OUTLINES OF PHYSICAL CHEMISTRY G. SENTER JC-NRLF TEXT- BOOKS OF SCIENCE UNIVERSITY OF CALIFORNIA LIBRARY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW 5w-10,'22 OUTLINES OF PHYSICAL CHEMISTRY OUTLINES OF PHYSICAL CHEMISTRY GEORGE SENTER D.Sc. (LOND.), PH.D. (LEIPZIG), F.I.C. PRINCIPAL AND HEAD OF THE CHEMISTRY DEPARTMENT, BIRKBECK COLLEGE, LONDON EXAMINER IN CHEMISTRY, UNIVERSITY OF LONDON FORMERLY EXTERNAL EXAMINER IN CHEMISTRY, UNIVERSITY OF BIRMINGHAM READER IN CHEMISTRY IN THE UNIVERSITY OF LONDON LECTURER ON CHEMISTRY AT ST. MARY'S HOSPITAL MEDICAL SCHOOL AND EXAMINER IN CHEMISTRY TO THE ROYAL COLLEGE OF PHYSICIANS OF LONDON AND THE ROYAL COLLEGE OF SURGEONS OF ENGLAND NINTH EDITION NEW YORK D. VAN NOSTRAND COMPANY 25 PARK PLAGE 1921 PREFACE TO FIRST EDITION r I A HE present book is intended as an elementary in- troduction to Physical Chemistry. It is assumed that the student taking up the study of this subject has already an elementary knowledge of chemistry and phy- sics, and comparatively little space is devoted to those parts of the subject with which the student is presumed to be familiar from his earlier work. Physical chemistry is now such an extensive subject that it is impossible even to touch on all its important applications within the limits of a small text-book. I have therefore preferred to deal in considerable detail with those branches of the subject which usually present most difficulty to beginners, such as the modern theory of solutions, the principles of chemical equilibrium, elec- trical conductivity and electromotive force, and have devoted relatively less space to the relationships between physical properties and chemical composition. The prin- ciples employed in the investigation of physical proper- ties from the point of view of chemical composition are illustrated by a few typical examples, so that the student should have little difficulty in understanding the special works on these subjects. Electrochemistry is dealt with vi OUTLINES OF PHYSICAL CHEMISTRY rather more fully than has hitherto been usual in ele- mentary works on Physical Chemistry, and the book is therefore well suited for electrical engineers. From my experience as a student and as a teacher, I am convinced that one of the best methods of familiarising the student with the principles of a subject is by means of numerical examples. For this reason I have, as far as possible, given numerical illustrations of those laws and formulae which are likely to present difficulty to the be- ginner. Thi$ is particularly important with regard to cer- tain formulae more particularly those in the chapter on Electromotive Force which cannot easily be proved by simple methods, but which even the elementary student must make use of. The really important thing in this connection is not that the student should be able to prove the formula, but that he should thoroughly understand its meaning and applications. I have throughout the book used only the most ele- mentary mathematics. In order to make use of some of the formulae, particularly those in the chapters on Velo- city of Reaction and Electromotive Force, an elementary knowledge of logarithms is required, but sufficient for the purpose can be gained by the student, if necessary, from a few hours' study of the chapter on " Logarithms " in any elementary text-book on Algebra. The experiments described in the sections headed " Practical Illustrations " at the conclusion of the chap- ters can in most cases be performed with very simple apparatus, and as many as possible should be done by the student. The majority of them are also well adapted for lecture experiments. The more elaborate experi- PREFACE vii ments which are usually performed during a course of practical Physical Chemistry are also mentioned for the sake of completeness ; for full details a book on Practical Physical Chemistry should be consulted. In drawing up my lectures, which have developed into the present book, I have been indebted most largely to the text-books of my former teachers, Ostwald and Nernst, more particularly to Ostwald's Allgemeine Chemie (2nd Edition, Leipzig, Engelmann) and to Nernst's Theo- retical Chemistry (4th Edition, London, Macmillan). 1 The following works, among others, have also been consulted : Van't HofT, Lectures on Physical Chemistry ; Arrhenius, Theories of Chemistry ; Le Blanc, Electrochemistry; Dan- neel, Elektrochemie (Sammlung Goschen) ; Roozeboom, Phasenlehre ; Findlay, The Phase Rule ; Mellor, Chemi- cal Statics and Dynamics ; Abegg, Die elektrolytische Dissociationstheorie. In these books the student will find fuller treatment of the different branches of the subject. References to other sources of information on particular points are given throughout the book. The importance of a study of original papers can scarcely be overrated, and I have given references to a number of easily accessible papers, both in English and German, some of which should be read even by the beginner. In the summarising chapter on " Theories of Solution" references are given which will enable the more advanced student to put himself abreast of the pre- sent state of knowledge in this most interesting subject. In conclusion, I wish to express my most sincere thanks to Assistant-Professor A. W. Porter, of University l The fifth German edition of Nernst's text-book has now appeared. viii OUTLINES OF PHYSICAL CHEMISTRY College, London, for reading and criticising the sections on osmotic pressure and allied phenomena, and for valu- able advice and assistance on many occasions; also to Dr. H. Sand, of University College, Nottingham, and Dr. A. Slator, of Burton, for criticising the chapters on Electromotive Force and on Velocity of Reaction respec- tively. Lastly, I wish to acknowledge my indebtedness to my assistant, Mr. T. J. Ward, in the preparation of the diagrams and for reading the proofs. G. S. November, 1908 PREFACE TO SECOND EDITION AS less than two years have elapsed since the appear- ance of the First Edition, only a few slight altera- tions have been rendered necessary by the progress of the subject in the interval. The opportunity has, how- ever, been taken to revise the text thoroughly ; in one or two places the wording has been slightly altered for the sake of greater clearness, and some misprints have been corrected. A few additions of some importance have also been made. In conformity with the elementary character of the book, the mathematical proofs of the connection be- tween osmotic pressure and the other properties of solu- tions which can be made use of for molecular weight determinations were omitted from the first edition. The book has, however, been more largely used by advanced students than was anticipated, and at the request of several teachers the proofs in question have now been inserted as an appendix to chapter V. The section dealing with the relationship between physical properties and chemical constitution has been rendered more com- plete by the insertion of brief accounts of absorption spectra and of viscosity. is x OUTLINES OF PHYSICAL CHEMISTRY I am again indebted to Professor Porter for much kind advice and assistance, and take this opportunity of expressing to him my grateful thanks. I wish also to acknowledge my indebtedness to a number of friends and correspondents, more particularly to Dr. A. Lapworth, F.R.S., Dr. J. C. Philip, Dr. A. E. Dunstan, Dr. W. Maitland and Mr. W. G. Pirie, M.A.. for valuable sug- gestions. G. S. December, IQIO. PREFACE TO FIFTH EDITION THE fact that a fifth large edition is called for within seven years of the first appearance of this book shows that the object with which it was written to assist in spreading a knowledge of the principles and methods of Physical Chemistry is being satisfactorily fulfilled. The opportunities afforded by the calls for successive editions have been taken advantage of to keep the book up to date and further to increase its usefulness by in- troducing certain new sections and amplifying others. Thus for the Third Edition a new chapter on Colloidal Solutions was written and a selection of questions and numerical problems was added. In the Fourth Edition the latter important section was amplified, and the last chapter, on Electromotive Force, was considerably ex- tended. For the Present Edition additions have been made to the chapters on Thermochemistry and on Heterogeneous Equilibrium, and a number of minor alterations have been made. In the Preface to the First Edition the great educa- tional value of numerical problems and examples was emphasized, and further experience has served to con- firm and strengthen the opinion then stated. In addition to working out the problems in the book, the student would do well to make use of one or other of the excel- lent books on Physico-chemical Calculations which have recently appeared. G. S. LUMSDEN, ABERDEENSHIRB, September, 1915. TABLE OF CONTENTS (The numbers refer to pages) CHAPTER I PAGE FUNDAMENTAL PRINCIPLES OF CHEMISTRY. THE ATOMIC THEORY T Elements and compounds, i Laws of chemical combination, 3 Atoms and molecules, 5 Fact. Generalisation or natural law. Hypothesis. Theory, 6 Determination of atomic weights. General, 8 Volumetric method. Gay-Lussac's law of volumes. Avogadro's hypothesis, g Dulong and Petit's law, n Isomorphism, 13 Determination of atomic weights by chemical methods, 14 Relation between atomic weights and chemical equivalents. Valency, 15 The values of the atomic weights, 16 The periodic system, 20. CHAPTER II GASES 25 The gas laws, 25 Deviations from the gas laws, 28 Kinetic theory of gases. General, 29 Kinetic equation for gases, 30 Deduction of gas laws from the equation pv = |wwc 2 , 31 Van der Waals' equation, 33 Avogadro's hypothesis and the molecular weight of gases. General, 36 Density and molecular weight of gases and vapours, 36 Results of vapour density determinations. Abnormal molecular weights, 40 Association and dissociation in gases, 41 Ac- curate determination of molecular and atomic weights from gas densities, 42 Specific heat of gases. General, 43 TABLE OF CONTENTS Specific heat at constant pressure, Cj,, and constant volume, C,, 44 Specific heat of gases and the kinetic theory, 46 Experimental illustrations, 47. CHAPTER III LIQUIDS General, 49 Transition from gaseous to liquid state. Critical phenomena, 49 Behaviour of gases on compression, 51 Application of Van der Waals* equation to critical pheno- mena, 53 Law of corresponding states, 56 Liquefaction of gases, 58 Relation between physical properties and chemi- cal composition of liquids. General, 59 Atomic and mole- cular volumes, 60 Additive, constitutive, and colligative properties, 62 Refractivity, 63 Rotation of plane of polarization of light, 66 Absorption of light, 69 Viscosity, 73 Practical illustrations, 77 CHAPTER IV SOLUTIONS General 80 Solution of gases in gases, 81 Solubility of gases in liquids, 82 Solubility of liquids in liquids, 84 Distilla- tion of homogeneous mixtures, 87 Distillation of non- miscible or partially miscible liquids ; steam distillation, 90 Solution of solids in liquids, 91 Effect of change of tem- perature on the solubility of solids in liquids, 92 Relation between solubility and chemical constitution, 94 Solid solutions, 94 Practical illustrations, 95. CHAPTER V DILUTE SOLUTIONS General, 97 Osmotic pressure. Semi-permeable membranes, 97 Measurement of osmotic pressure, 99 Van't Hoff's theory of solution, 101 Recent direct measurements of osmotic pressure, 104 Other methods of determining osmo- tic pressure, 105 Mechanism of osmotic pressure, 106 Osmotic pressure and diffusion, 108 Molecular weight of dissolved substances. General, IOQ Molecular weights x-'v OUTLINES OF PHYSICAL CHEMISTRY PAGE from osmotic pressure measurements, no Lowering of vapour pressure, in Elevation of boiling-point, 114 Ex- perimental determination of molecular weights by the boiling-point method, 116 Depression of the freezing-point, 119 Experimental determination of molecular weights by the freezing-point method, 120 Results of molecular weight determinations in solution. General, 121 Abnormal mole- cular weights, 123 Molecular weight of liquids, 125 The results of measurements, 127 Nature of surface tension, 129 Practical illustrations, 129. Mathematical deduction of formulae, 131. CHAPTER VI THERMOCHEMISTRY I39 General, 137 Hess's law, 139 Representation of thermo- chemical measurements. Heat of formation. Heat of solution, 141 Heat of combustion, 145 Thermochemical methods, 145 Results of thermochemical measurements, 147 Relation of chemical affinity to heat of reaction, 148 Practical illustrations, 153. CHAPTER VII EQUILIBRIUM IN HOMOGENEOUS SYSTEMS. LAW OF MASS ACTION . . . 154 General, 154 Law of mass action, 155 Strict proof of the law of mass action, 160 Decomposition of hydriodic acid, 161 Dissociation of phosphorus pentachloride, 163 Equili- brium in solutions of non-electrolytes, 164 Influence of temperature and pressure on chemical equilibrium. General, 166" Le Chatelier's theorem, 169 Relation between chemi- cal equilibrium and temperature. Nernst's views, 169 Practical illustrations, 170. CHAPTER VIII HETEROGENEOUS EQUILIBRIUM. THE PHASE RULE 172 General, 172 Application of law of mass action to hetero- geneous equilibrium, 172 Dissociation of salt hydrates, 17 \ TABLE OF CONTENTS xv PAGE Dissociation of ammonium hydrosulphide, 176 Analogy between solubility and dissociation, 177 Distribution of a solute between two immiscible liquids, 177 The phase rule. Equilibrium between water, ice and steam, 179 Equilibrium between four phases of the same substance. Sulphur, 183 Systems of two components. Salt and water, 186 Freezing mixtures, 189 Systems of two components. General, 190 Hydrates of ferric chloride, 194 Transition points, 197 Practical illustrations, 197. CHAPTER IX VELOCITY OF REACTION. CATALYSIS . .200 General, 200 Unimolecular reaction, 202 Other unimolecular reactions, 205 Bimolecular reactions, 207 Trimolecular reactions, 209 Reactions of higher order. Molecular- kinetic considerations, 211 Reactions in stages, 212 Determination of the order of a reaction, 213 Complicated reaction velocities, 215- Catalysis. General ,217 Charac- teristics of catalytic actions, 217 Examples of catalytic action. Technical importance of catalysis, 219 Biological importance of catalysis. Enzyme reactions, 221 Mechan- ism of catalysis, 222 Nature of the medium, 224 Influence of temperature on the rate of chemical reaction, 225 Formulae connecting reaction velocity and temperature, 228 Practical illustrations, 229. CHAPTER X ELECTRICAL CONDUCTIVITY . . . .234 General, 234 Electrolysis of solutions. Faraday's laws, 236 Mechanism of electrical conductivity, 238 Freedom of the ions before electrolysis, 240 Dependence of conductivity on the number and nature of the ions, 242 Migration velocity of the ions, 243 Practical determination of the relative migration velocities of the ions, 246 Specific, molecular and equivalent conductivity, 249 Kohlrausch's law. Ionic velocities, 251 Absolute velocity of the ions. Internal xvi OUTLINES OF PHYSICAL CHEMISTRY friction, 253 Experimental determination of conductivity of electrolytes, 254 Experimental determination of molecular conductivity, 257 Results of conductivity measurements, 258 Electrolytic dissociation, 260 Degree of ionisation from conductivity and osmotic pressure measurements, 261 Effect of temperature on conductivity, 263 Basicity of acids from conductivity measurements, 264 Grotthus' hypo- thesis of electrical conductivity, 264 Practical illustrations, 264. CHAPTER XI EQUILIBRIUM IN ELECTROLYTES. STRENGTH OF ACIDS AND BASES. HYDROLYSIS . The dilution law, 266 Strength of acids, 269 Strength of bases, 274 Mixture of two electrolytes with a common ion, 276 Isohydric solutions, 277 Mixture of electrolytes with no common ion, 278 Dissociation of strong electrolytes, 279 Electrolytic dissociation of water. Heat of neutrali- sation, 283 Hydrolysis, 285 Hydrolysis of the salt of a strong base and a weak acid, 287 Hydrolysis of the salt of a weak base and a strong acid, 290 Hydrolysis of the salt of a weak base and a weak acid, 292 Determination of the dissociation constant for water, 293 Theory of indica- tors, 296 The solubility product, 298 Applications to analytical chemistry, 300 Experimental determination of the solubility of difficultly soluble salts, 301 Complex ions, 303 Influence of substitution on degree of ionisation, 304 Reactivity of the ions, 306 Ampho'reric electrolytes, 307 Practical illustrations, 308. CHAPTER XII COLLOIDAL SOLUTIONS. ADSORPTION. . Colloidal solutions. General, 313 Preparation of colloidal solu- tions, 315 Osmotic pressure and molecular weight of colloids, 316 Optical properties of colloidal solutions, 317 Brownian movement, 318 Electrical properties of col- loids, 319 Precipitation of colloids by electrolytes, 320 PAGE TABLE OF CONTENTS xvii Suspensions, suspensoids and emulsoids, 322 Filtration of colloidal solutions, 323 Adsorption, general, 324 Adsorp- tion of gases. Adsorption formulae, 328 The cause of adsorption, 329 Further illustrations of adsorption, 330. CHAPTER XIII THEORIES OF SOLUTION 333 General, 333 Evidence in favour of the electrolytic dissociation theory, 335 lonisation in solvents other than water, 337 The old hydrate theory of solution, 339 Mechanism of electrolytic dissociation. Function of the solvent, 342 Hydration in solution, 345. CHAPTER XIV ELECTROMOTIVE FORCE . . .. , . .348 The Daniel cell, 348 Relation between chemical and electrical energy, 351 Measurement of electromotive force, 354 Standard of electromotive force. The cadmium element, 356 Solution pressure, 358 Calculation of electromotive force at a junction metal/salt solution, 360 Differences of potential in a voltaic cell, 362 Influence of change of con- centration of salt solution on the E.M.F. of a cell, 365 Concentration cells, 367 Cells with different concentrations of the electrode materials (substances producing ions), 371 Electrodes of the first and second kind. The calomel elec- trode, 373 Single potential differences. The capillary electrometer, 378 Gas cells, 383 Potential series of the elements, 387 Cells with different gases, 391 Oxidation- reduction cells, 393 Electromotive force and chemical equilibrium, 396 Electrolysis and polarization, 398 Sep- aration of ions (particularly metals) by electrolysis, 400 The electrolysis of water, overvoltage at electrodes, 401 Electrolysis and polarization (continued) 404 Accumulators, 405. The electron theory, 407 Practical illustrations, 410. b DEFINITIONS AND UNITS 1 In this section the centimetre-gram-second (C.G.S.) system of units is used throughout, length being measured in centimetres (cms.), mass in grams, and time in seconds. Density is mass per unit volume : unit, gram per c.c. (cubic centi- metre). Specific Volume (i/density) is volume per unit mass : unit, c.c. per gram. Velocity is rate of change of position : unit, cm. per sec. or cm. /sec. Acceleration is rate of change of velocity : unit, cm. per sec. per sec. or cm./sec. 2 . Momentum is mass x velocity : unit, gram-cm, per sec. Force is mass x acceleration (rate of change of momentum). Unit, the dyne, is that force which is required to produce an acceleration of i cm. per sec. per sec. in a mass of i gram. As a gram-weight, falling freely, obtains an acceleration of 980-6 cm. per sec. (owing to the attraction of the earth) the force represented by the gram-weight = 980*6 dynes at a latitude of 45 and at sea-level. Energy may be defined as that property of a body which diminishes when work is done by the body ; and its diminution is measured by the amount of work done. Work Done is force x distance (the work done by a force is measured by the product of the force and the distance through which the point of application moves in the direction of the force). The unit of work 1 The more important constants made use of in physical chemistry are collected here for convenience of reference. DEFINITIONS AND UNITS xix (which is also the unit of energy) is the dyne-centimetre or erg. The gram-centimetre unit is sometimes used; i gram-centimetre = 980*6 ergs ; also the joule (= io 7 ergs) is frequently used, especially in electrical work (see below). Power is rate of doing work, unit, erg per second. There are six chief forms of energy: (i) mechanical energy, (2) volume energy, (3) electrical energy, (4) heat, (5) chemical energy, (6) radiant energy. These forms of energy are mutually convertible, and according to the law of conservation of energy, there is a definite and invariable relationship between the quantity of one kind of energy which disappears and that which results. The unit of energy, the erg, has already been defined. It is some- times convenient to express certain forms of energy in special units, heati for example, in calories ; in the following paragraphs the equivalents in ergs of these special units are given. Volume Energy is often measured in litre-atmospheres. When a volume, !, of a gas expands to the volume v 2 against a constant pressure p, say that of the atmosphere, the external work done by the gas (gained) is p (#2 - *>i). The (average) pressure of the atmosphere on unit area (i sq. cm.) supports a column of mercury 76 cm. high and i sq. cm. in cross-section. Hence the pressure on i sq. cm. = 76 x 13*596 = 1033*3 grams weight (as the density of mercury is 13*596), or 1033*3 x 980*6 = 1,013,200 dynes. As the work done is the product of the constant pres- sure and the increase of volume, i litre-atmosphere (the work done when the increase in the volume of a certain quantity of a gas is i litre or 1000 c.c.) = 1,013,200 x 1000 ^= 1,013,200,000 ergs. Electrical Energy is the product of electromotive force and quantity of electricity, and is usually measured in volt-coulombs or joules. The practical unit of quantity of electricity is the coulomb; it is that quantity of electricity which under certain conditions liberates 0*001118 grams of silver from a solution of silver nitrate. If a coulomb passes through a conductor in i second, the strength of current is i ampere; the latter is therefore the practical unit of strength of current. The practical unit of resistance is the o/tw, which is the resistance at o offered by a column of mercury 106*3 cm l n g an< ^ weighing 14*4521 grams. The practical unit of electromotive force is the volt ; when a current of i ampere passes in i second through a conductor of resistance i ohm, the electromotive force is i volt. xx OUTLINES OF PHYSICAL CHEMISTRY The definitions of the C.G.S. units of electromotive force, current strength and resistance are to be found in text-books of physics, and cannot be given here. It can be shown that i ohm = io 9 C.G.S. units and i ampere = i/io C.G.S. unit; hence, by Ohm's law, i volt =* io 8 C.G.S. units. Further, i volt-coulomb or i joule =* io 8 x io- 1 io 7 C.G.S. units or io 7 ergs. Heat Energy is measured in calories. The mean calorie is i/ioo of the amount of heat required to raise i gram of water from o to 100 and does not differ much from the amount of heat required to raise i gram of water from 15 to 16. i calorie = 42,650 gram-centimetres = 41,830,000 ergs (the mechanical equivalent of heat) = 4*183 joules. One joule =s 0*2391 calories. There is no special unit for chemical energy ; it is usually measured in volt-coulombs or calories. The value of R, in the general gas equation (p. 27) for a mol of gas = 34,760 gram-centimetres = 83,150,000 ergs = 8-3 15 joules = 1-985 calories 0*08205 litre-atmospheres. USE OF SIGNS IN ELECTRO-CHEMISTRY. There has always been much confusion in Electro-chemistry as to the proper use of positive and negative signs, and even now no general agreement has been reached on the subject. Recently, however, a simple convention has been suggested by the German Electro-chemical Society (Bunsen-Gesellschaft) which promises to find general acceptance. The potential difference has the positive sign if the metal is charged positively with respect to the solution^ and negative if the metal is negatively charged, when metal and solution are combined with a comparison electrode to form a cell (cf. p. 358). In the present book, while this con- vention is adopted for the potential series of the elements, etc., the potential differences are often given in absolute value and the E.M.F. of combinations illustrated by the graphic method described on pp. 365, 377, 386 and elsewhere. As a result of considerable experience, it has been found that the graphic method is much more useful in avoiding errors of sign than any convention with regard to the use of signs. OUTLINES OF PHYSICAL CHEMISTRY CHAPTER I FUNDAMENTAL PRINCIPLES OF CHEMISTRY. THE ATOMIC THEORY Elements and Compounds Definite chemical substances are divided into the two classes of elements and chemical com- pounds. Boyle, and later Lavoisier, defined an element as a substance which had not so far been split up into anything simpler. The substances formed by chemical combination of two or more elements were termed chemical compounds This definition proved to be a very suitable one, and retained its value even when many of the substances classed as ele- ments by Lavoisier proved to be complex. In course of time it came to be recognised that the substances which resisted further decomposition possessed certain other properties in com- mon, for example, the so-called atomic heat of solid elements proved to be approximately 6*4 (p. 12), and it was found possible to assign even newly-discovered elements with more or less certainty to their appropriate positions in the periodic table of the elements p. 21). There are, therefore, conclusive reasons, apart from the fact that they have so far resisted decomposi- tion, for regarding elements as of a different order from chemical compounds, and these reasons remain equally valid when full allowance is made for the remarkable discoveries of the last few years in this branch of knowledge. 2 OUTLINES OF PHYSICAL CHEMISTRY Until lately no case of the transformation'of one element into another was known, but recent work on radium, by Ramsay and Soddy and others, has shown that this element is continuously undergoing a series of transformations, one of the final products of which is the inactive gas helium. It might at first sight be supposed that the old view of the impossibility of transforming the elements could be maintained, radium being looked upon as a chemical compound of helium with another element, but further consideration shows that this suggestion is not tenable, as radium fits into the periodic table, and, so far as is known, possesses all those other properties which have so far been con- sidered characteristic of elements as distinguished from chemical compounds. Evidence is gradually accumulating which indicates that the slow disintegration, with final production of other elements, is not confined to radium alone, but is shown more particularly by certain elements of high atomic weight such as uranium and thorium. It is true that the change is spontaneous, as so far there is no known means of initiating it or even of influencing its rate, but further progress in this direction is doubtless only a matter of time. As the phenomenon in question is probably a general one, it seems desirable to retain the term " element " to indicate a substance which has a definite position in the periodic table, and has the other properties usually regarded as characteristic of elements. From what has been said, it will be evident that it is difficult to define an element in a few words, but in practice there will probably not be much difficulty in drawing the distinction between elements and compounds. Ostwald : (1907) defines an element as a substance which only increases in weight as the result of a chemical change, and which is stable under any attainable conditions of temperature and pressure, but in this definition the question of radio-active substances is left out of account. 1 Prinzipien der Chemie, Leipzig, 1907, p. 266, FUNDAMENTAL PRINCIPLES OF CHEMISTRY 3 Laws of Ghemioal Combination Towards the end of the eighteenth century, Lavoisier established experimentally the law of the conservation of mass, which may be expressed as follows : When a chemical change occurs, the total weight (or mass) of the reacting substances is equal to the total weight (or mass) of the products. As the weight is proportional to the mass or quantity of matter, the above law may also be stated in the form that the total quantity of matter in the uni- verse is not altered in consequence of chemical (or any other) changes. It is, of course, impossible to prove the law with absolute certainty, but the fact that in accurate atomic weight determinations no results in contradiction with it have been obtained shows that it is valid at least within the limits of the unavoidable experimental error. The enunciation of the law of the conservation of mass by Lavoisier, and the extended use of the balance, facilitated the investigation of the proportions in which elements combine, and soon afterwards the first law of chemical combination was estab- lished by the carefal experimental investigations of Richter and Proust. This law is usually expressed as follows : A definite compound always contains the same elements in the same proportions. The truth of this law was called in question by the famous French chemist Berthollet. Having observed that chemical processes are greatly influenced by the relative amounts of the reacting substances (p. 155), he contended that when, for example, a chemical compound is formed by the combination of two elements, the proportion of one of the elements in the compound will be the greater the more of that element there is available. This suggestion led to the famous controversy between Berthollet and Proust (1799-1807), which ended in the firm establishment of the law of constant proportions. All subsequent work has shown that the law in question is valid within the limits of experimental error. In certain cases, elements unite in more than one proportion 4 OUTLINES OF PHYSICAL CHEMISTRY to form definite chemical compounds. Thus Dalton found by analysis that two compounds of carbon and hydrogen methane and ethylene contain the elements in the ratios 6 : 2 and 6 : i by weight respectively ; in other words, for the same amount of carbon, the amounts of hydrogen are in the ratio 2:1. Similar simple relations were observed for other compounds, and on this experimental basis Dalton (1808) formulated the Law of Multiple Proportions, as follows : When two elements unite in more than one proportion, for a fixed amount of one element there is a simple ratio between tfo amounts of the other element. Dalton 's experimental results were not of a high order of accuracy, but the validity of the law was proved by the subsequent investigations of Berzelius, Marignac and others. Finally, there is a third comprehensive law of combination, which includes the other two as special cases. It has been found possible to ascribe to each element a definite relative weight, with which it enters into chemical combination. The Law of Combining Proportions, which expresses this conception, is as follows : Elements combine in the ratio of their combining weights } or in simple multiples of this ratio. The combining weights are found by analysis of definite com- pounds containing the elements in question. When the com- bining weight of hydrogen is taken as unity, the approxi- mate values for chlorine, oxygen and sulphur are 35*5, 8 and 1 6 respectively. These numbers also represent the ratios in which the elements displace each other in chemical com- pounds. Water, for example, contains 8 parts by weight of oxygen to i of hydrogen, and when the former element is dis- placed by sulphur (forming hydrogen sulphide) the new com- pound is found to contain 16 parts by weight of the latter element. 16 parts of sulphur are therefore equivalent to 8 parts of oxygen, and the combining weights are therefore often termed chemical equivalents. The chemical equivalent of an element is FUNDAMENTAL PRINCIPLES OF CHEMISTRY 5 that quantity of it which combines with, or displaces, one part (strictly 1*008 parts) by weight of hydrogen (cf. p. 18). It must be clearly understood that the above generalisations or kws are purely experimental ; they express in a simple form the results of the investigations of many chemists on the com- bining powers of the elements, and are quite independent of any hypothesis as to the constitution of matter. As they have been established by experiment, we are certain of their validity only within the limits of the unavoidable experimental error, and cannot say whether they are absolutely true. It is possible that when the methods of analysis are greatly improved, it will be possible to detect small variations in the composition of definite compounds, but up to the present the most careful investigations, in the course of atomic weight determinations, have failed to show any deviation from the results to be expected according to the laws. Atoms and Molecules The question now arises as tu whether a theory can be suggested which allows of a convenient and consistent representation of the laws enunciated above. The atomic theory, first brought forward in its modern form by Dalton (1808), answers these requirements. Following out an idea of the old Greek philosophers, Dalton suggested that matter is not infinitely divisible by any means at our disposal, but is made up of extremely small particles termed atoms ; the atoms of any one element are identical in all respects and differ, at least in weight, from those of other elements. By the association of atoms of different kinds, chemical compounds are formed. The laws of chemical combination find a simple explanation on the atomic theory. Since a chemical compound is formed by the association of atoms, each of which has a definite weight, it must be of invariable composition. Further when atoms combine in more than one proportion, for a fixed amount of atoms of one kind the amount of the other must in- crease in steps, depending on the relative atomic weight which is the law of multiple proportions. It is here assumed that 6 OUTLINES OF PHYSICAL CHEMISTRY the ultimate particles of a compound are formed by the associa- tion of comparatively few atoms, and this holds in general for inorganic compounds. Finally, the law of combining weights is also seen to be a logical consequence of the atomic theory, the empirically found combining weights, or chemical equiva- lents, bearing a simple relation to the (relative) weights of the atoms (p. 15). When Dalton brought forward the atomic theory, the number of facts which it had to account for was comparatively small. As knowledge has progressed, the atomic theory has proved capable of extension to represent the new facts, and its applica- tion has led to many important discoveries. At the present day, the great majority of chemists consider that the atomic theory has by no means outgrown its usefulness. Fact. Generalisation or Natural Law. Hypothesis. Theory 1 Chemistry, like most other sciences, is based on facts, established by experiment. A few such facts have already been mentioned, for example, that certain chemical compounds, which have been investigated with the greatest care, always contain the same elements in the same proportions. A mere collection of facts, however, does not constitute a science. When a certain number of facts have been established, the chemist proceeds to reason from analogy as to the behaviour of systems under conditions which have not yet been investigated. For example, Proust showed by careful analyses that there are two well-defined oxides of tin, and that the composition of each is invariable. From the results of these and a few other investigations, he concluded from analogy that the composition of all pure chemical compounds is invariable, although of course very few of them had then been investigated from that point of view. To proceed in this way is to generalise , and the short statement of the conclusion arrived at is termed a generalisation 1 H. Poincare", La Science et VHypothese, Paris, Flammarion ; Ostwald, Vorlesungen uber Natur philosophic, Leipzig, 1902; Alexander Smith, General Inorganic Chemistry, London, 1906. FUNDAMENTAL PRINCIPLES OF CHEMISTRY 7 or law. It will be evident that a law is not in the nature of an absolute certainty ; it comprises the facts experimentally estab- lished, but also enables us (and herein lies its value) to foretell a great many things which have not been, but which if necessary could be, investigated experimentally. The greater the number of cases in which a law has been found to hold, the greater is the confidence in its validity, until finally a law may attain practically the same standing as a statement of fact. We may confidently expect that however greatly our views regarding natural pheno* mena may change, such generalisations as the law of constant proportions will remain eternally true. Natural laws can be discovered in two ways : (i) by corre- lating a number of experimental facts, as just indicated ; (2) by a speculative method, on the basis of certain hypotheses as to the nature of the phenomena in question. The meaning to be at- tached to the term " hypothesis " is best illustrated by an example. In the previous section we have seen that the laws of chemical combination are accounted for satisfactorily on the view that matter is made up of extremely small, discrete particles, the atoms. Such a mechanical representation, which is more or less inaccessible to experimental proof, is termed a hypothesis A hypothesis may then be defined as a mental picture of an unknown, or largely unknown, state of affairs, in terms of some- thing which is better known. Thus, the state of affairs in gases, which is and will remain unknown to us, is represented, according to the kinetic theory, in terms of an enormous number of rapidly moving perfectly elastic particles, and on this basis it is possible, with the help of certain assumptions, to deduce certain of the laws which are actually followed by gases (p. 25). There does not appear to be any fundamental distinction in the use of the terms hypothesis and theory. A theory may be defined as a hypothesis, many of the deductions from which have been confirmed by experiment, and which admits of the con- venient representation of a large number of experimental facts. There is some difference of opinion as to the value of ft OUTLINES OF PHYSICAL CHEMISTRY hypotheses and theories for the advancement of science. 1 The majority of scientists, however, appear to consider that the advantages of hypotheses, regarded in the proper light and not as representing the actual state of affairs, are much greater than the disadvantages Boltzmann, 2 indeed, maintains that "new discoveries are made almost exclusively by means of special mechanical conceptions ". DETERMINATION OF ATOMIC WEIGHTS General Aftei the laws of chemical combination had been established, the next problem with which chemists had to deal was the determination of the relative atomic weights of the elements. This might apparently be done by fixing on one element, say hydrogen, as the standard ; a compound containing hydrogen and another element may then be analysed, and the amount of the other element combined with one part of hydrogen will be its atomic weight. It is clear, however, that this will be the case only when the binary compound contains one atom of each element, and it was just this difficulty of deciding the relative number of atoms of the two elements present that rendered the decision between a number and one of its multi- ples or sub-multiples so difficult. It has already been pointed out that the amount of an ele- ment which combines with, or displaces, part by weight of hydrogen (strictly speaking, 8 parts by weight of oxygen) is termed the combining weight or chemical equivalent of an ele- ment. The first step in determining the atomic weight of an element is to find the chemical equivalent as accurately as pos- sible by analysis and then to find the relation between the atomic weight and chemical equivalent by one of the methods described below. The atomic weight may be equal to, or a simple multiple of, the chemical equivalent. 