. The numbers for nitric acid are given, and 
 beside them are placed the equivalent conductivities of 
 methane sulphonic acid: 
 
 
 3 
 
 2 
 
 
 3 
 
 2 
 
 J-Slt* \ 
 
 
 2 
 
 2 
 
 331 
 
 285 
 
 32 
 
 367 
 
 347 
 
 512 
 
 377 
 
 376 
 
 4 
 
 342 
 
 3" 
 
 64 
 
 371 
 
 356 
 
 1024 
 
 378 
 
 378 
 
 8 
 
 352 
 
 326 
 
 128 
 
 375 
 
 364 
 
 2048 
 
 375 
 
 380 
 
 i6 
 
 36i 
 
 337 
 
 256 
 
 376 
 
 370 
 
 4096 
 
 
 
 378 
 
 The behaviour of tribasic acids resembles that of dibasic 
 acids. Phosphoric acid, for instance, resembles dichloracetic 
 acid; dilution increases the molecular conductivity from 131 
 at 2 litres, to 293 at 64 litres, and 345 at 2048 litres. The 
 maximum of a fairly strong monobasic acid is reached 
 but not surpassed; the third atom of replaceable hydrogen 
 probably takes very little part in the electrolysis. Strong 
 tribasic acids would probably reach a maximum conductivity 
 approximately equal to three times the maximum of the 
 strong monobasic acids, and the equivalent conductivities of 
 these acids would probably be very similar to the molecular 
 conductivities, which in this case are also the equivalent con- 
 ductivities, of the strong monobasic acids. But very few 
 tribasic acids have yet been examined. (See also par. 232.) 
 
 The researches of Kohlrausch and Ostwald 1 have esta- 
 blished a connexion between the molecular conductivities 
 of bases and the dilution of solutions of these bases similar to 
 that which exists between the conductivities and the dilution 
 of acids. 
 
 228 The molecular conductivities of the strong bases, soda, 
 potash, lithia, and thallia, increase as dilution increases in 
 much the same way as the conductivities of the strong mono- 
 basic acids increase ; the maxima for the bases seem to be 
 about | of those for the acids. 
 
 The following numbers 8 shew that there is a close paral- 
 
 1 See Ostwald's Lehrbuck, 2. 839 and 886. 
 3 Ostwald, Lehrbuch, 2. 839. 
 
 282
 
 436 CHEMICAL AFFINITY. [BOOK II. 
 
 lelism between the electrical conductivities and the reaction- 
 velocities of bases ; the reaction-velocities were determined by 
 observing the rate of saponification of ethylic acetate by the 
 different bases; the numbers are stated in empirical units for 
 convenience sake. 
 
 
 Saponification- 
 
 Electrical 
 
 BASE. 
 
 velocities. 
 
 conductivities. 
 
 Soda 
 
 162 
 
 161 
 
 Potash 
 
 161 
 
 149 
 
 Lithia 
 
 165 
 
 142 
 
 Thallia 
 
 158 
 
 156 
 
 Ammonia 
 
 '3 
 
 4-8 
 
 Methylamine 
 
 19 
 
 2O'2 
 
 Ethylamine 
 
 19 
 
 20-5 
 
 Propylamine 
 
 18-6 
 
 1 8'4 
 
 Isobutylamine 
 
 14-4 
 
 I5-2 
 
 Amylamine 
 
 18-5 
 
 1 8'6 
 
 Allylamine 
 
 4 
 
 6-9 
 
 Dimethylamine 
 
 22 
 
 23-5 
 
 Diethylamine 
 
 26 
 
 28-3 
 
 Trimethylamine 
 
 7'3 
 
 97 
 
 Triethylamine 
 
 22 
 
 20'2 
 
 Piperidine 
 
 27 
 
 2? 
 
 Tetra-ethylammonium 
 
 131 
 
 128 
 
 229 It has been shewn in pars. 223 and 224 that the 
 affinities of acids are closely connected with the relative 
 conductivities of these acids stated in terms of their maxi- 
 mum conductivities ; and that it is necessary to determine 
 the conductivities of acids at varying dilutions, until the 
 maximum is reached, in order to arrive at exact measure- 
 ments of the affinities of these acids by the electrical method. 
 Pars. 224 and 225 contain an account of Ostwald's method 
 for finding the relative and maximum conductivities of mono- 
 basic acids. 
 
 Let us now see how the results thus obtained are applied 
 to find the affinities of the monobasic acids. Ostwald's 
 treatment of this subject 1 is based on the extension by 
 Arrhenius to electrolytic phenomena of van't HofFs law of 
 
 1 Zeitschr. fur physikal. Chemie, 2. 270.
 
 CII.III.228,229] ELECTRICAL CONDUCTIVITIES OF ACIDS. 437 
 
 osmotic pressure (v. post pars. 235, 237). The hypothesis of 
 Arrhenius states that the molecular conductivity of an electro- 
 lyte in solution depends on the number of molecules of the 
 electrolyte which are dissociated into their ions, and on the 
 velocity of transference of these ions. The differences be- 
 tween the conductivities of different acids depend, on this 
 hypothesis, chiefly on differences in the degrees of dissocia- 
 tion of the molecules of these acids. At infinite dilution, 
 all the molecules of the electrolyte are supposed to be dis- 
 sociated into their ions. 
 
 As the hypothesis rests on the identity of the laws ex- 
 pressing gaseous dissociation and dissociation in solution, it 
 follows that deductions may be drawn from gaseous dissocia- 
 tion-phenomena and applied to dissociations in solution. Now 
 if a gaseous body is dissociated into two gases, temperature 
 being constant, the pressure of the undissociated portion, /, 
 bears a constant relation to the square of the pressure of the dis- 
 sociated portion, /,, so that , = c. At a stated temperature, 
 
 the pressure of a gas is proportional to its mass, #, and in- 
 versely proportional to the volume, v. But van't Hoff's law 
 of osmotic pressure states that the osmotic pressure of an 
 undissociated compound in solution is equal to the pressure 
 which the same mass of that substance would exert did 
 it exist as a gas occupying the same volume as is occupied 
 by the solution ; hence in the solution, this pressure, /, may 
 
 be put as proportional to - ; and therefore from the above 
 
 *U 
 
 uv 
 equation ^ = C . 
 
 Now let fji x = molecular conductivity of a binary electro- 
 lyte at infinite dilution, and let /* = molecular conductivity 
 of volume v (i.e. conductivity of v litres containing one 
 molecular weight in grams of the electrolyte) ; then (by the 
 
 hypothesis) the fraction -"- expresses the portion of the elec- 
 
 A^oo 
 
 trolyte which is dissociated in terms of the total mass of the 
 electrolyte taken as unity. Putting this fraction as
 
 438 CHEMICAL AFFINITY. [BOOK II. 
 
 and the undissociated portion of the electrolyte as u, we 
 have 
 
 Then substituting these values in the equation , = C, we 
 
 u \ 
 
 have 
 
 This equation may be put in the more convenient form 
 i m _ 
 
 where m= , i.e. the molecular conductivity at any stated 
 dilution referred to the maximum molecular conductivity. 
 
 This equation states that ^ v must have the same value 
 
 m* 
 
 for all dilutions of any one binary electrolyte. 
 
 Ostwald has proved that the value of ^- v is constant 
 
 for each of a great many monobasic acids 1 ; in these cases 
 m varied from "j to 76, and the value of C varied for different 
 acids from '129 to 15 '3. 
 
 Now the affinity of an acid is a number which quanti- 
 tatively conditions the chemical reactions of the acid, and this 
 number is nearly proportional to the electrical conductivity 
 of the acid in aqueous solution. The value of the affinity- 
 coefficient of an acid, according to the hypothesis of van't 
 Hoff and Arrhenius, depends chiefly upon the degree of dis- 
 sociation of that acid, for the greater the amount of dissocia- 
 tion into hydrogen and a negative ion the more readily will 
 these ions enter into chemical reactions; and inasmuch as 
 the amount of dissociation is independent of the nature of 
 
 1 Ostwald (loc. cit.} shews how the application of corrections for the changes 
 in molecular volumes and in viscosity which accompany the concentration of 
 solutions of binary electrolytes, brings the observed values of C yet more near to 
 absolute constancy.
 
 CH. III. 229, 230] AFFINITY AND CONSTITUTION. 439 
 
 the reactions brought about by the acid, it follows that the 
 affinity of an acid is independent of the nature of the re- 
 actions in which the acid takes part. 
 
 The constant obtained by applying the equation 
 
 i - m 
 
 v = C 
 m 
 
 to a monobasic acid, represents then the affinity of the acid 
 in question. 
 
 SECTION II. Connexions between tJie affinity -coefficients and 
 tJte constitution of acids, 
 
 230 Ostwald has shewn that the affinity-coefficients of many 
 monobasic acids are very nearly proportional to their mole- 
 cular electrical conductivities in solution stated as fractions 
 of the maximum conductivities. This statement asserts that 
 a number can be found for each acid which measures its 
 readiness to conduct electricity in solution, and also its 
 readiness to take part in chemical reactions, and that this 
 number depends only on the nature of the acid, and is in- 
 dependent of the degree of dilution. Put into the form of 
 an equation by which the number in question can be deter- 
 mined, the statement is 
 
 i m ~ 
 * v=C; 
 m* 
 
 where m = ; 
 
 Moo 
 
 fj, v being the conductivity of a solution of one molecular 
 weight in grams in v litres of water, and /i^ being the maxi- 
 mum molecular conductivity at infinite dilution. 
 
 In applying this equation to the measurement of affinities 
 of acids, Ostwald 1 prefers to put it in the following form : 
 
 ( i in) v 
 where & = -> The reason for this form is, that C has small 
 
 1 Konigl. Sachsischen Geselhchaft der Wissenschaften (rnath.-physische Classe), 
 Bd. 26 [1889]. (Also in Zeitschr.fiirphysikal. Chemie, 3. 170.)
 
 440 CHEMICAL AFFINITY. [BOOK II. 
 
 values for strong acids and large values for weak acids. To 
 avoid small fractions, Ostwald multiplies m by 100, and also k 
 by 100; he gives values for look at dilutions varying from 8 
 to 1024 litres, and finally he expresses the most probable 
 value for look as K. 
 
 231 Ostwald has determined K for more than 100 mono- 
 basic acids. The following are selections from his results for 
 various series of acids. 
 
 ACETIC ACIDS, CnH^ + ^COOH AND THEIR DERIVATIVES. 
 
 ACID. 
 
 
 K. 
 
 Formic 
 
 H.COOH 
 
 0214 
 
 Acetic 
 
 CH 3 .COOH 
 
 0018 
 
 Propionic 
 
 C 2 H 5 .COOH 
 
 00134 
 
 Butyric 
 
 C 3 H-.COOH 
 
 00149 
 
 Isobutyric 
 
 CH(CH 3 ) 2 .COOH 
 
 00144 
 
 Valeric 
 
 C 4 H 9 .COOH 
 
 00161 
 
 Caproic 
 
 C 6 H n .COOH 
 
 00145 
 
 Monochloracetic 
 
 CH 2 C1.COOH 
 
 155 
 
 Dichloracetic 
 
 CHCLj.COOH 
 
 5'H 
 
 Trichloracetic 
 
 Cdg.COOH 
 
 121* 
 
 Monobromacetic 
 
 CH 2 Br.COOH 
 
 138 
 
 Cyanacetic 
 
 CH 2 Cy.COOH 
 
 '37 
 
 Sulphocyanacetic 
 
 CH 2 SCy.COOH 
 
 265 
 
 I sosulphocyanacetic 1 
 
 C 3 H 3 2 SN 
 
 000024 
 
 Carbaminthioglycollic 2 
 
 CH 2 (SCONH 2 ).COOH 
 
 '0246 
 
 Thio-acetic 
 
 CH 3 .COSH 
 
 0469 
 
 Thioglycollic 
 
 CH 2 SH.COOH 
 
 0225 
 
 * Approximate only. 
 
 OXYACETIC ACIDS, C n H 2B OH . COOH, AND THEIR DERIVATIVES. 
 
 ACID. K. 
 
 Glycollic CH 2 OH.COOH -0152 
 
 Methoxy-acetic CH 2 (OCH 3 ). COOH -0335 
 
 Ethoxy-acetic CH 2 (OC 2 H 6 ). COOH -0234 
 
 Phenoxy-acetic CH 2 (OC 6 H 5 ). COOH -0756 
 
 0-Nitrophenoxy-acetic CH 2 (OC 6 H 4 . NO 2 ). COOH -158 
 
 P- '153 
 
 1 By action of chloracetic acid on sulphocarbamide (Volhard, J. fur prakt. 
 Chemie, 1874. 6; Claesson, Ber. 10. 1352). 
 
 2 Claesson, Ber. 10. 1350.
 
 CH. III. 230, 231] AFFINITY AND CONSTITUTION. 441 
 
 ACIDS DERIVED FROM AMIDOACETIC, CH 2 . NH 2 . COOH. 
 
 ACID. K. 
 
 Amidophenyl-acettc CH 2 (C 6 H 4 N H 2 ) . COO H -0039 
 
 Hippuric CH 2 (C 6 H 5 . NH . CO). COOH -0222 
 
 Aceturic CH 2 (NH . C,H 3 O). COOH '023 
 
 ACIDS DERIVED FROM PROPIONIC, CH 3 . CH,. COOH. 
 
 ACID. K. 
 
 Lactic CH 3 .CHOH.COOH -0138 
 
 Oxypropionic CH 2 OH . CH 2 . COOH '00311 
 
 ' Glyceric CH 2 OH . CHOH . COOH -0228 
 
 Laevulic CH 2 . C 2 H 3 O. CH 2 . COOH -00255 
 
 lodopropionic CH 2 I . CH 2 'COOH '009 
 
 Trichlorolactic CC1 3 . CHOH .COOH -465 
 
 DERIVATIVES OF HIGHER ACETIC ACIDS. 
 ACID. K. 
 
 Trichlorobutyric C 3 H 4 C1 3 .COOH io'o 
 
 Oxyisobutyric (CH 3 ) 2 . CHOH . COOH -0106 
 
 Nitrocaproic C 6 H 10 . NO,. COOH -0123 
 
 Dinitrocaproic C ft H 9 . (NO 2 ) 2 . COOH -0694 
 
 BENZOIC ACID AND ITS OXY-DERIVATIVES. 
 
 ACID. K. 
 
 Benzole C 6 H 5 .COOH '006 
 
 i : 2 Oxybenzoic C 8 H 4 OH.COOH -102 
 
 I : 3 '00867 
 
 1:4,, -00286 
 Oxysalicylic 
 
 COOH : OH : OH=i 12:3 -114 
 
 Oxysalicylic 1:2:5 * IQ 8 
 
 1:2:4 -0515 
 
 ,,1:2:6 5-0 
 Dioxybenzoic 
 
 COOH : OH : OH = i : 3 : 4 -0033 
 
 Dioxybenzoic I : 3 5 '0091 
 
 HALOGEN DERIVATIVES OF BENZOIC ACID. 
 ACID. K. 
 
 o- Chlorobenzoic C 6 H 4 C1.COOH -132 
 
 m- ' OI 55 
 
 P- -0093 
 
 0-Bromobenzoic C 6 H 4 Br.COOH '145 
 
 '- ' OI 37 
 
 w-Fluobenzoic C 6 H 4 F.COOH -0136 
 
 w-Cyanobenzoic C 8 H 4 . CN . COOH -0199
 
 442 
 
 CHEMICAL AFFINITY. 
 NlTROBENZOIC ACIDS. 
 
 [BOOK ii. 
 
 ACID. 
 
 o- Nitrobenzoic 
 m- 
 
 P- 
 
 C 6 H 4 .N0 2 .COOH 
 
 K. 
 616 
 
 0345 
 0396 
 
 AMIDOBENZOIC ACIDS AND THEIR DERIVATIVES. 
 
 The values of K for the three isomeric amidobenzoic acids 
 vary ; the acids are all very weak ; the meta acid is the 
 strongest of the three. 
 
 ACID. K. 
 
 o- Acetamidobenzoic C 6 H 4 . NHC 2 H 3 O . COOH '0236 
 m- '0085 
 
 P- 
 
 00517 
 
 ACID. 
 o- Acetoxybenzoic 
 
 DERIVATIVES OF OXYBENZOIC ACID. 
 C 6 H 4 (OC 2 H 3 0)COOH 
 
 m- 
 
 o- Methoxybenzoic 
 
 P- 
 
 K. 
 
 333 
 
 -00422 
 
 -00986 
 
 C 6 H 4 (OCH a )COOH -00815 
 
 n '00302 
 
 HOMOLOGUES OF BENZOIC ACID. 
 
 C 6 H 4 .CH 3 .COOH -012 
 
 00514 
 
 ACID. 
 0-Toluic 
 
 Phenylacetic C 6 H 5 . CH 2 . COOH -00556 
 
 UNSATURATED ACIDS. 
 
 ACID. 
 
 
 K. 
 