1 In one or two recent books, Ostwald has treated certain branches of chemistry on a system free from hypotheses. a (ras Theorie, Leipzig, 1896, p. 4. FUNDAMENTAL PRINCIPLES OF CHEMISTRY 9 Dalton, working on the assumption that when two elements unite in only one proportion one atom of each is present, drew up the first table of atomic weights. Water was found by analysis to contain i part of hydrogen to 8 parts of oxygen by weight ; the atomic weight of oxygen was therefore taken as 8. In the same way, since ammonia contained i part of hydrogen to 4*6 parts of nitrogen, the atomic weight of the latter element was taken as 4*6. Great advances in this subject were then made by the Swedish chemist Berzelius. For fixing the pro- portional numbers, he depended to some extent, like Dalton, on the assumption of simplicity of composition, but was able to check the numbers thus obtained by the application of Gay- Lussac's law of volumes and Dulong and Petit's law. Later still, the discovery of isomorphism by Mitscherlich afforded yet another means of checking the atomic weights. Besides these physical methods, chemical methods may also be used for fixing the atomic weights of the elements. Each of these methods will now be shortly referred to. (a) Volumetric Method. Gay-Lussac's Law of Volumes Avogadro's Hypothesis Gay-Lussac, on the basis of an extensive series of experiments on the combining volumes of gases, established the law of gaseous volumes, which may be expressed as follows : Gases combine in simple ratios by volume, and the volume oj the gaseous product bears a simple ratio to the volumes of the re- acting gases ', when measured under the same conditions. A few years before, the same chemist had discovered that all gases behave similarly with regard to changes of pressure and temperature, and this fact, taken in conjunction with the law of volumes and the atomic theory, seemed to point to some simple relation between the number of particles in equal volumes of different gases. Berzelius suggested that equal volumes of different gases, under corresponding conditions of temperature and pressure, contain the same number of atoms. It was soon found, however, that this assumption was untenable, and the io OUTLINES OF PHYSICAL CHEMISTRY view held at the present day was first enunciated by the Italian physicist Avogadro. He drew a distinction between atoms, the smallest particles which can take part in chemical changes, and molecules, the smallest particles which can, exist in a free con- dition, and expressed his hypothesis as follows : Equal volumes of all gases, under the same conditions oj temperature and pressure, contain the same number of molecules. In expressing the results of determinations of the densities of different gases, hydrogen, as the lightest gas, is taken as standard, and the number expressing the ratio of the weights of equal volumes of another gas (or vapour) and hydrogen, measured under the same conditions, is the density of the gas (or vapour density in the case of a vapour). From Avogadro's hypothesis it follows at once that the ratio of the vapour densities of another gas and hydrogen, being a comparison of the relative weights of an equal number of molecules, is also the ratio of the molecular weights. It is usual to refer both atomic and mole- cular weights to the atom of hydrogen as unity, 1 and therefore the molecular weight, being referred to a standard half that to which the vapour density is referred, is double the vapour density. When the molecular weight is known, it is a comparatively simple matter to establish the atomic weight. As an example, we may employ the volumetric method to fix the atomic weight of beryllium, a matter of great historical interest. It was found by analysis that beryllium chloride contains 4*55 parts of beryllium to 35*5 parts of chlorine by weight; in other words, the chemi- cal equivalent of beryllium is 4*55. If beryllium be regarded as a bivalent metal (p. 16), the formula for the chloride will be BeCl 2 , and its' atomic weight 2 x 4*55 = 9*1. If, however, it is trivalent, the formula for the chloride must be BeCl 3 , and, to obtain the ratio for Be : Cl found experimentally, its atomic weight must be 4-55 x 3 -= 13*65. The vapour density of the chloride was de- termined by Nilson and Petterson, and from the result the mole- cular weight calculated as 8o'i. The molecule of beryllium 1 Strictly speaking, to the atom of oxygen as 16 (p. 18). FUNDAMENTAL PRINCIPLES OF CHEMISTRY n chloride cannot therefore contain more than 35-5 x 2 = 71 parts of chlorine, the formula for the chloride is BeCL^, and the atomic weight of beryllium 9*1. The determination of atomic weights by the volumetric method thus reduces to finding the smallest quantity of an element present in a molecule, referred to the atom of hydrogen as unity. If the molecular weights of a large number of vola- tile compounds containing a particular element are determined, it is practically certain that at least some of the compounds will contain only one atom of the element in question, and the pro- portion in which the element is present in these compounds is its atomic weight. In the above example, for instance, it has been assumed that only one atom of beryllium is present in the molecule of beryllium chloride of weight 80* i, and the justification for this assumption is that no compound is known the molecule of which contains less than 9*1 parts of beryllium. It is clear that the numbers thus obtained are maximum values, and the possibility is not excluded that the true values may be fractions of those thus arrived at. The values generally accepted are, however, confirmed by so many independent methods that every confidence can be placed in their trustworthiness. (b) Dulong and Petit's Law In 1818, the French chemists Dulong and Petit enunciated the important law that for solid elements the product of the specific heat and atomic weight is constant^ amounting to about 6*4. This law is a very striking one when the great differences in the magnitude of the atomic weights are taken into account. Thus, the specific heat of lead the ratio of the quantity of heat required to raise i gram of the metal i in temperature to that required to raise the temperature of the same weight of water i is 0-031, and its atomic weight 207, the product being 6*4 ; whilst for lithium, with a specific heat of 0*9 and an atomic weight of 7, the product is 6-3. Since quantities of the different elements in the proportion of their atomic weights require the same amount 12 OUTLINES OF PHYSICAL CHEMISTRY of heat to raise the temperature by a definite number of degrees, the law may also be expressed as follows : The atoms of all de- ments have the same capacity for heat. It is clear that this law can be used to determine the atomic weight of an element when the specific heat is known, the quotient of the constant by the specific heat giving the re- quired value. Dulong and Petit's law was largely used by Berzelius in fixing the values of the atomic weights. Like many other empirical laws, that of Dulong and Petit is only approximately true, the " constant " varying from about 6'o to 6*7. This degree of concordance is, of course, quite sufficient for fixing the values of the atomic weights, as it is only necessary for this purpose to choose between a number and a simple multiple or submultiple. Moreover, the specific heat varies with the allotropic form of the element and with the temperature, and there is much uncertainty as regards the proper conditions for comparison. Regnault, who made a series of very careful determinations of specific heats, showed that most elements of small atomic weight, more particularly carbon, silicon and boron, have exceptionally small atomic heats. Later, how- ever, it was found that the specific heats of these elements increase rapidly with rise of temperature, and at high tempera- tures their behaviour is in approximate accordance with Dulong and Petit's law. This is clear from the accompanying table, showing the behaviour of carbon (diamond) and boron. CARBON (DIAMOND). BORON. Temp. Sp. Heat. Atomic Heat. Temp. Sp. Heat. Atomic Heat. 10 206 600 1000 0-1128 0-2733 0-4408 0-4589 l'33 3-25 5-28 5'5i 2 7 126 177 233 0-2382 0-3069 0-3378 0-3663 2-61 3-40 3-70 4*02 The few elements which show this abnormal behaviour are of FUNDAMENTAL PRINCIPLES OF CHEMISTRY 13 low atomic weight, but the converse does not hold, as the atomic heat of lithium is normal. Some years after the introduction of Dulong and Petit's law, a similar law for compounds was enunciated by Neumann. He showed that, for compounds of similar chemical character, the product of specific heat and molecular weight is constant in other words, the molecular heats of similarly constituted com- pounds in the solid state are equal. In 1864, Kopp extended Neumann's law by showing that the molecular heat of solid compounds is an additive property, being made up of the sum of the atomic heats of the component atoms. It follows that in certain cases atoms have the same capacity for heat before and after entering into chemical combination. For ex- ample, the specific heat of calcium chloride is 0^174, the mole- cular heat is therefore 0*174 x in = 19*3, and the atomic heat of each atom 6 '4. This law may be used to estimate the atomic heats of sub- stances which cannot be readily investigated in the solid form, The atomic heat of solid oxygen in combination is about 4*0 and of solid hydrogen 2 '3. (c) Isomorphism Mitscherlich observed that the corre- sponding salts of arsenic acid, H 3 AsO 4 , and phosphoric acid, H 3 PO 4 , crystallize with the same number of molecules of water, are identical, or nearly so, in crystalline form, and can be obtained from mixed solutions in crystals containing both salts, so-called mixed crystals. On the basis of these and similar observations, Mitscherlich established the Law of Isomorphism, according to which compounds of the same crystalline form are of analogous constitution. Thus, when one element replaces another in a compound without altering the crystalline form, it is assumed that one element has displaced the other atom for atom. The replacing quantities of the different elements are therefore in the ratio of their atomic weights, and if the atomic weight of one of them is known, that of the other can be calculated. This principle was largely used by Berzelius for fixing atomic i 4 OUTLINES OF PHYSICAL CHEMISTRY weights before the establishment of Dulong and Petit's law, and afforded a welcome corroboration of those obtained by the use of the law of volumes. The converse to the law of isomorphism does not hold, as elements may displace one another atom for atom with complete alteration of crystalline form. The principle of isomorphism is, however, somewhat in- definite, inasmuch as even the most closely related compounds are not completely identical in crystalline form, and it is difficult to decide where the line between similarity and want of similarity is to be drawn. Thus the corresponding angles for the naturally-occurring crystals of the carbonates of cal- cium, strontium and barium are: Aragonite, 116 10'; Stron- tianite, 117 19'; Witherite, 118 30'. Tutton, 1 from a careful comparative study of the sulphates and selenates of potassium, rubidium and caesium, has shown that each salt has its own specific interfacial angle, but the differences produced by dis- placing one metal of the alkali series by another does not exceed i of arc, and is usually much less. The three most important characteristics for the establishment of isomorphism are : (1) The capacity of forming mixed crystals. The miscibility must be complete, or within fairly wide limits of concentration. (2) Similarity of crystalline form, which must include at least approximate agreement in the values of the geometrical con- stants. (3) The capacity of crystals of one substance to increase in size in a saturated solution of the other. ( jn p 1 1 m M * vo N ^ r^ 5 * 00 . ffi O H CO N II o\ ^* CO * a& II O II C/3 T^ ii n O D W M 4 ' I > EO M II H CO II PL. ^ H z< o N Si II ^ "b ^^5 "128 n "I 1 > r rt S H ^ ^ in <* 1 8- in > fficf > > M H % * H* IT ? M CO M w w II 99 II ^ (5 W OJ 1 1 E= o m 1 ** M o M M co t** M s 3 w* fl OQ 1 ^ nj ||0 f-s M M II rt jz 1 C/3 > J >H T- Tf * 1 vo ^c o> cT in o vo *P H co ^ N 1-1 & II 3 ii bo ra o "if T3 bjo J ,ffi 1 i vp oo IK^ co in o 0^ . o9 w iT II a f CO H J? II 1 & 3 rt ^o J-5? i ,< 1 04 u 1 Tf s Q N 8 1 rf Cl II II OO H CM E OJ 55 i II II will be proportional to the quantity of gas taken. Further, according to Avogadro's hypothesis, the molecular weight in grams of all gases occupies the same volume under the same conditions. It follows that for these quantities the constant r will have the same value for all gases, quite independent of the conditions under which the gases are measured. This special value of the constant may conveniently be represented by R, and we then obtain the equation PV = RT, where V is the volume occupied by the molecular weight of a gas in grams, at the absolute temperature T and under the pressure P an equation which is of fundamental importance for the behaviour of gases and also for dilute solutions. The molecular weight of a gas in grams, which, according to the atomic theory, represents the weight of the same number of molecules in each case, is conveniently termed a mol (Ostwald). GASES 27 The numerical value of R, in C.G.S. units, may readily be calculated from the accurate observations of the densities of gases made by Regnault, Rayleigh and others. There is, how- ever, a little uncertainty in the calculation owing to the fact that the volumes occupied by a mol of different gases under equiva- lent conditions are not quite the same, although very nearly so. Thus 2 'oi 6 grams of hydrogen, 32*00 grams of oxygen and 28*02 grams of nitrogen occupy 22*43, 22 '39 an d 22*40 litres respectively at o and 76 cms. Taking 22*40 litres as a mean value, and substituting the values for T (273) and P (76 x I 3'59 ~ I0 33'3 grams per sq. cm.), we obtain PV 101 V3 x 22,400 R- = - 84,76ogram-cms. = 83, 150,000 ergs As the pressure is measured in gram/cm. 2 , the volume is of the dimensions cm. 8 , and T is merely a number, the above value for R is of the form gram x cms. or gram -centimetres. The calorie, the ordinary heat unit, is equal to 42,640 gram-centi- metres = 41,830,000 ergs, so that the value of R is almost ex- actly double (accurately 1*99 times) that of a calorie. We may therefore write the gas equation in the simplified form PV = i*99T, but the approximate form PV = 2T is sufficiently accu- rate for many purposes. In this form the gas equation is repre- sented in thermal units. The product P V in the gas equation is of the nature of energy, as is clear from the fact that when a volume, v, of a gas is gener- ated under constant external pressure (say that of the atmosphere) the work done is proportional to the volume and to the pressure overcome, and therefore to their product. The work done by or upon a gas when it changes its volume under a constant ex- ternal pressure can readily be obtained in thermal units by using the second form of the gas equation given above. Thus if a mol of a gas is generated at o under the pressure of the atmos- phere, the amount of heat absorbed in performing the external work of expansion, PV, is 2T = 2 x 273 =* 546 cal. Since PV is constant, the pressure under which a definite 28 OUTLINES OF PHYSICAL CHEMISTRY mass of a gas is generated at a definite temperature has no influence on the external work of expansion. Thus, to take the above illustration, if a mol of a gas is generated under a pressure of atmosphere, the volume will be 2 2 '4 x 10 224 litres, and the work done will again be 546 cal. at o. Deviations from the Gas Laws Careful experiment shows that although the gas laws, which are summarised in the general formula PV = RT, give a general idea of the behaviour of gases, yet they do not represent accurately the behaviour of any single gas, the deviations depending both on the conditions of observation and on the nature of the gas. It may be said, in general, that the laws are the more nearly obeyed the higher the temperature and the smaller the pressure, and, as regards the nature of the gas, the further it is removed from the temperature of liquefaction, A gas which would follow the gas laws accurately is called a perfect or ideal gas, and ordinary gases approach more or less nearly to this ideal behaviour. The accompanying figure (Fig. i) gives a graphic representa- tion of the behaviour of the three typical gases, hydrogen, nitrogen and carbon dioxide, according to Amagat. The pro- duct PV, in arbitrary units, is represented on the vertical axis and the pressure P, in atmospheres, along the horizontal axis. If PV were constant (Boyle's law), the curves would be straight lines parallel to the horizontal axis. Actually, PV increases continuously with the pressure in the case of hydrogen, and for nitrogen and carbon dioxide it first decreases, reaches a mini- mum, and beyond that point increases with increase of pres- sure. All gases except hydrogen show a minimum in the curve, which indicates that the compressibility is at first greater than corresponds with Boyle's law, reaches a point (which differs for different gases) at which for a short interval Boyle's law is followed, and beyond that point is less compressible than the law indicates. Hydrogen, on the other hand, is always less GASES 29 compressible than the law requires at ordinary temperatures, but at very low temperatures it would also probably show a minimum in the curve. That the deviations from the simple litw become less the higher the temperature, is very well illus- trated by the curves for carbon dioxide at 35*1 and 100. I SO 40 6O 8O TOO 1 2O 140 l6o 1 80 2OO 22O 240 260 280 $00 - FIG. i. The general behaviour of gases, and the deviations from the simple laws, find a very satisfactory interpretation on the basis of the kinetic theory of gases, which we are now to consider. KINETIC THEORY OF GASES General The fact that the laws followed by gases are so simple in character makes it readily intelligible that attempts to account for their properties on a mechanical basis were made very early in the history of science (Bernoulli, 1738). Our present views on the subject, known as the kinetic theory 30 OUTLINES OF PHYSICAL CHEMISTRY of gases, are due more particularly to the labours of Clerk Maxwell, Clausius and Boltzmann. According to the theory, gases are regarded as being made up of small, perfectly elastic particles (the chemical molecules) which are in continual rapid motion, colliding with each other and with the walls of the containing vessel. The space actually filled by the gas particles is supposed to be small compared with that which they inhabit under ordinary conditions, so that the particles are practically free from each other's influence except during a collision. Owing to the comparatively large free space in which the particles move, an individual particle will move over a certain distance before colliding with another particle ; the average value of this distance is termed the " mean free path " of the molecule. On this theory the pressure exerted by the gas on the walls of the containing vessel (which is equal to the pressure under which it is confined) is due to the bombardment of the walls of the vessel by the moving particles. It is clear that the magnitude of the pressure must depend on the frequency of the collisions, as well as on the mass and velocity of the particles. Kinetic Equation for Gases The pressure exerted by a gas can be calculated quantitatively in terms of the number and velocity of the molecules as follows : Imagine a definite mass of a gas contained in a cube, the sides of which are of length /; let n be the number of particles, each of mass m and velocity c. The particles will impinge on the walls in all direc- tions, but the velocity of each may be resolved into three com- ponents, x, y and z, parallel to the edges of the cube, the components being related to the original velocity c by the equation x* + y 2 + z 2 = 4 x 273X/X0 A shorter method is to use the alternative expression for the gas equation 1 pv n RT, where n represents the number of gram-molecules of gas in the volume v. Since n /M we have pv Density and Molecular Weight of Gases and Vapours The determination of the volume occupied by a known 1 Care must be taken to express R in the proper units, corresponding with those in which the pressure and volume are given. (Cf. p. in.) GASES 37 weight of a gas or vapour under definite conditions is equivalent to determining its density, which is the mass per unit volume. The actual determinations may be made in various ways. It will be sufficient for our present purpose to describe Regnault's method, which is particularly suitable for the permanent gases, and the method first suggested by Victor Meyer, which is now used almost exclusively for determining the density, and therefore the molecular weight, of vapours. (i) Regnaulfs Method Two glass bulbs of approximately equal capacity and provided with well-ground stop-cocks are used. One is exhausted as completely as possible by means of a pump, weighed, filled at a known temperature and pressure with the gas the density of which has to be determined, and again weighed, the other bulb being used as counterpoise. The volume of the bulb may be obtained by weighing it empty and then filled with distilled water at a known temperature. One of the advantages of using a second bulb is that any risk of error arising from a change in the temperature, pressure or humidity of the air in the balance-case during the weighing is avoided. From the results, the density referred to hydrogen as unity can readily be calculated, and hence the molecular weight, which is double the density (p. 10). The molecular weight can also be obtained by substituting in the formula given above. This method, with slight modifications, has been employed in recent years by Lord Rayleigh, Morley, Ramsay and others for determining the densities of the permanent gases, and is cap- able of giving results of the highest accuracy. (2) Victor Meyer's Method This method differs from all the others inasmuch as it is not the volume of the vapour itself which is measured, but that of an equal volume of air which has been displaced by the vapour. The apparatus consists of a cylindrical vessel, A, of about 200 c.c. capacity, ending in a long neck provided with two side tubes, as shown in Fig. 2. One of these side tubes, /, from which the displaced air issues during an experiment, is OUTLINES OF PHYSICAL CHEMISTRY bent in such a way that its free end can conveniently be brought under the surface of water in a suitable vessel. Into the other tube, / 2 , fits a rubber tube enclosing a glass rod which can be moved outwards and inwards, and, at the commencement of the experiment, serves to retain in place the small glass bulb shown in the figure, containing a weighed quantity of the liquid, the vapour density of which is to be determined. The top of the main tube is closed by a cork which is kept in place throughout an experiment, and a little asbestos or mercury is placed in the bottom to guard against fracture of the glass when the bulb drops. The apparatus is heated at a con- stant temperature throughout the greater part of its length by means of the vapour of a liquid boiling in the outer bulb-tube, B ; the temperature should be at least 20 above the boiling point of the liquid to be vaporized. At the commencement of an experi- ment, the bulb and rod are placed in position and the cork inserted, the jacket- ing liquid is then boiled till air ceases to issue from the end of the tube, /, and bubble through the water, showing that the temperature inside the bulb, A, is constant. A graduated measuring tube, C, full of water, is then inverted over the end of the delivery tube, and the small bulb allowed to drop by drawing back the glass rod. When air ceases to issue from the end of the delivery tube, the graduated tube is closed by the thumb, removed to a deep vessel containing water, allowed to stand till the temperature is constant, and the volume of air read off when the water outside and inside are at the same level. The temperature inside the tube, A, is the same before and after the experiment, the only difference in the conditions is FIG. 2. GASES 39 that a certain volume of air is displaced by an equal volume of vapour. The observed volume of air is therefore that which the vapour would occupy after reduction to the temperature and pressure at which the air is measured (provided that the vapour and air are equally affected by changes of temperature and pressure, which is approximately the case under suitable conditions). The temperature is that of the water, and the pressure that of the atmosphere less the vapour pressure of water at the temperature of observation. It is clear that it is not necessary to know the temperature at which the substance is vaporized, and this is one of the advantages of the method. The mode of calculating molecular weights from the observed data may be illustrated by the following example: 0*220 grams of chloroform when vaporized displaced 45*0 c.c. of air, measured at 20 and 755 mm. pressure. As the vapour pressure of water at 20 is 17*4 mm., the actual pressure exerted by the gas is 755-17*4 737*6 mm. Therefore, as 0*220 grams of vapour, at 20 and 737*6 mm. pressure, occupy 45*0 c.c., we have to find what weight in grams will occupy 22,400 c.c., at 273 abs. and 760 mm. pressure, and this will be the required molecular weight. Substituting in the general formula (p. 36) we have 0*220 x 760 x 22,400 x (273 -f 20) 2 73 x 737'6x45 This result is in fair agreement with the molecular weight of chloroform (119*5) calculated from its formula. The results obtained by this method are only accurate if the vapour follows the gas laws as closely as air (since only under these circumstances will the vapour replace an exactly equivalent quantity of air), and as the vapour is often not very remote from its temperature of condensation, this condition is not in general fulfilled. In the great majority of cases, however, the results are sufficiently near for the purpose, as the composition of the substance can be determined with great accuracy by chemical analysis, and the vapour density method is only used 40 OUTLINES OF PHYSICAL CHEMISTRY to distinguish between simply related numbers. In the example given above, for instance, analysis shows that the molecular weight of chloroform must be 119*5 or a simple multiple of that number, and the density determination proves that the former alternative is correct. Results of Yapour Density Determinations. Ab- normal Molecular Weights The most important result of the numerous molecular weight determinations which have been made by this method is that in general the values obtained are in complete agreement with those based on chemical considera- tions. There are certain exceptions to this rule, but for all these plausible explanations have been suggested. In the case of elements, the values found are simple multiples of the atomic weights (very often twice the atomic weight), whilst in the case of compounds they are simple multiples of the sum of the atomic weights. All the metals which have been obtained in gaseous form, including mercury, zinc, cadmium, potassium, sodium, antimony and bismuth, 1 are monatomic, as are the rare elements argon, helium, krypton, etc., discovered in the atmosphere by Ramsay and his co-workers. Many of the non-metals, such as oxygen, nitrogen and chlorine, are diatomic under ordinary conditions. Whilst arsenic and phosphorus are tetratomic, sulphur at low temperatures gives results corresponding with the formula S 8 . Several elements, such as carbon and silicon, and many metals have not yet been obtained in the gaseous form. The determination of molecular weights at high temperatures has been greatly developed in recent years, more particularly by Victor Meyer and his co-workers, and by Nernst. The air- displacement method has proved most suitable for this purpose, but the chief difficulty has been to obtain vessels which stand high temperatures, and are not porous for the contained vapours. Victor Meyer at first replaced glass by porcelain, 1 Compare H. von Wartenberg, Zeitsch. anorg, Chem., 1907, 56, 320; Abstracts Chem. Society, 1908, ii., 86. GASES 41 and the latter by an alloy of platinum and iridium, and at the time of his death was experimenting with vessels of magnesium oxide. Satisfactory results were obtained up to 1700-1800. One of the most striking results obtained by Victor Meyer is that the molecular weight of iodine, which at 600 corresponds with the formula I 2 , becomes smaller as the temperature is further raised, until at 1500 it reaches half the initial value, indicating that at the latter temperature it is completely split up into iodine atoms. Bromine is also partially decomposed at 1500, and chlorine commences to split up about the same temperature. It had previously been shown by Deville and Troost that the molecular weight of sulphur also diminishes with increasing temperature, and above 800 gives results which indicate that only diatomic molecules are present. Nernst l has quite recently succeeded in extending this method up to 2000 by using a vessel of iridium coated outside and inside with a paste of magnesia and magnesium chloride, and heated in an electric furnace. At this temperature, the molecular weight of mercury is 201, indicating that the atoms of this element have undergone no further simplification, whilst sulphur, between 1800 and 2000, has a density of about 24, indicating that the diatomic molecules are split up, to the ex- tent of about 33 per cent., into single atoms. Association and Dissociation in GasesWe have al- ready seen that such substances as sulphur and arsenic have abnormally high molecular weights at low temperatures ; such substances are said to be associated. This peculiarity is not confined to elements, as the molecular weight of acetic acid, which, as determined by chemical methods, is 60, exceeds 100 when determined by the vapour density method at comparatively low temperatures. The conclusion that acetic acid in the form of vapour at comparatively low temperatures consists largely of double molecules (CH 8 COOH) 2 , is in satisfactory agreement with other considerations. 1 Compare Wartenberg, loc. cit. 42 OUTLINES OF PHYSICAL CHEMISTRY An apparent deviation from Avogadro's hypothesis of a different nature is met with, for example, in the case of gaseous ammonium chloride. On chemical grounds, the molecular formula, NH 4 C1, is given to this substance, corresponding with a molecular weight of 53-5, whereas the observed value, obtained from its vapour density, is only half as great. This behaviour could be accounted for on the assumption that, at the tem- perature of the experiment, the molecule is to a great extent split up, or dissociated, into NH 3 and HC1 molecules, and the experimental justification for this assumption has been obtained by Pebal (1862), who effected a partial separation of the decomposition products by taking advantage of their different rates of diffusion. It may be added that in the complete absence of moisture, ammonium chloride can be vaporized without dissociation, and then has the normal molecular weight deduced by means of Avogadro's hypothesis. 1 Accurate Determination of Molecular and Atomic Weights from Gas Densities We have seen that Avogadro's hypothesis does not hold strictly for actual gases, and that the reason for this is probably to be found in the mutual attractions and finite volumes of the gas particles.- We may, therefore, assume that it would be strictly true for an ideal gas, and, on the basis of van der Waals' equation, apply a correction to actual gases to find their true molecular weights, that is, the relative masses which would occupy equal volumes at great rarefaction, when the gas laws would be strictly followed (p. 28). The method followed is therefore to determine the volume of a definite mass of a gas under two or more pressures (the Compressibility of the gas), and find by extrapolation the relative densities of different gases as the pressure approaches zero. This method has been used more particularly by Daniel Berthelotand by Lord Rayleigh. From the results, the follow- 1 H. Brereton Baker, Trans. Chem. Society, 1894, 65, 611 ; 1898,73, 422. Compare Johnston, Zeitsch. physikal Chem., 1908, 61, 457. GASES 43 ing molecular weights (vapour density x 2) were calculated by Berthelot (oxygen = 3 2 being taken as the standard) : H 2 N 2 CO 2 C0 2 N 2 O HC1 2-0145 28-013 28*007 32*000 44-000 44*000 36*486 From these observations, the following atomic weights have been obtained, the values derived by chemical methods being placed below for comparison : O H C N Cl Gas density 16*000 1*0075 12*000 14*005 35*479 Chemical 16-000 roo8 12*00 14-01 35*45 The agreement, except in the case of chlorine, is excellent. As a matter of fact, the chemical value for chlorine is probably too low ; the recent investigations of Richards and Wells l appear to show that the true value is 35*473, almost identical with that obtained by the density method. The above striking results lend strong support to the assump- tion that in the limit Avogadro's hypothesis is strictly valid for all gases. SPECIFIC HEAT OF GASES General The specific heat of any substance may be defined as the ratio of the amounts of heat required to raise i gram of the substance in question and i gram of water through a given range of temperature. The amount of heat required to raise i gram of water i in temperature is termed a calorie, and hence the specific heat may also be defined as the quantity of heat in calories required to raise i gram of the substance i in tem- perature. This statement has only a definite meaning, however, when the conditions under which the heating is carried out are stated, and this is particularly true of gases. If a gas is suddenly compressed it becomes warmer, although no heat has been supplied to it, and, conversely, if a gas is allowed to expand against pressure it becomes cooled, although no heat has been abstracted from it. According to the above definition, 1 y. A mer. Chem. Soc., 1905, 27, 459. 44 OUTLINES OF PHYSICAL CHEMISTRY amount of heat supplied Specific heat => -i : ; " rise in temperature so that if a gas is warmed by compression its specific heat is zero Moreover, if, while a gas is expanding against pressure, sufficient heat is supplied to keep its temperature constant, the heat supplied has a certain finite value whilst the change of tempera- ture is zero, so that the specific heat, according to definition, is infinite. It is clear that the specific heat of a gas may have any value whatever, unless the conditions under which it is measured are stated. Specific Heat at Constant Pressure, C p , and Constant Volume, C, There are two important cases in which the term " specific heat of a gas " is clearly defined : (a) the specific heat at constant volume, C t , () the specific heat at constant pressurs, C,,. In the former case, the volume is kept constant whilst the gas is being heated, and no external work is done. In the latter case, the volume is allowed to increase whilst heat is being supplied, work is therefore done against the pressure of the atmosphere, which tends to cool the gas. Sufficient heat must therefore be supplied not only to raise the temperature, but to make up for the cooling due to the external work performed. It is clear that the specific heat at constant pressure is greater than that at constant volume, and the difference is the heat equi- valent of the amount of work done against the external pressure. The difference between the two specific heats may readily be obtained in thermal units by using the general gas equation. For this purpose, it is convenient to deal with a mol of a gas. It has already been shown (p. 27) that when a gas expands at constant pressure, the work done is measured by the product of the pressure and the change of volume. If at first the absolute temperature is T lt we have the equation PVj = RT X where V l is the molecular volume. If the temperature is raised to T 2 , and the new molecular volume is V s , the work done during the expansion is P(V,-V L )- RiTj-Tj). GASES 45 In the present case, T a - T x is i, therefore P(V 3 - V^ - R. Further, the difference in the molecular heats of a gas at constant pressure and constant volume is the external work done when a mol of gas is raised i in temperature, and there- fore M (C P - C v ) (where M is the molecular weight of the gas) is also P (V 2 - V^. Hence M (C p - Q) R. In thermal units, R is approximately 2 calories, so that the difference of the specific heats of a mol of any gas in other words, the difference of the molecular heats of any gas at constant pressure and at constant volume is 2 calories. The specific heat of a gas at constant pressure can readily be determined by passing a known quantity of it, heated to a definite temperature, through a metallic worm in a calorimeter, at such a rate that there is a constant difference of temperature between the entering and issuing gas. It is more difficult to determine directly the specific heat at constant volume, and this has only been accomplished satisfactorily in comparatively recent times. 1 The molecular heats MC, and MQ, (molecular weight x specific heat) of a few of the commoner gases are given in the accompanying table, the values of C, being obtained from those of C p by subtracting 2 calories : Specific Gas. Heat, C P MC p MC,, eye. Argon . 4*98 2-98 1-66 Helium 1*66 Mercury 2*965 1*66 Hydrogen 3'409 6*880 4-880 412 Oxygen 0*2175 6*960 4*960 40 Hydrogen chloride Chlorine 0-1876 0*1241 6-84 8-820 4*84 6*820 409 29 Nitrous oxide 0*2262 9*99 7*99 247 Ether . 0-4797 35'5i 33-51 060 1 Joly, Proc. Roy. Soc., 18 Heat, p. 239. 