 Acrylic 
 
 C 2 H 3 .COOH 
 
 0056 
 
 Crotonic 
 
 C 3 H 2 .COOH 
 
 00204 
 
 Isocrotonic 
 
 J5 
 
 0036 
 
 Tiglic 
 
 C 4 H 7 .COOH 
 
 0009 
 
 Angelic 
 
 
 
 00501 
 
 Hydrosorbic 
 
 C 5 H 9 .COOH 
 
 00241 
 
 Sorbic 
 
 C 6 H r .COOH 
 
 00173 
 
 Parasorbic 
 
 C 6 H r .COOH 
 
 00173 
 
 Methylacrylic 
 
 C 5 H 9 .COOH 
 
 ooin
 
 CH. III. 23 I, 232] AFFINITY AND CONSTITUTION. 443 
 
 ClNNAMIC ACID AND DERIVATIVES. 
 
 ACID. K. 
 
 Cinnamic CH (C 6 H 5 ) . CH . COOH -00355 
 
 a- Bromo-cinnamic CH (C 6 H 5 ). CBr. COOH 1-44 
 
 0- CBr (C 6 H fi ).CH. COOH "093 
 
 Phenylpropiolic C 6 H 5 .C 2 .COOH -59 
 
 0-Nitrophenylpropiolic C 6 H 4 NO 2 . C 2 . COOH ro6 
 
 DERIVATIVES OF THE BENZENOID SULPHONIC ACIDS. 
 The benzenoid sulphonic acids are so strong that their 
 affinity-constants cannot accurately be determined by the 
 electrical method ; at moderate dilutions as much as 90 per 
 cent, of an acid of this group seems to be dissociated. When 
 the amido-group (NH 2 ) is introduced in place of hydrogen, 
 the affinity of a sulphonic acid is decreased, and measure- 
 ments can be made by the electrical method. 
 
 ACID. K. 
 
 o- Amidobenzene sulphonic C 6 H 4 . NH 2 . SO 3 H '33 
 
 m- '0185 
 
 P- -0581 
 
 Diamidobenzene sulphonic 
 
 SO 3 H : NH 2 : NH,= i = 2:3 -005 
 Bromamidobenzene sulphonic 
 
 SO 3 H : NH 2 : Br=i 12:5 1-67 
 
 Bromamidobenzene sulphonic 1:3:6 '072 
 
 Dibromamidobenzene sulphonic 1:2:4:5 7-9 
 
 1:2:3:5 very strong ; 
 
 K shews irregularities. 
 
 1:3:4:6 2-5 
 
 Toluidine sulphonic SO 3 H : NH 2 : CH 3 =i : 3 : 4 '0236 
 
 1:4=2 -0357 
 
 J It has already been mentioned (par. 227) that many 
 dibasic acids conduct as if they were separated by the 
 current into hydrogen and a negative ion HR, and on 
 further dilution into hydrogen and the negative radicle R. 
 Electrolysis probably takes place in accordance with the 
 two schemes (i) H 2 R = H + HR, (2) HR=H+R; both of 
 these occur more or less together, but until the conductivity, 
 and hence, by hypothesis, the electrolytic dissociation, reaches 
 about half its maximum value, the first scheme fairly accu- 
 rately represents the course of the electrolysis. Dissociation-
 
 444 CHEMICAL AFFINITY. [BOOK IT. 
 
 constants can be determined for dibasic acids by the method 
 already described, provided only those values of the con- 
 ductivity are used for which m is less than -5. If the con- 
 ductivities are greater than half the maximum values for 
 monobasic acids, the dissociation-constants cannot be accu- 
 rately determined ; yet even in these cases comparison of 
 the dilutions at which the relative conductivities of the 
 different acids are equal, or nearly equal, gives data for com- 
 paring the dissociation-constants of the acids; the constants 
 are inversely as the corresponding dilutions '. 
 
 Ostwald has determined the conductivities of many di- 
 basic acids, and, by using the numbers representing relative 
 conductivities at varying dilutions approximately up to that 
 dilution whereat the second phase of the electrolysis begins, 
 he has found values for K which enable the affinities of these 
 acids to be compared. 
 
 The following numbers are selected from his results. 
 
 OXALIC ACIDS AND DERIVATIVES. 
 
 The constant for oxalic acid itself could not be accurately 
 determined ; even at a dilution of 32 litres, the acid is much 
 more than half dissociated. From his observations, Ostwald 
 concludes that K for oxalic acid may be taken in round 
 numbers as about 10. 
 
 ACID. 
 
 K. 
 
 Malonic CH 2 (COOH) 2 
 
 158 
 
 Succinic C 2 H 4 (COOH) 2 
 
 00665 
 
 Glutaric C 3 H 6 (COOH) 2 
 
 00475 
 
 Adipic C 4 H 8 (COOH) 2 
 
 00371 
 
 Pimelic C 5 H 10 (COOH) 2 
 
 00359 
 
 Methylmalonic CH (CH 3 ) . (COOH) 2 
 
 087 
 
 Ethylmalonic CH (C 2 H 5 ) . (COOH) 2 
 
 127 
 
 Dimethylmalonic C (CH 3 ) 2 . (COOH) 2 
 
 077 
 
 Methylsuccinic C 2 H 3 (CH 3 ) . (COOH) 2 
 
 0086 
 
 Oxamic CONH 2 .COOH 
 
 80 
 
 Oxaluric CONH (CONH 2 ). COOH 
 
 4'5 
 
 Oxanilic CONH (C 6 H 5 ) . COOH 
 
 I '21 
 
 o- Chloroxanilic CONH (C 6 H 4 C1) . COOH 
 
 2-03 
 
 P- 
 
 1'4 
 
 Ostwald, I.e.
 
 CH. III. 232] AFFINITY AND CONSTITUTION. 445 
 
 Malic C 2 H 3 (OH).(COOH) 2 '0395 
 
 Inactive malic ,, '0399 
 
 Dextro-tartaric C 2 H 2 (OH) 2 (COOH) 2 -097 
 
 Laevo-tartaric '097 
 
 Racemic -097 
 
 BENZENE DICARBOXYLIC ACIDS. 
 ACID. K. 
 
 0-Phthalic C 6 H 4 (COOH) 2 -121 
 
 m- '0287 
 
 Oxyterephthalic C 6 H 3 (OH). (COOH) 2 -25 ' 
 Nitrophthalic C 6 H 3 (NO 2 ). (COOHU 
 COOH : NO 2 : COOH = i : 2 : 5} 
 
 I : 3 : 5 -60 
 
 ACIDS DERIVED FROM PYRIDINE 1 . 
 
 ACID. K. 
 
 Picolinic C 5 H 4 N.COOH -0003 
 
 Nicotinic C 5 H 4 N.COOH '00137 
 
 Isonicotinic -00109 
 
 Lutidinic C 6 H 3 N (COOH) 2 (a y ) -60 
 
 Cincomeronic (/Sy) '21 
 
 Isocincomeronic (a#) -43 
 
 Quinolinic (a/3) '30 
 
 Pyridine dicarboxylic ($3') "15 
 
 a- Methyl pyridine dicarboxylic C 6 H 2 . CH 3 . N (COOH) 2 '20 
 
 aa- Dimethyl pyridine dicarboxylic C 5 H (CH 3 ) 2 N (COOH) 2 -34 
 
 y- '55 
 
 The following results exhibit the influence of geometrical 
 isomerism (v. pars. 93 95, Book I.). The formulae are 
 written in accordance with the notation of Wislicenus. 
 
 ACID. K, 
 
 H\_ ^/COOH 
 Crotonic TI ^C C\ '00204 
 
 ^"3 
 
 TT -v 
 
 Isocrotonic _ u J>C C\ ^ '0036 (approximate). 
 
 L.ti 3 ^ 
 
 The values of K for isocrotonic acid vary from '0028 to 
 
 1 The positions of the carboxyl groups in the dicarboxyl derivatives of pyridine 
 are indicated by the scheme 
 
 :M:
 
 446 CHEMICAL AFFINITY. [BOOK II. 
 
 '00347 ; this is because of the impossibility of completely 
 separating the acid from admixed crotonic acid. The axially 
 symmetric isocrotonic acid is certainly stronger than the 
 plane symmetric crotonic acid. 
 
 The values of K for tiglic and angelic acids, C 6 H 8 O 2 , are ; 
 tiglic acid ='000957, angelic acid = '00501. It is therefore 
 probable that angelic acid is analogous to isocrotonic acid, 
 and has the constitution 
 
 r r 
 CH 3 ^ 
 
 while tiglic acid is probably 
 
 CH 3 \ 
 
 H/ \CH 3 
 
 In the cases of maleic and fumaric acids, C 2 H 2 (COOH) 2 , 
 the values are; maleic acid = ri 7, fumaric acid '093. In 
 maleic acid, which is about twelve times stronger than fumaric 
 acid, the carboxyl groups are probably nearer one another 
 than in fumaric acid ; the structure is indicated by the 
 formulae 
 
 ^ r _ 
 H^- COOH and COOK/- >H 
 
 (maleic) (fumaric) 
 
 If the formulae of Wislicenus for citraconic and mesaconic 
 acids are adopted, viz. 
 
 COOH . ,/-CH 3 
 
 VL^ \COOH H-^ "\COOH- 
 
 (citraconic) (mesaconic) 
 
 we should expect citraconic to be the stronger of the two 
 acids. The values obtained for K are, for citraconic '34, 
 and for mesaconic '079. The third isomeride, itaconic acid is 
 very weak; ^ = '012. The constitution of this acid is 
 probably 
 
 C CH!> C - C \COOH- 
 
 233 The results obtained by Ostwald, some of which are 
 recorded in the preceding paragraphs, enable conclusions to 
 be drawn regarding connexions between the constitutions 
 and the affinities of acids. In the acetic series, for example,
 
 CH. III. 232,233] AFFINITY AND CONSTITUTION. 447 
 
 affinity decreases from formic to propionic acid and then 
 remains nearly constant until caproic acid is reached. The 
 substitution of chlorine for hydrogen in an acetic acid is 
 attended with an increase of affinity ; the value of K is in- 
 creased to a smaller extent when bromine replaces hydrogen ; 
 on the other hand the group CN increases the affinity more 
 than chlorine does, so does the group SCN, but SCN is less 
 energetic in this way than CN. In the benzoic acids, substi- 
 tution of hydrogen by CN increases K a little more, but 
 only a little more, than is effected by putting chlorine for 
 hydrogen, the position of the CN group in one case being 
 the same as that of the Cl atom in the other case. Substitu- 
 tion of sulphur for oxygen in the group COOH in acetic 
 acid, raises K from '0018 to '0469; but if the group SH 
 is substituted for hydrogen in the same acid, K is raised 
 from -0018 to -0225 only. 
 
 The change from an acetic acid to the corresponding 
 oxyacid, i.e. the substitution of OH for H, raises the affinity, 
 but the increase is much less than when Cl is put in place 
 of H. The group OCH S is more acidic than OH. The 
 acidic character of the group OC tf H 8 is very marked. When 
 OC 6 H 4 NO 2 is substituted for H, in an acetic acid, the increase 
 of K is approximately equal to that which occurs when Cl 
 is substituted for H. On the other hand, the basic character 
 of ammonia derivatives is seen by comparing K for 
 
 CH 2 (OC 6 H 6 ) COOH [# = -0756], 
 with K for CH 2 (C 6 H 4 NH 8 ) COOH [K = -0039] : 
 
 with this decrease may be contrasted the increase due to 
 putting in the acidic group CO 
 
 [K for CH 2 (C 6 H 8 . NH . CO) COOH = -0222], 
 or the acidic group C 2 H 3 O 
 
 [K for CH 2 (NH . C 2 H 3 O) COOH = -023]. 
 
 The influence of the relative positions of the different 
 groups is apparent when we compare the affinities of pro- 
 pionic, oxypropionic, lactic, and glyceric acids ;
 
 448 CHEMICAL AFFINITY. [BOOK II. 
 
 CH 3 .CH 2 .COOH K= -00134 
 
 CH 2 OH.CH 2 .COOH ^='00311 
 
 CH 3 .CHOH.COOH ^='0138 
 
 CH 2 OH.CHOH.COOH ^='0228 
 
 The influence of relative position is well shewn in the 
 values of K for the three oxybenzoic acids; the affinity of 
 the ortho-acid is nearly twelve times greater than that of the 
 meta-acid, and the affinity of the meta-acid is about three 
 times greater than that of the para-acid. Substitution of a 
 second OH group in benzoic acid raises the affinity a little 
 if the second OH group is placed in the position next to 
 the first, but if the second OH group is placed in the position 
 next to the COOH group, the increase in the value of K 
 is very great ; 
 
 C 6 H 4 .COOH.OH 1:2 K= -102 
 
 C 6 H 3 .COOH.OH.OH 1:2:3 K= "114 
 C 6 H 3 .COOH.OH.OH 1:2:6 K=$-o 
 
 A comparison of the affinities of the isomeric chloro- 
 and bromo-benzoic acids shews the influence of the arrange- 
 ment of the substituting groups ; the nearer the acidic groups 
 are placed the greater is the affinity of the acid. Again 
 the effect of replacing H by Cl, and by NO 2 , exhibits at 
 once the more acidic character of the NO 2 group, and also 
 the influence of position : 
 
 Cl substituted for H in C 6 H 5 .COOH in the meta-position raises 
 K from '006 to '0155. 
 
 NO 2 substituted for H in C 6 H 8 .COOH in the meta-position raises 
 K from '006 to '0345. 
 
 Cl substituted for H in C 6 H 5 .COOH in the ortho-position raises 
 .AT from -006 to '132. 
 
 NO 2 substituted for H in C 6 H 6 .COOH in the ortho position raises 
 K from -006 to '616. 
 
 The effect of the character and position of the replacing 
 groups is also shewn in the change of affinity brought about 
 by passing from benzoic acid to ortho- and para-acetoxy- 
 benzoic acids, and from benzoic acid to ortho- and para- 
 methoxy-benzoic acids ; both groups raise the affinity when 
 they are placed in the ortho-position, and both lower the
 
 CH. III. 233] AFFINITY AND CONSTITUTION. 449 
 
 affinity when they are placed in the para-position; the 
 change of position in the case of the group O . C 2 H 8 O from 
 ortho to para decreases the affinity to about ^ of its value, 
 the corresponding change of position in the case of the 
 group O . CH S decreases the affinity to about ^ of its value : 
 
 O.C 2 H 3 O substituted for H in C H 5 .COOH in the ortho-position 
 raises K from -006 to '0333. 
 
 O.CH-, substituted for H in C 6 H fi .COOH in the ortho-position 
 raises K from '006 to '00815. 
 
 O . C 2 H 3 O substituted for H in C 6 H 5 . COOH in the para-position 
 lowers K from '006 to -00422. 
 
 O . CH 3 substituted for H in C 6 H 5 .COOH in the para-position 
 lowers K from '006 to '00302. 
 
 That the affinity of an acid is dependent not only on the 
 character of the radicles, but also on their relative positions, 
 is shewn in a very marked way by comparing the values of 
 K for the two bromo-cinnamic acids : 
 
 CH(C 6 H 5 ).CH.COOH K= '00355 
 CH(C 6 H 5 ).CBr.COOH ^=1-44 
 CBr(C 6 H 5 ).CH.COOH K= '093 
 
 Substitution of Br for H in one case increases the affinity 
 about 400 times, and in the other case only about 26 times. 
 
 The affinities of the pyridine dicarboxylic acids also ex- 
 hibit the influence of position ; what one may perhaps call 
 the strongest position for the COOH group is that nearest 
 the nitrogen atom, and the position para to the nitrogen atom 
 is stronger than that which is meta to the nitrogen atom. 
 
 These results, regarded as a whole, point to a close con- 
 nexion between the affinities of acids and the space-arrange- 
 ments of the atoms which form the molecules of the acids. 
 This is confirmed by the measurements of the affinities of 
 crotonic and isocrotonic, maleic and fumaric, and citraconic, 
 mesaconic, and itaconic, acids 1 . 
 
 1 For further data, and discussion of the data, Oswald's memoir must be 
 consulted. 
 
 M. C. 29
 
 45 CHEMICAL CHANGE. [BOOK II. 
 
 SECTION III. Chemical change. 
 
 234 In considering Guldberg and Waage's general equation of 
 equilibrium 
 
 the quantities k and ^'were treated as the 'coefficients of affinity' 
 of the direct and reverse changes, respectively; in a later con- 
 sideration of the subject k and k' were regarded as represent- 
 ing the velocity-coefficients of the two parts of the complete 
 change. In pars. 214 220 it is shewn that to each acid may 
 be assigned a certain number which is the affinity-coefficient 
 of that acid, and that the value of this coefficient quantita- 
 tively conditions the different reactions in which the acid takes 
 part. Pars. 221 229 are devoted to a sketch of the electrical 
 methods whereby values are obtained for the affinities of the 
 acids. The explanation of these electrical methods rests on 
 a development of the molecular dissociation-hypothesis of 
 Williamson which was first applied to electrolysis by Clausius 
 (v. par. 192). 
 