3, 47, 218. Compare Preston, Theory of 46 OUTLINES OF PHYSICAL CHEMISTRY For diatomic molecules, the average value of the molecular heat at constant volume is about 4*8 calories in the neighbour- hood of 100; but chlorine and bromine are exceptions. For triatomic molecules the average value of MC t is 6*5 cal. and the value increases with the complexity of the compound, as is illustrated in the table. Specific Heat of Oases and the Kinetic Theory Much light is thrown on the question of the specific heat of gases by the kinetic theory. According to this theory the energy- content of a gas is made up of three parts : ( i ) energy of transla- tion (rectilineal motion of the molecules), often termed simply kinetic energy (p. 32); (2) energy of vibration of the atoms within the molecule, which is partly kinetic and partly potential ; (3) energy of rotation ; l and when heat is supplied to a gas at con- stant volume all three factors of the energy may be affected. For monatomic gases, however, such as mercury vapour, the factors (2) and (3) are presumably absent, and the heat supplied must simply be employed in increasing the kinetic energy of the molecules. We have already learnt (p. 32) that the kinetic energy of i mol of any gas -|PV = 3T if expressed in thermal units. When a gas is raised at constant volume from the absolute temperature T 1 to T 2 we have for the kinetic energies at the two temperatures the equations f P X V = 3^ and |P 2 V = 3X3, where P l and P 2 are the pressures at T x and T 2 respectively. Subtracting the first equation from the second, we obtain i (Pj-Pi)V = sCTj-TJ and for a rise of temperature of i f (P 2 - PjJV 3 (calories). Therefore the molecular kinetic energy of a monatomic gas is increased by 3 calories for a rise of i in temperature, or, in other words, the molecular heat MC. of a monatomic gas at constant volume is 3 calories. As the specific heat at constant pressure is 3 + 2 = 5 calories, the ratio, MC P /MC V , for a monatomic gas must be r66, if the assumptions we have made on the basis of the kinetic theory are justified. As has already been mentioned, C, is somewhat difficult to 1 Boltzmann, he. cit., D. 54.. GASES 47 determine directly, and to test the above deduction from the kinetic theory it is simpler to determine the ratio C P /C. in- directly, which can be done in various ways, for example, by measuring the velocity of sound in a gas. Kundt and Warburg (1876) therefore determined the velocity of sound in mercury vapour and obtained for the above ratio the value r66, in exact accord with the theoretical value, undoubtedly one of the most striking triumphs of the kinetic theory. Conversely, a gas for which the ratio C P /C 9 is r66 must be monatomic, and by this method Ramsay showed that the rare gases argon and helium are monatomic. For gases containing two or more atoms in the molecule, the heat supplied is employed not only in accelerating the rectilinear motion of the particles, but also in performing internal work in the molecule. As the former effect alone requires 3 calories, the total molecular heat of a polyatomic gas will be 3 -f a calories, where a is a positive quantity, constant for any one gas, The value of MCp will be 5 + a calories, and the ratio of the specific heats will be MQ, 5 + a -' less than 1*67 but greater than i. A comparison of the numbers given in the table shows that this deduction is in complete accord with the experimental facts. It may be expected that the more complex the molecule the greater will be the amount of heat expended in performing internal work and therefore the greater will be the specific heat. In accordance with this, MC, for i mol of ether vapour is 33*5 calories, and for turpentine (C 10 H 16 ) 66*8 calories. The specific heat of monatomic gases is independent of temperature, that of polyatomic gases usually increases slowly with temperature. Experimental Illustrations Experiments with gases are usually somewhat difficult to perform, and require special ap- paratus. Experimental illustrations of the simple gas laws are 48 OUTLINES OF PHYSICAL CHEMISTRY described in all text-books on physics, and need not be con- sidered here. The determination of the density l and hence the molecular weight of such a gas as carbon dioxide by Regnault's method may be performed as follows : One of the bulbs is first exhausted as completely as possible by means of a pump, the stop-cock closed, and the bulb weighed. It is then filled with water by opening the stop-cock while the end of the tube dips under the surface of water and again weighed. The volume of the bulb is obtained by dividing the weight of the water by its density at the temperature of the experiment. The water is removed from the bulb by means of a filter-pump, the interior of the bulb is dried (by washing out with alcohol and ether and warming), pkced nearly to the stop-cock in a bath at constant temperature, the end is then connected to a T piece by means of rubber tubing ; one of the free ends of the T piece is connected, through a stop-cock or rubber tube and clip, to a pump, the other, also through a stop-cock or rubber tube and clip, to an apparatus generating carbon dioxide. The bulb is evacuated by means of the pump, the stop-cock connecting it with the latter is then closed, that connecting it with the carbon dioxide apparatus opened, the bulb filled with carbon dioxide, disconnected and weighed. As the apparatus fills it with carbon dioxide at rather more than atmospheric pressure, the stop-cock is opened for a moment to adjust it to atmospheric pressure before weighing. The weight of a known volume of the gas at known temperature and pressure having thus been determined, its density and molecular weight can readily be calculated. The determination of vapour densities by Victor Meyer's method is fully described on page 38, and may readily be performed by the student with ether or chloroform, steam being used as jacketing vapour. 1 For full details as to the manipulation of gases, consult Traverg* Experimental Study of Gases (Macmillan, 1901). CHAPTER III LIQUIDS General Liquids, like gases, have no definite form, but, unlike the latter, they have a definite volume, which is only altered to a comparatively small extent by changes of tempera- ture and pressure. In contrast to the simple gas laws, the formulae connecting temperature, pressure and volume of liquids are very compli- cated and empirical in character, and depend also on the nature of the liquid. This is, of course, connected with the fact that liquids represent a much more condensed form of matter than gases. i c.c. of liquid water at 100*, when converted into vapour at the same temperature, occupies a volume of over 1600 c.c. It seems plausible to suggest that the main reason why the formulae representing the behaviour of liquids are so much more complicated than the gas laws is that the mutual attraction of the particles, which is almost negligible in the case of gases (p. 34), is of predominant importance for liquids. As is well known, gases can be liquefied by increasing the pressure and lowering the temperature ; and, conversely, by raising the temperature and diminishing the pressure a liquid can be changed to a gas. It is shown in the next section that there is no difference in kind, but only a difference in degree, between liquids and gases. Transition from Gaseous to Liquid State. Critical Phenomena If gaseous carbon dioxide, below 31, is con- fined in a tube and the pressure on it gradually increased, a point will be reached at which liquid makes its appearance in 4 4Q go OUTLINES OF PHYSICAL CHEMISTRY the tube, and the whole of the gas can be liquefied without appreciable increase of pressure. If, however, carbon dioxide above 31 is continuously compressed, no separation into two layers (liquid and gas) occurs, no matter how high the pressure applied. Similarly, if carbon dioxide is contained in a sealed tube, under such conditions that both liquid and gas are present, and the temperature is gradually raised, it will be noticed that when the temperature reaches 31* the boundary between liquid and vapour disappears, and the contents of the tube become homogeneous. Other liquids show the same remarkable phenomena, but at tem- peratures which are characteristic for each sub- stance. This temperature is known as the critical temperature; above its critical temperature no pressure, however great, will serve to liquefy a gas, below its critical temperature any gas can be liquefied by pressure. That pressure which is just sufficient to liquefy a gas at the critical tem- perature is termed the critical pressure, and the specific volume under these conditions is called the critical volume. The critical phenomena may be observed, and rough measurements of the constants obtained, with an apparatus (Fig. 3) used by Cagniard de la Tour, who discovered these phenomena in 1822. The upper part of the branch A contains a suitable volume of the liquid to be examined, the branch B, the upper part of which is gradu- ated, contains a little air to act as a manometer, the remainder of the apparatus (the shaded part in the figure) is filled with mercury. The tube at first contains both vapour and liquid, but on gradually raising the temperature, a point is ultimately reached at which the boundary between liquid and vapour becomes faint, and finally disappears ; the tube is momentarily filled with peculiar flicker- FIG. 3. LIQUIDS 5' ing striae, and then the contents become quite homogeneous. On allowing to cool, a mist suddenly appears in the tube at a certain temperature, and separation into liquid and vapour again occurs. The temperature at which the boundary dis- appears on heating or reappears on cooling approximates to the critical temperature, and the critical pressure can be cal- culated from the volume of air in B. Accurate measurements of the constants may be made by methods described by Young l and others. As the temperature rises, the density of the liquid in the sealed tube naturally decreases, whilst that of the vapour increases, and it has been shown that at the critical temperature the densities of liquid and vapour are equal. The critical temperatures and pressures of a few substances are given in the accompanying table : Critical Temperature, C. Critical Pressure (Atmospheres). Helium - 267-268 2*3 Hydrogen -2 3 8 15 Nitrogen . - 149 27 Oxygen . - IIQ 58 Carbon dioxide 31 72 Ethyl ether 195 35 Ethyl alcohol . 243 63 Behaviour of Gases on Compression We have already learnt that if gaseous carbon dioxide is compressed at a tem- perature below 31 it can be liquefied, but if the compression is carried out above 31 no separation into two layers occurs. These relations are best shown diagrammatically, as in Fig. 4, in which the ordinates represent the pressures and the abscissae the corresponding volumes at constant temperature. If the gas in question obeys Boyle's law, the curves obtained by plotting the pressures against the corresponding volumes at constant temperature (the so-called isothermals) are hyperbolas, corresponding with the equation/^ = constant, and this condi- tion is approximately fulfilled by air, as shown in the upper right- 1 Phil. Mag., 1892, [v.], 33, 153- OUTLINES OF PHYSICAL CHEMISTRY hand corner of the diagram. An examination of the isothermals for carbon dioxide shows that the same is nearly true of this gas at 48*1, but at 35-5, and still more at 32*5, the isothermals deviate from those of an ideal gas. At the latter temperature it is very interesting to observe that the compressibility at 75 60 85 so 75 70 65 60 55 50 Air. Carbon Dioxide. B FIG. 4. atmospheres is very great for a short part of the curve, and beyond that point extremely small ; in the latter respect the highly compressed gas resembles a liquid. At the critical point, 31*1, the curve is for a short distance practically hori- zontal, thus representing a great decrease of volume for a small change of pressure in other words, a high compressibility. Finally, at 21*1 and 13'!, separation of liquid takes place, the LIQUIDS 53 curves run horizontal whilst the gas is changing to liquid at constant pressure, and then the curves run almost vertical, indicating a small decrease of volume with increase of pres- sure (/. ponding with one real root of the equation under these conditions. Some light is thrown on the question of the missing third real volume when the isothermal curves for carbon dioxide are plotted by substituting the values of a and b, found experi- mentally (p. 34) in equation (i). The wavy curve ABCDE shown in Fig. 5 was obtained in this way ; on comparison with the experimental curve for carbon dioxide (Fig. 4), it will be \ FIG. 5. LIQUIDS 55 seen that whereas the points D and E in the latter isothermal for 13 are joined by a straight line DE, in the former the corresponding points E and A are joined by the dotted line ABCDE, which represents a change from the gaseous to the liquid form without discontinuity. The point C, at which the line of constant pressure cuts the isothermal, represents the third of the volumes required by the above cubic equation, but it probably cannot be realised in practice, as the part DCB of the curve on which it occurs represents decrease of volume with diminishing pressure, quite contrary to our usual experi- ence. On the other hand, the sections AB and ED have a real meaning. When a vapour is compressed till saturated, it does not necessarily liquefy; in the complete absence of liquid it may be compressed considerably beyond the point at which liquefaction occurs in the presence of traces of liquid ; in other words, a part of the curve ED may be experimen- tally realised. Similarly, water may be heated in a carefully cleaned vessel several degrees above its boiling point, that is, it does not necessarily pass into vapour when the superincum- bent pressure is less than its vapour pressure, and a part of the curve AB may thus be experimentally realised. Simikr phenomena will be met with later ; it often happens that when a system is under such conditions that the separation of another phase (form of matter) is possible, the change does not occur in the absence of the new phase. Van der Waals' equation can also be employed to obtain important relations between the critical constants and the other characteristic constants representing the behaviour of gases. It has already been pointed out that the densities and consequently the volumes of liquid and gas become equal at the critical temperature, and as this must also be true for the intermediate third volume, it follows that the three roots of the equation become equal under these conditions. If, in this general 56 OUTLINES OF PHYSICAL CHEMISTRY equation, we call the three roots V v V 2 and V 3 , then the equation (V-VjXV- V 2 )(V- V 8 )-o, must hold, which, when the roots are equal, becomes (V - V*) 3 - V* - 3 V*V 2 + 3 V* 2 V - V* - o (2), where V* is the critical volume. Equating the coefficients of the identical equations (i) and (2), we have ^ + ^ = 3V*(i);^- 3 vj (ii); Jj = v(iii). From the last three equations, the values of the critical con- stants can readily be obtained in terms of R, a and b. We have Critical volume V* = 3^ (from ii and iii), Critical pressure PA -^ (from ii), Critical temperature T* =* ^ (from i). We thus reach the interesting result that the critical constants may be calculated from the deviations from the gas laws, when the latter are expressed in terms of the constants a and b of Van der Waals' equation. As an illustration of the satisfactory agreement between the observed and calculated values, we will take the data for ethylene, for which a = 0-00786, b = 0-0024, R = 0-0037. V k = 0-0072 (observed value 0*006), 5 ' 5 (observed value 5 r 27 x ( 8 x 0-00786 , . T A = - - -262 Abs. (observed value 282 ). 27 x 0-0024 x 0-0037 Law of Corresponding States Van der Waals has further pointed out that if the pressure, volume and temperature of a substance are expressed as multiples of the critical values, that is, if we put P = aP*, V - fiV k) T = yT k , and then substitute in the equation (P + a/V 2 )(V - 6) = RT, P A , V* and T* being LIQUIDS 57 replaced by their values in terms of a, b and R, the equation simplifies to This equation does not contain the constants characteristic of any particular substance, and ought therefore to hold for all substances in the gaseous and liquid state. Experiment shows, however, that it is only to be regarded as a first ap- proximation, the deviation in many cases being much greater than the experimental error. For our present purpose, these considerations are chiefly of importance as affording information regarding the proper con- ditions for comparison of the physical properties of liquids. If we wish, for example, to compare the molecular volumes of ether and alcohol, it would probably not be satisfactory to compare them at the ordinary temperature of a room, as this would be near the boiling-point of ether, 35, but much below that of alcohol, 78. According to van der Waals, the proper temperatures for comparison, the so-called " corresponding tem- peratures/' are those which are equal fractions of the respective critical temperatures. Thus, if we choose 20, or 293 Abs., as the temperature of experiment for ether, the critical tem- perature of which is 195, or 468 Abs., the proper temperature, /, for comparison with alcohol (critical temperature, 243 C.) will be given by 273 ^g 2 - ^M' whence '-S^ The same considerations apply to the pressures. The theoretical basis for this method of comparison is that, as mentioned above, the choosing of pressures, volumes or tem- peratures which for different substances bear the same proportion to their respective critical constants leads, when substituted in van der Waals' equation, to an equation which is the same for all substances, and the practical justification for choosing these as corresponding conditions is that more regularities are actually 58 OUTLINES OF PHYSICAL CHEMISTRY observed by this method than when the comparison is made under other circumstances. Liquefaction of Gases As already indicated, all gases can be liquefied by cooling them below their respective critical temperatures and applying pressure. The methods employed for this purpose by Cailletet, Pictet, Wroblewski and others are fully described in text-books of physics. In recent years the older methods have been- almost completely displaced, in the case of the less condensible gases, such as air and hydro- gen, by a method introduced almost simultaneously by Linde and by Hampson. The principle of the method is that when a gas is allowed to pass from a high to a low pressure through a porous plug without performing external work it becomes cooled (Joule-Thomson effect). The cooling effect is due to the performance of internal work in overcoming the mutual attrac- tion of the particles, and is therefore only observed for "im- perfect " gases (p. 34). The effect is the greater the lower the temperature at which the expansion takes place, and the greater the difference of pressure on the two sides of the plug. The cooling effects thus obtained are summed up in a very ingenious way by the principle of " contrary currents," the same quantity of gas being made to circulate through the apparatus several times, and after passing through the plug being caused to flow over and cool the tube through which a further quantity of gas is passing on its way to the plug (or small orifice). The apparatus employed is represented diagrammatically in Fig. 6. By means of the pump A, the gas is compressed in B to (say) 100 atmospheres, the heat given out in this process being absorbed by surrounding B with a vessel through which a continuous current of cold water is passed. The cooled, com- pressed gas then passes down the central tube G, towards the plug E, being further cooled on the way by the gas passing up the wide tube D, which has just expanded through the plug. After passing through E and thus falling to its original pressure, the gas passes upwards over the central tube G and again LIQUIDS 59 B reaches A by the tube C and the left-hand valve at the bottom of A. The direction of the circulating stream of gas is indicated by the arrows. In course of time, the temperature becomes so low that part of the gas is liquefied and collects in the vessel F. More air is drawn into the appar- atus as required, and the process is continuous. By means of an apparatus con- structed on this principle Dewar, and, somewhat later, Travers, succeeded in obtaining liquid hydrogen in quantity. All known gases have now been liquefied. The liquefaction of helium was effected quite recently by Kam- merlingh Onnes. RELATION BETWEEN PHYSI- CAL PROPERTIES AND CHEMICAL CONSTITUTION General The foregoing para- graphs of this chapter represent an introduction to the relation- ship between the physical pro- perties of liquids and their chemi- cal composition, inasmuch as in- formation has been gained as to the conditions under which measurements should be made with different liquids in order to obtain comparable results (theory FlG - of corresponding states). Although in this chapter we are mainly concerned with the physical properties of pure liquids, it is convenient to include also some observations with solu- 60 OUTLINES OF PHYSICAL CHEMISTRY tions. We will deal shortly with the following physical pro- perties: (i) Atomic and molecular volumes; (2) refractivity ; (3) rotation of plane of polarization of light; (4) absorption of light ; (5) viscosity. Atomic and Molecular Volumes In the case of gases, we have seen that simple relations are obtained when the volumes occupied by different substances in the ratio of their molecular weights are compared ; at the same temperature and pressure, the volumes are equal. The justification for taking the molecular weights (in grams, for instance) as comparable quantities is that, according to the molecular theory, equal numbers of molecules of different substances are thus compared. Similarly, in dealing with liquids, it is usual to determine the molecular volume of the liquid, /. v> V*> tthOOK>.bipt.OOOho-fe>a>OD O ho 4x O OD O IV -fc. 2000 1.500 1000 500 :400 250 200 100 50 30 20 15 10 5 3 2 1 0-6 1 A 1 1 / \ / / j / . / \ / \ [ / X. *s 72 OUTLINES OF PHYSICAL CHEMISTRY It may be mentioned that most of the measurements have been made in the ultra-violet region of the spectrum, but a certain number of observations have also been made in the visible and ultra-red regions. A great deal of discussion has taken place as to the mechanism of light absorption, and a dynamical explanation has found most favour. According to Drude, absorption in the ultra-violet and visible regions is connected with the presence of negative electrons (valency electrons), and there is doubtless some intimate connection between the rate of vibration of the electrons and the frequency of the light waves absorbed. It appears, however, that absorption in the ultra-red region is due, not to electrons, but to particles of much greater magnitude, probably atoms or even groups of atoms. As already indicated, the absorption spectra of chemical compounds are closely related to their constitution, and in recent years this method of elucidating chemical constitution has come increasingly into use. The progress made in this branch of investigation is mainly due to Hartley, and within the last few years to Baly and his co-workers. 1 It is impossible here to do more than to indicate in the briefest way the broad differences between the absorption spectra of the main groups of organic compounds. According to Hartley, 2 all compounds which exert selective absorption are of aromatic character, for example, benzene, pyridine, and their derivatives. Those showing strong general absorption have also a cyclic structure, but are not typical aro- matic compounds ; examples, thiophene, piperidine, etc. Finally, compounds which exert only a weak general absorption are open chain compounds; examples, fatty alcohols, esters, etc. Although recent investigation has led to the discovery of one or two exceptions to these generalisations, they remain sub- stantially accurate. Apart from these broad differences in the absorption curves 1 Trans. Chem. Soc. from 1904 onwards. 2 British Association Report, 1903. LIQUIDS 73 of different groups of organic compounds, it has been shown by Hartley that substances of closely allied constitution have absorption curves of similar type. The recent progress in the establishment of the chemical constitution of organic compounds from measurements of their absorption spectra is entirely due to the application of this important rule. Thus if the con- stitution of one compound is known with certainty from its chemical behaviour, and a second compound can be represented by alternative formulae, of which one is analogous to that of the compound of known constitution, a comparison of absorp- tion spectra often enables a decision to be made. Like the other physical methods of determining chemical constitution, the one under discussion should be used with considerable caution in the present very imperfect state of our knowledge of absorption phenomena. As a supplement to purely chemical methods of determining constitution, however, especially when such methods lead to contradictory results, it is rendering valuable service. As regards the additive character of absorption spectra, comparatively little is known with certainty. The determina- tion of the effect of different groups of atoms on the character of the absorption spectrum is attended with considerable diffi- culty, but some progress has been made in this direction. Ultra-red absorption spectra have a pronounced additive char- acter ; this is probably connected with the generally accepted view that absorption in this case is connected with the vibrations of the atoms themselves. Viscosity The measurement of internal friction, or vis- cosity, gives information as to the work done in the relative displacement of the particles of a solid, liquid, or gas. In the case of liquids, for which the property has been most fully investigated, the viscosity is most conveniently studied by observing the rate of flow through capillary tubes. We may assume that the layer of liquid in contact with the wall of the tube is at rest, that the layer next to it is moving slowly parallel to the axis of the tube, and that the rate of movement gradually 74 OUTLINES OF PHYSICAL CHEMISTRY increases towards the interior, attaining its maximum at the centre of the tube. It is evident that the rate of displacement of the layers with regard to each other must be mainly deter- mined by the amount of friction between them, and hence measurements of the rate of flow afford information as to the viscosity of liquids. The converse of viscosity is termed fluidity ; a liquid of small viscosity, such as ether, is said to have a high degree of fluidity. The magnitude of the viscosity depends greatly on the nature of the liquid. Thus the viscosity of warm ether is very small, whereas that of treacle and of pitch is so great that they approximate to the behaviour of solids, the internal friction of which is extremely high. The internal friction of gases is very small (p. 25). The coefficient of viscosity, 77, is usually defined as the force required to move a layer of unit area in unit time through a distance of unit length past an adjacent layer unit distance away. For water at 15, 77 = o 0134 in absolute units; for glycerine at the same temperature, 77 = 2*34. The coefficient of viscosity of a liquid can be calculated from the rate of outflow from a cylindrical tube by means of the equation where v is the volume of liquid discharged in the time /, p the pressure under which the outflow takes place, r the radius and / the length of the tube. In practice, however, the rate of flow of the liquid is compared with fhat of a standard liquid, usually water, under the same experimental conditions, and its absolute viscosity, 77, calculated by means of the formula nh = //C where rj M is the absolute viscosity of water at the temperature of the experiment, and t and t M are the times required for the discharge of equal volumes of the liquid and water respectively. The viscosity of liquids diminishes rapidly as the temperature LIQUIDS 75 rises, but so far no simple relationship of general applicability connecting change of viscosity and temperature has been dis- covered. Measurement of Viscosity The determination of vis- cosity by the comparative method may be conveniently carried out with the apparatus described by Ostwald and illustrated in Fig. 9. It consists essenti- ally of a capillary tube, db t connected at its upper part with a bulb /, and at its lower end with a wider tube, bent into U-shape and provided with a bulb e. Marks are etched c on the capillary tube at c and d above and below the bulb k. The apparatus is filled at / , with a definite volume of the liquid, which c is then sucked into the other limb till the surface rises above the mark c. The time required for the level of the liquid to fall from c to d is then noted. Observations have previously been made with water under similar conditions. As the pressures under which the discharge takes place are in the ratio of the density, d, of the liquid to that of water, the relative viscosity, x = rj/vj^ is given by the equation x = dtldj^. On account of the great influence of temperature on the viscosity, the measure- ments must be made at constant temperature, and for this purpose the apparatus is so constructed that it can conveniently be immersed in a thermostat. Results of Viscosity Measurements 1 Reference has already been made to the enormous differences in the viscosity of liquids, and also to the fact that temperature has a great influence on the magnitude of the viscosity. In comparing 1 Smiles, loc. cit. pp. 51-105. FIG. g. 76 OUTLINES OF PHYSICAL CHEMISTRY different liquids with regard to viscosity, we are again confronted with the difficulty of deciding at what temperatures the measure- ments should be made. The choice of the boiling-points as corresponding temperatures (p. 57) did not in this case lead to very satisfactory results, and most regularities were observed by using the data for points at which the rate of change of viscosity with temperature is the same (Thorpe and Rodger). A comparison of substances of allied chemical constitution shows that viscosity is to some extent an additive property, but is greatly affected by constitutive influences. The absolute viscosity of a number of pure liquids at o and at 25 is given in the accompanying table (Walden) : Liquid. >j at o. rj at 25. Acetone 0-00397 0-00316 Methyl alcohol 0*00846 0*00580 Acetic anhydride 0*0130 0*00860 Water 0*0178 0*00891 Ethyl alcohol 0*0179 0*0108 Benzonitrile 0*0194 0*0125 Nitrobenzene 0*0307 0-0182 In recent years the viscosity of mixtures of liquids has been the subject of a good deal of investigation. If for simplicity we confine our attention to mixtures of two components only, three classes may be distinguished : (1) The viscosity of the mixture lies between those of the pure components. Example, ethyl alcohol and carbon disul- phide. (2) The viscosity of the mixture in certain proportions is greater than that of either component. Example, pyridine and water. (3) The viscosity of the mixture in certain proportions is less than that of either constituent. Example, benzene and acetic acid. A few numbers illustrating the behaviour of the mixtures LIQUIDS 77 cited as examples of classes (2) and (3) are given in the accompanying table. Pyridine and Water.l Benzene and Acetic Acid. 2 Per cent. Pyridine. 7, at 25. Per cent. Benzene. TJ at 25. O'OO 0*00890 O'OO 0-01174 19-28 0-01336 34*93 0-00734 39-84 0-01833 48-29 0-00666 59*70 0-02187 77-26 0-00597 66-65 0-02225 8973 0-00591 80-15 0-01894 97*25 0-00594 lOO'OO 0-00885 100-00 0-00598 The results are very similar to those for the vapour pressures of binary mixtures, described later (p. 87). No general agreement has so far been reached as to the explanation of these remarkable differences in the behaviour of binary mixtures (compare p. 322). Measurements of the viscosity of salt solutions (solutions which conduct the electric current) have also led to interesting results, but they cannot be usefully considered at the present stage. Practical Illustrations, (a) Critical Phenomena The critical phenomena can be observed in an apparatus, con- structed like that of Cagniard la Tour, but more simply as fol- lows : A tube 3-4 mm. internal diameter and 3-4 cm. long is constructed out of a piece of glass tubing, the walls of which are 07-0-8 mm. thick, by closing one end in the blow-pipe and drawing out the other at a distance 3-4 cm. from the closed end into a fairly long (5-6 cm.) thick- walled capillary tube. The capillary is then bent, at a point about i cm. from the commence- ment of the wide part of the tube, at right angles to the latter and then partly filled with ether as follows. The tube is warmed and the capillary end dipped into ether, which is drawn into the tube 1 Hartley, Thomas and Appleby, Trans. Chem. Soc., 1908, 94, 538. a Dunstan, ibid., 1905, 87, 16. 78 OUTLINES OF PHYSICAL CHEMISTRY as the latter cools. The ether in the tube is then boiled gently to expel all the air, the end of the capillary dipping all the time in ether, and on again allowing to cool, ether is drawn in so as practically to fill the tube. The excess of ether is then boiled off till the tube is about three-quarters full, the end of the capillary being in ether throughout, and then allowed to cool till the liquid just begins to rise up the capillary tube, showing that the pressure inside is somewhat less than atmospheric ; the capillary is then rapidly sealed off near the bend on the side remote from the tube. In order to observe the capillary phenomena in the tube thus prepared, the latter is suspended by a wire and heated by means of a Bunsen burner held in one hand, the face being protected, in the event of an explosion, by a large plate of glass held in the other hand. In this way, the complete dis- appearance of the liquid above a certain temperature, and its reappearance on cooling, may be observed without the least danger. When practicable, the tube may be heated in an iron or copper vessel provided with mica windows, and the critical temperature may be read off on a thermometer placed side by side with the tube in the air bath. (b) Determination of Molecular Volume The determination of the molecular volume of a liquid reduces to a determination of its density at a definite temperature compared with that of water as unity, and any of the well-known methods for deter- mining the density of liquids may be employed for this purpose. A direct method for determining the density, and hence the mole- cular volume, of a liquid at its boiling-point has been described by Ramsay. A tube is drawn out to a long neck and the latter bent in the form of a hook. The vessel is then filled with liquid, heated in the vapour of the same liquid till equilibrium is reached and then weighed. If the volume of the vessel and its coefficient of expansion are known, the molecular volume of the liquid can at once be calculated. LIQUIDS 79 Measurements of the refractive index of liquids (water alcohol, benzene) and of the rotation of the plane of polarization of light by liquids or solutions (cane sugar in water) should be made by the student ; the methods are fully described in text- books of physics. The experiments on rotation of the plane of polarization may conveniently be made in connection with the hydrolysis of cane sugar in the presence of acids (p. 230). CHAPTER IV SOLUTIONS General Up to the present, we have dealt only with the properties of pure substances which may exist in the gaseous, liquid or solid state, or simultaneously in two or all of these states. We now proceed to deal with the properties of mixtures of two or more pure substances. When these mixtures are homogeneous, they are termed solutions^ There are various classes of solutions, depending on the state of the components. The more important are : (i) Solutions of gases in gases ; (ii) Solutions of (a) gases, (b) liquids, (c) solids in liquids ; (iii) Solutions of solids in solids, so-called solid solutions ; and each of these classes will be briefly considered. A distinction is often drawn between solvent and dissolved substance, but, as will appear particularly from the sections dealing with the mutual solubility of liquids, there is no sharp distinction between the two terms. The component which is present in greater proportion is usually termed the solvent. The dissolved substance is sometimes called the solute. When one of the compounds is present in very small pro- portion, the system is termed a dilute solution, and as the laws term solution is also applied to mixtures which appear homo- geneous to the naked eye but heterogeneous when examined with a micro- scope or ultramicroscope, e.g., colloidal solution of arsenic sulphide. The usual definition of a solution is "a homogeneous mixture which cannot be separated into its components by mechanical means," but the last part of this definition is open to objection. 80 SOLUTIONS 81 representing the behaviour of dilute solutions are comparatively simple, they will be dealt with separately in the next chapter. Solution of Gases in Gases This class of solution differs from the others in that the components may be present in any proportion, since gases are completely miscible. If no chemical change takes place on mixing two gases, they behave quite in- dependently and the properties of the mixture are therefore the sum of the properties of the constituents. In particular, the total pressure of a mixture of gases is the sum of the pressures which would be exerted by each of the components if it alone occupied the total volume a law which was discovered by Dalton, and is known as Dalton s law of partial pressures. Dalton's law is of the same order of validity as Avogadro's hy- pothesis ; it is nearly true under ordinary conditions, and would in all probability become strictly true at great dilution. Dalton's law can of course be tested by comparing the sum of the pressures exerted separately by two gases with that after admixture, but it is of interest to inquire into the possibility of measuring the partial pressure of one of the components in the mixture itself. It was pointed out by van't Hoff that this is always possible if a membrane can be obtained which allows only one of the gases to pass through. This suggestion was experimentally realised by Ram- say x in the case of a mixture of nitrogen and hydrogen as follows : P (Fig. 10.) is a palladium vessel containing nitrogen, the pressure of which can be determined from the difference of level between A and B in the manometer, which contains mercury. P is enclosed in another vessel, which can be filled 1 Phil. Mag., 1894, [v.], 38, 206. H FIG. 10. 