 The further development of the Clausian hypothesis is due 
 in great measure to the labours of van't Hoff, Arrhenius, and 
 Ostwald. An account has been given in the preceding sections 
 of this chapter of the results of some of Ostwald's work in this 
 direction, and reference has been made, from time to time, to 
 the 'law of osmotic pressure' as stated by van't Hoff. It now 
 remains to glance at the investigations whereby this law has 
 been gained and at the extensions of the law to explain the 
 phenomena of chemical change occurring among substances 
 in solution. As the subject is not yet fully elucidated, and 
 as the principles involved are rather physical than chemical, 
 although the chemical applications are of paramount import- 
 ance, a brief account of the fundamental researches will suffice. 
 235 In 1887 van't Hoff published an important memoir 1 , in 
 which he sought to establish similarities, and, under certain 
 conditions, identities, between substances in dilute solution 
 and in the gaseous state. If an aqueous solution of a sub- 
 
 1 Zeitschr. fur physikal. Chemie, 1. 481 (Translation in Phil. Mag., August, 
 1888).
 
 CH. III. 234,235] OSMOTIC PRESSURE. 451 
 
 stance is contained in a vessel the walls of which are perme- 
 able by water molecules but not by the molecules of the 
 dissolved substance, and the vessel is immersed in water, 
 water will enter the vessel, and the pressure on the walls will 
 increase until equilibrium results, after which no more water 
 will enter. The pressure on the walls of the vessel is called 
 osmotic pressure. If the vessel had been furnished with a 
 movable piston, the same condition of equilibrium might have 
 been obtained, without the entry of water, by compressing the 
 solution with a pressure equal to the osmotic pressure. With 
 such an arrangement the concentration of the liquid could 
 be altered by increasing or decreasing pressure by means of 
 the piston ; as the process would be reversible, the second 
 law of thermodynamics may be applied. 
 
 Experiments on osmotic pressure have been conducted by 
 de Vries 1 , Pfeffer 2 , and others; the results shew that the 
 osmotic pressures of dilute solutions are proportional to the 
 concentrations of the solutions. Now the statement that the 
 alteration of concentration of a dilute solution is proportional 
 to the pressure exerted by the solution, is equivalent to saying 
 that Boyle's law holds good for dilute solutions. Moreover 
 the proportionality of concentration to osmotic pressure may 
 be theoretically deduced. If we assume, as seems justifiable, 
 that osmotic pressure is due to the impact of the molecules of 
 the dissolved substance, then the number of impacts in unit 
 time must be proportional to the number of molecules in unit 
 volume. But this is the molecular conception of the pressure 
 of a gas ; and as in gases volume is inversely as pressure, the 
 same proportionality should hold good in dilute solutions, in 
 other words, Boyle's law should apply to these solutions. 
 
 van't Hofif then proceeds to deduce, by thermodyna-mical 
 reasoning, that osmotic pressure is proportional to absolute 
 temperature, provided concentration remains constant; this 
 conclusion is equivalent to the law of Charles for gases, inas- 
 much as concentration in one case corresponds with volume 
 in the other. 
 
 1 See especially Zeitschr. fitr physikcd. Chemie, 2. 415. 
 8 Osmotische (Jntersiichungen [Leipzig, 1887]. 
 
 2 9 2
 
 45 2 CHEMICAL CHANGE. [BOOK II. 
 
 The experimental results obtained by Pfeffer, and also 
 by Soret l , are, on the whole, in keeping with the statement 
 that the laws of Boyle and Charles hold good in dilute solu- 
 tions. 
 
 Further thermodynamical reasoning applied to isotonic 
 solutions, i. e. solutions exerting equal osmotic pressures, 
 leads to the conclusion that the osmotic pressure of a stated 
 mass of a gasifiable substance in dilute solution is equal 
 to the pressure exerted by the same mass of the same sub- 
 stance existing as a gas at the same temperature. If then 
 osmotic pressure may be substituted for gaseous pressure, 
 Avogadro's law may be extended to substances in dilute solu- 
 tion. This extension of Avogadro's law is thus stated by 
 van't Hoff, " Equal volumes of different solutions, at the same 
 temperature and osmotic pressure, contain equal numbers of 
 molecules, which numbers are the same as would be contained 
 in equal volumes of gases at the same temperature and pres- 
 sure? 
 
 This is van't Hoffs law of osmotic pressure. 
 
 The first experimental proof of the accuracy of this law is 
 obtained from the results of Pfeffer's experiments on the 
 osmotic pressure of sugar solutions at different temperatures, 
 ,by comparing these with the pressures exerted at the same 
 temperatures by a volume of hydrogen containing the same 
 number of molecules as the sugar-solution. The second proof 
 of the accuracy of the law is obtained by proving thermo- 
 dynamically that the vapour-pressures of solutions containing 
 equal numbers of molecules of different substances are equal ; 
 but this statement has already been established experi- 
 mentally by Raoult (Compt. rend. 44. 1431; 87. 167). The 
 third proof of the accuracy of the law also rests on thermo- 
 dynamical reasoning ; van't Hoff shews that solutions in the 
 same solvent having the same freezing point are isotonic, 
 i.e. exert equal osmotic pressures, at their freezing points ; 
 and from this he deduces the conclusion that solutions which 
 contain equal numbers of molecules in equal volumes, and 
 
 Ann. Chim. Phys. (5) 22. -293.
 
 CH. III. 235] OSMOTIC PRESSURE. 453 
 
 which are therefore isotonic by the law of osmotic pressure, 
 have the same freezing point. But this statement is identical 
 with Raoult's law of molecular lowering of freezing point 
 which was gained by laborious experimental investigation 
 (v. Book I. par. 35). This third proof of the law furnishes a 
 convenient method for finding osmotic pressures from deter- 
 minations of the lowering of freezing points of dilute solutions. 
 
 But there are many exceptions to Raoult's law of mole- 
 cular lowering of freezing point. These exceptions are ex- 
 plained, if we assume, with Arrhenius, that compounds whose 
 behaviour is not expressed by this law are partially disso- 
 ciated in solution. Here again there is a marked analogy 
 between gases and dilute solutions ; as the pressure of ammo- 
 nium chloride vapour is greater than that calculated by 
 applying Avogadro's law on the assumption that the vapour 
 consists of molecules of NH 4 C1, but as the observed pressure 
 agrees with the calculated pressure when it is assumed that 
 the vapour consists of equal numbers of molecules of NH 8 
 and HC1, so the apparently abnormal osmotic pressures of 
 many solutions may be reconciled with the law of osmotic 
 pressure by assuming that the compounds in these solutions 
 are more or less dissociated into simpler molecules. 
 
 The osmotic pressures of certain solutions agree with 
 those calculated by van't Hoff s law from observations of the 
 lowering of the freezing points of the solutions ; these solu- 
 tions are generally, if not always, non-electrolytes. The 
 exceptions to the law of van't Hoff occur chiefly, if not 
 wholly, among electrolytes. The hypothesis of Arrhenius 
 (par. 237) regards such electrolytes as more or less dissociated 
 into their ions when they are dissolved in water. 
 
 Dealing with exceptions to the law of osmotic pressures, 
 van't Hoff calculates the ratio of the observed pressures to 
 the pressures which would be exerted did the law fully express 
 the behaviour of the compounds in question. This ratio he 
 designates by the symbol i\ values are obtained for i from 
 Raoult's freezing-point determinations 1 . The law of mass- 
 
 1 For more recent and more trustworthy determinations of i for 40 compounds 
 v. Raoult, Zeitschr.fur physikul. Chcmie, 2. 488; and Arrhenius, ibid. 2. 491.
 
 454 CHEMICAL CHANGE. [BOOK II. 
 
 action of Guldberg and Waage is then considered by van't 
 Hoff, formulae being used in which the ratio i occurs ; the 
 results agree very fairly with the calculated numbers. 
 
 The law of osmotic pressure has been placed on a fairly 
 firm basis by van't Hoff, who has also shewn that the hypo- 
 thesis that many compounds, and especially electrolytes, are 
 partially dissociated in dilute solutions, serves to explain many 
 if not all the apparent exceptions to the law. 
 
 236 Planck, in memoirs 1 published independently of van't Hoff, 
 by purely thermodynamical reasoning, arrived at the con- 
 clusion that, in the case of compounds which do not obey 
 Raoult's law of lowering of freezing point, van't Hoff's co- 
 efficient i expresses the ratio of the number of molecules 
 actually present in solution to the number which would 
 have been present had no dissociation occurred. In other 
 words, Planck concludes that the observed phenomena re- 
 garding the freezing points of dilute solutions can be brought 
 into accordance with thermodynamical laws only by assuming 
 that, in many cases, dissociation of the molecules of the dis- 
 solved body has occurred, and that the ratio of the observed to 
 the calculated osmotic pressure of substances which do not 
 obey the law of freezing points is also the ratio of the number 
 of molecules actually present to the total number which would 
 have been present if dissociation had not occurred. 
 237 Arrhenius 2 has developed the Clausian hypothesis of elec- 
 trolytic dissociation, and in doing this he has made use of 
 van't Hoff's law of osmotic pressure. 
 
 Arrhenius applies the term 'active' to the molecules of 
 an electrolyte which are supposed to be dissociated in solu- 
 tion; the undissociated molecules he calls 'inactive'. The 
 ratio between the number of active molecules and the sum of 
 all the molecules, whether active or inactive, is called by 
 Arrhenius the 'activity-coefficient' of the solution (this is the 
 same as the 'dissociation-ratio' of Lodge 3 ), and is represented 
 by the symbol a. At infinite dilution all the molecules of an 
 
 1 Wied. Ann. 32. 462; 34. 139; Zeitschr. fiir physikal. Ckemie, 1. 577. 
 
 2 Especially Zeitschr. fur physikal. Chemie, 1. 631; 2. 284, 491. 
 
 3 Brit. Ass. Reports, 1886. 756.
 
 CH. III. 235 2 37] ELECTROLYTIC DISSOCIATION. 455 
 
 electrolyte are supposed to be active, and therefore the 
 activity-coefficient is equal to unity; in less dilute solutions, 
 but still so dilute that the effects of internal friction, &c. may 
 be overlooked, the activity-coefficient may be taken as the 
 ratio between the observed molecular conductivity and the 
 limiting value at infinite dilution. (For Ostwald's method of 
 rinding this ratio v. ante, pars. 225, 226.) The value of van't 
 Hoff's coefficient i can be calculated if a is known 1 . Putting 
 m as the number of inactive molecules, ri as the number of 
 active molecules, and k as the number of ions into which each 
 active molecule is separable (e.g. KC1 is separable into 2 ions, 
 K + Cl, and K a SO 4 into 3 ions, K + K + SOJ, we have 
 
 . _ m + k.n t 
 m + n ' 
 
 n 
 but a = - ; 
 
 m + n 
 
 hence i = i + (k i) a. 
 
 Arrhenius then calculates i from observations of a for a great 
 many compounds ; he also calculates i for the same bodies 
 from determinations of the lowering of the freezing points of 
 solutions of these bodies 2 . The two series of values for i agree 
 very well on the whole. For non-conducting liquids such as 
 methylic alcohol, ethylic acetate, &c., i is approximately 
 equal to unity ; for bases, acids, and salts, i varies from i to 
 about 2-5. 
 
 We have already seen (pars. 225, 226) that Ostwald's 
 measurements of the molecular conductivities of monobasic 
 acids have led to results in keeping with those deduced from 
 the hypothesis of electrolytic dissociation. In two memoirs 8 , 
 Arrhenius uses the same hypothesis to explain the conduc- 
 tivities of solutions of mixtures of different electrolytes ; the 
 
 1 See also van't Hoff and Reicher, Zeitschr.fiir physikal. Chemie, 3. 198. 
 
 2 Let lowering of freezing point of water produced by dissolving i gram- 
 molecule of given body in i litre water = /; then i = -^ ; v. van't Hoff, Phil. 
 
 Mag., August, 1888, p. 100. 
 
 3 Zeitschr. fur physikal. Chemie, 1. 631 ; 2. 284.
 
 456 CHEMICAL CHANGE. [BOOK II. 
 
 results obtained agree very closely with the calculated re- 
 sults. To follow the reasoning here would lead us too far 
 afield. One point however must be noted ; Arrhenius shews 
 that the hypothesis enables the retarding influence of am- 
 monium salts on the saponification of ethylic acetate by 
 ammonia to be quantitatively determined, and that the 
 numbers theoretically calculated agree well with those 
 actually observed. Arrhenius also extends the hypothesis to 
 the case of any number of electrolytes in solution together ; 
 the equation arrived at 1 expresses the conditions of chemical 
 equilibrium for a mixture of electrolytes, and the quantitative 
 applications of this equation give good results. 
 
 The work of van't Hoff and Arrhenius establishes a large 
 probability in favour of the statement that the properties of 
 dilute solutions can be deduced from two principles, viz. the 
 principle of the close analogy, and in some respects even the 
 agreement, between the gaseous state and the state of dilute 
 solution, and the principle of electrolytic dissociation 2 . 
 238 Arrhenius 3 points out that many physico-chemical proper- 
 ties of salts in solution can be represented as approximately 
 the sums of the properties of parts of the solution ; such pro- 
 perties are the heats of neutralisation of acids by bases in 
 dilute solution, the specific volumes and specific gravities, the 
 specific refractive powers, and the conductivities, of dilute 
 solutions of salts. The fact that such properties as these 
 are additive, as distinguished from cumulative properties, is 
 entirely in keeping with the hypothesis of electrolytic disso- 
 ciation, inasmuch as this hypothesis regards a dilute solution 
 of an electrolyte as composed, for the most part, of the ions of 
 the electrolyte, each ion having its own characteristic properties 
 which are generally independent of the properties of the other 
 
 1 Zeilschr. fur physikal. Chemie,Z. 294. 
 
 2 The agreements between the observed and calculated numbers do not, of 
 course, finally establish the accuracy of these two principles. 
 
 The law of van't Hoff gives a means for determining the molecular weights 
 of. salts in solution ; but the work of Arrhenius points to the existence in many 
 salt solutions of molecules of different degrees of complexity, and suggests that in 
 many cases we cannot speak (A the molecular formula of a salt in solution. 
 
 3 Ibid. 1. 6 4 o.
 
 CH. III. 237 239] ELECTROLYTIC DISSOCIATION. 457 
 
 ion. The solutions of salts which have been used for measure- 
 ments of specific gravity, refractive power, lowering of freezing 
 points, &c., have not, as a rule, been so dilute as to ensure 
 complete dissociation of the dissolved bodies ; hence the pro- 
 perties mentioned appear as approximately the sums of certain 
 constants, each of which belongs to one part of the solution. 
 When we deal with fairly dilute solutions of the salts of strong 
 acids with strong bases, or with dilute solutions of the strong 
 acids and bases themselves, no large errors are introduced by 
 generally assuming that such properties as those named are 
 the sums of the properties of the ions. The weak acids and 
 bases, and several salts e.g. ammonia and the amines, phos- 
 phoric, boric, hydrocyanic, and sulphhydric, acids, and many 
 salts of mercury, cadmium, and zinc do not appear to be 
 largely dissociated in solution ; the properties of such com- 
 pounds in solution are not so distinctly additive as are the 
 properties of the strong acids and bases and the salts formed 
 by the interactions of these. It is then necessary to distin- 
 guish between different classes of compounds ; some are 
 almost wholly dissociated in dilute solutions into their ions, 
 others are partially dissociated, and others are dissociated only 
 to a small extent 1 . 
 
 239 In par. 229 was given a short account of Ostwald's applica- 
 tion of the law of osmotic pressure, and the hypothesis of 
 electrolytic dissociation, to find the affinities of monobasic 
 acids. The equation given by Ostwald 
 
 ought to express completely the electrical conductivity of 
 binary electrolytes, if the hypothesis of electrolytic disso- 
 ciation is well founded. Ostwald 2 notes six generalisations 
 regarding aqueous solutions of binary electrolytes which have 
 been established empirically. These are : 
 
 1 The degree of dissociation is determined from measurements of the coeffi- 
 cients i and a : v. pars. 235, 237. 
 
 2 Zeitschr, fiir physikal. CAewie, 2. 275.
 
 45^ CHEMICAL CHANGE. [BOOK II. 
 
 1. The molecular conductivities of solutions of electrolytes 
 increase with increasing dilution, and asymptotically approach 
 maximum values. 
 
 2. The maximum values for equivalent quantities of 
 acids, bases, and salts, are of the same order but they are not 
 identical. 
 
 3. The maxima may be expressed as sums of two quan- 
 tities, one of which depends only on the positive ion, and the 
 other only on the negative ion. 
 
 4. The last statement does not hold good for somewhat 
 concentrated solutions, nor for solutions of weak acids or 
 bases. 
 
 5. The molecular conductivities of bad conductors, such 
 as weak acids and bases, increase rapidly as dilution increases; 
 the conductivities of monobasic acids and mono-acid bases are 
 proportional to the square root of the dilution. 
 
 6. Increase of molecular conductivity follows the same 
 course in solutions of all monobasic acids and mono-acid 
 bases ; the dilutions at which the conductivities of these acids 
 and bases are equal fractions of their maximum conductivities 
 bear a constant proportion to one another. 
 
 Ostwald then proceeds to shew that the equation already 
 given contains these six generalisations. The equation is 
 
 1*9 
 
 where /^= molecular conductivity for volume v, //,, = maximum 
 conductivity for infinite dilution, v = volume of solution. 
 i. If v increases without limit, the expression 
 
 must approach zero. As both p v and //, have finite values, 
 /itoo /JL V must become smaller, i.e. /^will increase continuously 
 until it reaches the limiting value fj, x . 
 
 2 and 3. As //,*, expresses the molecular conductivity of 
 the completely dissociated electrolyte, and as the ions move 
 in this solution independently of one another, the value of //.^
 
 CH. III. 239] ELECTROLYTIC DISSOCIATION. 459 
 
 can be regarded as the sum of two quantities, which are 
 measured by the velocities of the ions, quite apart from the 
 nature of the compound which was formed by the union of 
 these ions. If compounds are compared which have one 
 common ion, and the other ions of which do not shew great 
 differences in their velocities of transference, then the sums 
 of the two velocities must be of the same order of magni- 
 tude. 
 