82 OUTLINES OF PHYSICAL CHEMISTRY with hydrogen at any desired pressure. The vessel P is heated and a stream of hydrogen at known pressure passed through the outer vessel. As palladium at high temperatures is permeable for hydrogen, but not for nitrogen, the former gas enters P till its pressure outside and inside are equal. The total pressure in P, as measured on the manometer, is greater than the pressure in the outer vessel, and it is an experimental fact that the excess pressure inside is approximately equal to the partial pressure of the nitrogen. If, on the other hand, we start with a mixture of hydrogen and nitrogen, and wish to find the partial pressure of the latter, all that is necessary is to put the mixture inside a palladium bulb, keep the latter at a constant high temperature and pass a current of hydrogen at known pressure through the outer vessel till equi- librium is attained, as shown on the manometer. The difference between the external and internal pressure is then the partial pressure of the nitrogen. This very instructive experiment will be referred to later in connection with the modern theory of solutions (p. 101). Solubility of Gases in Liquids In contrast to the com- plete miscibility of gases, liquids are only capable of dissolving gases to a limited extent. When a liquid will not take up any more of a gas at constant temperature it is said to be saturated with the gas, and the resulting solution is termed a saturated solution. The amount of a gas taken up by a definite volume of liquid depends on (a) the pressure of the gas, () the tem- perature, (c) the nature of the gas, (d) the nature of the liquid. The greater the pressure of a gas, the greater is the quantity of it taken up by the solvent. For gases which are not very soluble, and do not enter into chemical combination with the solvent, the relation between pressure and solubility is expressed by Henry's law as follows : The quantity of gas taken up by a given volume of solvent is proportional to the pressure of the gas. Another way of stating Henry's law is that the volume of a gas taken up by a given volume of solvent is independent of the SOLUTIONS 83 pressure. This is clearly equivalent to the first statement, be- cause when the pressure is doubled the quantity of gas absorbed is doubled, but since its volume, by Boyle's law, is halved, the original and final volumes dissolved are equal. The question may be regarded from a slightly different point of view, which is instructive in connection with later work. When a definite volume of liquid is saturated with a gas at a certain pressure, there is an equilibrium between the dissolved gas and that over the liquid, and Henry's law may be expressed in the alternative form : The concentration of the dissolved gas is proportional to that in the free space above the liquid. We may consider that the gas distributes itself between the solvent and the free space in a ratio which is independent of the pressure. The solubility of gases in liquids diminishes fairly rapidly with rise of temperature. For purposes of comparison, the solvent power of a liquid for a gas is best expressed in terms of the " coefficient of solubility," which is the volume of the gas taken up by unit volume of the liquid at a definite temperature. 1 The so-called " absorption coefficient " of Bunsen, in which solubility measurements are still often expressed, is the volume of a gas, reduced to o and 76 cm. pressure, which is taken up by unit volume of a liquid at a definite temperature under a gas pressure equal to 76 cm. of mercury. With regard to the influence of the nature of the gas on the solubility, it may be said in general that gases which have distinct basic or acidic properties, for example, ammonia and hydrogen chloride, are very soluble, whilst neutral gases, such as hydrogen, oxygen and nitrogen, are comparatively insoluble. Further, gases which are easily liquefied, for example, sulphur dioxide and hydrogen sulphide, are fairly soluble. As regards the relation between solvent power and the nature of the liquid, very little is known. In general, the order of the solubility of gases in different liquids is the same, and the solvent power of a liquid therefore appears to be to soma extent a specific property. 1 Alternatively ; the ratio of the concentration in liquid and in gas space. OUTLINES OF PHYSICAL CHEMISTRY The above remarks are illustrated by the following table, in which the coefficients of solubility of some typical gases in water and in alcohol are given : Gas. Water. Alcohol. Ammonia 1050 Hydrogen sulphide 80 18 Carbon dioxide 1-8 4'3 Oxygen . 0-04 0-28 Hydrogen 0'02 0-07 It may be mentioned that the solubility of gases in water is greatly diminished by the addition of salts, and to a much smaller extent by non-electrolytes. The interpretation of these results has given rise to considerable difference of opinion. 1 Solubility of Liquids in Liquids As regards the mutual solubility of liquids, three cases may be distinguished : (i) The liquids mix in all proportions, e.g., alcohol and water ; (2) the liquids are practically immiscible, e.g., benzene and water ; (3) the liquids are partially miscible, e.g., ether and water. (i) and (2) Complete miscibility and non-miscibility Very little is known as to the factors which determine the miscibility or non-miscibility of liquids. The separation of the compon- ents by fractional distillation is discussed in succeeding sections. (3) Partial miscibility If ether, in gradually increasing amounts, is added to water in a separating- funnel, and the mix- ture well shaken after each addition, it will be noticed that at first a homogeneous solution is formed, but when sufficient ether has been added, a separation into two layers takes place on standing. The upper layer is a saturated solution of water in ether, the lower layer a saturated solution of ether in water. As long as the relative quantities of ether and water are such that a separation into two layers takes place on standing, the 1 Compare Philip, Trans. Chem. Soc., 1907, 91, 711 ; Usher, ibid., IQIO, 97, 66. SOLUTIONS 85 composition of these layers is independent of the relative amounts of the components present, since the composition is determined by the solubility of ether in water and of water in ether at the temperature of experiment. Further, the saturated vapours sent out by the two layers have the same pressure and the same com- position this follows from the fact that they are in equilibrium with the two layers which are in equilibrium with each other. In the majority of cases, the solubility of two partially miscible liquids increases with the temperature, and it may therefore be anticipated that liquids which in certain propor- tions form two layers at the ordinary temperature may be com- pletely miscible at higher temperatures. Several such cases are known, for example, phenol and water, which has been investigated by Alexieeff. At room temperature a saturated solution of phenol in water contains about 8 per cent, of the former component. When more phenol is added two layers are formed and the temperature has to be raised in order to secure complete miscibility. For further additions of phenol up to 36 per cent, the temperature at which complete miscibility occurs rises progressively to 68 '4. In this way the solubility- temperature curve of phenol in water is obtained. Similarly, a saturated solution of water in phenol at 20 contains 28 per cent, of the former component and on further additions of water the temperature of complete miscibility rises progres- sively to 68*4, at which point the two solubility-temperature curves meet. These results are represented graphically in Fig. n, the composition of the mixture being measured on the horizontal axis and temperatures along the vertical axis. The point D represents o per cent, phenol (100 per cent, water), E represents 100 per cent, phenol. At all points outside the curve ABC there is complete miscibility, at points inside the curve two layers exist. The maximum represents the tem- perature, 6 8 '4, above which phenol and water are miscible in all proportions. If, therefore, we start with a homogeneous solution of phenol in water of the composition represented 86 OUTLINES OF PHYSICAL CHEMISTRY by the point x, and gradually add phenol at constant tem- perature, the composition of the solution will alter along the dotted line xx until the curve AB is reached at z. This point represents a saturated solution of phenol in water, and on further addition of phenol a separation into two layers takes place, the compositions of which are represented by the points z and z' respectively. As more phenol is added, the composition of the layers remains unaltered, but the relative amount of the second layer increases until at the point z' only this layer is present, and its composition then alters along zx' . 100 /o Phenol Phenol Miscibility of Phenol and Water. FlG. II. % KK>% NICOT'NC NICOTINE Miscibility of Nicotine and Water. FIG. 12. If, however, phenol is added to the same solution at the tem- perature corresponding with the point y the composition alters along yy but no separation into two layers takes place. It is evident that there is a striking analogy between the miscibility of two liquids and the critical phenomena represented in Fig. 5. In both cases there is only one phase outside the curves AOE and ABC respectively, and two phases at points inside the curves. Further, above a certain temperature only one phase can exist in each case, and the temperature of com- plete miscibility for binary mixtures may therefore be termed the critical solution temperature. Moreover, just as we can SOLUTIONS 87 pass without discontinuity from a gas to a liquid (p. 53), we can pass from a solution containing excess of water to one contain- ing excess of phenol without discontinuity. Starting with a mixture represented by the point x, the temperature is raised above the critical solution temperature along xy, phenol is then added till the pointy is reached and the homogeneous mixture then cooled along y'x. In some cases, however, the solubility of one liquid in another diminishes with rise of temperature, thus if a saturated solution of ether in water, prepared at the ordinary temperature, is gently warmed, it becomes turbid, indicating partial separation of the ether. An interesting example of this behaviour is seen in nicotine and water, which are miscible in all proportions at the ordinary temperature, but separate into two layers when the temperature reaches 60. If a temperature can be reached beyond which the mutual solubility again begins to increase with rise of temperature, the components may again become miscible in all proportions. This has been experimentally realised so far only for nicotine and water, which again be- come completely miscible when the temperature exceeds 210. The remarkable solubility relations of these two liquids are therefore represented by a closed curve (Fig. 12), which will be readily understood by comparison with Fig. n. Distillation of Homogeneous Mixtures A very impor- tant matter with reference to binary homogeneous mixtures is the possibility of separating them more or less completely into their components by distillation. Much light is thrown on this question by the investigation of the vapour-pressure of the mix- ture as a function of its composition at constant temperature. Experimental investigation shows that the curve representing the relation between vapour pressure and composition at constant temperature usually belongs to dne of the three main types a, b and c represented in Fig. 13, in which the abscissae represent the composition of the mixture and the ordinates the corres- ponding vapour pressures. 88 OUTLINES OF PHYSICAL CHEMISTRY (a) The vapour-pressure curve of the mixture may have a minimum, as represented by the point U in the curve RUS ; example, hydrochloric acid and water. (In the diagram the ordinate PR represents the vapour-pressure of B, and QS that of the other pure substance A.) () The vapour-pressure curve may show a maximum, repre- sented by the point T on the curve RTS ; example, propyl alcohol and water. P(o/ A) Composition FIG. 13. Q doo / A) (<:) The vapour-pressure of the binary mixture may lie between those of the pure components A and B, as repre- sented by the curve RWS ; example, methyl alcohol and water. In considering these three typical cases with regard to their bearing on the separation of two liquids by fractional distilla- tion, the important question is the relation between the com- position of the boiling liquid and that of the escaping vapour. For a pure liquid, the composition of the escaping vapour is necessarily the Game as that of the liquid, but this is not in general the case for a mixture of liquids, and therefore the SOLUTIONS 89 composition of the mixture may alter continuously during dis- tillation. Case (a). Since a liquid boils when its vapour pressure is equal to the external pressure, it is clear that if a mixture the vapour-pressure curve of which has a minimum (as in the curve RUS) be boiled, the composition of the liquid will alter in such a way that it tends to approximate to that represented by the point U, since all other mixtures have a higher vapour pressure, and will consequently pass off first. When finally only the mixture U remains, it will distil at constant tempera- ture like a homogeneous liquid, since the composition of the vapour is then the same as that of the liquid. The best- known example of such a constant-boiling liquid is a mixture of hydrochloric acid and water, which boils at 110. If a mixture containing the components in any other proportion be heated, either hydrochloric acid or water will pass off, and the com- position of the liquid will move along the curve to the point of minimum vapour pressure, beyond which it distils as a whole, without further change of composition. Case (). When, on the other hand, there is a maximum in the vapour-pressure curve, the mixture which has the highest vapour tension will pass over first, and the composition of the residue in the retort will tend towards the component which was present in excess in the initial mixture. In the case of propyl alcohol and water, for example, the mixture which has the highest vapour tension contains from 70 to 80 per cent, alcohol (the maximum being very flat) ; a mixture of this com- position would boil at constant temperature, whilst for one con- taining more water, some of the latter would finally remain in the retort. Case (c). In this case the composition of the vapour, and therefore the composition of the liquid remaining, alter continu- ously on distillation. The vapour, and therefore the distillate, will contain the more volatile liquid, A, in greater proportion, and the residue excess of the less volatile liquid, a partial separation 90 OUTLINES OF PHYSICAL CHEMISTRY being thus effected. If the distillate rich in A is again distilled a mixture still richer in A is at first given off, and the process may be repeated again and again. The more or less complete separation of liquids by this method is termed fractional dis- tillation. It was long thought that constant-boiling mixtures were definite chemical compounds of the two components for example, HC1, 8H 2 O in the case of hydrochloric acid and water, but this view was shown by Roscoe to be untenable. He found that the composition of the mixtures does not correspond with simple molecular proportions of the com- ponents, and, further, that the composition alters con- tinuously with alteration of the pressure under which the distillation is conducted, which is not likely to be the case if definite chemical compounds are present. Distillation of Non-Miscible or Partially Miscible Liquids. Steam Distillation If two immiscible liquids are distilled from the same vessel, since one does not affect the vapour pressure of the other, they will pass over in the ratio of the vapour pressures till one of them is used up. The tem- perature at which the mixture boils is that at which the sum of the vapour pressures is equal p(o/ B) Composition Q 100 /o B) to the superincumbent FIQ. 14. pressure. The curve re- presenting the relation between vapour pressure and composition of the mixture is therefore a straight line (UU' f Fig. 14) parallel to the axis of composition, PU representing the sum of the vapour pressures SOLUTIONS 9* RP and QT, of the two components at the temperature in question. These considerations are very important in connection with steam-distillation. This process is usually employed for the separation of substances with a high boiling-point, such as aniline, and will be familiar to the student. The relative volumes of steam and the vapour of the liquid which pass over are in the ratio of the vapour pressures, p^ and / 2 , at the tem- perature of the experiment, and the relative weights which pass over are therefore in the ratio p^ :/ 2 ^ n wmcn ^i and FIG. 15. becomes turbid on warming. In the case of calcium sulphate, the solubility increases at first with rise of temperature and then diminishes, so that there is a maximum in the solubility curve, as shown in the figure. Solubility curves are usually continuous, but that representing the solubility of sodium sulphate shows a distinct change of direction at 33. This is owing to the fact that we are dealing 94 OUTLINES OF PHYSICAL CHEMISTRY with the solubility curves of two distinct substances. Below 33, the dissolved salt is in equilibrium with the solid deca- hydrate Na 2 SO4, ioH 2 O, but the latter splits up into the anhydrous salt and water at 33, so that the solubility curve at higher temperatures is that of the anhydrous salt. That this explanation of the phenomenon is correct is shown by the fact that the solubility of the anhydrous salt can be determined for a few degrees below 33 in the complete absence of crystals of the decahydrate ; the part of the curve thus obtained, repre- sented by the dotted line, is continuous with the right-hand curve. It is important to remember that the change to which the break in the solubility curve of sodium sulphate is due takes place in the solid phase and not in the solution. No well- defined case is known of a sharp break in a curve representing the variation of a physical property in a homogeneous system with temperature or composition. Relation between Solubility and Chemical Constitution Very little is known as to causes influencing the mutual solubility of substances and its variation with temperature. In general, it may be said that substances of similar chemical com- position are mutually soluble, thus the paraffins are miscible with each other in all proportions, and organic compounds containing the hydroxyl group are all fairly soluble in water. In these cases it does not seem probable that the solubility is connected with anything in the nature of ordinary chemical combination. Phenomena of an apparently different nature are met with in the solubility of gases in liquids, already referred to (p. 83), where it was pointed out that the solvent power is in general a specific property of the solute, and to some extent independent of the nature of the gas. The solubility of indifferent gases appears in the first instance to depend upon the relative ease with which they can be liquefied. Solid Solutions * In general, when the temperature of a dilute solution is lowered until partial solidification takes place, 1 Compare Bruni, Feste Losiingen und Isomorphisms, Leipzig, 1908. SOLUTIONS 95 the solvent separates in the solid form, practically uncontami- nated with the solute. When, however, a solution of iodine in benzene is partially frozen, crystals containing both substances separate, and when solutions of varying concentration are used, there is a constant ratio between the iodine remaining in solution and that in the solidified benzene. This is illustrated in the accompanying table ; in the top line is given the concentration G! of the iodine in the liquid benzene, in the second line the iodine concentration C 2 in the solid benzene, and in the third line the ratio of the concentrations in solid and liquid, which is approximately constant : G! 3-39 2-587 0-945 percent. C 2 I<2 79 o*9 2 5 o'S 1 ? percent. 0-377 0-358 0-336 This phenomenon exactly corresponds with Henry's law regard- ing the solubility of gases in liquids (p. 82), and as the crystals containing the two substances are quite homogeneous, they may be regarded as a solid solution of iodine in benzene. Similar phenomena have been observed for many other pairs of sub- stances, more particularly for certain metals (p. 192). Besides crystalline solid solutions, of which an example has just been given, non -crystalline or amorphous solid solutions are known. The hydrogen absorbed by palladium appears to be in solid solution in the metal, but the phenomenon is com- plicated, and is not yet thoroughly understood. Van't Hoff suggests that two solid solutions are present, hydrogen dissolved in palladium and palladium dissolved in solid hydrogen, corre- sponding with the two liquid layers formed by phenol and water. There is evidence that in some cases the dissolved substances can diffuse slowly through the solid solvent, which indicates that the solute exerts osmotic pressure (p. 97). Practical Illustrations. (a) Partial Miscibility The fact that certain liquids, such as phenol and water, are onlr 9 o OUTLINES OF PHYSICAL CHEMISTRY partially miscible at ordinary temperatures, but completely miscible above 69, may be illustrated as follows: 5-6 grams of crystals of phenol are placed in a small separating funnel, and on adding a little water and shaking it will be found that a clear solution is formed, mainly due to the effect of water in lowering the freezing-point of phenol. On further addition of water two layers will be formed, which only disappear when a large excess of water has been added. If, on the other hand, phenol is warmed to 75 in a test tube, and water at the same temperature is gradually added, no separation into two layers will occur, corresponding with the fact that the critical solution temperature has been exceeded. () Solubility and Temperature The solubility in water of a salt such as sodium chloride may conveniently be determined as follows. A large test tube is partially filled with distilled water and excess of powdered sodium chloride, and partially immersed in a bath kept at constant temperature. The tube is closed by means of a rubber cork through which passes a glass stirrer, driven by means of a motor. At intervals samples of the solution are removed by means of a pipette, a weighed portion of the solution evaporated to dryness, and the residue weighed. When the concentration of the solution no longer alters, it is saturated. Observations should be made at differ- ent temperatures at intervals of 10 and the results plotted on squared paper, the temperatures being plotted as abscissae, and the solubility expressed as grams of the salt in 100 grams of solvent, as ordinates (Fig. 15). (c) Supersaturated Solutions A supersaturated solution of sodium sulphate may be prepared by heating the salt with half its weight of water in a flask till a perfectly clear solution is obtained; the flask is then plugged with cotton wool and set aside to cool. If a small crystal of the sulphate is added to the cold solution, crystallization at once starts, but crystals not isomorphous with sodium sulphate (e.g., sodium chloride crystals) are not efficient in starting crystallization. CHAPTER V DILUTE SOLUTIONS General So far, we have dealt in a general way with the properties of solutions, mainly on the lines of the older methods of investigation, as they were practised up to about twenty years ago. In 1885, however, a new turn was given to the subject by the enunciation of the modern theory of solution by van't Hoff. Many of the experimental facts on which this theory is based had previously been established by the work of Ostwald, Raoult and others, and these results were correlated, and many fresh avenues opened for investigation, by van't HofFs theory, the most important point in which is the conception of osmotic pressure, which will now be considered. It has already been shown that the laws applicable to gases are very simple and that these laws are most strictly followed in the rarefied condition ; on the molecular theory this is accounted for by assuming that the particles are then so far apart as to exert little or no mutual influence, and that the space filled by the material of the particles is negligible in comparison with the space occupied. Similarly, we may reasonably anticipate that the laws expressing the behaviour of dissolved substances mil be most simple in dilute solution, in other words, when one of the components (the solvent) is present in large propor- tion compared with the other (the solute), and this is quite borne out by the facts. Osmotic Pressure. Semi-permeable Membranes When a few drops of bromine are carefully placed by means 7 97 9 8 OUTLINES OF PHYSICAL CHEMISTRY of a pipette at the bottom of a jar full of hydrogen or air, and the jar is covered and allowed to stand, it will be found after some time that the heavy bromine vapour has distributed itself uniformly throughout the confined space against the force of gravity. We may say that the bromine vapour exerts a pressure in virtue of which it diffuses into those parts of the confined space where the pressure is less, and equilibrium is only attained when the pressure is equal throughout. In an exactly similar way, if a sugar solution is carefully covered with a layer of water, the dissolved sugar exerts a pressure with the result that it ultimately becomes uniformly distributed in the solution. This pressure cannot be determined directly, since the external pressure is the sum of this and the pressure of the liquid, but the principle of the method used for measuring it will be under- stood from its analogy with the method already described for measuring the partial pressure of a gas in a mixture (p. 81). In the latter case, it will always be possible to determine the partial pressure of a gas, A, mixed with another gas, B, when a membrane is known which allows B, but not A, to pass through. Such a membrane is said to be semi-permeable, and for 3 mixture of nitrogen and hydrogen heated palladium answers the purpose. It is clear that, if we could find a membrane which allows water, but not dissolved sugar, to pass through, the pressure exerted by the latter in solution, its so-called osmotic pressure, could be measured. Such membranes were discovered by Traube, in the course of his experiments on so-called artificial vegetable cells. The most suitable membrane for the purpose was found to be copper ferrocyanide, and the formation of this membrane and its im- permeability for certain dissolved salts may be illustrated as follows. A glass tube, provided with a rubber tube and clip at one end and open at the other, is partly filled by suction with an aqueous solution of copper acetate (about 2'8 per cent.) and ammonium sulphate (0-5 per cent.), and the open end, in which the surface of the liquid has been made parallel by DILUTE SOLUTIONS 99 adjustment, is then dipped carefully into a 2-4 per cent, aqueous solution of potassium ferrocyanide, containing a little barium chloride, and the tube supported in that position. A thin membrane of copper ferrocyanide forms across the lower end of the tube, and if the experiment has been carefully performed, it will be found that even after standing some hours there is no white precipitate (of barium sulphate) in the lower solution, showing that the membrane is impervious to ammonium sul- phate. Traube tried many other membranes, but none proved so efficient as copper ferrocyanide. Measurement of Osmotic Pressure The semi-permeable membranes prepared by Traube were much too weak to with stand fairly large pressures, and their use for actual measurements was only ren- dered possible by Pfeffer's idea of deposit- ing them in the walls of a porous pot A (Fig. 1 6) such as are used for experiments on gas diffusion. The pot is first carefully washed, soaked in water for some time, then nearly filled with a solution of copper sulphate (2*5 grams per litre), dipped nearly to the neck in a solution of potas- sium ferrocyanide (2-1 grams per litre) and allowed to stand for some hours. The salts diffuse through the walls of the pot and at their junction form a membrane of copper ferrocyanide, which, since it is im- permeable for the salts from which it is formed, remains quite thin but is capable of withstanding fairly large pressures, owing to its being supported by the walls. The cell is then taken out, washed, filled with a strong solution of sugar, and closed with a well-fitting rubber cork through which an open glass tube, B, passes. To ensure the tightness of the apparatus, it is of ioo OUTLINES OF PHYSICAL CHEMISTRY advantage, before forming the membrane, to dip the upper part of the pot, to the depth of about two inches, into melted paraffin, and after the pot is filled and the cork and tube placed in position, the upper surface should be covered with melted paraffin. When a cell thus prepared is placed in water, the water passes in, the pressure inside slowly increases (as shown by the rise in level of the solution in the tube), and finally reaches a point at which, when the cell has been properly prepared, it remains constant for days. The maximum pressure thus attained, in other words, the excess of pressure which must prevail inside the cell in order to prevent more water flowing in through the semi-permeable membrane, is termed the osmotic pressure of the solution. In accurate measurements, it is preferable to close the cell with a cork carrying a closed manometer, containing a definite volume of air confined over mercury. Dilution of the solution by the entry of a large volume of water is thus avoided. This arrangement was used by Pfeffer in his original experiments. The osmotic pressures measured in this way are very con- siderable thus a i per cent, solution of cane sugar exerts a pressure of more than half an atmosphere, and a i per cent, potassium nitrate solution over two atmospheres. The question as to the relation between osmotic pressure and concentration of the solution was investigated by Pfeffer, and the results obtained for aqueous solutions of sugar and of potassium nitrate at room temperature are given in the ac- companying table, in which C represents the concentration of the solution (in grams per ioo c.c. of solution) and P the osmotic pressure (in cm. of mercury). Cane Sugar. Potassium Nitrate. C P P/C C P P/C 1 53*5 53*5 0-8 130-4 163 2 101-6 50-8 1-43 218-5 J 53 4 208-2 52-1 3-33 436-8 133 6 307*5 5i'3 It is clear from these results that the ratio P/C is approximately DILUTE SOLUTIONS 101 constant for any one solution, in other words, the osmotic pres- sure of a' solution is proportional to its concentration. It will be observed that the ratio is somewhat less for potassium nitrate at the higher pressures, a result due in part to the slight per- meability of the membrane for the salt under these conditions. It was also shown by Pfeffer that the osmotic pressure at constant concentration increases with the temperature ; some of the results obtained in this connection are quoted on the next page. The magnitude of the osmotic pressure observed with different membranes was not quite the same, but this must be ascribed to the imperfection of most of the membranes, as it can be shown theoretically that the numerical value of the osmotic pressure is independent of the nature of the membrane, provided the latter is perfectly semi-permeable. Yan't Hoff s Theory of Solutions Pfeffer's investiga- tions were undertaken for botanical purposes, and their great general importance was only recognised in 1885 by van't Hoff, who used them as the experimental basis of a new theory of solution. We have already seen that osmotic pressure may be regarded as in some respects analogous to gas pressure, and as ihe former can be measured as described in the previous section we are now in a position, following van't Hoff, to investigate the relationship between osmotic pressure, volume and tem- perature as has already been done for gases. As regards the relation between osmotic pressure and volume at constant temperature, we have seen in the previous section that P/C is constant for any one substance, and as the concen- tration is inversely as the volume in which a definite weight of substance is dissolved, we obtain, by substituting i/V for C, the equation PV = constant, the exact analogue for solutions of Boyle's law for gases. With reference to the relation between osmotic pressure and temperature at constant concentration, van't Hoff showed from Pfeffer's observations that the osmotic pressure, P, like the gas 102 OUTLINES OF PHYSICAL CHEMISTRY pressure, is proportional to the absolute temperature, T. Some of the observations on which this conclusion is based are given in the accompanying table : Cane Sugar. Sodium Tartrate. / T P / T P 14-2 287-2 51-0 13-3 285-3 90-8 32-0 305-0 54-4 (54-6) 37-0 310-0 98-3 (98-2) The observed values are given in the third column, with the calculated values in brackets ; the agreement is within the limits of experimental error. From these two equations, PV = const, and P oc T, we can derive an equation for dilute solutions corresponding to that already obtained for gases (p. 26), PV = rT, in which P represents the osmotic pressure of a solution con- taining a definite weight of a solute in the volume, V, of solution, and r is a constant. It remains to calculate the numerical value of r for a definite amount, say a mol of a dissolved substance, as has already been done for gases. This can readily be done from Pfeffer's observa- tion that a i per cent, solution of cane sugar at o exerts an osmotic pressure of 49*3 cm. of mercury. The molecular weight of cane sugar is 342, the volume in which it is contained 34,200 c.c., the pressure is 49-3 x 13*59 gram/cm. 2 , and the absolute temperature 273. Hence PV 49-3x13-59x34,200 ,. .. r - - = 83,900 (in gram-cm, units), a value which almost exactly corresponds with that obtained for gases. As the same value for r is obtained for a mol of other organic compounds, such as urea and glucose, we will represent it by R, to indicate that it is a factor of general im- portance. We have thus obtained two results of the greatest importance : (i) the equation PV = RT is valid for dilute solu- DILUTE SOLUTIONS 103 tions ; (2) the numerical value of R is the same for dissolved substances as for gases. The latter statement implies, as is clear from the general equation, that the osmotic pressure of a definite quantity of cane sugar or other substance in solution is equal to the gas pressure which it would exert if it occupied the same volume in the gaseous form. We may therefore say with van't Hoff that " the osmotic pressure exerted by any substance in solution is the same as it would exert if present as gas in the same volume as that occupied by the solution, provided that the solution is so dilute that the volume occupied by the solute is negligible in comparison with that occupied by the solvent"* This statement holds for all temperatures, as is at once clear from the fact that the solution obeys the gas laws. Certain important exceptions to the above rule, more particularly in the case of solutions which conduct the electric current, will be discussed in a later chapter. Some important consequences of the validity of the general equation, PV = RT, for dissolved substances will be dealt with in detail later. In particular, the molecular weight of a dis- solved substance is the quantity in grams which, when dissolved in 22*4 litres at o, exerts an osmotic pressure of i atmosphere, a definition almost exactly analogous to that for gases (p. 36). The same fact may be expressed somewhat differently as fol- lows : Quantities of different substances in the ratio of their molecular weights, when dissolved in equal volumes of the same solvent, exert the same osmotic pressure. So far, we have considered only the experimental basis of the theory of solution. It has, however, been shown theoretically by van't Hoff, by thermo dynamical reasoning, that the osmotic pressure and gas pressure must have the same absolute value, if the solution is sufficiently dilute, and this conclusion has been confirmed by Lord Rayleigh and by Larmor, among others. The latter writer puts the matter as follows : " The change of available energy on further dilution, with which alone we are concerned in the transformations of dilute solu- io 4 OUTLINES OF PHYSICAL CHEMISTRY tions \cf. p. 150], depends only on the further separation of the particles . . . and so is a function only of the number of dissolved molecules per unit volume and of the temperature, and is, per molecule, entirely independent of their constitution and that of the medium," l the assumption being made that the particles are so far apart that their mutual influence is negligible. "The change of available energy " is thus brought into exact correlation with that which occurs in the expansion of a gas. Recent direct Measurements of Osmotic Pressure It is a remarkable fact that, although Pfeffer's osmotic pres- sure measurements were made as early as 1877, the degree of accuracy attained by him has not been improved upon until quite recently. Accurate measurements are, however, very desirable, because although the relation between osmotic pres- sure and concentration can be calculated from the gas laws in dilute solution, there is still much uncertainty as to how far the gas laws are applicable, or what is the exact relationship between osmotic pressure and concentration, in concentrated solutions. In particular, it is, or was until quite recently, uncertain whether V in the general equation, PV = RT, should represent the volume of the solvent or that of the solution. This uncertainty has been to some extent removed by the very careful measurements carried out by Morse and Frazer 2 since 1903 by Pfeffer's method with slight modifications. Their results show that, if V in the general equation be taken as the volume of the solvent, aqueous solutions of cane sugar approximately follow the gas laws up to a concentration of 342 grams of the solute in 1000 grams of water. A few of their results, illustrating the above statement, are given in the accompanying table; the numbers under "gaseous" are calculated on the assumption that the sub- stance as gas occupies the same volume as the solvent in the solution. 1 Larmor, Encyc. Britannica, loth ed., vol. xxviii., p. 170. *Amer. Ghent. ?., 1905,34, iJ 1906, 36, i, 39! 1007, 37, 324, 425. 558; 38, 175; 1908, 39, 667; 40, i, 194; 1909, 41, i, 257; 1911, 45, 554, etc. DILUTE SOLUTIONS 105 Concentration of Solution. Pressure at constant temp. Ratio of (20) (atmospheres). osmotic pres- tfols per looo grams Mols per litre oi ^ A ^ sure to gas of water. solution. Gaseous. Osmotic. pressure, O'lO 0-09794 2*39 2-522 055 0*20 0*19192 4-78 5'23 051 0-40 0-36886 9'56 9-96 038 0*60 0-53252 i4'34 15-20 060 0-80 0-68428 19-12 20*60 077 I"OO 0-82534 23-90 26*12 093 The table shows that only when concentrations are referred to a definite weight (or volume) of solvent is there proportionality between concentration and osmotic pressure ; if they are re- ferred to a constant volume of solution (column 2) the osmotic pressure increases faster than the concentration. The numbers in the fifth column show, however, that the osmotic pressure at 20 is on the average about 6 per cent, greater than the gas pressure. Curiously enough, the ratio is about the same at all temperatures from o to 25. Other Methods of Determining Osmotic Pressure The difficulties inherent in the direct determination of osmotic pressure can often be avoided by determining it indirectly by comparison with a solution of known osmotic pressure. Solutions which have the same osmotic pressure are said to be isotonic or isosmotic. One such method, used by de Vries, 1 depends on the use of plant cells as semi-permeable membranes. The protoplasmic layer which surrounds the cell-sap is permeable to water, but impermeable to many substances dissolved in the cell-sap, such as glucose and potassium malate. If such a cell is placed in contact with a solution of higher osmotic pressure than the cell-sap, water is withdrawn from the cell (just as a sugar solution absorbs water through a semi-permeable membrane) and the protoplasm shrinks away from the cell-wall ; a pheno- menon which is termed plasmolysis. If, however, the solution has a smaller osmotic pressure than that of the cell-sap, water enters the cell, the protoplasm expands and lines the cell-wall. The behaviour of the protoplasm, especially if coloured, can be 1 Zeitsch. physikal. Chem. t 1888, 2, 415. 106 OUTLINES OF PHYSICAL CHEMISTRY followed under the microscope, and by trial a solution can be found which has comparatively little effect upon the appearance of the cell, and is therefore isotonic with the cell contents. A method depending on the same principle, in which red blood corpuscles are used instead of vegetable cells, has been described by Hamburger, 1 and the cell-walls of bacteria may also be used as semi-permeable membranes. The following table contains some " isotonic coefficients " as given by de Vries and by Hamburger ; the numbers represent the ratio of the osmotic pressures of equimolecular or equimolar solutions of the compounds mentioned. Isotonic Coefficients. Plasmolytic With Red Blood Substance. Method. Corpuscles. Cane sugar . . 1*81 172 Potassium nitrate . .3*0 3*0 Sodium chloride . .3*0 3*0 Calcium chloride . 4'33 4' 5 It will be observed that, although the results obtained by the two methods agree fairly well, the osmotic pressures for equi- valent solutions are not equal, as would be expected according to Avogadro's hypothesis. The deviation from the expected result is such that potassium nitrate, for example, exerts an osmotic pressure about 1*7 times greater than that due to an equimolar solution of cane sugar. This observation is of fundamental importance in connection with modern views as to salt solutions. The Mechanism of Osmotic Pressure The foregoing considerations are quite independent of any hypothesis as to the exact nature of osmotic pressure, and so far no general agreement has been reached on this point. Van't Hoff inclines to the view that the pressure is to be accounted for on kinetic grounds, 2 perhaps as being due to the bombardment of the 1 Zeitsch. physikal. Chetn., 1890, 6, 319. 2 For a discussion between van't Hoff and Lothar Meyer on this point, see Zeitsch. physikal. Chetn, , iSgOj 5, 23, 174. DILUTE SOLUTIONS 107 walls of the vessel by solute particles, in the same way as the pressure of a gas is produced according to the kinetic theory, and the fact that the osmotic pressure is proportional to the absolute temperature appears rather to support this suggestion. Other views are that it is connected with attraction between solvent and solute, or perhaps with surface tension effects. It may be pointed out that the equivalence of osmotic pressure and gas pressure in great dilution is no evidence that they arise from the same cause. As regards semi-permeable membranes, their efficiency does not depend, as might at first sight be sup- posed, on anything in the nature of a sieve action, only the smaller molecules being allowed to pass, but rather upon a difference in their solvent power for the two components of the mixture. The action of the palladium in Ramsay's experiment (p. 81) is very probably to be accounted for in this way, and that the same is true for solutions is well illustrated by an in- structive experiment due to Nernst and illustrated in Fig. 17. The wide cylin- drical glass tube A is closed at the bottom with an animal membrane (bladder) which has previously been thoroughly soaked in water; it is then filled with a mixture of ether and benzene and fitted with a FIG. 17. cork and narrow tube, as shown in the figure. The cell is supported on a piece of wire gauze in a beaker partly filled with moist ether and loosely closed by a cork, B. After a time it will be observed that the liquid has risen to a considerable height in the narrow tube. What occurs in this case is that the etner dissolves in the water with which the membrane is soaked, and in this way is transferred inside the cell, whilst the benzene, being insoluble in water, is unable to pass out. io8 OUTLINES OF PHYSICAL CHEMISTRY Similarly, the efficiency of the copper ferrocyanide membrane may depend on its solvent power for water but not for sugar. Osmotic Pressure and Diffusion It has already been pointed out that there is a close connection between osmotic pressure, as defined above, and diffusion ; it is the difference in the osmotic pressure of cane sugar in different parts of a system which causes it in time to be uniformly distributed through that system. The diffusion of dissolved substances was very fully investigated by Graham, but the general law of diffusion was first enunciated by Fick. Fick's law is comprised in the equation ds DA^<#, dx which states that the amount of solute, ds, which passes through the cross-section of a diffusion cylinder is proportional to the area, A, of the cross-section, to the difference of concentration, dc, at two points at a distance dx from one another, to the time, dt, and to a constant, D, characteristic for the substance, and termed the diffusion-constant. As an illustration of the above formula, it was found that when dc=* i gram per c.c., dx*=i cm., A i sq. cm. and ^/= one day, that 0-75 grams of sodium chloride passed between the two surfaces. This is excessively slow, in comparison with the high osmotic pressures set up even by dilute solutions, and the explanation is to be found in the great friction due to the smallness of the particles. As the driving force the osmotic pressure and the rate of diffusion are known, the resistance to the movement of the particles can be obtained. It has been calculated that the enormous force of four million tons weight is needed to force i gram mol of cane sugar through water at a velocity of i cm. per sec. The more rapid diffusion in gases may plausibly be ascribed to the much smaller resistance to the movement of the particles. The rate of diffusion is much influenced bv temperature and, curiously enough, to about the same extent for all solutes DILUTE SOLUTIONS 109 the average increase is about ^ of the value at 18 for every degree C. MOLECULAR WEIGHT OF DISSOLVED SUBSTANCES. General It has already been pointed out (p. 103) that since Avogadro's hypothesis is valid for solutions, the molecular weight of a dissolved substance can readily be calculated when the osmotic pressure exerted by a solution of known concentration at known temperature and pressure is known. An illustration of this is given on the next page. As, however, the direct measure- ment of osmotic pressure is a matter of considerable difficulty, it has been found more convenient for the purpose to measure other properties of solutions, the relationship of which to the osmotic pressure is known, The only three methods which can be dealt with here are : (1) The lowering of vapour pressure ; (2) The elevation of boiling-point ; (3) The lowering of freezing-point, brought about by adding a known weight of solute to a known weight or volume of solvent. It can be shown by therm odynamical reasoning (p. 1 3 1) that un- der certain conditions the lowering of vapour pressure, the eleva- tion of the boiling-point and the lowering of the freezing-point due to the addition of a definite quantity of solute to a definite volume of solvent are each proportional to the osmotic pressure of the solution. Further, the equations expressing the exact relation- ships between these three factors and the osmotic pressure have also been established, 1 and all these theoretical deductions have been fully confirmed by experiment. // follows that just as equimolecular quantities of different substances in equal volumes of the same solvent exert the same osmotic pressure, so equimole- cular quantities of different substances in equal volumes of the same solvent raise the boiling-point ', lower the freezing-point, and lower the vapour tension to the same extent. These statements find a very simple representation on the molecular theory. Since 1 Appendix, pp. 131-138. no OUTLINES OF PHYSICAL CHEMISTRY equimolecular quantities of different substances contain the same number of molecules, it follows that the magnitude of the osmotic pressure, lowering of vapour pressure, etc., depends only on the number of particles present and is independent of their nature (colligative properties, p. 63). The molecular weight of the solute could, of course, be obtained by determining one of the factors (i), (2), (3) and then calculating the value of the osmotic pressure, but it is much simpler to obtain the molecular weight by comparison with a substance of known molecular weight. It may be mentioned that besides the methods just indicated, there are other analogous methods for determining molecular weights which, from considerations of space, cannot be referred to here. Nernst has pointed out that any process involving the separation of solvent and solute can be used for determining molecular weights, and a little consideration will show that the four methods just mentioned come under this heading. Moreover, the osmotic effect of the solute is to diminish the readiness with which part of the solvent may be separated from the solution, and the effect of the solute on the boiling- and freezing-points of the solvent must therefore be in the direction already indicated. The mathematical proof of the connection between these four properties depends upon the equivalence of the work done in removing part of the solvent from the solu- tion (Appendix). The four different methods for determining molecular weights in solution and the general nature of the results obtained will now be considered in detail. Molecular Weights from Osmotic Pressure Measure- ments, (a) from absolute values of the osmotic pressure The principle of this method has already been discussed (p. 103). If 8 grams of substance, dissolved in v c.c. of solvent, gives an osmotic pressure of p cm. at T abs., the molecular weight, m, will be that quantity which, when present in 22,400 c.c. of solvent, will give an osmotic pressure of 76 cm. Hence, since is proportional to the amount of substance used (p. 26), DILUTE SOLUTIONS m pv 22,400 x 76 273 + / :: m :: 273 % x 22,400 x 76 x (273 + /) or m = " - As an example, we will take an experiment of Morse and Frazer (p. 105) in which a solution containing 34*2 grams of sugar in 1000 c.c. (really 1000 grams) of water gave an osmotic pressure of 2*522 atmospheres = 191*6 cm. at 20. Hence m = 34'2 x 22.400 x 76 x 293 , ^. Q 273 x 191*6 x 1000 as compared with the theoretical value jf 342. Alternatively, by formula (2) p. 36 m = g RT -342 x 0*08205 x 293 ^ g pv 2*522 x i (b) By comparison of osmotic pressures Since equimolecular solutions in the same solvent have the same osmotic pressure, it is only necessary to find the strengths of two solutions which are in osmotic equilibrium (isotonic), and if the molecular weight of one solute is known that of the other can be calculated De Vries found that a 3*42 per cent, solution of cane sugal was isotonic with a 5-96 per cent, solution of rafrmoEe, the molecular weight of which was then unknown. If it be re- presented by x, then 3-42 : 5*96 : : 342 : : x, whence # = 596. This result has since been confirmed by chemical methods. Lowering of Yapour Pressure It has long been known that the vapour pressure of a liquid is diminished when a non- volatile substance is dissolved in it, and that the diminution is proportional to the amount of solute added. In 1887 Raoult, on the basis of a large amount of experimental work, established the following important rule : Equimolecular quantities of differ- ent substances, dissolved in equal volumes of the same solvent^ lower the vapour pressure to the same extent. On comparing the relative lowering (i.e., the ratio of the observed lowering and the original pressure) in different solvents, the same observer discovered another important rule, which may be expressed as follows : The relative lowering of vapour pressure is equal to the ratio of the number of molecules of solute and the total number oj ii2 OUTLINES OF PHYSICAL CHEMISTRY molecules in the solution. Putting f l and p^ for the vapour pressures of solvent and solution respectively, the rule may be put in the form A -A . * Pi N -I- n in which n and N represent the number of molecules of solute and solvent respectively, In order to illustrate the validity of this rule, some results given by Raoult are quoted in the ac- companying table ; the relative lowering is that due to the addition of i mol of solute to 100 mols of the various sol- vents : Solvent. H 2 PC1 3 CS 2 CC1 4 CH 3 I (C 2 H 5 ) 2 O CH 3 OH Relative lowering 0*0102 0*0108 0*0105 0*0105 0*0105 0*0096 0*0103 The results agree excellently among themselves, and fairly well with the calculated value, i/ioi = 0*0099. About the same time van't Hoff introduced the conception of osmotic pressure, and showed by a thermodynamical method that the relation between the relative lowering of vapour pres- sure and the osmotic pressure is given by the equation AzA__M_ p Pi * RT ' where M molecular weight of solvent, in the form of vapour, s is its density, and the other symbols have their usual significance. The expression M/jRT is therefore constant, since it depends only on the nature of the solvent, and consequently the relative lowering of vapour-pressure is proportional to the osmotic pres- sure P. By using the general equation, PV = RT (where n is the number of mols of solute), P in equation (i) can be elimin- ated, 1 and we finally obtain wRT * P = -y , where V is the volume of the solvent. If N represents the number of mols of solvent, M its molecular weight and $ its density, the volume V of the solvent = MN/s. Hence P when this value is substituted in equation (i) we obtain &- DILUTE SOLUTIONS "3 A -A J? A * N- This equation differs from that of Raoult in that the de- nominator on the right-hand side is N instead of N 4- , but they become identical " at infinite dilution " when the volume of the solute is negligible in comparison with that of the solvent. By substituting for n and N gjm and W/M, where g and W are the weights of solute and solvent respectively, m is the (unknown) molecular weight of the solute and M that of the solvent in the form of vapour, we obtain the equation A ~A jM /! 3 Wm which enables us to calculate the molecular weight of a dissolved substance when the relative lowering produced by a known weight of solute in a known weight of solvent is known. As an illustration, an experiment of Smits may be quoted. He found that at o the lowering of vapour pressure produced by adding 29*0358 grams of sugar to 1000 grams of water is 0*00705 mm., the vapour pressure of water at that temperature being 4/62 mm. Hence x 18 , and m = 342, in exact agreement with the theoretical value. As the lowering of vapour pressure is very small and not very easy to determine accurately by a statical method, it has not been very largely used for molecular weight determinations, the closely allied method depending on the elevation of the boiling-point being preferred. It has, however, one great advantage, inasmuch as, unlike the boiling-point and freezing- point methods, it can be used for the same solution at widely different temperatures. For this purpose, a dynamical method suggested by Ostwald and worked out by Walker l has certain advantages. A current of air is drawn in succession through (i) a set of Liebig's bulbs containing the solution of vapour 1 Zeitsch. physikal. Chem., 1888, 2, 602. ri4 OUTLINES OF PHYSICAL CHEMISTRY pressure / 2 (2) similar bulbs containing the pure solvent vapoui pressure p l (3) a U-tube containing concentrated sulphuric acid. In the first set of bulbs it becomes saturated up to / 2 with the vapour of the solvent, in the second set up to p v in the U-tube the moisture is completely absorbed. The loss of weight in the second set of bulbs is proportional to p l -/. 2 , and the gain in the U-tube to/j (cf. p. 91).* Elevation of Boiling-point A little consideration shows that there is a close connection between this method of deter- mining molecular weights and that depending on the lowering of vapour pressure. A liquid boils when its vapour pressure is equal to that of the atmosphere. The presence of a solute lowers the vapour pressure, and to reach the same pressure as before we require to raise the temperature a little; it is evident that, to a first approximation, this elevation must be proportional to the lowering of vapour pressure. It follows that, in this case also, equimolecular quantities of different solutes, in equal volumes of the same solvent, raise the boiling- point to the same extent. The molecular weight of any soluble substance may therefore be found by comparing its effect on the boiling-point of a solvent with that of a substance of known molecular weight. For this purpose, it is convenient to determine the molecular elevation constant, K, for each solvent, that is, the elevation of boiling-point which would be produced by dissolving a mol of any substance in 100 grams or 100 c.c. of the solvent. Actually, of course, the elevation is determined in fairly dilute solution, and the value of the constant calculated on the assumption that the rise of boiling-point is proportional to the concentration. Then the weight in grams of any other compound which, when dissolved in 100 grams or 100 c.c. of the solvent, produces a rise of K degrees in the boiling-point is the molecular weight. If g grams of substance, of unknown molecular weight, m, dissolved in L grams of solvent raises the boiling-point 8 1 A modification of this method has recently been used by Lord Berkeley and Hartley for the indirect determination of the osmotic pressure of con- centrated solutions of cane sugar (Proc. Roy. Soc., 1906, 7?A, 156. DILUTE SOLUTIONS 115 degrees, whilst m grams in 100 grams of solvent give a rise of K degrees, it follows, since loog/L, is the number of grams of substance in 100 grams of solvent, that IOOP- . loo^K _ : 8 : : m : : K, whence m = =~ . L Lo In the course of the last few years, the constants for 100 grams and 100 c.c. have been very carefully determined for a large number of solvents, and some of the more important data are given in the accompanying table : Solvent. IVlUlC^UJctl JJ/1CV. 100 grams. AllUll V-sUlloLi 100 C.C. Water 5*2 5*4 Alcohol ii-5 15-6 Ether 2I'O 3'3 Acetone . 167 22*2 Benzene . 267 32 -8 Chloroform 39' 2.77 Van't Hoff has shown that these constants, some of which had previously been obtained empirically by Raoult, can be calculated from the latent heat of vaporization, H, per gram of solvent, and its boiling-point, T, on the absolute scale, by means of the formula _ 0-02T2 ~H~ As an example, the calculated value for the molecular elevation constant for water, the latent heat of vaporization of which at its boiling-point is 537 calories, is K - (0-02 x (373) 2 )/537 - 5'* in satisfactory agreement with the experimental value. For all solvents which have been carefully investigated, the experi- mental and calculated values are in good agreement. 1 1 The observed and calculated values for a large number of solvents are given in Landolt and Bornstein's tables. n6 OUTLINES OF PHYSICAL CHEMISTRY Experimental Determination of Molecular Weights by the Boiling-point Method The ease and certainty with which such determinations can now be made is largely due to the work of Beckmann. One of the methods sug- gested by him will first be considered, and then a method due to Landsberger, based on a different principle. (a) Beckmann s Method The apparatus used is represented in Fig. 1 8. The boiling-tube, A, is provided with two side tubes, /p by means of which the solute (solid or liquid) is introduced, and / 2 , which is connected to a small condenser, by the action of which the amount of solvent is kept fairly constant. The solution is made to boil by the heat from a small screened burner, B, which can be carefully regulated, and the boiling liquid is insulated by means of an air jacket between the outer cylindrical glass tube, G, and the boiling tube. As the temperature of the vapour which escapes from a boiling solution is little, if any, above the boiling-point of the pure solvent, it is necessary to place the thermometer in the boiling liquid so that the bulb is completely immersed. The liquid tends to become superheated, and to eliminate this source of error Beckmann recommends filling up the boiling-tube nearly to the level of the liquid with glass beads or garnets, or, still better, with platinum tetrahedra. The thermometer repre- sented in the figure, which was specially designed by Beck- mann for this work, has a large bulb and an open scale, covering only 5- 6, and graduated in y^ . To render the thermometer available for widely different temperatures, there is an arrangement by means of which the amount of mercury in the bulb can be so adjusted that the top of the thread can be brought on the scale at any desired temperature. The sol- vent, of which 10 to 15 grams is usually sufficient, is measured with a pipette, or weighed by difference in the boiling-tube itself ; the solute, if solid, may be conveniently introduced in the form of a compressed pastille or, if liquid, by means of a pipette. The boiling-point of the solvent is determined DILUTE SOLUTIONS n; by causing it to boil fairly vigorously, and the temperature should remain constant within o'oi 0*015 for about twenty minutes FIG. 18. while readings are being taken. The temperature is then allowed to fall several degrees by removing the source of heat, the solute n8 OUTLINES OF PHYSICAL CHEMISTRY rapidly introduced, the boiling-point again determined, a fresh quantity of solute introduced, the boiling-point re-determined, and so on. The thermometer should be tapped before each reading. The amount of solute added may conveniently be such that the boiling-point is raised o*i5-o*2 after each addi- tion. It may be pointed out that more satisfactory results are usually obtained when differences produced by the addition of more solute are used in the calculation than when differences in the boiling-point of solvent and solution are used. As an illustration of the calculation of the results, an experi- ment with camphor in ethyl alcohol may be quoted. The addition of 0*56 grams of camphor to 16 grams of the solvent raised its boiling-point 0*278. Hence 100 x 0*56 x 11*5 ~T$~ 16 x 0-278 the theoretical value for C 10 H 16 O being 142. With proper precautions, the results obtained by this method are accurate within 3-4 per cent. (b) Landsberger 's Method This method depends upon the fact that a solution can be heated to its boiling-point by passing into it a stream of the vapour of the boiling solvent. In this case there is little or no risk of superheating, as the temperature of the vapour is lower than the boiling-point of the solution. The boiling-point of the solvent is first determined by passing in vapour till the temperature ceases to rise, some of the solute is then added, and more vapour passed in until the boiling- point of the solution is reached. As, during the heating, the amount of solvent increases by condensation of vapour, the final amount of solution, upon which of course the observed boiling-point depends, is obtained by weighing after the experi- ment. If no great accuracy is required, the final volume may be read off in the boiling-tube, graduated for the purpose. Radiation may be minimised by jacketing the inner tube with the vapour of the boiling solvent. DILUTE SOLUTIONS 119 Depression of the Freezing-point This is the most accurate and most largely employed method for the deter- mination of molecular weights in solution. The two necessary conditions for its applicability are (i) the pure solvent, free from any of the solute, must separate out when the freezing-point is reached ; (2) only a little of the solvent must have separated when the measurement is taken, otherwise the concentration of the solution will be appreciably altered. As in solubility determinations, we are dealing with an equilibrium (p. 84) in this case between ice and solution, and the experimental fact is that the more concentrated the solution the lower is the tem- perature at which equilibrium is reached. It is thus evident that if a large amount of the solvent separates in the solid form, the observed freezing-point is the temperature of equilibrium with a more concentrated solution than that originally prepared. In this case also, the osmotic pressure, and hence the mole- cular weight, could be calculated from the formula connecting osmotic pressure and depression of the freezing-point (p. 138), but the comparison method is always used. Just as for the boiling- point (p. 114) the molecular freezing-point depression^ i.e., the depression produced by dissolving i mol of solute in 100 grams or 100 c.c. of the solvent, has been determined for a large number of solvents, and some of the more important data are given in the accompanying table. Molecular Depression. Solvent. 100 grams. 100 c.c. Water . .18-5 18-5 Benzol . 50 56 Acetic acid .39 4 1 Phenol . . 74 Naphthalene . 69 The molecular depression, K, can be calculated from the latent heat of fusion, H, of the solvent and its freezing point on the absolute scale by means of the expression. 120 OUTLINES OF PHYSICAL CHEMISTRY 0-02T 2 K H analogous to that which holds for the boiling-point elevation, Thus for water we have K = (0*02 x (273) 2 )/8o = 18*6. It may be mentioned, as a matter of historical interest, that the experimental values for K obtained with solutions of cane sugar by Raoult, Jones and others, were at first much greater than 1 8*6, but the careful experiments of Abegg, Loomis, Wildermann, and later of Raoult himself made it clear that the high values previously obtained were due to experimental error, and that, with proper precautions, the value of K deduced on the basis of the theory of solution was fully confirmed by experiment. If g grams of solute, in L grams of solvent, caused a depres- sion, A, of the freezing-point of the solvent, the molecular weight of the solute can be calculated from the formula which exactly corresponds with that already given for elevation of boiling-point. Experimental Determination of Molecular Weights by the Freezing-point Method The apparatus which is used almost exclusively for this purpose was also designed by Beckmann, and is shown in Fig. 19. The inner tube, A, which contains the solvent, has a side tube by which the solute may be introduced, and is provided with a Beckmann thermometer, D, and a stirrer, preferably of platinum. The remainder of the apparatus consists of a tube, B, rather wider than A, and fitted into the loose cover of the large beaker, C, which contains water or a freezing -mixture (ice, or ice and salt), the temperature of which is 2-3 below the freezing-point of the solvent. In making an experiment, 15-20 grams of the solvent are weighed or measured into the tube, A, the stirrer and ther- mometer are put in place, and A is then placed in the wider DILUTE SOLUTIONS 121 tube B, which acts as an air mantle. The liquid is then continuously and the thermometer observed. Owing to cooling, the temperature falls below the freezing-point solvent, but as soon as solid begins to separate, it rises rapidly, owing to the latent heat set free, and the highest temperature observed is taken as the freezing-point of the solvent. The tube is then removed from the bath, the solid allowed to melt, a weighed amount of the solute added, and the determination of the freezing-point repeated. A further por- tion of solute may then be added, and another reading taken. With some sol- vents there is considerable supercooling, and as this would be a source of error owing to separation of much solvent when solidification finally occurs, a small par- ticle of solid solvent is added to start solidification when the temperature has fallen 1-2 below the freezing-point. As an illustration of the calculation of the results, an experiment with napthalene in benzene may be quoted. The addition of 0*142 grams of the compound to 20*25 grams of the solvent lowered the freezing-point 0*284. Hence stirred super- of the 100 x 0-142 x 51*2 ! 126 AL 0*284 x 20*25 as compared with the theoretical value FIG. ig. 128. Results of Molecular Weight Determinations in Solu- tion. General The most important result of the numerous molecular weight determinations of dissolved substances which 122 OUTLINES OF PHYSICAL CHEMISTRY have been made in recent years is that in general the molecular weight in dilute solution is the same as that deduced from the simple chemical formula of the solute > as based on vapour density deter- minations or on its chemical behaviour. For example, the empirical formula of naphthalene is C 5 H 4 , and since one-eighth of the hydrogen can be replaced, the simplest chemical formula must be C 10 H 8 , and the molecular weight 128. Cryoscopic determinations in benzene gave a value 126, so that naphthalene is present as simple molecules in solution. The Van't Hoff-Raoult formulae (p. 112) on which the determination of molecular weights in solution depend, have been deduced on certain assumptions which hold only for dilute solutions, and it is of the utmost importance to bear in mind that there is no a priori reason why they should give trust- worthy results for concentrated solutions. The question as to how far the gas laws hold for concentrated solution, or what modifications are necessary, has been much debated, but so far no definite conclusions have been arrived at. It is mainly a matter for further experiment. It has already been shown (p. 105) that when V in the general formula is taken as the volume of the solvent, the normal molecular weight is obtained for cane sugar up to very high concentrations on the assumption that the gas laws are valid for these solutions. The same is true for other compounds, more particularly in organic solvents, as may be illustrated by the values obtained by Beckmann for camphor in benzene 1 (theoretical value 152) : Concentration. Value of m. Concentration. Value of m. o'4ii 144 12*11 149 1-253 143 2 3* 12 I S 2 2-791 145 26-59 J 54 5*897 147 The observed molecular weights depend not only on the nature of the solute and on the concentration, but also very largely on the nature of the solvent. Examples will be given in the follow- ing pages showing that in certain solvents the observed mole- 1 Concentration in grams per 100 grams of benzene. DILUTE SOLUTIONS 123 cular weights are often higher than those deduced from the chemical formula of the solute. The solute is then said to form complex molecules or to be associated, and the solvent is termed an associating solvent. In other solvents, on the contrary, the molecular weight may be equal to or less than that deduced from its chemical formula. In the latter case the solute is said to be dissociated, and the solvents in question are termed dissociating solvents. Abnormal Molecular Weights In order to illustrate the results of molecular weight determinations from a slightly differ- ent point of view, the following table contains the values for the molecular freezing-point depression, K, for three typical sol- vents, water, acetic acid and benzene. The data are mainly due to Raoult, and in calculating K it is assumed that the molecular weight corresponds with the ordinary chemical formula of the solute : Solvent Water. Solvent Acetic Acid. Solvent Benzene. Solute. K. Cane sugar 18*6 Acetone . 17*1 Glycerol . ij'i Urea . . 18*7 Solute. K. Methyl iodide . 38-8 Ether . . . 39-4 Acetone . .38-1 Methyl alcohol 357 Solute. K. Methyl iodide . 50*4 Ether . . .49-7 Acetone . . 49-3 Aniline . . .46*3 HC1 . .39*1 HN0 3 . 35'8 KN0 3 . . 35-8 NaCl . . 36-0 HC1. . , . 17-2 H 2 SO 4 . . .18-6 (CH 3 COO) 2 Mg 1 8' 2 Methyl alcohol 25*3 Phenol . . .32*4 Acetic acid . 25-3 Benzoic acid . 25-4 This very instructive table shows that, for all three solvents, there are two sets of values for K, one of which is approximately double the other. The question now arises as to which of these are the normal values, obtained when the solute exists as single molecules in solution. This can at once be settled by using van't Hoffs formula, K(o'02T 2 )/H (p. 120), and we find that the normal depressions are 18*6, 39*0 and 51*2 for water, acetic acid and benzene respectively. This means that acetic acid, phenol and some other compounds dissolved in i2 4 OUTLINES OF PHYSICAL CHEMISTRY benzene produce only half the depression, in other words, exert only about half the osmotic pressure that would be expected ac- cording to their formulae, whilst in water certain acids and salts have an abnormally high osmotic pressure. The osmotic pressure of certain mineral acids in acetic acid is abnormally low. On the molecular theory, an abnormally small osmotic pressure shows that the number of particles is smaller than was anticipated. The experimental results can be satisfactorily accounted for on the view that acetic acid and benzoic acid exist as double molecules in benzene solution, and that phenol is polymerized to a somewhat smaller extent. This explanation seems the more plausible inasmuch as acetic acid contains com- plex molecules in the form of vapour (p. 41). It is mainly compounds containing the hydroxyl and cyanogen groups which are polymerized in non -dissociating solvents ; in dissociating solvents, such as water and acetic acid, 1 these com- pounds have normal molecular weights. It may be anticipated that the molecular complexity of solutes will be greater in concentrated solutions, and the avail- able data appear to show that such is the case. The results are, however, somewhat uncertain, inasmuch as in concentrated solution the gas laws are no longer valid (p. 122). Solvents such as benzene are sometimes termed associating solvents, but this probably does not mean that they exert any associating effect. There is a good deal of evidence to show that the substances existing as complex molecules in benzene and chloroform solution are complex in the free condition, and that the complex molecules are only partly broken up in so-called associating solvents. The explanation of the behaviour of solutes in water is by no means so simple, and can only be dealt with fully at a later stage. The data in the table indicate that cane sugar, urea, acetone, etc., are present as single molecules in solution, but hydrochloric acid, potassium nitrate, etc., be- have as if there were nearly double the number of molecules to 1 That acetic acid is in some cases at least a dissociating solvent is evident from the fact that the molecular weight of methyl alcohol in it is almost normal. DILUTE SOLUTIONS 125 be anticipated from the formulae. When van't Hoff put forward his theory of solutions he was quite unable to account for this behaviour, and contented himself with putting in the general gas equation a factor, /, to represent the abnormally high os- motic pressure, so that for salts and the so-called " strong " acids and bases in aqueous solution the equation became PV = iRT. The factor /can of course be obtained for aqueous solutions by dividing the experimental value of the molecular depression by the normal constant, 18*6, so that for potassium nitrate, for example, / = 35'8/i8'6 = 1*92. Van't Hoff recalled the fact that ammonium chloride, in the form of vapour, exerts an abnormally high pressure, which is simply accounted for by its dissociation according to the equa- tion NH 4 C1 = NH 3 + HC1, but it did not appear that the results with salts, etc., could be explained in an analogous way. We shall see in detail later that the elucidation of the signifi- cance of the factor i was of the highest importance for the further development of the theory of solution. According to our present views, the substances which show abnormally high osmotic pressures are partially dissociated in solution, not into ordinary atoms, but into atoms or groups of atoms associated with electrical charges. The equation representing the partial splitting up of potassium nitrate, for example, may be written + KNO 3 = K + NO 3 , which indicates that the solution contains potassium atoms associated with positive electricity, and an equal number of NO 3 groups, associated with negative elec- tricity. These charged atoms, or groups of atoms, are termed ions. Molecular Weight of Liquids Our knowledge as to the molecular weight of pure liquids is due mainly to the investi- gations of Eotvos (1886) and of Ramsay and Shields (1893), and is based on the remarkable rule, discovered by Eotvos, that the rate of change of the "molecular surface energy " of many 126 OUTLINES OF PHYSICAL CHEMISTRY liquids with temperature is the same. If y represents the sur- face tension and therefore the energy per sq. cm. of surface and s the " molecular surface," the rule in question may be writlen where c is a constant. 1 The molecular surface, j, can be ex- pressed in terms of readily measurable quantities as follows : The molecular volume of any liquid is represented by M# where M is the molecular weight and v the specific volume. If the molecular volume is regarded as a cube, one edge of the cube will measure (Mz/)*, and the area of one side of it (Mz;)?. (Mz;)f may therefore be called the molecular sur- face, s, and just as the relative molecular volumes of different liquids contain an equal number of molecules so the relative molecular surfaces for different liquids are such that an equal number of molecules lie on them. Equation (i) then becomes dt ll - , _ - 1 The student should make himself familiar with this method of repre- senting rate of change, as it is largely used in physical chemistry. It is perhaps most readily understood by considering the rate of change of position of a body as discussed in mechanics. If a body is moving with uniform velocity, the velocity can at once be found by dividing the distance, 5, traversed by the time, *, taken to traverse it, hence velocity = I/. The velocity may, however, be continually altering, and it is often desirable to express the velocity at any instant. It is not at first sight evident how this can be done, as it requires som* time for the particle to traverse any measurable distance, and the velocity may be altering during that time. The nearest approach to the real velocity at any instant will be obtained by taking the time, and therefore the distance traversed, as small as possible. We might then imagine an ideal case in which s and t are taken so small that any error due to the variation of speed during the time t can be neglected. If we represent these values of 5 and t by ds and dt respectively, the speed of the particle at any instant will be given by ds/dt. In the example given in the text d(ys)/dt represents the rate of change of the product with temperature, and the equation shows that the rate of change is constant DILUTE SOLUTIONS 127 where y x and y 2 are the surface tensions of a liquid at the temperatures t^ and / 2 respectively. From equation (2) we obtain, for the molecular weight M, M The surface tension of a large number of pure liquids at different temperatures has been measured by Ramsay and Shields by observing the height to which they rose in capillary tubes. The results show that, if M is taken as the molecular weight corresponding with the simplest formula of the liquid, the value of c for the majority of substances is about - 2-12. The method may be illustrated l by a determination of the molecular weight of liquid carbon disulphide. The experi- mental data are that y 33-6 ergs per sq. cm. at 19*4, and 29*4 ergs at 46-1: the specific volume (i/density) of carbon disulphide at 19*4 is i/i'264; at 46'! it is 1/1*223. Hence as compared with the value 76 calculated from the formula. As already indicated, the surface tension of a liquid in contact with its vapour diminishes as the temperature rises and becomes zero at the critical temperature, where the surface of separation beween liquid and vapour disappears (p. 50). If temperatures are measured downwards from the critical tem- perature as zero, dt in equation (i) p. 126 has a positive value, and therefore c is positive. In the next section for convenience positive values of the constant will be used. It should be added that the rule regarding the constancy of the expression d (ys)fdt only holds for temperatures at some distance (say 50) below the critical temperature. Results of Measurements Among the liquids which give values for c about 2*12 are the following : benzene 2 -17, carbon tetrachloride 2-11, silicon tetrachloride 2*03, ethyl iodide 2-10, ethyl ether 2*17, benzaldehyde 2-16, aniline 2 '05. On the other 1 Ramsay and Shields, Trans. Chem. Soc. % 1893, 63, 1096. 