 4. The conductivities of fairly concentrated solutions are 
 conditioned by the degree of dissociation of the solutions, and 
 as this varies in different solutions, especially in weak acids 
 and bases, the conductivities of these solutions cannot be 
 expressed as the sums of two quantities one of which depends 
 only on each ion. Salts, however, of similar composition are 
 nearly equally dissociated in solutions of equal dilution ; the 
 molecular conductivities of such salts are equal fractions of 
 their maximum values, and they can be expressed as the sums 
 of two quantities which are the velocities of the ions multiplied 
 into the degree of dissociation. 
 
 5. In the cases of weak acids and bases /* is small com- 
 pared with /ia,, and p x p v is nearly constant, and the equa- 
 tion gives nJ v const. In other words, when conductivity is 
 small, it increases proportionately to the square root of the 
 dilution. 
 
 6. In the equation, the constant c depends on the nature 
 of the electrolyte ; if the dilutions at which the relative con- 
 ductivities of various electrolytes are equal are put as v t v a ... 
 then the values of 
 
 /*. 
 
 are equal, and v l : v^\ v a . . . = c t : c a : C 3 . . . ; 
 
 i.e. the dilution at which the conductivities of different electro- 
 lytes are equal bear a constant relation to one another, and 
 this relation depends only on the nature of the electrolytes. 
 
 In these six points then, there is complete agreement 
 between the empirically determined data and the deductions 
 from the equation which expresses the conductivity of binary 
 electrolytes. But this equation is itself deduced from the
 
 460 CHEMICAL CHANGE. [BOOK II. 
 
 principles of electrolytic dissociation and of agreement be- 
 tween the gaseous state and the state of bodies in dilute 
 solution. We have already seen (par. 229) how Ostwald has 
 modified the equation expressing the behaviour of binary 
 electrolytes so as to obtain measurements of the constant 
 which is dependent on the nature of the electrolyte. In the 
 case of acids, this constant expresses the affinity of the elec- 
 trolyte ; the agreement between the affinities of acids thus 
 determined and the affinities determined by other physical 
 and chemical methods, is a further proof of the trust- 
 worthiness of the principles on which the electrical method 
 is based. 
 
 240 The hypothesis of the dissociation of electrolytes in solu- 
 tion is connected with van't Hoff's extension to solutions of 
 the law of Avogadro, in much the same way as the hypothesis 
 of gaseous dissociation is connected with Avogadro's law in 
 its original form. Planck's thermodynamical investigations 
 give independent support to the hypothesis. The hypothesis 
 gives a fairly complete account of the conductivities not only 
 of electrolytes in solution, but also of mixtures of electrolytes. 
 The results of determinations of the molecular lowering of the 
 freezing points of solutions strikingly confirm the hypothesis, 
 and afford a convenient method for determining the ratio of 
 the number of molecules actually present to the number which 
 would have been present had no dissociation occurred. The 
 hypothesis gives an explanation of the retarding influence 
 -of neutral salts on the rates of chemical actions brought 
 about by weak acids. From the hypothesis of electrolytic 
 dissociation, taken along with van't Hoff's law of osmotic 
 pressure, an equation is deduced which enables measurements 
 to be made of the affinities of acids, and these affinities are in 
 keeping with the values obtained by wholly different methods, 
 both physical and chemical 1 . 
 
 241 If we accept the law of van't Hoff, and the principle of 
 electrolytic dissociation, we must regard the chemical re- 
 actions of acids and bases in solution, as, at any rate very 
 
 1 For a brief statement of the present position of the electrolytic dissociation- 
 hypothesis, v. Arrhenius, Zeitschr.fiirphysikal. Cheinie, 2. 504 (July, 1888).
 
 CH. III. 239 241] ELECTROLYTIC DISSOCIATION. 461 
 
 largely, dependent on the extent to which these compounds 
 are dissociated into their ions, and on the velocities of trans- 
 ference of these ions. Inasmuch as hydrogen moves so 
 much more rapidly than any of the negative ions of acids, 
 the chemical reactions of acids in solution will chiefly depend 
 on the degree of dissociation. The exact form in which this 
 conception is applied in order to find the affinities of acids 
 has been given in par. 229 ; it is 
 
 m 
 
 2 
 m* 
 
 where ;;/ = molecular conductivity at any stated dilution, 
 referred to the maximum molecular conductivity, and c = a 
 constant = affinity of the acid. 
 
 In comparing gaseous dissociation with dissociation in 
 solution, it is important to note that just as all gases are not 
 dissociated by heat, so all salts, acids, and bases, are not 
 dissociated in solution ; nevertheless, if the hypothesis of 
 dissociation is adopted, and the law of van't Hoff is taken 
 to be true, the data shew that dissociation is a much more 
 frequent occurrence among compounds in solution than 
 among gases. The compounds which most readily and most 
 completely undergo dissociation in solution are electrolytes ; 
 the greater the conductivity the more complete is the dis- 
 sociation. Now if a compound is a good electrolytic con- 
 ductor it is also ready to take part in chemical reactions. 
 The strong acids and bases e.g. HC1, HNO 8 , KOH, NaOH 
 are chemically very energetic, and their conductivities are 
 very large. Hence, if we adopt the hypothesis of electrolytic 
 dissociation, we must regard the readiness shewn by the 
 strong acids and bases in solution to exchange hydrogen and 
 hydroxyl in chemical reactions, as due to the large extent 
 to which they are dissociated in solutions, into hydrogen and 
 negative ions on the one hand, and hydroxyl and positive 
 ions on the other hand. At the first glance it is difficult to 
 accept the conception of such compounds as hydrochloric 
 and nitric acids, or soda and potash, as existing in solution 
 dissociated into their ions. But some of the difficulty arises,
 
 462 CHEMICAL CHANGE. [BOOK II. 
 
 as Ostwald points out 1 , partly from confounding the affinities 
 which hold together the elements of a compound with the 
 affinity which this compound exhibits towards other bodies, 
 and partly from forgetting that the ions of an electrolyte 
 which is dissociated in solution are not comparable with the 
 same bodies in the free state, because the ions carry with 
 them enormous electrical charges 2 . Because potassium hydr- 
 oxide is chemically extremely energetic, it does not follow 
 that ' the elements are held together in this compound ' as 
 is sometimes said ' by the strongest affinities.' The reverse 
 of this rather is true : it is in compounds which do not 
 readily enter into chemical reactions, such as the paraffins 
 and their derivatives, that the elements are firmly held by 
 strong affinities. 
 
 To meet the objection that we cannot suppose a solution 
 of potash to contain the ion potassium, because we know 
 that potassium and water at once react to form hydrogen 
 and potash, Ostwald brings forward the following considera- 
 tions 3 . Let two glass vessels contain potassium chloride 
 solution ; let the vessels be brought into communication by 
 a glass tube filled with the same solution ; now let a nega- 
 tively electrified body be brought near one of the vessels, 
 the contents of this vessel become positively electrified and 
 those of the other vessel become negatively electrified ; let 
 the connecting tube be now removed, and then let the nega- 
 tively electrified body be removed; the contents of the vessels 
 remain electrified, one positively and the other negatively. 
 Now, according to Faraday's law, electricity must travel in 
 an electrolyte with the ions ; therefore the vessel which 
 remains positively electrified must have positively electrified 
 potassium atoms accumulated in it, while negatively electrified 
 atoms of chlorine must have accumulated in the other vessel. 
 If a platinum wire, in connexion with the earth, is now 
 
 1 Zeitschr.furphysikal. Chemie. 2. 270. 
 
 2 It is to be remembered that the statement, that the ions of an electrolyte 
 are endowed with electrical charges and are thus different from the products 
 of dissociation of a gas, does not explain the difference in question, because we 
 are as yet ignorant what an electrical charge is. 
 
 3 Loc. cit. pp. 271273.
 
 CII. III. 241] ELECTROLYTIC DISSOCIATION. 463 
 
 brought into the positively electrified vessel, potash and 
 hydrogen are produced; and this is because the atoms of 
 potassium give up their electric charges and then at once 
 interact with the water. 
 
 From this experiment, Ostwald draws the conclusion that 
 the electrolyte must have been dissociated in the solution 
 before the electrified body was brought near. The measure- 
 ments of Kohlrausch shew that the rates at which ions travel 
 may be stated in not very many millimetres per second ; but 
 electrolytes take up electrostatic charges practically instan- 
 taneously ; hence, in the experiment described, the chlorine 
 atoms which accumulate in one vessel could not have been 
 originally in combination with the potassium atoms which 
 appear in the other vessel. A similar conclusion is drawn 1 
 from the results of the common experiment of placing amal- 
 gamated zinc and a platinum wire, at a considerable distance 
 apart, in dilute sulphuric acid, and then connecting the zinc 
 and platinum. Hydrogen instantly appears on the platinum ; 
 but this hydrogen cannot have been in combination with the 
 negative ion, SO 4 , which at the same moment combines with 
 the zinc, because the rates at which the ions hydrogen and 
 SO 4 travel during electrolysis are not rapid enough to have 
 enabled the hydrogen to pass to the platinum and the SO 4 to 
 pass to the zinc 8 . 
 
 The affinity-coefficients of the acids and bases in solution 
 are then, on this hypothesis, measures of the dissociation of 
 these compounds ; and as the amount of dissociation of an 
 acid or base is generally independent of the body with which 
 the acid or base chemically reacts, these affinity-coefficients 
 have constant values which depend only on the nature of the 
 acid or base. If however another body should be present 
 which modifies the dissociation of the acid or base, the pre- 
 sence of this body will also modify the affinity of the acid or 
 base. This explains the fact that the affinities of the acids are 
 modified by the presence of the normal salts of these acids 8 . 
 
 1 Zeitschr. fitr physikal. Chetnie, 2. pp. 271 273. 
 
 5 See also Ostwald and Nernst, Zeitschr. fur physikal. Chemie, 3. 1 10. 
 
 3 Arrhenius has worked out in detail the modifying influence of normal salts,
 
 464 CHEMICAL CHANGE. [BOOK II. 
 
 As the molecular conductivities of the acids depend on the 
 degree of dissociation of the acids, and also on the velocities 
 of transference of their ions, but chiefly on the former because 
 the positive ion hydrogen travels more than five times more 
 rapidly than the quickest travelling negative ion, so the 
 affinities of acids depend on the degree of dissociation of these 
 acids and on the velocities of transference of their ions. 
 
 But the affinities are dependent on the velocities of the 
 ions to a greater extent than the conductivities. In some 
 reactions, e.g. the solution of zinc in acids, the velocity of the 
 negative ion plays an important part ; in such cases the action 
 of acids which are all equally dissociated will vary in accord- 
 ance with the velocities of their negative ions. In other 
 reactions the negative ion will be of little importance ; in 
 these cases the actions of different acids which are equally 
 dissociated will be equal. Generally speaking, the readiness 
 with which acids react chemically will be chiefly dependent 
 on the degree of dissociation of the acids, because the positive 
 ion hydrogen travels so much more rapidly than the negative 
 ions, and the nature of the negative ion will be of secondary 
 importance 1 . 
 
 242 The hypothesis sketched in the preceding paragraphs, 
 whether accepted or not, presents a general conception of 
 those chemical changes which take place between electrolysable 
 bodies in solution. All compounds which in solution react 
 chemically with electrolytes are regarded by the hypothesis 
 as themselves electrolytes. 
 
 It is necessary to observe that the hypothesis, in its pre- 
 sent form at any rate, is applicable only to substances in 
 solution. If we regard the hydrogen chloride in a dilute 
 aqueous solution of this compound as dissociated to the ex- 
 tent of about 90 per cent, and if we assign the chemical 
 activity of the compound in this solution to the large prepon- 
 derance of 'active' over 'inactive' molecules (i.e. by hypo- 
 thesis, the preponderance of dissociated over undissociated 
 
 and has shewn that the amount of modification can be correctly deduced from the 
 hypothesis of electrolytic dissociation; v. Zeitschr. fiir physikal. Chemie, 2. 284. 
 1 Ostwald, Zeitschr. fiir physikal. Chemie, 2. 273275.
 
 CH. III. 241 243] ELECTROLYTIC DISSOCIATION. 465 
 
 molecules), it does not follow either that liquid hydrogen 
 chloride should be chemically active, or that gaseous hy- 
 drogen chloride should be easily dissociated by heat. The 
 hypothesis does not afford means for comparing the chemical 
 activity, or the stability, of gaseous or liquid compounds with 
 the activity of the same compounds when in solution. 
 
 It should also be remembered that the hypothesis does 
 not assert the occurrence of dissociation in solutions of all 
 compounds ; it distinguishes between non-electrolytes, solu- 
 tions of which it regards as not dissociated, and electrolytes, 
 which it looks on as more or less dissociated in solution ; and 
 it allows a gradation from one class to the other. 
 :3 The action of the solvent on the electrolyte dissolved in 
 it is not yet fully explained by the hypothesis of electrolytic 
 dissociation. The law of van't Hoff assumes that the volume 
 of the solvent is occupied by the molecules of the dissolved 
 body in the gaseous state. The molecules of those compounds 
 which are apparent exceptions to this law are supposed to be 
 dissociated ; in these cases, the volume of the solvent there- 
 fore contains more molecules than if dissociation had not 
 occurred, and, as a consequence, the osmotic pressure exceeds 
 that calculated from the law. This explanation regards the 
 solvent as in some way bringing about dissociation vithout 
 itself being changed. If the solvent acts merely as a medium 
 in which the dissolved electrolyte is dissociated, one would 
 expect the amount of dissociation of an electrolyte to be 
 independent of the composition of the solvent. But experi- 
 ments shew that the conductivities of certain salts dissolved 
 in alcohol are considerably less than those of the same salts 
 dissolved in water 1 ; Arrhenius says 2 that this decrease in 
 conductivity is probably due to the friction which the ions 
 must overcome being increased by the substitution of alcohol 
 for water. 
 
 Armstrong 3 seems to think that a non-conductor, say 
 
 1 Fitzpatrick, B. A. Reports, 1886. 333. 
 
 2 See B. A. Reports, 1888; " On Electrolysis in its Physical and Chemical 
 Bearings." 
 
 8 See the Reports of the B. A. Committee on Electrolysis, 188689. 
 M. C. 30
 
 466 CHEMICAL CHANGE. [BOOK II. 
 
 liquid hydrogen chloride, is composed of complex molecular 
 aggregates, which are broken down by the action of the solvent 
 into simple molecules; that these molecules flow past one 
 another, and that although their parts ' strain at one another,' 
 yet the molecules are not separated into their ions until elec- 
 tromotive force is applied. The objection to this view lies in 
 the fact that, so far as accurate experiment has gone, electro- 
 lytes obey Ohm's law, in other words, that electrolytes cannot 
 resist the smallest electromotive force directly applied to them. 
 This fact seems to require the presence of some ions in the 
 solution of an electrolyte before the current passes. 
 
 How then are these ions produced ? Energy must be 
 obtained somewhere to effect the separation of the molecules 
 of the electrolyte into ions. It may be that the water used as 
 a solvent is chiefly composed of aggregates of molecules, but . 
 that some molecules, H 2 O, are also present, and that the 
 combination of these with molecules of the electrolyte is the 
 source of the energy whereby some of the electrolytic mole- 
 cules are separated into their ions 1 . 
 
 Molecular aggregates are probably formed before electro- 
 lytic dissociation begins ; in our present ignorance of inter- 
 atomic forces, it seems enough to say that the production of 
 molecular aggregates brings the atoms into intra-molecular 
 relations which result in new arrangements of these atoms 2 . 
 Or, it may be said that 'the molecular aggregates in solution' 
 have ' an aptitude for directed decomposition,' and that when 
 the current is applied, electrolysis results (Lodge). 
 244 There can be no doubt of the existence of a marked 
 parallelism between the electrical conductivities and the 
 chemical activities of many compounds in solution. If the 
 former is connected with dissociation, however effected, the 
 latter is probably due to the same cause. As pure liquid 
 hydrogen chloride is an extremely bad conductor, if not 
 indeed non-conductive, so is this compound very inactive 
 chemically; the addition of water is accompanied by the 
 
 1 Cf. Pickering, C. S. Journal, Trans. 1889. 23. 
 
 2 Some such view as this seems to be favoured both by Lodge and Armstrong. 
 See B. A. Electrolysis Committee Reports.
 
 CH. III. 243, 244] ELECTROLYTIC DISSOCIATION. 467 
 
 manifestation of conductivity and chemical activity. We 
 cannot yet fully explain why the presence of water so largely 
 changes the properties of the hydrogen chloride ; but we 
 know other cases wherein the presence of a third body is 
 required before chemical action takes place between two 
 bodies. 
 
 Perfectly dry chlorine and hydrogen do not combine in 
 sunlight; the presence of a very small quantity of water 
 suffices to start the combination 1 . A mixture of perfectly dry 
 carbon monoxide and oxygen is not exploded by an electric 
 spark which at once produces explosion if the gases are 
 slightly moist 2 . Dry hydrogen chloride is unchanged when 
 mixed with dry oxygen and exposed to sunlight, but in the 
 presence of a little liquid water chlorine is produced ; if the 
 water present is all gaseous, chemical action does not occur 3 . 
 A mixture of dry hydrogen iodide and oxygen is, however, 
 said to be changed in sunlight 3 . 
 