128 OUTLINES OF PHYSICAL CHEMISTRY hand, many substances give values for c which are much smaller than 2-12 and which vary with the temperature. Thus for ethyl alcohol the values of d [y (Mz/) 2 / 3 ]/<# in the neighbourhood of the temperatures indicated are as follows : 1*18 at 30, 1*31 at 90, 1-46 at 130, 177 at 185 and 1*94 at 225. Among sub- stances which give low values for c are the alcohols, the organic acids (acetic acid 0*90 at 16-46), acetone and water. The most plausible explanation of these observations is that liquids which give constant values for c approximating to 2*12 are non-associated, whilst those giving smaller values for this factor are associated. We may assume that association would tend to lower the molecular volume and thus give a smaller value for <:, as is actually found. The fact that for liquids with abnormally small values for c the latter increases steadily with the temperature is also in harmony with this explanation, since it may be assumed that the molecular complexity diminishes with rise of temperature. Attempts have been made to deduce from the observed values of d (ys)jdt the degree of complexity of associated liquids, but the results are by no means conclusive. According to Ramsay, the association factor of water at 5, 25, 45 and 85 is 3*81, 3*44, 3*13 and 279 respectively; van der Waals, how- ever, deduces from the same data considerably smaller values for this factor. 1 It is quite certain that water under ordinary conditions is a complex mixture of molecules of the formulae H 2 O, (H 2 O) 2 , (H 2 O) 3 and perhaps still more complicated aggregates, but the average degree of association at any given temperature is not definitely known. Recently Walden 2 has shown that the value of d (ys)ldt for palmitic and stearic acids is greater than 5 between 60 and 120. On the basis of the above interpretation of abnormally small values of the temperature coefficient in question, this would appear to indicate that the two acids are highly dissociated, whilst direct determinations in solution show that the mole- cular weights are normal. This affords further evidence in l Zeitsch. Physikal Chem., 1894, 13, 713. See also General Dis- cussion, Trans. Faraday Soc. t 1910, 6, 71-123. *Zeihch. Physikal Chem. 1911, 75, 555. DILUTE SOLUTIONS 129 favour of the conclusion indicated above, that the rule of Eotvos is only approximately valid. The Nature of Surface Tension A deeper insight into surface tension is obtained on the basis of the molecular theory. We assume that liquid particles attract each other with a force which falls off very rapidly with the distance. A particle in the interior of a liquid is equally attracted on all sides, but a particle in the surface layer is attracted inwards by all the particles of liquid within its sphere of influence, the corre- sponding attraction by the few particles in the vapour space being negligible in comparison. It follows that at the surface of liquids there is a force the so-called surface tension act- ing inwards, the liquid behaving as if it were covered by an elastic skin. It is evident that work must be done against molecular attraction in bringing a particle to the surface layer, and there- fore the formation of a larger surface involves an expenditure of energy. The surface energy is proportional to the product of the surface tension y and the area of the surface, and therefore the molecular surface energy is represented by the expression y (Mfl) 2/3 , as already mentioned. A liquid tends to diminish the area of its surface as much as possible in virtue of the force tending to draw the particles on the surface towards the interior. The tendency of liquid drops to assume a spherical shape and of minute drops to aggregate to larger drops is thus readily explained. Practical Illustrations. Osmotic Pressure -The nature of semi-permeable membranes may readily be illustrated by Traube's experiment, described on page 98, and also by allowing drops of a fairly concentrated solution of potassium ferrocyanide to fall into a moderately dilute solution of copper sulphate in such a way that the drops, which are immediately surrounded by a film of copper ferrocyanide, remain suspended at the surface of the solution. It will be observed that the cells grow fairly rapidly owing to passage inwards of water from the copper sulphate solution, and, further, that in consequence 9 130 OUTLINES OF PHYSICAL CHEMISTRY of the increased concentration of the copper sulphate solution round the drop, the concentrated solution slowly flows down through the less concentrated solution. The stream of con- centrated solution can readily be recognised by the difference of refractivity, especially if a bright light is placed behind the vessel Selective Action of Semi-permeable Membrane This can be illustrated by Nernst's experiment, which is fully described and figured on page 107. A simple experiment illustrating the same principle has been described by Kahlenberg. 1 At the bottom of a cylindrical jar is placed a layer of chloroform, above that a layer of water, and at the top a layer of ether and the jar is then corked. After some time it will be noticed that the chloroform layer has increased in depth, the water layer having moved higher up the tube. This phenomenon depends on the fact that ether is much more soluble in water than chloroform. The water there- fore acts like a semi-permeable membrane, absorbing the ether and giving it up to the chloroform. At the same time the chloroform is dissolving in the water and passing through tc the ethereal layer, but owing to its much smaller solubility, the current upwards is negligible in comparison with that downwards. In the same paper, Kahlenberg describes a number of experi- ments with rubber membranes, which are in many respects instructive. Separation of Solvent and Solute in Freezing-point Experi- ments This point, which is of fundamental importance for the applicability of the freezing-point method of determining mole- cular weights, can be illustrated by partially freezing an aqueous solution of a highly coloured substance such as potassium permanganate (o'i per cent, solution). When the solution is poured off, it will be found that the ice which has separated is practically colourless. The determination of molecular weights by the boiling-point method (p. 116) and by the freezing-point method (p. 120) are fully described in the course of the chapter. 1 Physical Chem., 1906, 10, 141. APPENDIX. MATHEMATICAL DEDUCTION OF IMPORTANT FORMULA. In the course of the present chapter, several formulae of fundamental importance have been made use of, and their meaning has been fully illustrated by numerical examples. For the sake of the more advanced student, simple deductions of these formulae are given. It must be under- stood that the deductions are not mathematically strict, as certain of the assumptions on which they are based are only approximately true. The fundamental equation (p. 112), Pi ~ Pz _ M p / T \ "ft -- s'RT ' F ' ' ' ' ' which gives the connection between the relative lowering of vapour pressure and the osmotic pressure, and the Raoult-van't Hoff formula (P- H3), which is readily derived from equation (i) by means of the gas laws, can be deduced by a statical-thermodynamical method due to Arrhenius and also by a cyclical thermodynamical method due to van't Hoff. These deductions will now be given. (i) The Statical Method A long tube R containing a solution of n mols of a non-volatile solute in N mols of solvent, 1 is closed at its lower end by a semi-permeable membrane and placed upright in a vessel C which contains pure solvent (fig. 20). The arrangement is covered by a bell-jar and all air is removed from the interior. When equilibrium be- tween solvent and solution is established through the semi-permeable membrane it is evident that the osmotic pressure is measured by the hydro- static pressure of the column of liquid (height h) in the tube. Now the- pressure of vapour at the level, a, of the surface of the solution must be the same inside and outside the tube. If this were not the case, evapora- tion or condensation of vapour would take place at the surface, a, and in either case the concentration of the solution would be altered and the equilibrium between solution and solvent disturbed, which is contrary to the original postulate that the system is in equilibrium. If p l is the vapour pressure of the solvent and p 2 that of the solution, the difference Pi " /a * s tne difference of pressure at the surface of the solvent and at 1 In calculating the number of mols of solvent, its molecular weight, M, is taken as that in the form of vapour (p. 112). 132 OUTLINES OF PHYSICAL CHEMISTRY the level a. This difference is due to the weight of a column of vapour of height h on unit area, therefore where d is the density ot the vapour. We have now to express d and h in a. different form. If v is the volume of i mol of the vapour, and M the molecular weight of the vapour in the gaseous form, we have d = M/flj or tfj = M/d. When this value of v 1 is substituted in the general gas equation p-^v^ = RT, we obtain _ Mp 1 Further, as the osmotic pressure, P, is measured by the weight of the column h, therefore P = hs' where s' is the density of the solution. If very dilute solutions are used, no appreciable error will be committed by substituting 5, the density of the solvent, for s', the density of the solution. Substituting these values of d and h in equation (a) we obtain A-*-?. r Pi~P* = M p Pi . *RT' which is equation (i), p. 112. J From this equation, we obtain the formula, FIG. 20. as already described (p. 112). (2) The Cyclical Method This thermodynamical proof of the above formula depends upon the performance of a cyclic process in which the system is finally brought back to its initial condition reversibly at con- stant temperature. The fundamental point to bear in mind in connection with such processes is that they must be conducted throughout under equilibrium conditions. It has already been pointed out (p. no) that the thermodynamical proof of the connection between osmotic pressure and the lowering of vapour pressure depends on the work done in removing solvent reversibly from a solution. There are two principal methods by which removal (or addition) of solvent can be accomplished : (a) If the solution is brought into contact with its own saturated vapour at constant temperature, the slightest diminution of the external pressure will effect the removal of part of the solvent ; on the other hand, the slightest increase of the external pressure will bring about condensation of vapour. If the change of volume of the solution is in each case very small compared with the total volume, the change in concentration can be neglected. APPENDIX 133 (b) A solution is placed in a cylinder closed at the bottom with a semi-permeable membrane, the cylinder is immersed in the pure solvent, and a movable piston rests on the upper surface. The solution and solvent will be in equilibrium through the semi-permeable membrane when the pressure on the piston is equal to the osmotic pressure. If the pressure is diminished ever so slightly by raising the piston, solvent will enter; if the pressure on the piston is slightly increased, solvent will pass out through the membrane. We have, therefore, a second method by which solvent can be separated from a solution in a reversible manner, equilibrium being maintained throughout. The cyclic process, in which both these methods are used, will now be described. (1) From a solution containing n mols of solute to N mols of solvent, a quantity of solvent which originally contained i mol of solute is squeezed out reversibly by means of the piston and cylinder arrangement; the quantity thus removed is N/ mols. As the original quantity of solu- tion is supposed to be very great, its concentration, and therefore its osmotic pressure, are not appreciably altered in the process. As the volume removed is that which contained i mol of solute, the work done on the system, which is the product of the change of volume and the pressure on the piston (the osmotic pressure), is equal to - RT ..... (i) (p. 27) if the gas laws apply. (2) The quantity of solvent is now converted reversibly into vapour by expansion at the pressure, p lt of the solvent ; the work gained is ap- proximately piV-i for i mol of vapour (the volume of the liquid being regarded as negligible in comparison), or altogether. (3) The vapour is now allowed further to expand till its pressure falls to /> 2 , the vapour pressure of the solution : in this process, an amount of work is done by the system represented approximately by t per mol of vapour, where (/ x + / 2 )/2 * s tne mean pressure during the small expansion. The quantity of vapour actually used is N/w mols, hence the total work done by the system is ^h (4) The vapour, at the pressure ^ 2 , is now brought into contact with the solution, with which it is in equilibrium, and condensed reversibly, so that the system regains its initial state. The work done on the system in condensing the gas to liquid at the pressure / 2 is approximately -^ 2 ..... (iv) As the entire cycle is carried through at constant temperature, there has on the whole been no transformation of heat into work or vice versa ; as the system is finally brought back to its initial condition, the work done on the system must on the whole be equal to the work done by the system ; in other words (i) + (ii) + (iii) + (iv) must be zero. 134 OUTLINES OF PHYSICAL CHEMISTRY Combining in the first place (ii), (iii), and (iv), we have N N which reduces to N N (v% + vA . - ( a J where w is the mean volume of i mol of vapour. Substituting for v its value from the general gas equation, v RT//, we have finally l n pi as the work done by the system in the last three stages of the cycle. This must be equa( to the work done on the system during the osmotic removal of solvent, hence _ RT = as before. The same result may be obtained still more simply by integration. The work done by the system in step (ii) is exactly balanced by that done on the system in (iv), as is evident from the factors themselves, if the gas laws hold. In (iii) both the pressure and the volume change during the exoansion, hence work done by the system for I mol of vapour is equal to v = pRT = RT log*^ - RT log? V 1 J V 1 V a - RT log 2 - - RT , - - Pi \ Pi approximately, 2 or, for the total volume of vapour, n Pi The remainder of the proof is as above. Lowering of Freezing-point The above formula has been deduced by an isothermal cyclic process, but the cyclic process by which the freezing-point formula is deduced cannot be carried through at constant temperature. We are therefore concerned with a new question, that of the relationship between heat and work. The law which applies in this case is the second law of thermodynamics, the deduction of which is to be 1 When the solution is dilute, p in the denominator may be put equal to p l without sensible error. 2 RT^ 1 ~ ^ 2 is the first term of the expansion of the logarithmic function. The more accurate form of the van't Hoff-Raoult formula is log/> 1 // 2 = ;^-, to which the usual form approximates in dilute solution. APPENDIX 135 found in any advanced book on Physics, and which states that the maxi- mum work, dA, obtainable from a given quantity of heat Q, in a reversible cycle is given by dT <*A= q^ where the symbols have the usual significations (p. 151). A solution containing n mols of solute in N mols (W grams) of solvent is contained in the cylinder with semi-permeable membrane and movable piston already described. The freezing-point of the solvent is taken as T and that of the solution as T - dl. The stages in the cyclic process are as follows : (1) At the temperature T - dT an amount of solvent which originally contained i mol of solute is frozen out ; the amount in question is N/w mols or MN/n grams. The separation can be carried out at constant temperature provided that the amount of solution is so great that its con- centration is not thereby appreciably affected. The solidified solvent is then separated from the solution and the temperature of both raised to T. MN (2) The solidified solvent is fused, in which process H . -- calories are taken up, H being the heat of fusion per gram. (3) The fused solvent is then brought into contact with the solution through the semi-permeable membrane under equilibrium conditions, that is, when the pressure on the piston is equal to the osmotic pressure of the solution (p. 133) and is allowed to mix reversibly with the solution. The work done by the system in this process is represented by the product of the osmotic pressure, P, and the volume, v, in which i mol of solute was dissolved and is, therefore, according to the gas laws, equal to RT. (4) The system is finally cooled to the original temperature, T dT, in order to complete the cycle. We have now to consider the work done in the different stages of the cycle. The heat expended in warming solution and solvent in (i) is practically compensated 1 by the heat given out in (4). Further, an amount of heat HW/w is taken in at the higher temperature T and a somewhat less amount given out at T - dT ; hence, by the second law ol thermodynamics, the work done on the system is The only work done by the system is that expended in the osmotic readmission of the solvent, hence RT H W dT H '1T' T , T RT 2 n or dT -^~ . yf . . . (i) 1 The two amounts are not exactly equal, but the difference can be made negligible in comparison with the heat taken up in the second stage of the cycle. 136 OUTLINES OF PHYSICAL CHEMISTRY If instead of H we use the molecular heat of fusion, A, we have A. =* MH, and, further, N = W/M. Substituting these values in equation (i), the latter reduces to RT 2 n . . "-IT-N ...... < 2 > From this it is evident that the lowering of the freezing-point, like the relative lowering of vapour pressure, is proportional to the ratio of the number of mols of solute to the number of mols of solvent. From the above formula, or more readily from equation (i), above, an expression for K, the depression produced when i mol of solute is dissolved in 100 grams of solvent, can readily be obtained. R is approxi- mately = 2 when expressed in calories, n = i and W = 100. Hence we obtain, for this particular value of dT, _-- _ ' H ' I^o - ~H~~' which is the formula given on p. 120. Elevation Of Boiling-point By means of a cyclic process exactly corresponding with that already used in establishing the freezing-point formula, the formula connecting the elevation of the boiling-point with the latent heat of vaporisation of the solvent is obtained in the form 0-02T* ~H~ where H is the heat of vaporisation of i gram of solvent at the tempera- ture of the experiment, and T is the boiling-point of the solvent on the absolute scale. Summary Of Formulae (#) Osmotic pressure and relative lowering of vapour -pressure. From formula (i) (p. 112) we obtain by substitution P = 82 ;p A"* atmospheres ; M . p l where P is the osmotic pressure, expressed in atmospheres, s is the density of the solvent at the absolute temperature T, M is the molecular weight of the solvent in the form of vapour, and/>j and p 2 are the vapour-pressures of solvent and solution respectively. (b) Osmotic pressure and lowering of freezing-point From formula (i) (p. 137), by substitution zoooHs dT P = - . -=r- atmospheres ; 24-22 T where H is the latent heat of fusion of the solvent in calories per gram, T is the freezing-point of the solvent on the absolute scale and dT is the freezing-point depression. Osmotic pressure and elevation of boiling-point The formula, which corresponds exactly with that for the freezing-point depression, is __ zoooHs dT 24-22 'T where H is the latent heat of vaporisation for i gram of solvent at its boiling-point, T is the boiling-point of the solvent on the absolute scale, and dT is the boiling-point elevation. CHAPTER VI THERMOCHEMISTRY General It is a matter of every-day experience that chemical changes are usually associated with the develop- ment or absorption of heat. When substances enter into chemical combination very readily, much heat is usually given out (for example, the combination of hydrogen and chlorine to form hydrogen chloride), but when combination is less vigorous, the heat given out is usually much less, and, in fact, heat may be absorbed in a chemical change. These facts, which were noticed very early in the history of chemistry, led to the suggestion that the amount of heat given out in a chemical change might be regarded as a measure of the chemical affinity of the reacting substances. Although, as will be shown later, this is not strictly true, there is, in many cases, a parallelism between chemical affinity and heat liberation. In thermochemistry, we are concerned with the heat equivalent of chemical changes. Heat is a form of energy, and therefore the laws regarding the transformations of energy are of importance for thermo- chemistry. It is shown in text-books of physics that there are different forms of energy, such as potential energy, kinetic energy, electrical energy, radiant energy and heat, and that these different forms of energy are mutually convertible. Further, when one form of energy is converted completely into another, there is always a definite relation between the amount which has disappeared and that which results. The 138 OUTLINES OF PHYSICAL CHEMISTRY best-known example of this is the relation between kinetic energy and heat, which has been very carefully investigated by Joule, Rowland and others. Kinetic energy may be measured in gram-centimetres or in ergs, and heat energy in calories (see p. xvii). The investigators just referred to found that i calorie = 42,650 gram-centimetres = 41,830,000 ergs, an equation representing the mechanical equivalent of heat. From the above considerations it follows that when a certain amount of one form of energy disappears an equivalent amount of another form of energy makes its appearance. These results are summarised in a law termed the Law of the Conservation of Energy, which may be expressed as follows : The energy of an isolated system is constant, i.e., it cannot be altered in amount by interactions between the parts of the system. The proof of this law lies in the experimental impossibility of perpetual motion it has been found impossible to construct a machine which will perform work without the expenditure of energy of some kind. In dealing with chemical changes, it has been found con- venient to employ the term chemical energy, and when two substances combine with liberation of heat, we say that chemical energy has been transformed to heat. To make this clear, we will consider a concrete case, the burning of carbon in oxygen with formation of carbon dioxide, a reaction which, as is well known, is attended with the liberation of a considerable amount of heat. The reaction can be carried out under such condi- tions that (the heat given out when a definite weight of carbon combines with oxygen can be measured, and it has been found that when 12 grams of carbon and 32 grams of oxygen unite, 94,300 calories are liberated. This result may conveniently be represented by the equation C + O 2 = CO 2 + 94,300 cal. in which the symbols represent the atomic weights of the reacting elements in grams. The above equation is an illus- tration of the conversion of chemical energy into heat 12 THERMOCHEMISTRY 1 39 grams of free carbon and 32 grams of free oxygen possess 94,300 cal. more energy than the 44 grams of carbon dioxide formed by their union. From these and similar considerations it follows that the free elements must have much intrinsic energy, but the absolute amount of this energy in any par- ticular case is quite unknown. Fortunately, this is a matter of secondary importance, as chemical changes do not depend on the absolute amounts of energy, but only on the differences of energy of the reacting systems. So far, we have implicitly assumed that the increase or de- crease of internal energy when a system A changes to a system B is measured by the heat absorbed or given out during the reactions ; but this is not necessarily the case. In particular, external work may be done during the change, by which part of the energy is used up, or heat may be produced at the expense of external work (cf. p. 27). If the total diminution of internal energy in the change A -> B is represented by U, the heat given out by - q, and the external work done by the reacting sub- stances during the transformation by A, we have, by the prin- ciple of the conservation of energy, U = A - q. When no external work is done the total diminution of energy, U, is numerically equal to Q, the heat evolved in the reaction. The factor A is only of importance when gases are involved in the chemical change. Hess's Law It is an experimental fact that when the same chemical change takes place between definite amounts of two substances under the same conditions the same amount of heat is always given out provided that the final product or products are the same in each case. Thus when 12 grams of carbon combine with 32 grams of oxygen with formation of carbon dioxide, 94,300 cal. are always liberated, quite independently of the rate of combustion or of the nature of the intermediate pro- ducts. This law was first established experimentally by Hess in 1 840, and may be illustrated by the conversion, by two different methods, of a system consisting of i mol of ammonia and of MO OUTLINES OF PHYSICAL CHEMISTRY hydrochloric acid respectively and a large amount of water, each taken separately, into a system consisting of i mol of ammonium chloride in a large excess of water. By the first method we measure (a) the heat change when i mol of gaseous ammonia and i mol of gaseous HC1 combine, (b) the heat change when the solid ammonium chloride is dissolved in a large excess of water ; by the second method we measure the heat changes when (c) i mol of ammonia, (d) i mol of hydrochloric acid are dissolved separately in excess of water, and (e) when the two solutions are mixed. The results obtained were as follows : First Way. (a) NH 3 gas + HC1 gas = +42,100 cal. (b) NH 4 C1 + aq = - 3,900 cal. 38,200 cal. Second Way. (c) NH 8 gas + aq = 4- 8,400 cal. (d) HClgas + aq + 17,300 cal. (e) HClaq + NH 3 aq = + 12,300 cal. 38,000 cal. As will be seen, a + b c + d+e within the limits of ex- perimental error. It can easily be shown that Hess's law follows at once from the principle of conservation of energy. This law is of the greatest importance for the indirect deter- mination of the heat changes involved in certain reactions which cannot be carried out directly. For example, we cannot determine directly the heat given out when carbon combines with oxygen to form carbon monoxide. The heat given out when 12 grams of carbon burn to carbon dioxide is 94,300 cal., which is, by Hess's law, equal to that produced when the same amount of carbon is burned to monoxide and the latter then converted to dioxide. The latter change gives out 68,100 THERMOCHEMISTRY 141 cal, and the reaction C + O = CO must therefore be associated with the liberation of 94,300 - 68,100 = 26,200 cal. Representation of Thermochemical Measurements. Heat of Formation. Heat of Solution As has already been pointed out, the results of thermochemical measure- ments may be conveniently represented by making the or- dinary chemical equation into an energy equation, for example, C + O 2 = CO 2 + 94,300 cal. Sometimes, if the final condition of the system is assumed to be known, the shorter form C, O 2 = 94>3 cal - may be used. When, as is frequently the case, the reacting substances are used in aqueous solution, this is indicated by adding aq to the formula in question. Thus the neutralisation of dilute hydro- chloric acid by sodium hydroxide is represented as follows : NaOH aq + HC1 aq = NaCl aq + 13,700 cal. The heat of formation of a compound is the heat given out when a mol of the compound is formed from its component ele- ments. Thus the heat of formation of carbon dioxide (at constant volume) is 94,300 cal. The above energy equations, e.g., that representing the formation of carbon dioxide, are, however, not complete, inasmuch as we do not know the in- trinsic energy associated with free carbon and oxygen re- spectively, nor do we know the differences of energy between the various elements, as they are not mutually convertible by any known means. We may therefore choose any arbitrary values for the intrinsic energies of the elements, and it has been found most convenient to put them all equal to zero. On this basis the intrinsic energy of carbon dioxide, being 94,300 cal. less than the sum of the intrinsic energies of the component elements, is 94,300 cal., and, in general, the in- trinsic energy of a compound is numerically equal to its heat of formation, but with the sign reversed. 142 OUTLINES OF PHYSICAL CHEMISTRY When the heats of formation of all the substances taking part in a reaction are known, the heat set free in the reaction can be calculated. One method of doing so is to apply the law that the heat of reaction is equal to the sum of the heats of formation of the substances formed minus the sum of the heats of formation of the substances used up. This law follows at once if we imagine the reacting substances first decomposed into their elements and these elements then combined to form the final products. In the first stage there would be absorbed an amount of heat equal to the sum of the heats of formation of the reacting substances, and in the second stage an amount of heat would be given out equal to the sum of the heats of formation of the products. An alternative method, the basis of which will be evident on a little consideration, is to write an energy equation in which the formulae of the various compounds are replaced by their intrinsic energies (the respective heats of formation with the signs reversed). As an example of the method, we may cal- culate the heat of reaction, x, when copper is displaced from copper sulphate in dilute solution by metallic zinc. The heat of formation of copper sulphate (from its elements) in dilute solution is 198,400 cal. and of zinc sulphate under the same conditions 248,500 cal. The energy equation for the chemical change is therefore Zn + CuSO 4 aq = Cu + ZnSO 4 aq o -f ( 198,400) = o + (- 248,500) + x cal. whence .#, the total heat liberated in the reaction, is 248,500 - 198,400 =* 50,100 cal. In the same way an unknown heat of formation can be cal- culated when all the other heats of formation and the heat of reaction are known a method which, as shown in the last section, is particularly useful for obtaining the heats of forma- tion of substances such as carbon monoxide and methane, which cannot be determined directly. As an example, the THERMOCHEMISTRY 143 heat of formation of methane will be calculated. The heat given out when i mol of this compound is burned completely in oxygen is 213,800 cal., and the heat of formation of the products, carbon dioxide and water, are 94,300 and 68,300 cal. respectively. Representing the heat of formation of methane by x, its intrinsic energy therefore by - x, we have the equation CH 4 + 2O 2 = CO 2 + 2H 2 O -x + o == - 94,300 + (- 2 x 68,300) + 213,800 cal. Whence x = 17,100 cal. A compound such as methane, which is formed with libera- tion of heat, is termed an exothermic compound, whilst one which is formed with absorption of heat is termed an endo- thermic compound. The majority of stable compounds are exothermic. Among the best-known endothermic compounds are carbon disulphide, hydriodic acid, acetylene, cyanogen and ozone. It is not always easy to determine directly whether a compound is exothermic or endothermic, but this may be done indirectly by carrying out a chemical change with the compound itself and with the components separately and comparing the heat changes in the two cases. The method may be illustrated by reference to carbon disulphide. When burnt completely in oxygen, the gaseous compound gives out 265,100 cal. accord- ing to the equation CS 2 + 3<3 2 = CO 2 + 2SO 2 + 265,100 cal. Hence, representing the intrinsic energy of the compound by - x, we have, for the energy equation, -# + o= +(- 94,300) + ( - 2 x 7 1,000) + 265,100, and - x = + 28,800 cal. The intrinsic energy of carbon disul- phide is therefore 28,800 cal. ; that is, the compound has 28,800 cal. more energy than the elements from which it is formed. The heat of solution is the quantity of heat given out or absorbed by the solution of a mol of the substance in so much 144 OUTLINES OF PHYSICAL CHEMISTRY of the solvent that no further heat change is observed when more of the solvent is added. The heat of solution as thus defined is usually different from the heat change observed when a mol of substance is dissolved in sufficient solvent to form a saturated solution, and the two quantities may even be of opposite sign. Thus the heat of solution of cupric chloride dihydrate, CuCl 2 , 2H 2 O, is positive in dilute and negative in very concentrated solution. It is the heat of solution in nearly saturated solution which is of importance in predicting the effect of temperature on the solubility in accordance with Le Chatelier's theorem (p. 169). It has already been mentioned (p. 141) that the heat given out in a chemical change differs according to whether changes of volume occur with the consequent performance of internal work by or on the system. When only solids and liquids are concerned, no appreciable changes of volume occur and the internal work is negligible. When 'gases are concerned, how- ever, the heat change at constant volume, when no internal work is done, differs slightly from that at constant pressure. As already pointed out (p. 27), the work associated with the production or disappearance of a mol of gas is 2 T calories = 2 x 290 = 580 calories at room temperature, 17, and the heat change at constant pressure, Q p , differs from that at constant volume, Q v , by 2 (n l -n^) T, where n l and n 2 represent the number of mols of gas in the initial and final products respectively. If (n l - n 2 ) is positive, then Q p > Q v ; if, on the other hand, (n-^ n 2 ) is negative, Q v > Qp. The heats of formation at constant volume of some important compounds are given in the accompanying table. The state- ments in brackets refer either to the state of the reacting sub- stances or of the product : THERMOCHEMISTRY Substance. I Heat of Formation (Calories). H 2 O (liquid) CO 2 (diamond) + 67,520 + 94,300 CO (diamond) + 26,600 SO 2 (rhombic sulphur) + 71,080 HF (gaseous fluorine) + 38,600 HC1 (gaseous chlorine) + 22,000 HBr (liquid bromine) + 8,400 HI (solid iodine) 6,100 NH 3 + 12,000 NO - 21,600 NO 2 - 7,700 KC1 f 105,600 KBr + 95,300 Heat of Combustion Whilst a great many inorganic re- actions are suitable for thermochemical measurements, this is not in general the case for organic reactions ; in fact, the only reaction which is largely used for the purpose is combustion in oxygen to carbon dioxide and water. The heat given out when a mol of a substance is completely burned in excess of oxygen is termed the heat of combustion, and from this, by application of Hess's law, the heats of formation can be cal- culated, as has been done for methane and carbon disulphide, in the preceding section. Further, the heat given out in a chemical change can readily be calculated by Hess's law when the heats of combustion of the reacting substances are known it will clearly be equal to the sum of the heats of combustion of the substances which disappear less the sum of the heats of combustion of the substances formed. As an example, the heat of formation of ethyl acetate from ethyl alcohol and acetic acid may be calculated. The heat of combustion of ethyl alcohol is 34,000 cal., of acetic acid 21,000 cal., and of ethyl acetate 55,400 cal., whence the heat of formation of ethyl acetate is 34,000 + 21,000 55,400 400 cal. Thermochemical Methods Two principal methods are employed in measuring the heat changes associated with chemical reactions. If the reaction takes place in solution, the water calorimeter, so largely used for purely physical measure- ments, may be employed. For the determination of heats of i 4 OUTLINES OF PHYSICAL CHEMISTRY combustion, on the other hand, in which solids or liquids are burned completely in oxygen, special apparatus has been de- signed by Thomsen, Berthelot, Favre and Silbermann and others. (a) Reactions in Solution The change (chemical reaction, dilution or dissolution), the thermal effect of which is to be measured, is brought about in a test-tube deeply immersed in a large quantity of water, and the rise of temperature of the water is measured with a sensitive thermometer. When the weight of the water and the heat capacity of the calorimeter are known, the heat given out in the reaction can readily be calculated. Allowance must, of course, be made for the heat capacity of the solution in the test-tube. A simple modification of Berthelot's calorimeter, used by Nernst, is shown in Fig. 21. It consists of two glass beakers, the inner one being supported on corks, as shown, and nearly filled with water. Through the wooden cover, X, of the outer beaker pass a thin-walled test-tube, A, in which the reaction takes place, an accurate thermometer B, and a stirrer C of brass, or, better, of platinum. The water in the calorimeter is stirred during the reaction, which must be rapid, and the heat of reaction can then be calculated in the usual way when the weight of water in the calorimeter and the rise of temperature are known. Experiments on neutralization and on heat of solution are conveniently made in the inner beaker, the solution itself serving as calorimetric liquid. For dilute aqueous solutions, it is sufficiently accurate to assume that the heat capacity of the solution is the same as that of water. The chief source of error in the measurements is the loss of heat by radiation, which is minimised (a) by choosing for investigation reactions which are complete in a comparatively short time ; (b) by making the heat capacity of the calorimeter system large. It is of advantage so to arrange matters that the temperature