 Whether the water in these reactions acts by directly 
 decomposing one of the gases, e.g. 
 
 (i) 
 (2) 
 
 or whether a compound of the water with the reacting bodies 
 is first formed, e.g. 
 
 OH 2 OCO OH 2 OCO 
 
 W O H 2 OCO () OH 2 OCO' 
 
 cannot yet be decided 4 . The presence of water is required in 
 order to render the molecules of the other bodies active. 
 
 Whether we accept the hypothesis of electrolytic disso- 
 ciation or not, we must admit that the conductivities and 
 chemical activities of many compounds are much increased 
 by solution in water. If we say that many of the molecules 
 of the dissolved body acquire 'an aptitude for directed decom- 
 
 1 Pringsheim, Wied. Ann. 32. 384. 
 
 2 Dixon, Phil. Trans. 1884. 617; and C. S. Journal, 49. 94. 
 
 3 Richardson, C. S. Journal, 51. 80 1. 
 
 4 Cf. Dixon, l.c. with Armstrong, C. S. Journal, 49. 112. 
 
 302
 
 468 CHEMICAL CHANGE. [BOOK II 
 
 position', and if we agree to call these molecules 'active', then 
 the ratio of active to inactive molecules is the chief condition 
 which quantitatively affects the electrical conductivity and 
 the chemical activity of the compound in solution. Ostvvald 
 has shewn us how to put this conception of chemical change 
 between electrolytes in solution into a form which enables 
 constant values to be found for the affinities of these electro- 
 lytes (par. 229). 
 
 245 There are definite connexions between the affinities, and 
 the composition, of acids (pars. 231-233). To trace definite 
 connexions between composition and properties has always 
 been the aim of chemistry. The study of composition has ad- 
 vanced further than the study of properties. The connexions 
 between composition and properties have been quantitatively 
 investigated only in a few cases. Great difficulties attend 
 the elucidation of the connexions between the composition 
 and the properties of bodies: some properties, such as weight, 
 are purely additive; the weight of a body is the sum of the 
 weights of its parts; other properties are purely cumulative, they 
 are dependent on the mode of combination of the parts and are 
 wholly independent of the nature and number of these parts ; 
 the volume occupied by gaseous molecules under standard 
 conditions belongs to this category, the volume is independent 
 of the nature and number of the atoms provided these are 
 all chemically combined ; but many properties, including 
 most chemical properties, are constitutive, i.e. they depend not 
 only on the number of the parts but also on their nature and 
 relative arrangement; such properties as boiling point, crystal- 
 line form, and specific rotatory power, belong to the category 
 of constitutive properties 1 . The affinities of acids and bases 
 are dependent on the constitutions of these compounds. Each 
 acid, and each base, has its own affinity-coefficient. If the 
 change of constitution in the passage from one of two acids 
 to the other were identical with the change of constitution in 
 the passage from one of a second pair of acids to the other, 
 the difference between the affinities of the first pair of acids 
 
 1 Ostwald, v. especially KonigL Scichsischen Gesellschaft der Wissenschaften 
 (math. phys. Classe) Bd. 26. [1889] 237.
 
 CH. III. 244 246] AFFINITY AND VALENCY. 469 
 
 would, almost certainly, be identical with the difference be- 
 tween the affinities of the second pair of acids ; but such a 
 case probably never occurs. 
 
 The chemists who have studied the subject of affinity 
 have belonged either to the school of Bergmann or to that of 
 Berthollet. To Ostwald, more than to any other chemist, 
 belongs the signal honour of finding the middle course, which, 
 neglecting the work of neither of these great naturalists, 
 leads to a well-founded and consistent method of measuring 
 affinities, and points the way to the elucidation of the funda- 
 mental problem of chemistry. Bergmann taught that every 
 body has a definite affinity, and in this he was doubtless 
 right ; he also taught that the contest of affinities always leads 
 to the occurrence of chemical change in one direction only, in 
 this he was certainly wrong. Berthollet was right in asserting 
 that chemical change is quantitatively conditioned by the 
 relative masses of the reacting bodies ; but his view that the 
 affinities between acids and bases are inversely proportional 
 to the equivalent weights of these bodies is not in keeping 
 with recent research. (Ostwald.) 
 
 246 But we have not yet gained a complete theory of chemical 
 change. Such a theory must shew us what chemical con- 
 stitution means, and it must quantitatively generalise the 
 relations of constitution to properties. In doing this, the 
 theory must bring into one point of view the scattered partial 
 hypotheses which at present are so numerous in chemistry. 
 The theory must, for instance, connect the valencies of atoms 
 with the other properties of atoms, and with the properties of 
 molecules. To do this requires a conception of valency more 
 exact and at the same time wider than we have at present, 
 and a more thorough elucidation of the way in which the 
 stabilities of molecules are connected with the valencies of 
 their atoms. 
 
 While holding that it is better at present to limit discus- 
 sions about atomic valencies to data obtained from the com- 
 positions and reactions of gaseous molecules, I am of opinion 
 that much progress will not be made in our knowledge of 
 the constitution of compounds, and the connexions between
 
 470 CHEMICAL CHANGE. [BOOK II. 
 
 constitution and properties, unless the chemical properties 
 of bodies in solution, and of solid bodies, are carefully and 
 exhaustively examined. The study of valency, and the 
 study of affinity, overlap ; yet I do not think that the study 
 of either will be materially advanced by confusing one with 
 the other 1 . The composition of the molecules of a certain 
 gaseous compound is known, and the valency of each atom in 
 the gaseous molecule is also known ; but when the compound 
 is dissolved in water, or when it is solidified, the interatomic 
 relations may be, and in many cases most probably are, 
 modified, so that the molecules are able to take part in 
 chemical changes which could not be brought about by the 
 gaseous molecules. The cause of the chemical reactions of 
 the molecules, in both cases, we call affinity ; the number of 
 atoms with which any specified atom is directly associated in 
 one of the gaseous molecules is called in this book the 
 valency of that atom in that molecule. It may be that the 
 electrical charges of the atoms are not fully neutralised in the 
 gaseous molecules (whatever this may mean), but that the 
 residual charges do not suffice to hold together a greater 
 number of atoms than that constituting these molecules, and 
 that on solution, or solidification, these residual charges are 
 able loosely to bind together complex molecular aggregates 
 the atoms in which are brought into such intra-molecular 
 relations that new atomic arrangements result, and so new 
 compounds are formed 2 . If something of this kind occurs, 
 we should expect to find series of bodies ranging from 
 mixtures to definite and stable compounds. Let two mole- 
 cules, one composed of atoms ab, and the other of atoms 
 cd y be brought together; the (hypothetical) residual electric 
 charges may just suffice to form an aggregate ab . cd, wherein 
 the properties of the constituent molecules, or radicles, ab and 
 cd, are recognisable, although they are to some extent merged 
 
 1 There is an interesting paper on The thermal phenomena of neutralisation, 
 by Pickering in C- S. Journal, 51. 593 ; the reasoning seems to me sometimes to 
 be marred by confusing together valency and affinity. 
 
 2 This view, or a view resembling this, seems to be favoured by Armstrong 
 (see Proc. R. S. 1886. 268; also Pickering).
 
 CH. III. 246, 247] AFFINITY AND ENERGY. 4/1 
 
 in those of the new body; or the residual charges may suffice 
 to cause a rearrangement of the atoms with production of the 
 new molecule abed; or lastly an exchange of atoms may occur 
 resulting in the formation of two new molecules ac and bd. 
 In the' first case two different substances would be obtained, 
 according as we started with ab and cd, or with ac and bd\ 
 but in the second case the same body would be produced 
 whether ab reacted with cd or ac with bd: which reaction 
 should occur would depend on the affinities of the reacting 
 bodies rather than on the valencies of the atoms 1 . 
 247 A complete theory of chemical change must elucidate and 
 accurately set forth the connexions between changes of pro- 
 perties, changes of constitution, and changes of energy. 
 
 In Book I. we learned that the primary object of thermal 
 chemistry is to measure the changes of energy which accom- 
 pany definite changes of composition. We found that de- 
 finite quantities of energy change form in the passage from 
 one isomeride to another (pars. 85 89). No discussion was 
 attempted in these paragraphs of the relations between 
 thermal changes and affinity, or between thermal changes 
 and chemical equilibrium. 
 
 A word or two must now be said on this subject. 
 
 The heats of neutralisation of most acids in aqueous 
 solution are independent of the nature of the base used, and 
 the heats of neutralisation of very many bases are inde- 
 pendent of the nature of the acid used ; hence it follows that 
 the heats of formation, in solution, of two similar salts of 
 different metals differ by a constant quantity which is in- 
 dependent of the nature of the acidic radicles of the salts * ; 
 or it may be said that the heat of formation of a salt, in 
 aqueous solution, is the sum of two constants, one of which 
 belongs to the basic, and the other to the acidic, radicle. 
 Arguing on these lines, Lothar Meyer 3 arrives at the con- 
 
 1 See Atkinson's experiments (C. S. Journal, 1885. 12 2), described in par. 102. 
 
 3 This is a development of the statement of the thermoneutrality of salts first 
 laid down by Hess in 1842; Pogg. Ann. 52. 79. Among more recent papers on 
 the subject, see Pickering, C. S. Journal, 51. 593. 
 
 3 Zeitschr. fiir physikal. Ckemie, 1. 134 (Translation in Phil. Mag., June, 1887).
 
 4/2 CHEMICAL CHANGE. [BOOK II. 
 
 elusion, that the heat produced in the formation of a salt is a 
 consequence of the change of state which the substances 
 undergo, and that it is not conditioned by the mutual actions 
 of the constituents, i.e. in ordinary chemical language, by the 
 affinity of one constituent for the other. Although each acid 
 and each base has a definite thermal constant which quanti- 
 tatively conditions the thermal phenomena accompanying 
 the formation of salts by that acid or base, and although each 
 acid and base has also a definite affinity-constant which 
 quantitatively conditions its salt-forming reactions, never- 
 theless, according to Meyer's view, the thermal constant 
 does not measure the affinity-constant. Meyer regards each 
 substance as having a definite quantity of available energy 
 which is increased or diminished by every change of state ; 
 one of those changes in which the available energy is dimi- 
 nished takes place when an acid and a base react to produce 
 a salt ; but the degradation of energy which accompanies this 
 change of composition is not the cause, but rather the con- 
 sequence, of the mutual action of the acid and the base ; the 
 cause of the change we call affinity; it is dependent on the 
 relations of the reacting bodies ; but the degradation of the 
 energy of each body is dependent only on the nature of that 
 body and on the change of state which it undergoes, and is 
 independent of the nature of the other body by the presence 
 of which the change of state is rendered possible. 
 
 The conclusions drawn by Meyer may be too sweeping. 
 The heats of formation of salts, even in aqueous solution, are 
 the algebraical sums of many thermal changes which as yet 
 we cannot disentangle. But, granting this, we have a large 
 probability in favour of the statement that the heats of for- 
 mation of many salts, when the physical conditions are kept 
 as constant as possible, can be represented as the sum of two 
 constants, one of which belongs to the basic radicle and one 
 to the acidic radicle, of the salts. This statement enables us, 
 I think, to say distinctly that the affinities of acids and bases 
 are not measured by the quantities of heat produced in their 
 reactions, unless indeed we use the term affinity as synony- 
 mous with potential energy of a body, and we assume that
 
 CH. III. 247, 248] AFFINITY AND ENERGY. 473 
 
 the heat produced in a reaction of this body with another 
 measures the total change of potential energy into kinetic 
 energy. 
 
 If we adopt the general conception of chemical change 
 between electrolytes in solution afforded by the hypothesis of 
 electrolytic dissociation, we should picture to ourselves the 
 ions of two electrolytes as giving up their electric charges 
 and so combining to form a new compound ; supposing, for 
 simplicity, each ion to be an elementary atom, we should 
 regard the valencies of the ions as determining the number of 
 atoms which combine to form the molecule of the new com- 
 pound ; we should say that the cause of the union is to be 
 found in the affinities of the ions, but what this affinity is we 
 do not know ; and we should look on the quantity of heat 
 produced as to some extent measuring the energy degraded 
 in the process. On this view, affinity is not identical with 
 potential energy 1 . The stability of the new compound is de- 
 termined by the condition that the entropy of the system 
 shall be a maximum ; but the measurement of the heat pro- 
 duced is not a complete determination of the change of 
 entropy, for entropy is a quantity of heat divided by a 
 temperature, and changes of entropy may be conditioned by 
 changes other than thermal. (See par. 191.) 
 
 If we assert that the quantity of heat produced in a re- 
 action measures the affinities of the interacting bodies, and 
 the affinities quantitatively condition the direction, and the 
 amount, of the chemical change, we must turn our backs on 
 the results gained by Guldberg and Waage, Ostwald, and 
 many other chemists, regarding the distribution of the inter- 
 acting bodies in the changes which occur when acids and 
 bases are mixed in equivalent quantities. 
 
 248 But surely there must be some connexion between the 
 quantity of heat produced in a chemical change and the 
 electromotive force of the arrangement. 
 
 1 The kinetic theory of gases obliges us to regard the atoms of a molecule as 
 in continual motion; the affinity of atoms cannot be looked on as altogether 
 potential energy. (There is an interesting paper by Pringsheim in Ztitschr. fur 
 pkysikal. Chcmie, 3. 145.)
 
 474 CHEMICAL CHANGE. [BOOK II. 
 
 In the course of his applications of the conception of the 
 conservation of energy, Joule undertook a series of researches 
 on the ' energetics ' of the electric current 1 . The case of the 
 passage of a current through a wire was considered, and the 
 quantity of heat produced was found to be expressed by the 
 equation 
 
 H=CE, 
 
 where H is the quantity of heat developed per second, and 
 C and E are the current and the electromotive force re- 
 spectively. 
 
 Since Joule had himself shewn that heat is changeable 
 into work, the equation took the form 
 
 W=JH=CE, 
 
 where J = the mechanical equivalent of heat. 
 
 The phenomena attending the production of heat during 
 the passage of a current through an electrolyte were then 
 examined by Joule, and it was shewn that the total quantity 
 of heat could be separated into two parts. One part was 
 expressible as the result of overcoming ordinary resistance, in 
 accordance with his previous law, and the other part was due 
 to chemical changes in the cell. He then determined the 
 quantity of heat produced, during a given time, in a process 
 of electrolysis by a current of given strength ; then, by ap- 
 plying Ohm's law, and the law stated connecting heat with 
 resistance and current, he found the heat which would have 
 been produced had a wire with resistance equal to that of 
 the electrolyte been substituted for the electrolyte. The 
 difference between these two quantities of heat is, Joule said, 
 ' equivalent to the heat which is due to the reverse chemical 
 combination by combustion or other means ' (loc. cit. (2) 3. 
 494)- 
 
 The problem was further considered by Sir W. Thomson *. 
 His reasoning was somewhat as follows. 
 
 1 Phil. Mag. 20. 98; 22. 204; and do. (2) 3. 481. See also the article 
 ' Electricity' in Encycl. Brit. Vol. 8. (gth Ed.) pp. 88-92. 
 
 2 Phil. Mag. for December, 1851; see Mathematical and Physical Papers, 
 1. 472.
 
 CH. III. 248, 249] ELECTROMOTIVE FORCE AND ENERGY. 475 
 
 Let unit 'quantity of electricity pass through a cell of 
 infinitely small resistance; then, by Joule's law, the work 
 done by the current is equal to E, the electromotive force. 
 But e gram of one of the elements of the electrolyte has 
 been electrolysed, in accordance with Faraday's law. Let 6 
 be the quantity of heat developed by the combination of one 
 gram of this element to reproduce the electrolyte, then, ac- 
 cording to Thomson, since no work is expended in any other 
 part of the circuit, 
 
 E = JeO, and therefore = -^ . 
 
 To realise this equation in practice a great many corrections 
 have to be applied. 
 
 This formula presents us with an electrical method for 
 determining the heats of combination of various elements, or, 
 we may say, the energy-changes attending the formation of 
 various compounds. In Joule's papers, the values of the 
 quantity 6 were regarded as affording measures of 'the in- 
 tensities of affinity ' of different substances (loc. cit. 20. 99) ; 
 but we have seen that this cannot now be held, except the 
 term ' affinity ' is used in a very vague sense. 
 
 Many investigations have been made into the accuracy of 
 Thomson's law ; but I cannot attempt to trace these here. 
 Some results shew great discrepancies between the observed 
 E. M. F.'s of cells and those calculated from thermal measure- 
 ments of the chemical changes which are supposed to occur 
 in the cells ; but unless the exact chemical changes which 
 occur are completely known, the discrepancies may be more 
 fanciful than real 1 . 
 
 Concluding Remarks. 
 
 249 We have thus tried to gain some answers to the questions 
 with which we started, What is the composition of compounds? 
 
 1 Among the more important researches may be mentioned ; Braun, Wied. 
 Ann. 16, 561 ; 17. 593; Wright, Phil. Mag. (5) 9. 237, 331 ; 11. 169, 261, 348; 
 13. 265 ; 14. 1 88; 16. 25 ; a general account of his work to the end of 1880 is 
 given by Wright in Chem. Naus, 42. 249 ; see also Proc. of the Physical Society. In 
 connexion with Wright's work, see Laurie's criticism, Phil. Mag., August, 1886. 
 See also B. A. 'Reports of the Electrolysis Committee? 1886-88.
 