of the calorimeter liquid is 1-2 below the atmospheric temperature before the reaction, and 1-2 above it after the reaction. THERMOCHEMISTRY T 47 B (b) Combustion in Oxygen This may conveniently be carried out in Berthelot's calorimetric bomb, a vessel of steel, lined with platinum and provided with an air-tight lid. The sub- stance for combustion is placed in the bomb, which is filled with oxygen at 20-25 atmo- spheres' pressure. The whole apparatus is then sunk in the water of the calorimeter, and the combustion initiated by heating electrically a small piece of iron wire placed in contact with the solid. Results of Thermochemi- cal Measurements Some of the more important results of thermochemical measure- ments have already been inci- dentally referred to in the preceding paragraphs. In stating the results of thermo- chemical measurements, the condition of the substances taking part in the reaction must always be clearly stated. This applies not only to the physical state, in connection with which allowance must be made for heat of vaporization, heat of fusion, etc., but also to the different allotropic modifications of the solid. Thus mono- clinic sulphur has 2300 cal. more internal energy than rhombic sulphur, and yellow phosphorus 27,300 cal. more than the red modification. The correction for change of state is often very great. For the transformation of water to steam at 100, it amounts to FIG. 21. i 4 8 OUTLINES OF PHYSICAL CHEMISTRY about 537 x 18 = 9566 calories per mol. If, instead of the heat of formation of liquid water, which is 68,300 cal., the heat of formation of water vapour is required, it is 68,300 - 957 58,730 cal. in round numbers. As regards the thermochemistry of salt solutions, one or two experimental results may be mentioned which will find an interpretation later. When dilute solutions of two salts, such as potassium nitrate and sodium chloride, are mixed, heat is neither given out nor absorbed. This important result is termed the Law of thermoneutrality of salt solutions (p. 279). Further, when a mol of any strong monobasic acid is neutralized by a strong base, the same amount of heat, 13,700 cal., is always liberated (p. 284). The heat of formation of salts in dilute aqueous solution is obtained by the addition of two factors, one pertaining to the positive, the other to the negative part of the molecule; in other words, the heat of formation of salts in dilute solution is a distinctly additive property. The same is true to some extent for the heat of combustion of organic compounds. For example, the difference in the heat of combustion of methane and ethane is 158,500 cal., and in general, for every increase of CH 2 , the heat of combustion increases by about 158,000 cal. From these and similar results, we can deduce the general rule that equal differences in composition correspond to approxi- mately equal differences in the heat of combustion. We may go further, and obtain definite values for the heat of combustion of a carbon atom and a hydrogen atom as has already been done for atomic volumes ; the molecular heat of combustion is then the sum of the heats of combustion of the individual atoms. Experience shows that when allowance is made for double and triple bindings, the observed and calcukted values for the heats of combustion of hydrocarbons agree fairly well. Relation of Chemical Affinity to Heat of Reaction- Very early in the study of chemistry, it becomes evident that chemical actions may be divided into two classes : (i) those THERMOCHEMISTRY 149 which under the conditions of the experiment are spontaneous or proceed of themselves, once they are started, e.g., the com- bination of carbon and oxygen ; (2) those which only proceed when forced by some external agency, e.g., the splitting up of mercuric oxide into mercury and oxygen. In this section we are concerned only with spontaneous changes. The direction in which a chemical change takes place in a system depends on the energy relations of the system. We are accustomed to say that the direction of the change is determined by the chemical affinity of the reacting substances, and it is a matter of the utmost importance to obtain a numerical expression for the chemical affinity or driving force in a chemical system, the driving force being defined in such a way that the chemical change proceeds in the direction in which it acts, and comes to a standstill when the driving force is zero. Most reactions in which there is a considerable transformation of chemical energy, and therefore a considerable development of other forms of energy, such as heat or electrical energy, proceed very rapidly (for example, the combination of hydrogen and chlorine), whilst reactions in which less chemical energy is transformed are usually much less vigorous (for example, the combination of hydrogen and iodine). It seems, therefore, at first sight plausible to measure the chemical affinity in a system by the amount of heat liberated in the reaction (Thomsen, Berthelot). As, however, chemical affinity has been defined as acting in the direction in which spontaneous chemical change takes place, it would follow that only reactions in which heat is given out can take place spontaneously. This deduction is contrary to experience. Water can spontaneously pass into vapour, although in the process heat is absorbed, and many salts, such as ammonium chloride, dissolve in water with absorption of heat. It is clear, therefore, that chemical affinity, as above defined, cannot be measured by the total heat liberated in the reaction. i5c OUTLINES OF PHYSICAL CHEMISTRY The importance for technical purposes of such a reaction as the burning of coal in oxygen is not so much the total heat obtainable by the change as the amount of work which the change may be made to perform. In a similar way, // has been found convenient to measure the chemical affinity of a system by the maximum amount of external work which, under suitable conditions, the reaction may be made to perform. This is a special case of a very comprehensive natural law, which may be expressed as follows : All spontaneous reactions (in the widest sense, including neutralization of electrical charges, falling of liquids to a lower level, etc.) can be made to perform work, and all reactions which can be made to per- form work are spontaneous, i.e., can proceed of themselves without the application of external forces. The available energy of a chemical reaction, that is, that part of the total energy which at constant temperature and under suitable condi- tions can be made to perform an equivalent of work, has been termed " free energy " by Helmholtz. The chemical affinity or driving force of a reaction is not proportional to the total change of energy, but to the change in the available or free energy. The total energy, U, of a chemical change can be obtained in the form of heat by carrying out the reaction under such conditions that no external work is done (p. 141). We have now to consider what is the connection between the total decrease of energy, U, and the decrease of available or free energy, which may be termed A. This question is closely connected with the conditions under which heat can be con- tinuously transformed into work. We have to find an expres- sion for the maximum work performed in a cycle in which the heat is taken in at the temperature T, and given out at the slightly lower temperature T - */T. The principle to be used for this purpose is that employed in the theory of the steam-engine, but it has universal applicability. According to this, the maxi- mum work, AB + C will be complete in the direction indicated by the arrow. These views found their expression in the so-called affinity tables drawn up by Stahl, Bergmann and others, in which the elements were arranged in the order in which they could displace each other from com- bination. Somewhat later, Berzelius developed his electro- chemical theory, according to which the attractions concerned in chemical changes are electrical in character, but this theory EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 155 proved in many respects unsatisfactory. The importance of the conditions, more particularly as regards the relative amounts of the reacting substances and the temperature, on the direction and amount of chemical change, only came to be recognised very gradually. In recent years, the question as to why certain chemical changes take place has been relegated to the background and attention has been directed to how they take place. As mentioned in the last chapter, it has been found possible in many cases to obtain numerical values for the chemical affinity, without troubling about its exact nature. When for any reaction the chemical affinities of the reacting substances are known, as well as the dependence of the reaction on the conditions, the reaction is completely described. Law of Mass Action The importance of the relative amounts of the reacting substances for the course of a chemical change was first clearly established by Wenzel and by Berth- ollet. The latter pointed out that though under ordinary circumstances sodium carbonate and calcium chloride react almost completely according to the equation Na 2 CO 3 + CaCl 2 -> 2NaCl + CaCO 3 , yet the sodium carbonate found on the shores of certain lakes in Egypt is produced according to the equation 2NaCl + CaCO 3 -> Na 2 CO 3 + CaCl 2 , the converse of the first equation. In the latter case, the sodium chloride is present in solution in such large excess that the re- action proceeds in the direction indicated by the arrow, so that, according to Berthollet, an excess in quantity can compensate for a weakness in specific affinity. An important step forward was made in this subject by Berthelot and Pean de St. Gilles in 1862, in the course of an investigation on the formation of esters from acids and alcohol. For acetic acid and ethyl alcohol, the reaction may be repre- sented by the equation C 2 H 5 OH + CH 3 COOH ^ CH 3 COOC 2 H 6 + H 2 O. If one starts with equivalent amounts of acid and alcohol, 156 OUTLINES OF PHYSICAL CHEMISTRY the reaction proceeds till about 66 per cent, of the reacting substances have been used up, and then comes to a standstill. Similarly, if equivalent quantities of ethyl acetate and water are heated, the reaction proceeds in the reverse direction (indicated by the lower arrow) until 34 per cent, of the compounds have been used up and the mixture finally obtained is of the same composition as when acid and alcohol are the initial substances. A reaction of this type is termed a reversible reaction, and the facts are conveniently represented by the oppositely-directed arrows. When, however, for a fixed proportion of acid, varying amounts of alcohol are taken, the equilibrium point is greatly altered, as is shown in the accompanying table. The first and third columns show the proportion of alcohol present for i equivalent of acetic acid, and the second and fourth columns the proportion of acid per cent, converted to ester. Ester Formed. 82-8 88-2 93*2 i'S 77*9 50*0 ioo-o We here measure the amount of chemical action by the extent to which the acid is converted into ester, and the table shows very clearly the influence of the mass of the alcohol on the equilibrium. The influence of the relative proportions of the reacting substances on chemical action was thus clearly recognised, but was not accurately formulated till 1867. In that year, two Nor- wegian investigators, Guldberg and Waage, enunciated the Laiu of mass action, which may provisionally be expressed as follows : The amount of chemical action is proportional to the active mass of each of the substances reacting, active mass being defined as the molecular concentration of the reacting substance. The im- portant part of this statement is that the chemical activity of Equivalents of Alcohol. Ester Formed. Equivalents of Alcohol. 0'2 19*3 2*0 0*5 I'O 42*0 66-5 4-0 12*0 EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 157 a substance is not proportional to the quantity present, but to its concentration, or amount in unit volume of the reaction mixture. The law applies in the first instance more particularly to gases arid substances in solution ; the active mass of solids will be considered later. The " amount of chemical action " exerted by a certain sub- stance can be measured (a) from its influence on the equilibrium, as in the formation of ethyl acetate, just referred to ; (b) from its influence on the rate of a chemical action, such as the inver- sion of cane sugar. The law of mass action can therefore be deduced from the results of kinetic or equilibrium experiments. Conversely, once the law is established, it can be employed both for the investigation of rates of reaction and of chemical equilibria, and it is the fundamental law in both these branches of physical chemistry. In the above form, the law of mass action cannot readily be applied, and it will therefore be formulated mathematically. For purposes of illustration, we choose a reversible reaction between two substances in which only one molecule of each reacts ; a typical case is the formation of ethyl acetate and water from ethyl alcohol and acetic acid, already referred to. Calling the molecular concentrations of the reacting substances a and b, the rate at which they combine is, according to the law of mass action, proportional to a and to b separately, and there- fore proportional to their product. We may therefore write for the initial velocity of reaction at the time / Rate <0 oc ab or Rate, = kab, where k is a constant an affinity constant depending only on the nature of the substances, the temperature, etc. As the re- action proceeds, the active masses gradually dimmish, since the original substances are being used up in producing the new substances. If, after an interval of time /, x equivalents of the ester and water have been formed, the rate of the original reaction will be 158 OUTLINES OF PHYSICAL CHEMISTRY Rate, = k(a- x)(b- x). That this must be so is clear when one bears in mind that a and b represent molecular concentrations, and that for every molecule of ester and of water which are formed, an equal number of molecules of acid and alcohol must be used up. We have now to take into account the fact that the substances formed react to produce the original substances. At the time /, when the concentration of the ester and water is x, the rate of the reverse reaction will be : Rate, = ^ 1 o; 2 , where k is another affinity constant. We then have two reactions pro- ceeding in opposite directions, the velocity of the direct reaction is continually diminishing owing to diminishing concentration, that of the reverse reaction is continually increasing owing to increasing concentration of the reacting substances. A point must ultimately be reached when the velocity of the direct is equal to that of the reverse reaction, and the system will no longer change ; this is the condition of equilibrium. If the particular value of x under these conditions is x l we have the equations Rate direct = k(a - x^(b - xj and rate reverse = k^, and since these are equal k(a - x^(b - #0 = Vi 2 > which may be written (a - x^(b - *i) ^ K _ _ _-. jv. X^ k The facts are made still clearer if we represent the reaction as follows, the initial concentrations being represented on the upper, and the equilibrium concentrations on the lower line : Commencement a b o o C 2 H 5 OH + CH 3 COOH^CH 3 COOC 2 H 5 + H 2 O Equilibrium a - x l b - x l #! x 1 It is important to note that, since K, which is usually termed the equilibrium constant, is the ratio of the two velocity con- EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 159 stants, which are independent of the concentration, the above equation holds for all concentrations. Hence, if the equilibrium constant for any chemical change is obtained from one experi- ment, the equilibrium conditions can be calculated for any value of the original concentrations. Numerous applications of this equation are given in the succeeding paragraphs. When more than one molecular equivalent of a compound takes part in a chemical change, each equivalent must be con- sidered separately, as far as the law of mass action is concerned. In order to illustrate this statement, we will consider the com- bination of hydrogen and iodine to form hydriodic acid. The reaction is reversible, and may therefore be represented by the equation H 2 + I 2 ljHI + HI. The rate of the inverse reaction = ^iC^ since it is propor- tional to the concentration of each of the two mols of hydriodic acid and therefore to their product. As the velocity of the direct reaction = CH 2 Ci 2 , we obtain for the conditions at equilibrium the equation 2 _l2 _!-, "K" CHI ^ The general equation for a reversible reaction may be written in the form where n molecules of the substance A 1 react with 2 molecules of the substance A 2 . . . to form n^ molecules of the substance A/ and n 2 ' molecules of the substance A 2 '. The rates of the direct and reverse actions are represented by the equations : Rate direct == ^C A 1 C A 2 an d rate inverse = AlC^C^/ .... and in equilibrium KK-i A-j Ao = k ~ n ' A/ A 2 ' The above is the strict mathematical form of the law of mass 160 OUTLINES OF PHYSICAL CHEMISTRY action, which in words may be expressed as follows: At equilibrium the product of the concentrations on one side, divided by the product of the concentrations on the other side^ is constant at constant temperature. Thus for the reaction represented by the equation : 2FeCl 3 + SnCl 2 =SnCl 4 + 2 FeCl 2 we have K = CFeCl 3 CsnCI 2 CsnCl 4 CpeCly Strict Proof of the Law of Mass Action The law of mass action, the meaning of which has been illustrated in the previous paragraphs, may be strictly proved by a thermo- dynamical method (van't Hoff, 1885, cf. p. 416), or by a molecular- kinetic method (van't Hoff, 1877). The latter proof is comparatively simple, and depends on the assumption that the rate of chemical change is proportional to the number of collisions between the reacting molecules, which, in sufficiently diluU solution, will be proportional to the respective concen- trations. Taking again ester formation as an example, the velocity of the direct change = C a i co hoi C ac id an( * that of the reverse change = /^Cester C wate r. At equilibrium, the rates will just balance, and therefore ^C a i c ohol ^acid = ^iC es ter C wa t e r As before, this equation may be put in the form ^alcohol ^acid &\ -rr where the respective concentrations are those under equilibrium conditions, and K is the equilibrium constant. It follows from the assumptions made both in the ther mo- dynamical and kinetic proofs that the law of mass action holds strictly only for very dilute solutions, but the experimental results show that it often holds with a fair degree of accuracy even for moderately concentrated solutions. EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 101 EQUILIBRIUM IN GASEOUS SYSTEMS (a) Decomposition of Hydriodic Acid A typical example of equilibrium in a gaseous system is that between hydrogen, iodine and hydriodic acid, investigated by Bodenstein. 1 The reaction, which is represented by the equation H 2 + I 2 ^ 2HI, is a completely reversible one, the concentration at equilibrium being the same whether one starts with hydrogen and iodine or with hydriodic acid, if the conditions otherwise are the same. Applying the law of mass action, we get at once 14 =K ' ' ' (I) as shown in the previous paragraph. It is clear from the equation that if from one observation the respective molecular concentrations of iodine, hydrogen and hydriodic acid are known, K, the equilibrium constant at the temperature in question, can be calculated. The question now arises as to how the progress of the reaction can be followed, so that it may be known when equilibrium is attained. It is further necessary to find a method of measurement such that the equilibrium does not alter while the observations are being made. In this case it happens that both the direct and inverse reactions are extremely slow at room temperature, but are fairly rapid at 445, the tem- perature of boiling sulphur. If then the mixture is heated for a definite time at a high temperature and then cooled rapidly, the respective concentrations at high temperatures can be deter- mined at leisure by analysis. The reacting substances, in varying proportions, are heated at a definite temperature in sealed glass tubes for definite periods, and the amount of hydrogen then present measured after absorption of the iodine and hydriodic acid by means of potassium hydroxide. For the present, only results will be considered in which the tubes were heated so long at 445 that equilibrium was attained. In one experiment, 20*55 mols of hydrogen were heated with 1 Zeitsch. physikal. Chem., 1897, 22, i. II 1 62 OUTLINES OF PHYSICAL CHEMISTRY 31*89 mols of iodine, and it was found that the mixture at equilibrium contained 2*06 mols of hydrogen, 13*40 mols of iodine and 36*98 mols of hydriodic acid in the same volume. Hence [H a ][IJ (2-06 x 13-40) "THIF (36W Equation (i) could, of course, be tested by finding if the same value of K is obtained for different initial concentrations of the reacting substances, but it is in some respects preferable to calculate by means of the equation the proportion of hydriodic acid formed at equilibrium when different initial concentrations of the reacting substances are taken, and to compare the results with those actually observed. In the calculation, K is taken as 0*0200 at 445. If i mol of hydrogen is heated with a mols of iodine, and 2X mols of hydriodic acid are formed, i x mols of hydrogen and a - x mols of iodine will remain behind. Substituting in equation (i), (i - x)(a - x) ^ i - 1\ - i = K = 0'0200 . . (2) 4# The first and second columns of the accompanying table contain the initial concentrations of hydrogen and iodine respectively, and the fourth and fifth columns the observed and calculated concentrations of hydriodic acid at equilibrium, the latter values being obtained from the expression * + a ~~ v' 1 + a 2 " 4*J s where s = i - 4K = 0*92 obtained by solving the quadratic equation (2) above. H 2 Is I 2 /H 2 = a HI found 2.x (calc.) 20*57 5*22 0*254 IO*22 10*19 20*6 14*45 0*702 25*72 2 5'54 20*55 31*89 i'55 2 36*98 37'I3 20*41 5 2*8 2 '53S 38*68 39*01 20*28 67*24 3*3 l6 39'5 2 39' 2 5 EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 163 The close agreement between observed and calculated values shows that the law of mass action applies in this case. It can easily be shown from the fundamental equation that in this case the position of equilibrium is independent of the pressure or of the volume. Calling a, b and c the amounts of hydrogen, iodine and hydriodic acid present at equilibrium, the concentrations are a/V, /V and c/V respectively, where V is the volume occupied by the mixture. Substituting in the general equation, we obtain abjc 1 = K; in other words, K is independent of the volume. Bodenstein found that this re- quirement of the theory was also satisfactorily fulfilled. (b) Dissociation of Phosphorus Pentachloride Another instructive example of equilibrium in a gaseous system is that between phosphorous pentachloride and its products of de- composition, represented by the equation PC1 5 ^ PC1 3 + C1 2 . A decomposition of this type, in which a chemical compound yields one or more products, is termed dissociation, and the student will have met with many examples of dissociation in his earlier work. As before, on applying the law of mass action, we obtain If we commence with a molecules of PC1 5 , and x molecules each of PC1 3 and C1 2 are formed, the concentrations of PC1 5 , PC1 3 and C1 2 at equilibrium are (a - x)/V 9 x/V and x/V re- spectively, and, substituting in the above equation, ~2 X = J (a - x)V It will be observed that the equilibrium in this case depends on the volume, and the larger the volume the smaller is (a x) in other words, the greater is the dissociation. An important point in connection with chemical equilibrium in general is the effect of the addition of excess of one of the products of decomposition (dissociation) on the degree of 164 OUTLINES OF PHYSICAL CHEMISTRY decomposition. If, for example, a mols of PC1 6 are vaporized in a volume V in which b mols of PC1 3 are already present, and if x l is the degree of dissociation of the pentachloride under these conditions, the relative concentrations of trichloride, penta- chloride and chlorine will be b 4 x l9 a - x l9 and x l respec- tively. The equilibrium equation is therefore _ (a - Xl )V where K has the same numerical value as for the pentachloride alone, provided that the volume V and the temperature are the same. If it is assumed that the degree of dissociation when PC1 5 is heated alone under the same conditions is > not more than say 25 per cent., it is clear that the proportion of undis- sociated compound cannot be very seriously increased by the presence of excess of PC1 3 . Hence when <, the initial amount of PC1 3 , is made very large, x lt the amount of chlorine present at equilibrium must become very small in order that the pro- duct K (a x^ may retain approximately the same value ; in other words, the dissociation of PC1 5 must then be very small. From these considerations we deduce the following important general rule : The degree of dissociation of a compound is diminished by addition of excess of one of the products of dissociation provided that the volume remains constant. Equilibrium in Solutions of Non-Electrolytes As a/i illustration of an equilibrium in solution, that between acid, alcohol, ester and water (p. 156) may be considered rather more fully. For this equilibrium, according to the law of mass action, we have Cacid Caicohoi ^ ~ ** If at the commencement a, b and c mols of acid, alcohol and water respectively are present in V litres, and under equi- librium conditions x mols of water and ester respectively have been formed, the respective concentrations are EQUILIBRIUM IN HOMOGENEOUS SYSTEMS 165 V b ~ x - r = - - y ^ester \r > C + X V V whence, substituting in the above equation, (*-*)(*-*) x(c + x) In this case also, the position of equilibrium is independent of the volume. The value of K may be obtained from the observation already mentioned, that when acid and alcohol are taken in equivalent proportions, two-thirds is changed to ester and water under equilibrium conditions. Hence K = 3* = j This equation may now be employed, as in the case of hydriodic acid, to calculate the equilibrium conditions for varying initial concentrations of the reacting substances. As an example, we take the proportion of i mol of acetic acid converted to ester by varying proportions of alcohol, when the initial mixture contains neither ester nor water. The equation in this case simplifies to (!-*)(*-*) X* i- whence x = |(i + b- ijb*-b + i). The observed and cal- culated values of x are given in the table, and it will be seen that the agreement is very satisfactory, although the solution is so concentrated that it is scarcely to be expected that the law of mass action will apply strictly. b x (found) x (calc.) b x (found) x (calc.) 0*05 0*05 0*049 0-67 0'5I9 0*528 0*08 0*078 0-078 I'O 0*665 0*667 0*18 0-171 0*171 r 5 0-819 0*785 0-28 O'226 0-232 2*0 0-858 0*845 o'33 0*293 0-311 2*24 0-876 0*864 0*50 0-414 0-42^ 8-0 0*966 o*945 1 66 OUTLINES OF PHYSICAL CHEMISTRY As regards the practical investigation of this equilibrium, the reacting substances are heated in sealed tubes at constant temperature (say 100) till equilibrium is attained, cooled, and the contents titrated with dilute alkali, using phenolphthalein as indicator. As the concentrations of acid and alcohol before the experiment are known and the acid concentration after the at- tainment of equilibrium is obtained from the results of the titration, the proportion of ester formed can readily be calcu- lated. The equilibrium in salt solutions will be more conveniently dealt with at a kter stage (Chapter XL). Influence of Temperature and Pressure on Chemical Equilibrium. General The equations for chemical equi- librium deduced by means of the law of mass action hold for all temperatures provided that all the components remain in the system : the only effect of change of temperature is to alter the value of the equilibrium constant. The displacement of equi- librium is connected with the heat liberated in the chemical change by the equation drr RT 2 which shows that the rate of change of the logarithm of the equilibrium constant with temperature is equal to the heat evolved in the complete reaction l divided by twice the square of the absolute temperature at which the change takes place. Strictly speaking, the above equation holds only for the dis- placement of equilibrium due to an infinitely small change of temperature FIG. 23. axis. Similarly, the curve AC represents the effect of pressure on the melting-point of monoclinic sulphur, and as it is less inclined away from the temperature axis than OC, the two lines meet at C at 131 under a pressure of 400 atmospheres. The curve AD is the vapour-pressure curve of liquid sulphur above 120, where the liquid is stable, and AB', continuous with DA, is the vapour-pressure curve of metastable liquid sulphur. As already indicated, B' represents the melting-point of metastable HETEROGENEOUS EQUILIBRIUM 185 rhombic sulphur ; in other words, it is a metastable triple point at which rhombic and liquid sulphur, both in the metastable condition, are in equilibrium with sulphur vapour. OB', as already indicated, represents the vapour-pressure curve of meta- stable rhombic sulphur, and the diagram is completed, both for stable and metastable phases, by B'C, which represents the effect of pressure on the melting-point of rhombic sulphur. Mono- clinic sulphur does not exist above the point C ; when fused sulphur solidifies at a pressure greater than 400 atmospheres, the rhombic form separates, whilst, as is well known, the monoclinic form first appears on solidification under ordinary pressure. The areas, as before, represent each a single phase, as shown in the diagram. Monoclinic sulphur is of particular interest, because it can only exist in the stable form within certain narrow limits of temperature and pressure, represented in the diagram by OAC. The phase rule is chiefly of importance in indicating what are the possible equilibrium conditions in a heterogeneous system, and in checking the experimental results. To illustrate this, we will use it to find out what are the possible non-variant systems in the case of sulphur, just considered. From the formula C - P + 2 = F, since C = i, P must be three in order that F may be zero ; in other words, the system will be non-variant when three phases are present. As any three of the four phases may theoretically be in equilibrium, there must be four triple points, with the following phases : (a) Rhombic and monoclinic sulphur and vapour (the point O). (b) Rhombic and monoclinic sulphur and liquid (the point C). (c) Rhombic sulphur, liquid and vapour (the point B'). (d) Monoclinic sulphur, liquid and vapour (the point A). The phase rule gives no information, however, as to whether the triple points indicated can actually be observed. In this particular case they are all attainable, as the diagram shows, but only because the change from rhombic to monoclinic sulphur above the triple point is comparatively slow. If it 1 86 OUTLINES OF PHYSICAL CHEMISTRY happened to be rapid, the point B' could not be actually observed. Systems of Two Components. Salt and Water The equilibrium conditions are somewhat more complicated on passing from systems of one component to those of two com- ponents, such as a salt and water. For simplicity, the equi- librium between potassium iodide and water will be considered, as the salt does not form hydrates with water under the con- ditions of the experiment. There will therefore be only four phases, solid salt, solu- tion, ice and vapour. There are three degrees 3 oo f- y i ,x / of freedom, as, in ad- dition to the tempera* ture and pressure, the concentration of the solution may now be varied. The equilibrium in this system is repre- sented in Fig. 24, the 10 20 30 40 50 60 70 80 90 ordinates representing FlG - 24- temperatures and the abscissae concentra- tions. At o (A in the diagram) ice is in equilibrium with water and vapour, as has already been shown. If, now, a little potassium iodide is added to the water, the freezing-point is lowered, in other words, the temperature at which ice and water are in equilibrium is lowered by the addition of a salt, and the greater the proportion of salt present, the lower is the temperature of equilibrium. This is represented on the curve AO, which is the curve along which ice, solution and vapour are in equilibrium. On continued addition of potassium iodide, however, a point must be reached at which the solution is saturated with the salt, and on further addition of potassium -300 Grams KI In 100 grams solution HETEROGENEOUS EQUILIBRIUM 187 iodide, the latter must remain in the solid form in contact with ice and the solution. It is clear that, since the progressive lowering of the freezing-point depends upon the continuous increase in the concentration of the solution, the temperature corresponding with the point O must represent the lowest temperature attainable in this way under stable conditions. To complete the diagram, it is further necessary to determine the equilibrium curve for the solid salt, the solution and vapour. Looked at in another way, this will be the solubility curve of potassium iodide, which is represented by the curve OB. This curve is only slightly inclined away from the tempera- ture axis, corresponding with the fact that the solubility of potassium iodide only increases slowly with rise of temperature. The point O, which is the lowest temperature attainable with two components, is known as a eutectic point ; in the special case when the two components are a salt and water, it is termed a cryohydric point. The meaning of the diagram will be clearer if we consider what occurs when solutions of varying concentration are pro- gressively cooled. If, for example, we commence with a weak salt solution above its freezing-point (x in the diagram) and continuously withdraw heat, the temperature will fall (along xy] till the line OA is reached ; ice will then separate, and as the cooling is continued the solution will become more con- centrated and the composition will alter along the line AO until O is reached ; salt then separates as well as ice, and the solution will solidify completely at constant temperature, that of the point O. Similarly, if we start with a concentrated salt solution and lower the temperature until it reaches the curve OB, salt will separate and the composition will alter along the curve BO until it reaches the point O, when the mixture solidifies as a whole. Finally, if a mixture corre- sponding with the composition of the cryohydric mixture is cooled, the line parallel to xy representing the fall of tem- perature will meet the curve first at the point O, and the j88 OUTLINES OF PHYSICAL CHEMISTRY mixture will solidify at constant temperature. At the cryohydric temperature, the composition of the solid salt which separates is necessarily the same as that of the solution. Guthrie, 1 who was the first to investigate these phenomena systematically, was of opinion that these mixtures of constant composition were definite hydrates, which were therefore termed cryohydrates. At first sight there seems much to be said for this view, as the separa- tion takes place at constant temperature, independent of the initial concentration, and the mixtures are crystalline. For the following reasons, however, it is now accepted that the cryo- hydrates are not chemical compounds : (a) the properties of the mixture (heat of solution, etc.) are the mean of the pro- perties of the constituents, which is seldom the case for a chemical compound; (b) the components are not usually present in simple molar proportions ; and (c) the heterogeneous character of the mixture can be recognised by microscopic examination. The magnitude of the cryohydric temperature is of course con- ditioned by the effect of the salt in lowering the freezing-point of the solvent, and by its solubility at low temperatures. The eutectic temperatures of solutions of sodium and ammonium chlorides are -22 and -17 respectively, that of a solution of calcium chloride - 37. The application of the phase rule to this system will be readily understood from what has been said above. When there are four phases, ice, salt, solution and vapour, and two com- ponents, we find, by substituting in the formula C-P-f 2 = F, that F = o, that is, the four phases can only be in equilibrium at a single point, the point O in the diagram. When there are three phases, there is one degree of freedom, and the equi- librium is represented by a line (OA and OB in the diagram). If, for example, the condition of affairs is that represented by a point on the line OA, and the concentration of the solution is increased and kept at the new value (by further addition of salt when necessary) ice will dissolve, and the temperature will fall till it corresponds with that at which ice is in equilibrium l Phil. Mag., 1884, [5], 17, 462. HETEROGENEOUS EQUILIBRIUM X 8 9 with the more concentrated solution and vapour. If, then, while the concentration is still kept at the above value, the tempera- ture is altered and kept at the new value, one of the phases will disappear. The system is therefore univariant. If, instead of the concentration, one of the other variables is changed, corre- sponding changes in the remaining two variables take place, and the system adjusts itself till the three phases are again in equilibrium. If there are only two phases, for example, solution and vapour, the phase rule indicates that the system is bi variant, and it can readily be shown, by reasoning analogous to the above, that such is the case. Freezing Mixtures The use of mixtures of ice and salt as " freezing mixtures " for obtaining constant low temperatures, depends upon the principles just discussed. Suppose, for example, we begin with a fairly intimate mixture of ice and salt and a little water. When a little of the salt dissolves, the solution is no longer in equilibrium with ice. It will strive towards equilibrium by some more ice dissolving to dilute the solution, the latter, being now more unsaturated with regard to the salt, will dissolve more of it, more ice will go into solution and so on. As a consequence of these changes, heat must be absorbed in changing ice to water (latent heat of fusion of ice), and in connection with the heat of solution of the salt if, as is usually the case, the heat of solution is negative. The temperature, therefore, falls till the cryohydric point is reached, and then remains constant, since it is under these conditions that ice, salt, solution and vapour are in equilibrium. As the temperature of a cryohydric mixture is so much below atmospheric temperature, heat will continually be absorbed from the surroundings, but as long as both ice and solid salt are present, the heat will be used up in bringing about the change of state, and the temperature will remain constant. When, however, either ice or salt is used up, the temperature must necessarily begin to rise. i 9 o OUTLINES OF PHYSICAL CHEMISTRY Systems of Two Components. General The particular case of a two-component or binary system already considered potassium iodide and water is very simple, for two reasons . (i) the solid phases separate pure from the fused mass, in other words, the phases are not miscible in the solid state ; (2) the components do not enter into chemical combination. Com- plications occur when chemical compounds are formed, and when the solid phases separate as mixed crystals (p. 95) con- taining the two components in varying proportions. We will consider three comparatively simple cases of equilibrium in binary systems, the components being in all cases completely miscible in the fused state : (a) The components do not enter into chemical combination, and are not miscible in the solid state. (If) The components do not enter into chemical combination, but are completely miscible in the solid state. (c) The components form one chemical compound, but are not miscible with each other or with the compound in the solid state. Case (a). One example of this case is potassium iodide and water which has just been discussed. Another, which will be briefly considered, is the equilibrium between the metals zinc and cadmium. 