 4/6 CONCLUDING REMARKS. [BOOK II. 
 
 What actions are compounds capable of performing ? A 
 complete answer to either question will be an answer to both, 
 and that answer will include the whole of chemistry. 
 
 The atom of the chemical element has been the unit with 
 which we have had to deal ; the properties of compounds have 
 been regarded as conditioned on the one hand by the nature, 
 the number, and the arrangement, of the elementary atoms 
 which together form the compound molecules, and on the other 
 hand, by the greater or smaller quantities of available energy 
 associated with these molecules. To determine the relations 
 between the properties of various molecules, and the nature, 
 number, and arrangement, of their constituent atoms was the 
 first part of our task ; to attempt an outline of a dynamical 
 explanation of chemical operations between molecules was 
 the object of the second part of the undertaking. 
 
 But inasmuch as the properties which chiefly concern us as 
 chemists are the properties, not of individual substances, but 
 rather of these considered as members of changing systems, it 
 has been impossible to consider the questions arising in the 
 first part without to a great extent making use of methods 
 and conceptions more strictly belonging to the second part 
 of our subject. 
 
 The facts connoted by the expression chemical statics were 
 to some extent classified by the help of the hypothesis of 
 valency, itself an outcome of the application of the molecular 
 and atomic theory to chemical phenomena, and by the hypo- 
 thesis regarding the relations between the atomic weights of 
 the elements and the properties of these elements and their 
 compounds which is known as the periodic law. The deter- 
 mination of physical constants, and more particularly the 
 quantities of heat which are produced or disappear during 
 chemical changes, the refraction-equivalents, the specific rota- 
 tory powers, and the relative volumes, of typical compounds 
 and classes of compounds, helped somewhat towards a defi- 
 nite knowledge of the composition of these compounds. 
 
 The study of chemical kinetics, we found, was much 
 advanced by the dynamical hypothesis of Guldberg and 
 Waage, concerning mass-action and chemical affinity, which
 
 CH. III. 249] CONCLUDING REMARKS. 477 
 
 in its primary form is nearly independent of any molecular 
 theory of the structure of matter, but in its development and 
 application by Ostwald forms a bridge connecting the in- 
 vestigation of the chemical properties of molecules with that 
 of the actions of the forces which come into play during 
 chemical operations. In the later outcome of the work on 
 affinity, we found a general theory of chemical change be- 
 tween electrolytes in solution. Whether we accept this theory 
 or not, we must admit that it has been prolific in work of 
 first-class importance. It has advanced our conception of 
 chemical change : it has given us definite measurements of 
 the affinities of very many acids, and in these numbers it has 
 presented us with quantitative connexions between the con- 
 stitutions, and the reactions, of those acids. 
 
 We are getting nearer the goal towards which chemists 
 have ever striven ; we are learning to recognise and formulate 
 definite connexions between properties and composition. 
 
 I have tried always to exhibit the hypotheses of chemistry 
 as at once arising from facts, and serving as guides in the 
 quest for facts It is especially necessary to do this, I think, 
 in dealing with the questions concerning structural formulae. 
 If these formulae are dissociated from the chemical facts which 
 they symbolise they become intellectual tyrants; if each 
 formula is considered simply as a summary of facts regarding 
 the compound formulated, they are to be classed with the 
 other ' brute beasts of the intellectual domain,' and cease to 
 have much interest for one who believes that chemistry is a 
 branch of science. 
 
 One great difficulty in using chemical hypotheses consists 
 in determining the limits of the class of phenomena to which 
 each hypothesis may be applied. Berzelius carried the hypo- 
 thesis of dualism too far, and it was destroyed by the more 
 elastic hypothesis of substitution ; in our own day the hypo- 
 thesis of valency has frequently been applied to phenomena 
 with which it has little or nothing to do. 
 
 But each failure to explain all in terms of one hypothesis 
 makes us more hopeful for the future, and convinces us that
 
 4/8 CONCLUDING REMARKS. [BOOK II. 
 
 we have to deal with a living and growing part of the study 
 of nature. And nature is finer than our finest analysis. 
 
 Much work has yet to be done before a general theory of 
 chemical change can be hoped for; a theory which shall 
 represent every process of change as a function of the atomic 
 weights of the elements, and the affinities of the reacting 
 substances concerned in the operation. When such a theory 
 is attained, will chemistry be complete ? I hope not ; for 
 
 'What's come to perfection perishes.'
 
 INDEX. 
 
 The numbers refer to pages. 
 
 ABNORMAL VAPOUR densities, so call- 
 ed, 391 
 
 Absorption-spectra and molecular 
 structure, connexion between, 314 
 
 Acetic acid, density of vapour of, 203, 390 
 
 Acids, action of metals on, 100, 264 
 ,, affinities, relative, of, 413, 421, 
 
 436, 439 
 
 ,, classification of, by help of ther- 
 mal data, 269 
 
 ,, Davy's and Dulong's views re- 
 garding, 116 
 
 ,, electrolysis of, 422, 436, 443 
 ,, Lavoisier's views regarding, 116 
 ,, Liebig's views regarding, 117 
 Additive, cumulative, constitutive, mean- 
 ing of terms, 456, 468 
 Affinity, a unit of, use of expression in 
 hypothesis of valency, 132,134 
 ,, and valency ought not to be 
 
 confused, 470 
 
 ,, Berthollet's work on, 342 
 ,, Berzelius' conception of, 1 1 3 
 ,, coefficients of, 348, 378, 409 
 
 et seq., 439 et seq., 463 
 ,, connexions between, and con- 
 stitution, 439 et seq. 
 ,, connexions between, and chan- 
 ges of energy, 279, 471 
 ,, general meaning of term, 340 
 ,, not to be identified with po- 
 tential energy, 473 
 
 ,, of acids, connexions between 
 and conductivities of same 
 acids, 422 et seq., 434, 443 
 ,, Ostwald's work on, 408 et seq., 
 
 4&etuf. 
 
 tables of, 341, 440445 
 ,, 'the carbon atom has four units 
 
 of,' 133 
 ,, thermally considered, 368, 410, 
 
 4?i 
 ,, Thomsen's thermal work on, 
 
 368, 410 
 ,, use of term by older chemists, 340 
 
 Affinities, relative, of acids, 413, 421, 
 
 436, 439 
 
 ,, ,, tables of, 
 
 421, 423, 440 et seq. 
 Alchemy, the conceptions underlying, 2 
 Allotropy, 142 
 
 ,, experiments by Spring bear- 
 
 ing on, 142, note 
 ,, thermally considered, 266 
 
 Ammonium carbamate, dissociation of, 
 
 401 
 ,, hydrosulphide, 
 
 400 
 
 ARMSTRONG, his views regarding elec- 
 trolysis, 465 
 ARRHENIUS, his work on electrolytic 
 
 dissociation, 454 et seq. 
 Asymmetric atoms of carbon, 304 
 ATKINSON, R. W., his experiments 
 bearing on molecular compounds, 219 
 Atom, Daltonian definition of, 9 
 
 ,, definition of, obtained by apply- 
 ing Avogadro's law, 38 
 ,, each, has a definite replacing 
 
 value, 122 
 
 ,, function of given, dependent on 
 
 structureof molecule, i6^etsey. 
 
 ,, molecule, and equivalent, the 
 
 terms contrasted, 24, 192 
 , , of phosphorus is trivalent, mean- 
 ing of this expression, 131 
 Atoms and molecules, distinction be- 
 tween, based on reactions, 106 
 ,, arrangement of, in molecules, 
 
 138 note, 154 note 
 
 ,, classification of, by their valen- 
 cies, 127 
 
 , , double, use of by Berzelius, 20 
 ,, equivalency of (see also valency), 
 
 121 et seq. 
 
 ,, formula for finding maximum 
 number of monovalent, in a 
 molecule, 144 
 
 ,, valency of (see also valency), 
 "5. "9
 
 480 
 
 INDEX. 
 
 Atoms, valency of, in non-gasifiable 
 
 compounds, 137, 242 
 Atomic heat of elements, 49, 60 
 ,, refractions of elements, 292 
 ,, ,, of carbon and oxy- 
 
 gen, 298 
 
 ,, synthesis, Berzelian rules of, 18 
 ,, ,, Daltonian ,, 9 
 
 ,, theory, shortcomings of the 
 
 Daltonian, 1 1 
 ,, volumes of elements, curve 
 
 shewing, 227 
 
 ,, weight of an element, defini- 
 tion of, 38 
 
 weights, Berzelius' table of, 19 
 ,, data required before 
 
 can be determined,38 
 ,, ,, determined by appli- 
 
 cation of Avogadro's 
 law, and of law of 
 Dulongand Petit, 65 
 ,, ,, determined by appli- 
 
 cation of Mitscher- 
 lich's law of isomor- 
 phism, 74 
 
 determined by chemi- 
 
 cal methods, 78 
 
 ,, of beryllium, tellu- 
 
 rium, and uranium, 
 determined by ap- 
 plication of periodic 
 law, 232 
 
 ,, of elements, connexion 
 
 between, and heats 
 of formation of ha- 
 loid salts, 229 
 ,, of elements, data for, 
 
 tables, 39, 86 
 
 ,, of elements, periodic 
 
 connexion between, 
 
 and properties of 
 
 elements, 223 et seq. 
 
 ,, ,, of elements, table of, 
 
 48 
 Atomicity of molecules, explanation of 
 
 term, 45 
 ,, ,, table shewing, 
 
 Avidity, meaning of term as used by 
 
 Thomsen, 412 
 
 AVOGADRO, application of his law to 
 determine atomic weights, 
 compared with applica- 
 tion of law of Dulong and 
 Petit, 65 
 his distinction between 
 
 atom and molecule, 1 3 
 ,, his law, 13, 27 
 
 accepted by Du- 
 
 mas, 20 
 
 AVOGADRO, his law applied to chem- 
 ical reactions, 29 
 
 ,, leads to definition 
 
 of atomic weight, 
 
 made basis of sys- 
 
 tem of Gerhardt 
 and Laurent, 24 
 ,, not accepted by 
 
 Berzelius, 7 
 
 Axially symmetric molecules, use of 
 term, 184 
 
 BASE, division of a, between two acids, 
 368, 37^ 
 
 Bases, classification of, by help of ther- 
 mal data, 272 
 
 BEMMELEN, VAN, his experiments bear- 
 ing on molecular compounds, 215 
 
 BERGMANN, his tables of affinity, 341 
 ,, his work in connexion 
 
 with the atomic theory, 7 
 
 BERTHELOT, his law of maximum work, 
 
 279' 3 8 3 
 
 his three principles of ther- 
 
 mal chemistry, 278 
 
 BERTHOLLET, his study of affinity, 342 
 ,, his views regarding 
 
 chemical change, 345 
 ,, his views regarding solu- 
 
 tion, 343 
 
 Beryllium, atomic weight of, 232 
 ,, fusibility of salts of, 227 
 ,, specific heat of, 62 
 BERZELIUS, his acceptance but limita- 
 tion of Gay-Lussac's law, 
 
 17 
 
 ,, his electro-chemical investi- 
 
 gations, 113 
 
 his rules with regard to 
 
 atomic synthesis, 18 
 
 ,, his table of atomic weights, 
 
 I 9 
 
 his use of double atoms, 
 
 20 
 
 ,, ,, the term pola- 
 
 rity, 114 
 
 ,, his work on atomic synthe- 
 
 sis, 17 
 , , refuses to accept Avogadro's 
 
 law, 17 
 
 ,, the dualistic theory of, 115 
 
 Boiling points of carbon compounds, 
 connexions between, and structure, 
 286- 
 
 Bonds, free and satisfied, 132 
 relative strength of, 198 
 single, double, and treble, 133, 
 
 145 
 
 saturation of, 132
 
 INDEX. 
 
 481 
 
 Bonds, Thomsen's thermal researches 
 
 connected with, 282 
 use of term in hypothesis of 
 
 valency, 133 et seq. 
 
 Boron, carbon, and silicon, Kopp's hy- 
 pothesis regarding atoms of, 67 
 ,, specific heat of, 63 et seq. 
 BRAUNER, his investigations connected 
 
 with the periodic law, 234 
 BRAUNER and WATTS, their work on- 
 
 specific volumes, 325 
 BRODIE, his work bearing on structure 
 
 of small particles of elements, 78 
 Bromine, relative density of gaseous, 
 
 203 
 
 BRUHL, his work on the refraction- 
 equivalents of carbon compounds, 291 
 et seq. 
 BUNSEN, his work on mass-action, 346 
 
 Calcium carbonate, dissociation of, 
 
 394 
 
 CANNIZZARO, his generalisations re- 
 garding specific heats of compounds, 
 5* 
 
 Capillarity-constants, 336 
 Carbon, boron, and silicon, Kopp's 
 hypothesis regarding atoms of, 
 67 
 
 ,, specific heat of, 63 
 Carbonyl grouping of carbon and oxy- 
 gen atoms, meaning of expression, 
 295 
 
 CARNELLEY, his determinations of fusi- 
 bility of elements, 228 
 ,, his papers on the periodic 
 
 la\v, 230 note, 244 note 
 CAYLEY, his mathematical examination 
 
 of isomerism, 146 note 
 Central nucleus, use of term, 168 
 Chain, closed, open, side, meanings of 
 
 terms, 166 
 Chemical and electrical forces, relations 
 
 between, 474 
 
 Chemical change, and changes of 
 energy, Berthollet's 
 views regarding, 345 
 ,, Berzelius's views re- 
 
 garding, 114 
 considered thermo- 
 
 dynamically, 379 
 ,, electrolytic hypothesis 
 
 of, 460 
 ,, general considerations 
 
 regarding, 369 
 influence of mass on, 
 
 339 
 
 Chemical changes are accompanied by 
 degradation of ener- 
 gy, 27 
 M.C. 
 
 Chemical changes consist of two parts, 
 
 269, 296, 300 
 
 ,, involving degradation 
 
 of energy usually oc- 
 cur, 259, 384 
 Chemical classification, i, 121 
 
 equilibrium, hypotheses re- 
 garding, 363 et seq. 
 force, use of term, 350, 355 
 ,, methods for determining 
 atomic weights, examples 
 of, 78 
 
 ,, methods for investigating affi- 
 nities of the acids, 409 et 
 seq. 
 
 ,, problems, need of considering 
 both reacting bodies and 
 forces in, 5 
 
 ,, Statics and Kinetics, use of 
 these terms explained and 
 illustrated, 6, 339, 476 
 Chemistry, methods by which, brought 
 under domain of dynamics, 
 5 
 
 thermal, 247 et seq. 
 the fundamental problem of, 
 
 4 IJI 373, 477 
 ,, the general scope of, i 
 ,, the sphere of, contrasted 
 with spheres of dynamics 
 and physics, 4 
 ,, the two lines of advance in, 
 
 i. 121,475 
 Chlorine, relative density of, 203 
 
 specific heat of, 55 
 CLARKE, F. W., his investigations 
 on hydrated and dehydrated salts, 
 
 327 
 Classification, chemical, based on theory 
 
 of types, 121 
 
 ,, of acids and bases by help 
 
 of thermal data, 269 et 
 seq. 
 
 ,, of elements and com- 
 
 pounds by help of ther- 
 mal data, 266 
 
 ,, of elements in accordance 
 
 with their atomic heats, 
 61 
 
 of elements in accordance 
 
 with the periodic law, 
 235 
 
 the two schemes of, adopt- 
 
 ed in chemistry, r, 121 
 CLAUSIUS, his molecular hypothesis of 
 
 electrolysis, 385 
 
 Closed chain, meaning of term, 166 
 Coefficients of affinity, 409 et seq., 436 
 
 ,, of velocity, 355, 378 
 Colloids and crystalloids, 215 
 
 31
 
 482 
 
 INDEX. 
 
 Combining weights of elements, defini- 
 tion of, 36 
 
 weights of elements do not 
 always represent equiva- 
 lent weights, 16, 23 
 Compound radicles, 116, 119, 151 
 
 ,, possess a definite 
 
 replacing power, 
 122 
 Compounds, atomic, 200 
 
 classification of, by help of 
 
 thermal data, 267 etseq, 
 
 ,, formulae of gaseous and 
 
 solid, 46, 137 
 ,, isomorphism of, 69 
 
 molecular, 199 et seq. 
 
 specific heats of, 50, 54 
 
 Conductivities of acids, connexions be- 
 ,, tween, and affinities, 
 
 422 et seq., 439 etseq. 
 of bases, 435 
 
 Conductivity, molecular, 424 
 Constitution, water of, 326 
 Constitutive properties, 468 
 COOKE, J. P., his experiments in con- 
 nexion with physical isomerism, 209 
 Copper sulphate, dissociation of, 396 
 COUPER, his work bearing on valency 
 
 of atoms, 123 
 Crystalline form, determination of, as 
 
 aid in fixing atomic weights, 69 
 Crystallisation, water of, 326 
 Ciimulative properties, 468 
 
 DALE (see GLADSTONE) 
 
 DALTON, development of the atomic 
 
 theory of, 8 
 ,, his New System of Chemical 
 
 Philosophy, 9 
 ,, his reasons for giving to water 
 
 the formula HO, 1 1 
 ,, his refusal to accept Gay- 
 
 Lussac's law, 12 
 
 ,, his remarks on specific heats of 
 
 solids, liquids and gases, 48 
 
 ,, his rules respecting atomic 
 
 synthesis, 10 
 ,, shortcomings of his atomic 
 
 theory, 1 1 
 
 DAVY, his electro-chemical investiga- 
 tions, 112 
 
 ,, his views regarding acids, 116 
 Dilution, influence of, on conductivities 
 
 of acids, 424 et seq. 
 Dimorphism, 73 
 
 Dissociation, cases of, considered, 389 
 ,, electrolytic, 454 
 
 ,, meaning of term, 389 
 
 ,, of acetic acid vapour, 
 
 39 
 
 Dissociation, of ammonium carbamate, 
 
 401 
 ,, of ammonium hydrosul- 
 
 phide, 400 
 
 ,, of calcium carbonate, 394 
 
 ,, of compounds of silver 
 
 chloride with ammonia, 
 394 
 
 of copper sulphate, 396 
 of hydrogen iodide, 393 
 of iodine, 206 
 of saltsin solution, 453,461 
 of sodium phosphate, 397 
 regarded as special case 
 of chemical equilibrium, 
 
 399. 45 
 
 ,, regarded from molecular 
 
 theory point of view, 
 402 
 
 ,, thermodynamically re- 
 
 garded, 403 
 ,, treatment of by Gibbs, 
 
 402 
 Divalent atoms, meaning of expression, 
 
 126 et seq. 
 
 Divalent, the atom of tin is, in given 
 molecule, but is tetravalent 
 in another molecule, 128 
 DIVERS, his experiments on the action 
 
 of tin, &c., on nitric acid, 109 
 DONATH, his determination of the spe- 
 cific heat of uranium oxide, 59 
 Dualism, opposed by Dumas, 118 
 
 ,, opposed to Faraday's electro- 
 lytic laws, 117 
 ,, system of, introduced by Ber- 
 
 zelius, 115 
 
 DULONG and PETIT, their law regard- 
 ing specific heats of solid elements, 
 49, 60 
 
 DUMAS, his early acceptance of Avo- 
 gadro's law, 20 
 
 ,, his system of notation partly 
 
 atomic, partly equivalent, 21 
 
 ,, introduces the conception of 
 
 types, 1 20 et seq. 
 
 opposes the dualistic system of 
 Berzelius, 118 
 
 Eka-aluminium, eka-boron, and eka- 
 silicon, 230 
 
 Electro-chemical investigations of 
 Arrhenius, 454 
 Berzelius, 113 
 Davy, 112 
 Faraday, 117, 451 
 Ostwald, 422 &c. 
 Joule, 474 
 Thomson, 475 
 
 Electrolysis of acids, 422 et seq.
 
 Electrolysis, Faraday's laws of, 337 
 Electrolytes, action of solvents on, 
 
 4 6 5 
 
 Electrolytic dissociation, hypothesis of, 
 
 Electrolytic hypothesis of chemical 
 
 change, 460 
 Element, the old conception of, i, 244 
 
 note 
 Elements, atomic heats of, 49, 60 
 
 ,, atomic volumes, curve of, 227 
 ,, atomic weights of, data for 
 finding, tables, 39 et seq., 
 86 et seq. 
 
 ,, atomic weights of, table, 48 
 ,, atoms of, have definite re- 
 placing values, 122 
 , , atoms of, valency of (see also 
 valency of atoms), 126 et 
 seq. 
 classification of, by help of 
 
 thermal data, 266 
 ,, classification of, in accord- 
 ance with their atomic 
 heats, 6 1 
 
 ,, classification of, in accord- 
 ance with the periodic law, 
 223 etseq. 
 
 ,, fusibility of, 228 
 ,, isomorphism of, 72 
 ,, periodic connexion between 
 atomic weights and pro- 
 perties of, 223 et seq. 
 ,, specific heats of, law of Du- 
 long and Petit regarding, 
 49, 60 
 
 ,, specific heats of some, deter- 
 mined indirectly, 54 et seq, 
 ,, specific heats of, table, 51 
 ,, study of properties of, by help 
 
 of the periodic law, 232 
 ,, unknown, properties of, pre- 
 dicted by the periodic law, 
 230 
 Elementary gases, table of molecular 
 
 weights of, 33 
 
 Endothermic and exothermic changes, 
 meaning and application of terms, 
 252 
 
 Energy-changes accompanying chemical 
 changes, 176, 259, 
 279, 384, 471 
 
 ,, connected with affinity- 
 
 changes, 471 
 
 ,, measurements of, by 
 
 electrical methods, 
 
 475 
 
 ,, measurements of, by 
 
 thermal methods, 
 250, 257, 288 
 
 INDEX. 483 
 
 Energy, degradation of, accompanying 
 chemical changes, 259, 384, 
 471 
 ,, free and bound, use of terms by 
 
 Helmholtz, 382 
 Entropy, 379 
 Equilibrium, chemical, 363 et seq. 
 
 ,, ,, equation of, 349, 
 
 374. 
 
 ,, ,, equation of, a- 
 
 dapted to dif- 
 ferent cases, 
 
 363.. 374 
 
 ,, equation of, ap- 
 
 plied to study 
 of affinity, 408 
 et seq. 
 of systems of four 
 
 bodies, 367 
 
 ,, molecular me- 
 
 thods applied 
 to, 385 
 
 ,, thermal methods 
 
 applied to, 368 
 
 ,, thermodynami- 
 
 cal methods ap- 
 plied to, 379 
 Equilibrium-pressure, use of term in 
 
 connexion with dissociation, 392 
 Equivalency of atoms (see also -valency), 
 
 \ 26 et seq. 
 Equivalent, atom, molecule, the terms 
 
 contrasted, 24, 192 
 ,, connected with function, 
 
 J 5 23 
 difficulty of determining the 
 
 true, of an element, 14 
 ,, notation, inconveniences of, 
 
 ,, term introduced by Wol- 
 
 laston, 14 
 
 ,, weights of elements deter- 
 mined by Laurent, 23 
 Equivalents, work of Dumas, Laurent, 
 
 and Gerhardt on, 22 
 Etherefication-values, connexion be- 
 tween, and molecu- 
 lar structure of al- 
 cohols, 331 
 meaning of term, 332 
 
 et seq. 
 
 Ethylene grouping of two carbon 
 atoms, meaning of expression, 295 
 
 FARADAY, his electro-chemical investi- 
 gations, 117, 337 
 
 FISCHER, his work in connexion with 
 the atomic theory, 7 
 
 Fluorine, specific heat of, 55
 
 4 8 4 
 
 INDEX. 
 
 Forms of oxides and salts as determined 
 by application of the periodic law, 
 
 239 
 
 Formulae, chemical, of gases compared 
 
 *" with those of solids, 46 
 chemical, structural, examples 
 of methods of obtaining, 
 146 et seq. 
 
 chemical, structural, general- 
 isations usually made in 
 obtaining, 156 et seq. 
 FRANKLAND recognises a substituting 
 
 value for each elementary atom, 122 
 Fusibility of elements, connexion be- 
 tween, and atomic weights, 228 
 
 Gallium, identical with eka-alitminium, 
 
 230 
 
 GARNIER and CANNIZZARO, their gene- 
 ralisation regarding specific heats of 
 compounds, 51 58 
 Gases, formulae of, compared with those 
 
 of solids, 46 
 GAY-LUSSAC, Berzelius modifies the law 
 
 of, 17 
 ,, Dalton refuses to accept 
 
 the law of, 12 
 
 ,, his law regarding volu- 
 
 metric combinations of 
 gases, 12 
 
 Geometrical isomerism, 182, 304, 445 
 GERHARDT, his law of even numbers, 
 
 84, 198 
 
 ,, his reasons for changing 
 
 the equivalents of carbon, 
 &c., 22 
 Germanium, identical with eka-silicon, 
 
 232 
 
 GIBBS, his investigation of the equili- 
 brium of heterogeneous systems, 380, 
 402 
 
 GLADSTONE,hisinvestigalions on chemi- 
 cal change, 347 
 
 GLADSTONE and DALE, their investiga- 
 tions on refraction-equivalents of 
 carbon-compounds, 291 
 GLADSTONE and TRIBE, their investiga- 
 tions in connexion with the electro- 
 lysis of acids, 100 
 GMELIN, his system of notation, 21 
 GOLDSTEIN, his investigations on the 
 connexion between boiling points and 
 molecular structure, 286 
 GRAHAM, his work on colloidal and 
 
 crystalloidal matter, 214 
 ,, his work on water of crystal- 
 lisation, 326 
 
 GROTH, his investigations regarding 
 morfhotropic relations, 173 
 
 Group, use of term in nomenclature of 
 
 the periodic law, 224 
 GULDBERG and WAAGE, 
 
 their equation of chemical equili- 
 brium, 349, 374 
 
 their equation of chemical equili- 
 brium applied to study of chemical 
 affinity, 408 et seq. 
 
 their law of mass-action, 347 et 
 seq. 
 
 their molecular hypothesis.of chemical 
 equilibrium, 386 
 
 Halogens, hydracids and oxyacids of, 
 
 considered thermally, 268 
 HARTLEY, his investigation of relations 
 of molecular structure to absorption- 
 spectra, 314 
 
 Heat, connexion between quantities of, 
 produced in chemical changes, 
 and structure of molecules of 
 changing substances, 174 et seq. 
 ,, of formation of compounds, mean- 
 ing of term, 257 et seq. 
 ,, of neutralisation of an acid by a 
 
 base, and vice versa, 269, 368 
 ,, produced in chemical changes, 
 
 study of, 247 et seq. 
 ,, produced in reactions of isome- 
 
 rides, 174, 282 
 
 ,, specific, of solid elements, 49,60 
 (See also thermal chemistry, and 
 
 thermal data. ) 
 
 HELMHOLTZ, his electro-chemical in- 
 vestigations, 382 
 ,, his use of the terms free 
 
 and bound energy, 382 
 ,, on chemical equilibrium, 
 
 383 
 HERMANN, R., his work in connexion 
 
 with specific heats, 50 
 HOFF, J. H. VAN'T, his gravitational 
 hypothesis regarding 
 atomic valency, 135, 
 note. 
 
 his hypothesis regarding 
 
 optically active com- 
 pounds, 304 et seq. 
 his law of osmotic pres- 
 
 sure, 452, 465 
 ,, his work on chemical 
 
 equilibrium, 374, 384 
 ,, his work on velocity of 
 
 chemical change, 360 
 HOOD, his experiments on the velocity 
 
 of chemical change, 360 
 HORSTMANN, his treatment of dissocia- 
 tion-phenomena, 379 
 HUMPIDGE, on spec, heat of beryllium, 
 63
 
 INDEX. 
 
 485 
 
 Hydrofluoric acid, density of vapour of, 
 
 126 note (s. Addenda). 
 Hydrogen iodide, dissociation of, 393 
 Hydrogen, replaceable, illustrations of, 
 
 163 &c. 
 ,, specific heat of, 56 
 
 latro-chemists, 2 
 
 Iodine, atomic weight of, fixed by help 
 
 of periodic law, 233 
 ,, relative density of vapour of, 
 
 206 
 
 Ions, free, in solutions, 461 
 ISAMBERT, his work on dissociation of 
 
 ammonium hyclrosulphide, 400 
 Isomerides, formula for finding maxi- 
 mum number of monad 
 atoms in molecules of, 144 
 ,, heat produced or used in 
 
 reactions of, 174,282 
 Isomerism, detailed consideration of, 
 
 143**?. 
 
 ,, exceptions to, generally 
 adopted explanation of, 
 180 
 
 geometrical, 182, 304, 445 
 ,, hypothesis by which ex- 
 
 plained, [39, 181 . 
 ,, mathematical examination 
 
 of, by Cay ley, 146 note 
 eaning of term, 
 
 g o term, 139 
 ,, thermally considered, 174^ 
 
 seq. 
 
 ,, physical, 211 
 
 ,, ,, Lehmann's work 
 
 on, 210 et seq, 
 
 ,, position, and saturation, 294 
 ,, study of, by optical methods, 
 
 292 et seq, 304, 311 
 ,, . study of, by thermal me- 
 
 thods, 174 et seq. 
 Isomorphism of compounds, 69 
 ,, of elements, 72 
 
 ,, Mitscherlich's law of, 69 
 
 Isomorphous crystals, meaning to be 
 
 given to this expression, 71 
 Isotonic solutions, 452 
 
 JOULE, his electro-chemical investiga- 
 tions, 474 
 
 KANONNIKOW, his work on refraction- 
 
 equivalents, 298 note 
 KEKULE, his use of the terms atomic 
 and molecular compounds, 
 200 
 KEKULE, his work on valency of atoms, 
 
 123 
 
 Kinetics, chemical, general remarks re- 
 garding, 339 
 
 Kinetics, chemical, use of term explain- 
 ed, 6 
 KOHLRAUSCH, his law of electrolytic 
 
 conductivity, 428 
 
 KOPP, his hypothesis regarding the 
 atoms of carbon, boron, and 
 silicon, 67 
 
 ,, his investigations regarding spe- 
 cificheatsof elements, $ietseq. 
 ,, his investigations regarding spe- 
 cific volumes, 319 et seq. 
 
 LANDOLT, his work on optical activity 
 of carbon compounds, 301 
 et seq. 
 LAURENT, his definition of molecule 
 
 and atom, 24 
 ,, his system based on Avo- 
 
 gadro's law, 24 
 his work on equivalents, 
 
 23 
 LAVOISIER, his views regarding acids, 
 
 116 
 Law, Berthelot's, of maximum work, 
 
 279. 383 
 
 ,, of Avogadro (see also AvOGAD- 
 RO), 13, 27 
 
 ,, of dilution, as regards conduc- 
 tivity, 424 et seq. 
 
 ,, of Dulong and Petit, 49, 60 
 
 ,, of Gay-Lussac (see also GAY- 
 
 LUSSAC), 12 
 
 ,, of Kohlrausch regarding electro- 
 lytic conductivity, 428 ' 
 ,, of mass-action, 348 
 of molecular lowering of freezing 
 
 point, 76, 452 
 
 ,, of osmotic pressure, 452 
 ,, periodic (see also periodic law), 
 
 222 et seq. 
 
 LflHM ANN, his work on molecular com- 
 pounds, 210 
 his work on physical isomer- 
 
 ism, 210 et seq. 
 LEMOINE, his studies on dissociation, 
 
 393 
 
 LIEBIG, his views regarding acids, 117 
 Links, or bonds, use of term, in hy- 
 pothesis of valency (see also bonds), 
 
 X 33 
 
 Long and short periods, 235 
 LOSSEN, his criticism of hypothesis of 
 
 bonds, 133, 193 et seq. 
 ,, his investigations in connexion 
 with specific volume of the 
 group CH 2 , 322 
 
 ,, illustrations of his views re- 
 garding valency, 145 
 
 Magnetic rotatory power, 311
 
 486 
 
 INDEX. 
 
 MALLET, his determination of the va- 
 pour density of hydrofluoric 
 acid, 126 note 
 
 MARIGNAC, his work on the supposed 
 element hyponiobium, 75 
 
 Mass-action, law of, 348 et seq. 
 
 Maximum work, Berthelot's law of, 
 
 279. 383 
 
 MENDELEJEFF, his researches in con- 
 nexion with theperiodiclaw, ii^etseq. 
 MENSCHUTKIN'S investigation of etheri- 
 fication-values of alcohols and acids, 
 331 et seq. 
 Metals, action of acids on, 100 
 
 ,, action of acids on, considered 
 
 thermally, 264 
 Metamerism, 143 
 
 ,, physical, 213 
 
 MEYER, L., his calculation of the spe- 
 cific heat of beryllium, 63 
 his remarks on affinity, 471 
 
 ,, his work in connexion with 
 
 specific volumes, 330 
 ,, his work in connexion with 
 
 the periodic law, 223 et 
 seq. 
 
 MITSCHERLICH, his law of isomor- 
 phism, 69 
 
 Molecular compounds, general remarks 
 on, 200, 207, 
 219 
 ,, ,, Lehmann's work 
 
 on, 208 
 
 ,, no definition of, 
 
 possible, 200 
 ,, conductivity, 424 
 , , groups, existence of, in gases, 
 
 203 
 
 ,, heats of solid compounds 
 help to determine atomic 
 weights of elements, 54 
 ,, heat of solid compounds, 
 meaning of expression, 54 
 note 
 ,, lowering of freezing point, 
 
 law of, 76, 452 
 
 ,, phenomena dealt with by 
 statistical methods, 99 note 
 ,, structure, 138, 154 note 
 ,, structure, connexion be- 
 tween, and absorption- 
 spectra, 314 
 
 ,, structure, connexion be- 
 tween, and affinity, 439 
 ,, structure, connexion between, 
 and arrangement of atoms 
 in space, 182 
 
 ,, structure, connexion between, 
 and etherification-values, 
 331 
 
 Molecular structure, connexions be- 
 tween, and magnetic ro- 
 tatory power, 3 1 1 et seq. 
 
 , , structure, connexion between, 
 and optical activity, 303 
 et seq. 
 
 ,, structure, connexionbetween, 
 and thermal changes, 174 
 et seq., 282 
 
 ,, structure, examples of de- 
 pendence of function of 
 part of a molecule on 
 arrangement of all the 
 parts, 163 et seq. 
 
 ,, structure, examples of pre- 
 sence of certain atomic 
 groups in molecules, 151 
 et seq. 
 
 ,, theory, general sketch of, 25 
 et seq. 
 
 volumes, 317 et seq. 
 
 weight of a gas, definition of, 
 32 
 
 ,, weight of a gas, examples 
 shewing how determined, 
 35 
 
 ,, weight, same substance may 
 have more than one, 35 
 
 ,, weights of elementary gases, 
 table of, 33 
 
 ,, weights of substances in so- 
 lution determined, 76, 456 
 note 
 
 Molecule, atom, equivalent, the terms 
 contrasted, 24, 192 
 
 ,, dynamical conception of, 26 
 
 ,, physical, compared with che- 
 mical, conception of, 
 220 
 
 Molecules and atoms, distinction be- 
 tween, based on reac- 
 tions, 1 06 
 
 ,, atomicity of elementary, 
 table, 45 
 
 ,, attempts to measure ther- 
 mal changes accompany- 
 ing separation of, into 
 atoms, 263 
 
 ,, in which isomerism may 
 occur, 146 
 
 ,, of hydrogen, &c., separate 
 into parts during chemical 
 changes, 29 
 
 ,, saturated and unsaturated, 
 use of terms, 145 
 
 ,, size of, 28 
 
 Monovalent atoms, formula for finding 
 maximum number of, in a molecule, 
 
 M4 
 Monovalent, meaning of term, 126
 
 INDEX. 
 
 487 
 
 Morphotropic relations, use of expres- 
 sion by Groth, 173 
 
 Nascent actions, examples of, 97 
 
 ,, explanation of, given 
 
 by the molecular 
 theory, 98 
 
 ,, ,, general remarks on 
 
 use of the expres- 
 sion, 109 
 ,, ,, Traube's experiments 
 
 on, 106 
 
 ,, state of compounds, 99 
 NASINI, his work on refraction-equi- 
 valents, 298 
 NEUMANN, his extension of the law of 
 
 Dulong and Petit, 50 
 NEWLANDS, his work in connexion . 
 
 with the periodic law, 223 
 NILSON and PETTERSSON, their deter- 
 mination of the specific heat of beryl- 
 lium, 62 
 
 NILSON and PETTERSSON, their work in 
 connexion with the periodic law, 233 
 Nitrogen, specific heat of, 55 
 
 . ,, tetroxide, relative density 
 
 of, 203 
 Nucleus, central, meaning of term, 168 
 
 Odd and even series, 237 
 
 ODLING introduces notation shewing 
 
 valencies of elementary atoms, 122 
 Open chain, meaning of term, 166 
 Optically active compounds, meaning 
 
 of expression, 299 
 
 Optically active compounds, van't 
 Hoff's hypothesis concerning, 304 
 et seq. 
 
 Optical activity, influence of inactive 
 
 solvents on, 301, 310 
 
 ,, ,, of solid compounds, 
 
 302 
 Optical methods applied to questions 
 
 of chemical statics, 289 et seq. 
 Osmotic pressures, 451 
 OSTWALD, his application of law of 
 mass-action to dissoci- 
 ation, 399 
 
 ,, his notation used in ther- 
 
 mal chemistry, 251 
 ,, his work on affinity-co- 
 
 efficients of acids and 
 bases, 409 et seq. 
 
 his work on conductivities 
 
 and affinities of acids, 
 422 et seq., 460 
 
 ,, his work on connexions 
 
 between affinities and 
 constitution of acids, 439 
 
 OSTWALD, his work on distribution of 
 a base between two acids, 
 
 353> 372 
 Oxygen, atomic weight of, data for 
 
 determining, 38 
 
 ,, in oxides, specific heat of, 58 
 ,, specific heat of, 56 
 
 Periodic law, applied to predict proper- 
 ties of unknown ele- 
 ments, 230 
 
 applied to study of forms 
 
 of oxides and salts, 
 239 
 
 ,, applied to study of pro- 
 
 perties of beryllium, 
 232 
 
 ,, applied to study of pro- 
 
 perties of known ele- 
 ments, 232 et seq. 
 applied to study of pro- 
 
 perties of uranium, 234 
 ,, applied to study of valen- 
 
 cies of elementary 
 atoms, 241 
 
 general remarks on, 244 
 illustrations of, 2 24 et seq. 
 nomenclature employed, 
 
 224, 230, 237 
 statement of, 223 
 tables shewing arrange- 
 ment of elements in 
 accordance with, 225, 
 236 
 
 Periods, long, short, and transition, use 
 of terms in nomenclature of the 
 periodic law, 235 
 
 PERKIN, on the connexions between 
 molecular structure and magnetic ro- 
 tation, 3 1 1 il seq. 
 
 PETIT and DULONG, their law regard- 
 ing specific heats of solid elements, 
 49, 60 
 
 PETTERSSON (see NILSON) 
 PFAUNDLER, his hypothesis regarding 
 chemical equilibrium, 
 386 
 
 Phosphorus, change from yellow to red, 
 a case of chemical equi- 
 librium, 366 
 
 , , pentachloride, relative den- 
 
 sity of vapour of, 202 
 Physical methods applied to questions 
 
 of chemical statics, 246 et seq. 
 PICKERING, his examination of the ac- 
 tion of sulphuric acid on copper, 
 
 94 
 Plane-symmetric molecules, use of term , 
 
 184 
 Polarity, use of term by Berzelius, 114
 
 INDEX. 
 
 Polymerism, 141 
 
 ,, physical, 213 
 
 Polymorphism, 73 
 
 POTILITZIN, his experiments on in- 
 fluence of mass in chemical changes, 
 276 
 
 Radicles, compound, 116, 119, 151 
 ,, ,, possess a definite 
 
 replacing power, 
 122 
 
 RAMSAY, his experiments in connexion 
 with specific volumes, 320 
 
 RAMSAY and YOUNG, their experi- 
 ments on vapour density of acetic 
 acid, 390 
 
 RAOULT, his law of molecular lowering 
 of freezing-points, 76, 452 
 
 RATHKE, on molecular compounds, 201 
 
 Refraction-equivalent of a compound, 
 is it equal to sum of equivalents of 
 elementary constituents? 292 et seq. 
 
 Refraction-equivalent, meaning of term, 
 
 Refraction-equivalents, connexion be- 
 tween and structure of carbon com- 
 pounds, 291 et seq, 
 
 Refraction-equivalents, formulae for de- 
 termining, 290 
 ,, of elementary 
 
 atoms, 295 
 
 ,, of solid com- 
 
 pounds, 298 
 note 
 REGNAULT, his researches on specific 
 
 heat, 50 
 REYNOLDS, R. E., his determination 
 
 of the specific heat of beryllium, 62 
 RICHTER, his work in connexion with 
 
 the atomic theory, 7 
 ROSE, H. , his supposed discovery of an 
 
 allotropic form of niobium, 75 
 Rotatory power, specific, determination 
 
 of, 300 
 
 specific, meaning of ex- 
 
 pression, 300 
 
 Saturated and unsaturated molecules, 
 
 use of terms, 145 
 
 Scandium, identical with eka-boron, 231 
 SCHIFF, his work in connexion with 
 
 specific volumes, 320 
 Series, use of term in nomenclature of 
 
 the periodic law, 237 
 Side chain, meaning of term, 166 
 Silicon, carbon, and boron, Kopp's hy- 
 pothesis regarding atoms of, 67 
 ,, specific heat of, 63 
 Silver chloride, compounds of with 
 
 ammonia, dissociation of, 394 
 
 Sodium phosphate, dissociation of, 397 
 Solution, Berthollet's views regarding, 
 
 37 
 Specific heat of beryllium, 62 
 
 ,, ,, boron, carbon, and 
 
 silicon, 63 
 
 ,, ,, oxygen in oxides, 58 
 Specific heats of compounds, generalisa- 
 tion of Gamier and 
 Cannizzaro regard- 
 ing. 5i 
 
 ,, ,, of compounds, generalisa- 
 tion of Neumann re- 
 garding, 50 
 
 ,, ,, of elements, law of Du- 
 long and Petit re- 
 garding, 49, 60 
 
 ,, ,, of elements, table, 51 etseq. 
 ,, ,, of some elements determin- 
 ed indirectly, Betsey. 
 Specific refractive energy, meaning of 
 
 expression, 290 
 ,, rotatory power, determination 
 
 of, 300 
 ,, rotatory power, meaning of 
 
 expression, 300 
 ,, unipolarity, use of expression 
 
 by Berzelius, 114 
 
 , , volume of a compound proba- 
 bly equal to sum of volumes 
 of elementary constituents, 
 3^9' 3^8 
 
 ,, volume of carbon and of oxy- 
 gen varies according to the 
 valency of the atom of each 
 element, 319 et seq. 
 ,, volume, meaning of expres- 
 sion, 317 
 
 ,, volumes of atoms in molecules 
 vary according to distribu- 
 tion of interatomic reac- 
 tions, 322 
 
 ,, volumes of hydrated and de- 
 hydrated salts, 327 
 ,, volumes of solid compounds, 
 
 325 
 SPRING, his experiments in connexion 
 
 with allotropy, 142 note. 
 Stability, vagueness of theterm, 178, 465 
 ST^DEL, his experiments on specific 
 
 volumes of carbon compounds, 323 
 Statics, chemical, questions of, studied 
 
 by physical methods, 246 
 ,, chemical, use of expression, ex- 
 plained and illustrated, 6, 329 
 
 Tables of affinity, 341, 440 445 
 Table, atomic weights of elements, 48 
 ,, atomic weights of elements, data, 
 39, 86
 
 INDEX. 
 
 489 
 
 Table, atomicity of elementary mole- 
 cules, 45 
 ,, data for finding maximum atomic 
 
 weight of oxygen, 36 
 ,, illustrating electrical conduc- 
 tivities and velocity-constants 
 of acids, 423 
 
 illustrating law of dilution as 
 regards conductivities of 
 acids, 425 
 
 ,, illustrating saponification - ve- 
 locities and electrical con- 
 ductivities of bases, 436 
 ,, molecular weights of element- 
 ary gases, 33 
 
 ,, periodic arrangement of ele- 
 ments, 225, 236 
 ,, relative affinities of the acids, 
 
 440445 
 
 ,, relative densities of halogens, 
 nitrogen tetroxide, and phos- 
 phorus pentachloride, 202, 
 203, 206, 207 
 
 ,, specific heats of elements, 51 
 ,, thermo-atomic weights (Reg- 
 
 nault), 50 
 Tellurium, atomic weight of, fixed by 
 
 application of the periodic law, 233 
 Thermal chemistry, attempts made in, 
 to distinguish between the 
 two parts of a chemical 
 change, 248, 262, 275 
 chemistry, Berthelot's three 
 
 principles of, 278 
 
 ,, chemistry, illustrations of me- 
 thods of calculation used in, 
 255 et seq. 
 
 ,, chemistry, need of considering 
 action of excess of reacting 
 substances in, 276 
 chemistry, need of considering 
 physical conditions of chang- 
 ing systems in, 275, 277 
 ,, chemistry, notation used in, 
 
 248, 251 
 chemistry, principles on which 
 
 based, 247 
 
 ,, chemistry, the law of maxi- 
 mum work in, 279, 383 
 data, applied to action of acids 
 
 on metals, 264 et seq. 
 data, applied to action of con- 
 centrated and dilute hydri- 
 odic acid, 253, 260 
 ,, data, applied to action of sul- 
 phuretted hydrogen on me- 
 tallic salts, 260 et seq. 
 data, applied to allotropy, 266 
 ,, data, applied to classification 
 of acids and bases, 269 et seq. 
 
 M. C. 
 
 Thermal data, applied to classification 
 
 of compounds, 268 et seq. 
 data, applied to classification 
 
 of elements, 266 
 
 ,, data, applied to study of affi- 
 nity, 368, 410, 471 
 data, applied to study of iso- 
 
 merism, 1 74 et seq. 
 ,, data, examples of attempts to 
 
 analyse, 277 
 data, influence of temperature 
 
 on, 275 
 
 ,, methods used in chemistry, 247 
 Thermodynamical methods applied to 
 
 chemical equilibrium, 379 
 THOMSEN, J., his attempt to measure 
 the thermal value of 
 each bond of the car- 
 bon atom, 282 
 
 , , his classification of acids 
 
 and bases, based on 
 thermal data, 269 et 
 seq. 
 
 ,, his experiments on the 
 
 connexions between 
 thermal changes and 
 molecular structure, 
 174 et seq., 282 
 
 ,, his thermal study of the 
 
 affinities of acids, 368, 
 410 
 
 his statement of the law 
 
 of maximum work, 280 
 ,, his use of the term avi- 
 
 dity, 412 
 
 his work on division of 
 
 a base between two 
 acids, 368 
 
 THOMSON, J. J., his conception of 
 
 equilibrium from the stand-point of 
 
 the theory of vortex-atoms, 387, 403 
 
 THOMSON, Sir W., his electro-chemical 
 
 investigations, 475 
 
 THORPE, his experiments on relative 
 density of hydrofluoric acid 
 gas, 126 note (s. Addenda) 
 ,, his investigations in connex- 
 ion with specific volumes, 
 
 3 2 3 
 
 ,, his investigations of the re- 
 ducing action of metals on 
 ferric sulphate, 105 
 ,, andWATTS, their experiments 
 in connexion with water of 
 crystallisation, 327 
 TOMMASI, his work in connexion with 
 
 nascent actions, 105 
 Transition-periods, use of expression in 
 nomenclature of the periodic law, 235 
 Transpiration-rates, 336 
 
 32
 
 490 
 
 INDEX. 
 
 TRAUBE, his experiments in connexion 
 with nascent actions, 106 
 
 TRIBE (see GLADSTONE) 
 
 Trimorphism, 73 
 
 TROOST and HAUTEFEUILLE, their ex- 
 amination of change of yellow to red 
 phosphorus, 366 
 
 Types, classification based on, 120 
 conception of, introduced by 
 Dumas, 118 et seq. 
 
 Typical elements, use of expression in 
 nomenclature of the periodic law, 237 
 
 Uranium, atomic weight of, fixed by 
 application of the periodic 
 law, 234 
 ,, specific heat of, 59 
 
 Valency, a, use of expression, 132, 
 
 136 note 
 
 Valency of atoms, conception of, applied 
 to explain molecular 
 structure, 154 et seq. 
 
 ,, conception of, applied 
 
 to finding best struc- 
 tural formula for a 
 given compound, 144 
 et seq. 
 
 ,, data for determining, 
 
 127 
 
 ,, definition of, 129 
 
 ,, discussion of notation 
 
 adopted in hypothe- 
 sis of, 132 et seq. 
 
 ,, geometrical notion re- 
 
 garding, 182 
 
 ,, gravitational notion of 
 
 van't Hoft, 135 note 
 
 ,, in non-gasifiable com- 
 
 pounds, 137, 241 
 
 ,, limitations made in 
 
 applying the concep- 
 tion of, 154 
 
 ,, Lossen's views regard- 
 
 ing, 145, 193 et seq. 
 
 , , meaning of expression, 
 
 I 3 l 
 
 ,, ought not to be con- 
 
 founded with affinity, 
 470 
 
 ,, probably varies period- 
 
 ically with relative 
 weights of the atoms, 
 241 
 
 Vapour densities, bearings of dissocia- 
 tion on determina- 
 tions of, 391 
 
 Vapour densities, definition of expres- 
 sion, 34 note 
 
 ,, methods of determin- 
 
 ing. 35 note 
 
 ,, must be supplemented 
 
 by analyses before 
 molecular weights of 
 compounds can be 
 found by means of, 35 
 Velocities of chemical actions, con- 
 nexion between, and affinities of re- 
 acting substances, 356 et seq. 
 Volume, atomic, of elements, curve of, 
 
 227 
 
 ,, specific, meaning of expres- 
 sion, 317 
 
 Volumetric methods of studying chemi- 
 cal operations adopted by Ost wald, 372 
 Vortex atoms, bearing of theory of, on 
 chemical equilibrium, 387, 403 
 
 WAAGE (see GULDBERG) 
 WARDER, his experiments on the af- 
 finities of bases, 360 
 Water, basic and saline, 326 
 
 ,, effect of traces of, in chemical 
 
 changes, 467 
 of constitution, 327 
 ,, of crystallisation, 328 
 WATTS (see BRAUNER, also THORPE 
 WEBER, his determinations of the spc 
 cific heats of boron, carbon, and sil 
 con, 63 
 
 WIEDEMANN, E., his attempt to mec 
 sure heat used in separating mol< 
 cule of hydrogen into atoms, 263 
 WILLIAMSON, his hypothesis regardin 
 chemical equilibriun . 
 385 
 ,, his researches on thv 
 
 ethers, 80 
 
 WITT, his experiments on the connex- 
 ion between molecular structure and 
 tinctorial properties, 172 
 WOLLASTON, introduces the use of the 
 
 term equivalent, 14 
 ,, objections to his method 
 
 of determining equiva- 
 lents, ty 
 
 YOUNG (see RAMSAY). 
 
 ZANDER, his experiments on specific 
 volumes of carbon compounds, 322 
 
 ZIMMERMANN, his determination of the 
 specific heat of uranium, 59 
 
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