1 To determine the equilibrium curves, mixtures of these metals in varying proportions are heated above the melting-point, and then allowed to cool slowly, the rate of cooling being observed with a thermocouple, one junction of which is placed in the mixture and the other kept at constant temperature. If the thermocouple is connected to a mirror galvanometer, the rate of cooling can be followed by the move- ment of a spot of light. Curves in which the times are plotted against the corresponding temperatures of the mixtures are represented in Fig. 25 B. The curves a, Z and b represent the cooling of mixtures corresponding with the points a, Z, b on the composition axis of the upper figure ; the curves o and 100 1 Hinrichs, Zeitsch. anorg. Chem., 1907, 55, 415. HETEROGENEOUS EQUILIBRIUM 191 represent the cooling of pure zinc and cadmium respectively. For the mixtures there are halts in the rate of cooling so- called "breaks" at two points; the first point varies with the composition of the mixture, whilst the second is practically con- stant at 270. The curve obtained by plotting the temperatures of the first break against the composition of the mixture is 270 Equilibrium Diagram for Zinc and Cadmium FIG. 25 A (top), 253 (bottom). represented in Fig. 25 A. The analogy of the diagram with that for potassium iodide and water will be evident, as is its interpretation. The point A represents the freezing-point of zinc, B that of cadmium, the curve AC represents the effect of the gradual addition of cadmium upon the freezing-point of zinc, and BC the effect of zinc in lowering the freezing-point of 1 92 OUTLINES OF PHYSICAL CHEMISTRY cadmium, C is the eutectic point at which solid zinc and cad- mium are in equilibrium with the fused mass. Consider first a fused mixture rich in zinc. As the temperature falls, a point is ultimately reached at which pure zinc begins to separate, and as the change from liquid to solid is, as usual, attended with liberation of heat, the rate at which the temperature falls will diminish this represents the first break on cooling. As zinc continues to separate, the composition of the mixture moves along the curve AC, at C the solution is also saturated with regard to cadmium, and therefore at the temperature repre- sented by C, both zinc and cadmium separate in a mixture of the same composition as the fused mass. This, as already mentioned, is the eutectic point, and as the mixture at that point behaves like a single substance, the temperature remains constant till the whole mass has solidified. This is the second break observed when the mixture cools. If, on the other hand, we commence with a mixture rich in cadmium, the latter separates along the curve BC till the point C is reached, and then the mixture solidifies as a whole. Finally, if a mixture is taken, the composition of which is that of the eutectic mixture, there is only one break in the cooling curve, at the eutectic point (curve Z). The composition of the eutectic mixture is represented by the point Z on the axis of composi- tion XY, and corresponds with 17-4 per cent, of zinc and 82-6 per cent, of cadmium by weight. Case (b). No chemical compound. Separation of mixed crystals. A good example of this case is the system palladium-gold, 1 the equilibrium diagram for which is repre- sented in Fig. 26. In this case, when the fused mass is allowed to cool, crystals containing both metals in varying proportions separate, and therefore the ordinary rule with regard to the lowering of melting-point of one substance by the addition of another does no.t apply, and there is no eutectic point (p. 187). &s the composition of the crystals and the solution does not 1 Ruer, Zeitsch. anorg. Chetn., 1906, 151, 391. HETEROGENEOUS EQUILIBRIUM 193 remain the same during solidification, there is in general an interval of temperature, termed the crystallisation interval, be- tween the beginning and end of crystallisation, and the cooling curve shows two breaks or changes of direction representing the beginning (curve ACB) and end (curve ADB) of solidi- fication. Gold and palladium are miscible in all proportions in the solid state, but in many cases the miscibility is limited. Case (c). One chemical compound. No miscibility in solid form. A typical freezing-point curve for a system of this type is given in Fig. 27, representing thal- lium -mercury amal- gams. It will be ob- served that there is a maximum on the curve, corresponding with the composition t LIQUID SOLID 6 O% Au COMPOSITION* IOO% AU Equilibrium Diagram for Palladium and Gold FIG. 26. of a compound Hg 2 Tl, containing two equivalents of mercury to one of thallium. This compound melts at a definite temperature, and it is evident from the curve that the melting-point is lowered both by the addition of mercury (along CB) and of thallium (along CD). From this it is clear that the components of a chemical compound lower the freezing-point of the compound just as foreign substances do. The remainder of the curve will readily be understood from the previous paragraphs. A repre- sents the freezing-point of mercury, AB the lowering of the freezing-point of mercury by the progressive addition of the '3 i 9 4 OUTLINES OF PHYSICAL CHEMISTRY LIQUID compound Hg2Tl, E the melting-point of thallium, and ED the effect on the melting-point of thallium produced by gradually increasing amounts of the same compound. The points B and D are eutectic points, the eutectic mixtures containing mercury and Hg2Tl, and Hg 2 Tl and thallium re- spectively. As in Fig. 25, above the curve ABCDE only liquid, and below the dotted line only solid is present. The intermediate regions represent heterogeneous systems in which both liquid and solid are present. The occurrence of a maximum on the freez- ing-point curve is usually an indication of chemical combination, but, on the other hand, chemical compounds are sometimes present, although there are no maxima on the curve, Y This occurs more par- Z(Hg 2 r/) IOO%TI ticularly when the COMPOSITION * , , j j ., .... . ... chemical compound de- Equihbrmm Diagram for Mercury and Thallium r p IGi 27< composes before its melting-point is reached. The systematic investigation of the freezing-point curve of a binary mixture is one of the best methods for detecting chemical compounds and establishing their formulae. This can be illustrated by the equilibrium curve of ferric chloride and water, which is of great historical interest, inasmuch as, in the course of the investigation of this system by Rooze- boom, many of the points we have been discussing were elucidated. The Hydrates of Ferric Chloride The freezing-point curve of this system is represented in Fig. 28, and will b t HETEROGENEOUS EQUILIBRIUM 195 readily understood by comparison with the previous diagrams, more particularly Fig. 27. For convenience, the concentrations in this case are expressed as the ratio of the number of mols of ferric chloride present to 100 mols of water. In interpreting the curve, we commence at the left-hand side of ,the diagram. A represents the freezing-point of water, and Moll. 10 15 20 25 30 35 to loo mols. H%O FlG. 23. AB the lowering of freezing-point produced by the progressive addition of ferric chloride. At the point B, - 55, the solution is saturated with regard to ferric chloride, and B is therefore the eutectic point, at which ice, solution, a hydrate of ferric chloride (Fe 2 Cl 6 , i2H 2 O) and vapour are in equilibrium. On adding more ferric chloride, the ice phase will disappear, and equilibrium will be attained at a point on the curve BC, at which the 196 OUTLINES OF PHYSICAL CHEMISTRY dodecahydrate, Fe 2 Cl 6 , i2H 2 O, is in equilibrium with solution and vapour. The curve BC may therefore be regarded as the solubility curve of the dodecahydrate, and corresponds exactly with the curve OB (Fig. 24). On continued addition of ferric chloride, the equilibrium temperature continues to rise up to the point C at 37, at which point the composition of the mixture corresponds with that of the dodecahydrate. Further addition of ferric chloride lowers the temperature along the line CD, so that C is a maximum on the curve. At this point, the solid dodeca- hydrate is in equilibrium with a liquid of the same composition ; in other words, C is the melting-point of the compound Fe 2 Cl 6> i2H 2 O, just as the point C (Fig. 27) represents the melting-point of Hg 2 Tl. On addition of more ferric chloride, the melting-point is lowered, as represented by the section CD of the curve. At the point D, the curve reaches another minimum, or eutectic point, which corresponds with the point B, except that a new hydrate, Fe 2 Cl 6 , 7H 2 O, takes the place of ice. On further addition of ferric chloride, another maximum is reached, which represents the melting-point of the hepta- hydrate. In an exactly similar way, the other two maxima at higher concentrations of ferric chloride indicate the existence of two other hydrates, Fe 2 Cl 6 , 5H 2 O and Fe 2 Cl 6 , 4H 2 O, in the solid state. At the last eutectic point, K, the four phases in equilibrium are the tetrahydrate, anhydrous ferric chloride, solu- tion and vapour, and KL represents the effect of temperature on the solubility of the anhydrous chloride. The application of the phase rule to this system should be made by the student. As at the point D (and the other corre- sponding points) the solubility curves of the dodecahydrate and heptahydrate intersect, D may be termed the transition point for the two hydrates. Since at these points there are four phases in equilibrium, they are also termed quadruple points. In recent years, many other systems have been fully investi- gated on analogous lines to that indicated above. The chief experimental difficulty is to avoid supercooling, a source of HETEROGENEOUS EQUILIBRIUM 197 error which is much more troublesome in some systems than in others. Transition Points In the preceding sections, mention has been made on several occasions of transition points. When a substance is polymorphic (*>., exists in more than one form) it is often possible, as in the case of sulphur, to find a temperature the so-called transition point at which two forms are in equilibrium ; at higher temperatures one of the forms is stable, at lower temperatures the other. It has been shown that at the transition point the two modifications have the same vapour pressure, but at other temperatures the metastable form has the higher vapour pressure. By similar reasoning it can be shown that the metastable phase has the higher solubility and the lower melt- ing-point. It may happen, however, as in the case of benzophenone, that the modification stable at low temperatures melts before the transition point is reached. It is evident that in this case the transition can only take place in one direction, from the modification the existence of which is favoured by high tem- perature to that stable at low temperatures. Substances such as sulphur, for which there is a reversible transition, are termed enantiotropic y substances for which the transition is only in one direction are termed monotropic. It may be asked how it is possible to obtain the metastable form of benzophenone, as it is necessarily unstable under all conditions. The explanation is that when a fused polymorphic substance is allowed to solidify, it is generally the most unstable form which separates first (e.g. y sulphur). Similarly, the transition point of two hydrates is that tempera- ture at which they are in equilibrium, and at which they have the same solubility and the same vapour pressure, Practical Illustrations. Distribution of a solute between two immiscible solvents To a nearly saturated aqueous solu- tion of succinic acid (say 100 c.c.) in a stoppered bottle an i 9 8 OUTLINES OF PHYSICAL CHEMISTRY approximately equal volume of ether is added, and the bottle kept at room temperature for half an hour, shaking it at intervals. When the separation into two layers is complete, part of the ethereal layer is pipetted off and titrated with barium hydroxide, and the same is done with the aqueous layer. Less concentrated solutions of succinic acid are then used, and the concentrations in the ethereal and aqueous layers determined as before. The value of the distribution constant Cj/Cg is then calculated from the results, and should be constant, as the molecular weight is the same in the two solvents (p. 178). In a similar way the distribution of benzoic acid between water and benzene may be investigated. In this case, as ben- zoic acid is unimolecular in water and bimolecular in benzene (p. 179), the ratio C x / \/C 2 , where Cj represents the concentration in the aqueous layer, C 2 the concentration in the benzene layer, should be approximately constant. Determination of transition points Transition temperatures, such as that above which rhombic sulphur is unstable and monoclinic sulphur stable, can be determined in various ways, which depend in principle on the difference in properties of the two phases. The dilatometer method is largely used ; it depends on the fact that there is a more or less sudden change of volume when the transition takes place. Into a fairly wide glass tube, provided with a capillary tube and scale at the upper end and open at the lower end, is placed a mixture of the two modifications, e.g., monoclinic and rhombic sulphur, the lower end is then sealed up, and the vessel filled to the lower end of the scale with an indifferent liquid such as oil. The dilatometer is then placed in a bath the temperature of which is gradually raised, and readings made of the level of the liquid in the dilatometer. The rate of change of level will be more or less steady till the neighbourhood of the transition point is reached, when a relatively rapid change of level will be observed. The chief drawback to the method is that the change seldom takes place rapidly when the transition point is HETEROGENEOUS EQUILIBRIUM 199 reached. To facilitate the change as far as possible, some of the second phase should always be present, (p. 55). By solubility or vapour-pressure measurements The fact that the two phases have the same solubility at the transition point may be employed to determine the latter. To determine the transition point in the system Na 2 SO 4 ,io H 2 O Jt Na 2 SO 4 + 10 H 2 O, it is only necessary to measure the solubility of the anhydrous salt and of the decahydrate in the neighbourhood of the transition point, and the point at which the solubility curves intersect will be the required point. Measurements of vapour pressure may be employed in a similar way. Thus Ramsay and Young determined the vapour pressures of solid and liquid bromine respectively and found that the curves intersected at - 7, which is therefore the transition temperature for solid and liquid bromine ; in other words, the melting-point of bromine. CHAPTER IX VELOCITY OF REACTION. CATALYSIS General In inorganic chemistry, the question as to the rate of a chemical change does not often arise, because in general the reactions are so rapid that it is impossible to measure the speed. The neutralization of an acid by a base, for instance, as shown by the change of colour of the indicator, is practically instantaneous. However, some instances of slow inorganic re- actions in homogeneous systems are known. The rate of com- bination of sulphur dioxide and oxygen to form sulphur trioxide is very slow under ordinary conditions, and the mixture of gases has to be heated in contact with platinum as an accelerating agent in order to obtain a good yield of trioxide. In organic chemistry, on the other hand, slow chemical reactions are very frequently met with. Thus the combination of an organic acid and an alcohol to form an ester is very slow under ordinary conditions, and the mixture of acid and alcohol, saturated with hydrogen chloride, has to be boiled for a considerable time in order to obtain a good yield of ester. In this chapter, as in the preceding one on chemical equili- brium, the law of mass-action is the guiding principle. It has already been pointed out (p. 158) that the rate of a chemical reaction at any instant may be regarded as the difference in the speeds of the direct and the reverse reaction at that instant. If we consider a simple reversible reaction, such as ester forma- tion, in which a, , c and d are the initial equivalent concentra- tions of the reacting substances, and if x is the amount of 200 VELOCITY OF REACTION. CATALYSIS 201 ester formed in the time /, the equation for the reaction velo- city at that instant may be written ~ = k(a - x)(b - *) - kjf + x)(d + x) . (i) in which dx represents the small increase in the amount of x during the small interval of time, dt. This equation is a direct consequence of the application of the law of mass action to the reaction in question. It very often happens, however, that the equilibrium lies very near one side, which can only mean that the rate of the reverse reaction is small in comparison with that of the direct reaction. This is clear from the following considerations. The splitting up of hydrogen peroxide into water and oxygen is represented by the equation H 2 O 2 ->H 2 O + -O 2 , and the equilibrium be- tween this compound and its decomposition products by the equation H 2 O 2 ^tH 2 O + -JO 2 . Applying the law of mass action, we have and [H 2 2 ] ._ [H 2 0][0 2 ]* k " Now it is an experimental fact that the concentration of hydrogen peroxide in equilibrium with water and oxygen at atmospheric pressure is so small that it cannot be detected by analytical means. It follows, from the above equation, that k^ is small in comparison with k ; otherwise expressed, the rate of the con- verse reaction, represented by the lower arrow, is negligible in comparison with that of the direct reaction, represented by the upper arrow. The same considerations apply to the more general case re- presented by equation (i). If k^ is negligible in comparison with k, the expression k^(c + x)(d + x) in equation (i) is negligible in comparison with the remainder of the right-hand side of the equation, and the latter therefore simplifies to 202 OUTLINES OF PHYSICAL CHEMISTRY -*(- *)(> - *). Reactions of this type, in which the rate of the inverse reaction is negligible, are by far the simplest from a kinetic standpoint, and will therefore be considered first. Unimolecular Reaction The simplest type of chemical reaction is that in which only one substance is undergoing change, and there is practically no back reaction. Such a reaction, which can be readily followed, is the splitting up of hydrogen peroxide to water and oxygen in the presence of colloidal platinum or of certain enzymes. The reaction, which is usually carried out in dilute aqueous solution, may be repre- sented by the equation H 2 O 2 = H 2 O + O, and there is the advantage that the solvent does not appreciably alter during the reaction. As the colloidal platinum or the enzyme remains of constant activity during the reaction, the course of reaction is determined solely by the peroxide concentration (cf. p. 205). The reaction in the presence of haemase (blood -catalase) can conveniently be followed by removing a portion of the solution from time to time, adding to excess of sulphuric acid, which immediately stops the reaction, and titrating with permanganate solution. Some of the results obtained in this way are repre- sented in the accompanying table : a x X t (mins.). (c.c. KMnO 4 ). (c.c. KMnO 4 ). k o 46-1 o 5 37*1 9* o*o435 10 29-8 16-3 0-0438 20 19*6 26-5 0*0429 30 12-3 33*8 0*0440 50 5*o 41-1 0*0444 The numbers in the second column represent the number of c.c. of dilute permanganate solution equivalent to 25 c.c. of the reaction mixture when the times represented in the first VELOCITY OF REACTION. CATALYSIS 203 column have elapsed after mixing the peroxide and enzyme, and therefore represent the concentrations of peroxide in the mixture at the times in question. By subtracting these numbers from that representing the initial concentration of the peroxide, 46*1 c.c., the amounts of peroxide split up at the times / are obtained ; these numbers are given in the third column. The numbers illustrate very clearly the falling off in the rate of the reaction as the concentration of the peroxide diminishes. Thus in the first ten minutes an amount of peroxide equivalent to 1 6*3 c.c. of permanganate is split up, whilst in the second interval of ten minutes only 26*5 - 16-3 10*2 c.c. are de- composed. According to the law of mass action, the rate of the reaction at the time / should be proportional to the concentration of the peroxide, a x, at that time, hence ~~ k(a-x) . . . (2) In this form, however, the equation cannot be applied directly to the experimental results, since dx, the amount of change of x in the time dt> would have to be taken fairly large in order to obtain accurate results, and during the interval a -x would naturally have diminished. Better results would be obtained if a -x were taken as the average concentration during the interval dt within which dx of peroxide is being decomposed, but even this method does not give accurate values for k. The difficulty is got over by integrating the equation on principles described in books on higher mathematics. In this way, and bearing in mind that, when /= o, x*= o, we obtain from equation (2) above 7 lo ^ = * ... (3) It is, however, much more convenient to work with ordinary logarithms (to the base 10) than with logarithms to the base and x the amount transformed in the time /, the velocity equation is g - *(a -*)(*-*) . . . (i) The simplest case is that in which the substances are present in equivalent quantities. The velocity equation then becomes which, on integration, gives the formula __ _ - / a(a - x) ' As an illustration of a bimolecular reaction, the hydrolysis of an ester by alkali may be adduced, a reaction which has been thoroughly investigated by Warder, Ostwald, Arrhenius and others. For ethyl acetate and sodium hydroxide, the equation is as follows : CH 8 COOC 2 H 6 + NaOH - CH 3 COONa + C 2 H 6 OH. In carrying out an experiment, 1/20 molar solutions of ethyl acetate and of sodium hydroxide are warmed separately in a thermostat at constant temperature (25) for some time, equal volumes of the solutions are then mixed, and from time to time a portion of the reaction mixture is removed and titrated rapidly with dilute hydrochloric acid. In the following table are given some results obtained by Arrhenius : t (mm.) a-x k t (min.) a-x o 8*04 2*31 4 5*30 0*0160 6 I*8 7 6 . 4-58 0*0156 12 i'57 8 3*91 0*0164 18 i*35 10 3*51 0*0160 24 1*20 12 3*12 0*0162 30 no 208 OUTLINES OF PHYSICAL CHEMISTRY 1/50 molar solution at 24-7. 1/170 molar solution at 247. o'oiyo 0*0170 0*0171 0*0167 0*0163 The numbers for a - x in the second and fifth columns re- present the concentrations of sodium hydroxide (and of ethyl acetate) expressed as the number of c.c. of hydrochloric acid required to neutralize 10 c.c. of the reaction mixture. The reaction is very rapid, and therefore the experimental error is somewhat large but the values obtained for k in the third and sixth columns show that the assumptions on which formula (2) is based are justified. Another bimolecular reaction, which differs from the former inasmuch as two molecules of the same substance react, is the transformation of benzaldehyde to benzoin under the influence of potassium cyanide. The reaction is represented by the equation 2 C 6 H 5 CHO - C 6 H 6 CHOHCOC 6 H 5 , the potassium cyanide remaining unaltered at the end of the reaction. When the reacting substances are not present in equivalent proportions, the calculation is somewhat more complicated. On integrating the equation dxjdt = k(a - x)(b - x), we obtain for this case In order to illustrate the application of this equation, some results obtained by Reicher for the saponification of ethyl acetate by excess of alkali may be adduced. The reaction was followed by titrating portions of the reaction- mixture from time to time with standard acid, as already described, and the excess VELOCITY OF REACTION. CATALYSIS 209 of alkali was determined by titration of a portion of the solution after the ethyl acetate was completely saponified (at the end of twenty-four hours). t (min.). a - x b - x k (alkali concentration). (ester concentration). O 61-95 47*3 4*89 50-59 35-67 0-00093 11-36 42-40 27*48 0*00094 29-18 29-35 14*43 0-00092 oo I4'92 o It is important to note that the value of k for a bimolecular reaction is not, as the case of a unimolecular reaction, indepen- dent of the units in which the concentration is expressed. If, for example, a unit i/th of the first is chosen, the value of ix. i nx ix i becomes - / a(a - x) t na.n(a-x) t a(a - x) ' n so that the value of k diminishes proportionally to the increase of the numbers expressing the concentrations. The truth of this statement can be tested by means of the data for ester saponification due to Arrhenius. If the titrations are made with acid of half the strength actually used, (n ** 2), the numbers expressing the concentrations will be doubled, and it will be found by trial that the value of k becomes half that given in the table. Trimolecular Reactions When three equivalents take part in a chemical change, the reaction is termed trimolecular, and several such reactions have been carefully investigated. If, as before, we represent the initial molar concentrations of the reacting substances by a, b and c respectively, and if x is the proportion of each transformed in the time /, the rate of reaction at that time will, according to the law of mass action, be represented by the differential equation 210 OUTLINES OF PHYSICAL CHEMISTRY dx =* k(a - x)(b - x)(c - x). Such an equation is somewhat difficult to integrate, and we will therefore confine ourselves to the simple case in which the initial concentrations are the same. The equation then becomes dxfdt = k (a - #) 3 , which on integration gives for k , _ i x(2a - x) " 1 2a\a - x)* Different cases arise according as the reacting molecules are the same or different. The simplest case, in which the three re- acting molecules are the same, is illustrated by the condensation of cyanic acid to cyamelide, represented by the equation 3 HCNO = H 3 C 3 N 3 3 . A case where two only of the reacting molecules are the same is the reaction between ferric and stannous chlorides, represented by the equation 2FeCl 3 + SnCl 2 = SnCl 4 + 2FeCl 2 . Finally, the reaction between ferrous chloride, potassium chlorate and hydrochloric acid, represented by the equation 6FeCl 2 + KC1O 3 + 6HC1 - 6FeCl 3 + KC1 + 3 H 2 O, has been shown by Noyes and Wason to be proportional to the respective concentrations of the three reacting substances, and is therefore of the third order. As an illustration of a trimolecular change, some of Noyes' results for the reaction between ferric and stannous chlorides are given in the table. The reacting substances were mixed together at constant temperature, and from time to time a measured quantity of the solution was removed with a pipette, the stannous chloride decomposed with mercuric chloride, and the ferrous salt still remaining titrated with potassium per- manganate in the usual way. VELOCITY OF REACTION. CATALYSIS 211 SnCl 2 FeClg =* 0-0625 normal = = a. t (mm.) a x X k 0*0625 o I 0*04816 0*01434 88 3 0*03664 0*02586 8,1 7 0*02638 0*03612 84 17 0*01784 0*04502 89 25 0*01458 0*04792 89 Reactions of Higher Order. Molecular Kinetic Con- siderations Whilst reactions of the first and second order are very numerous, reactions of the third order are compara- tively seldom met with, and reactions of a still higher order are practically unknown. This is at first sight surprising, as the equations representing many chemical reactions indicate that a considerable number of molecules take part in the change, and a correspondingly high order of reaction is to be expected. The oxidation of ferrous chloride by potassium chlorate in acid solu- tion, for example, is usually represented by the equation 6FeCl 2 + KC1O 3 + 6HC1 - 6FeCl 3 + KC1 + 3H 2 O. Applying the law of mass action (p. 143), we have therefore ~ - [FeCl 2 ] 6 [KC10 3 ][HCl], that is, the reaction should be of the thirteenth order, whilst it is actually of the third order (p. 210). To account for this result, it has been suggested by 'van't Hoff that complicated chemical reactions take place in stages, and that the reaction whose speed is actually measured is one in which only two or three molecules take part, the velocity of the other reactions being very great in comparison. This view is further considered in the next section. The molecukr theory throws a good deal of light on this question. On the assumption that the rate of chemical reaction is proportional to the number of collisions between the reacting molecules (p. 160), it follows that in a trimolecular reaction the 212 OUTLINES OF PHYSICAL CHEMISTRY three reacting molecules must collide simultaneously to produce a chemical change. The probability of such a collision is ex- tremely small compared with that between two molecules ; there- fore, if at all possible, the reaction will take place between two molecules or by the change of a single molecule. The proba- bility of the simultaneous collision of four molecules is so small as to be almost negligible. Reactions in Stages It has just been pointed out that many reactions which are represented by rather complicated equations prove on investigation to be of the second or third order, which seems to show that the reaction, the speed of which is being measured, is in reality a comparatively simple one. When a chemical change takes place in stages, a little consideration shows that it is the slowest of a series of reactions which is the determining factor for the observed velocity. This process has been fittingly compared by Walker to the sending of a telegram ; the time which ekpses between dispatch and receipt is con- ditioned almost entirely by the time taken by the messenger between receiving-office and destination, as that is by far the slowest in the successive stages of transmission. An instructive example of a reaction which takes place in stages is the burning of phosphorus hydride in oxygen, investi- gated in van't Hoff s laboratory by van der Stadt. The change is usually represented by the equation 2 PH 3 + 4 2 = P 2 6 + 3 H 2 0, according to which it would be a reaction of the sixth order whilst the rate was actually found to be proportional to the respective concentrations of the two gases, the reaction being therefore of the second order. On allowing the gases to mix gradually by diffusion, it was then found that the first stage of the reaction is represented by the equation PH 8 + O 2 - HPO 2 + H 2 that of a bimolecular reaction the subsequent changes by VELOCITY OF REACTION. CATALYSIS 213 which water and phosphorus pentoxide are produced being very rapid in comparison. Many other reactions proceed in stages, and in some cases evidence as to the nature of the intermediate compounds has been obtained. Thus the reaction between hydrobromic and bromic acid, usually represented by the equation HBrO 3 + sHBr - 3 H 2 O + 3Br 2 , is bimolecular in the presence of excess of acid, arid it is probable that the first stage (the slow reaction) is as follows : HBrO 8 + HBr - HBrO + HBrO 2 , the subsequent changes, by which bromine and water are finally produced, being comparatively rapid. It is very probable that the equations which we ordinarily use represent only the initial and final stages in a series of changes, and the determination of the " order " of the reaction is one of the most important methods for elucidating the nature of the relatively unstable intermediate compounds. Determination of the Order of a Reaction Three im- portant methods which are largely used in determining the order of reactions may be mentioned here. (a) The Method of Integration According to this method, the values of k given by the integrated equations for reactions of the first, second and third order are calculated from the ex- perimental results, and the order of the reaction is that in which constant values are obtained for k. The method can be applied to the numbers obtained for the reaction between equivalent amounts of ethyl acetate and sodium hydroxide, when it will be found that the values for k, calculated from the equation k = i //log aj (a - x), continually decrease throughout the reaction; the values obtained with an equation of the third order continu- ally increase, and only for the equation k i/t.xja(a - x) is k actually constant. The disadvantage of this method is that disturbing causes, such as secondary reactions or the influence of the reaction oroducts on the velocity, may so complicate the 214 OUTLINES OF PHYSICAL CHEMISTRY results that a decision as to the order of the reaction is impossible or an erroneous conclusion may be drawn. (b) Ostwald's " Isolation " Method It has already been pointed out that if one or more of the reacting substances is taken in great excess, so that their concentration does not alter appreciably during the reaction, the velocity, as far as these substances is concerned, may be regarded as constant. It is on this principle that the " isolation" method is based. Each of the reacting substances in turn is taken in small concentra- tion and all the others in excess, and the relation between the reaction velocity and the concentration of the substance present in small amount determined experimentally. As an example, we will consider the reaction between potassium iodide and iodate in acid solution, investigated by Dushman. 1 Regarding the action of the acid as due to H' ions (p. 125), the reaction velocity, according to the law of mass action, must be repre- sented by the equation When iodide and acid are used in large excess, the velocity is proportional to the iodate concentration (n^ = i) ; with a large excess of iodate and acid it is proportional to the square of the iodide concentration (n^ = 2) ; and finally, when iodide and iodate are in large excess, it is proportional to the square of the acid concentration (n z = 2). Hence the velocity equation becomes and when neither of the reagents is present in great excess, is of the fifth order. (c) Time taken to Complete the same Fraction of the Reaction Measurements are made with definite concentrations of the reacting substances, and with double and treble those con- i y. Physical Chem., 1904, 8, 453. As the rate of reaction does not depend upon the particular iodate or iodide used, we employ the formulae for the iodate ion IO 3 ' and the iodide ion I'. VELOCITY OF REACTION. CATALYSIS 215 centrations, and the times taken to complete a certain stage (say one- third) of the reaction noted. The order of the reaction can then be determined from the following considerations (Ostwald) : (1) For a reaction of the first order the time taken to com- plete a certain fraction of the reaction is independent of the initial concentration. (2) For a reaction of the second order, the time taken to complete a certain fraction of the reaction is inversely propor- tional to the initial concentration, e.g., if the concentration is doubled, the time taken to complete a certain fraction of the reaction is halved. (3) In general, for a reaction of the nth order, the times taken to complete a certain fraction of the reaction are inversely proportional to the (n - i) power of the initial concentra- tion. In the experiments by Arrhenius, quoted on page 208, it will be noticed that in the second experiment, in which the con- centrations are less than J of those in the first experiment, the time taken to complete half the reaction is about three times as long in the former case as in the latter. Complicated Reaction Velocities In the present chapter, it has so far been assumed that chemical reactions proceed only in one direction, and are ultimately complete, or practically so, but in many cases these conditions are not fulfilled and the course of the reaction is complicated. The more im- portant disturbing causes are (a) side reactions; (b) counter reactions ; (c) consecutive reactions. Each of these will be briefly considered. (a) Side Reactions In this case the same substances react in two (or more) ways with formation of different products ; in general the reactions proceed side by side without influencing each other. An example is the action of chlorine on benzene, 1 which may substitute or form an additive product according to the equations 1 Slator, Trans. Chem. Soc., 1903, 83, 729. n6 OUTLINES OF PHYSICAL CHEMISTRY (1) C 6 H g + C1 2 - C 6 H 5 C1 + HC1, (2) C 6 H 6 + 3 C1 2 - C 6 H 6 C1 6 . The relative amounts of the products formed in side reactions depend on the conditions of the experiment, and it is usually possible so to choose the conditions that one of the reactions greatly predominates and can be investigated independently. (b) Counter Reactions This term is applied when the pro- ducts of a reaction interact to reproduce the original substances, so that a state of equilibrium is finally reached, all the re- acting substances being present (p. 201). Using the same terminology as before, the rate of formation of an ester, for example, will be represented by the differential equation The conditions can, however, usually be chosen in such a way that either the direct or the reverse reaction predominates, and the values of k and k^ can thus be determined separately. In this way it has been shown experimentally by Knoblauch 1 that the ratio k^k K, the equilibrium constant, as the theory requires (p. 158). (c) Consecutive Reactions Consecutive reactions are those in which the products of a chemical change react with each other or with the original substances to form a new substance or substances. They appear to be of very frequent occurrence (p. 212). A good example is the saponification of ethyl succi- nate, investigated by Reicher. It proceeds in the following two stages : ( i) C a H 4 (COOC 2 H B ) 2 + NaOH = W<' + C 2 H 5 OH, , , p /COOC 2 H 6 (2) C * H 4\ + NaOH = C 2 H 6 (COONa) 2 + C 2 H 6 OH, the product of the first reaction, ethyl sodium succinate, re- acting further with sodium hydroxide to form the normal sodium salt. 1 Zeitsch. physikal. Chem., 1897, 22, 268. VELOCITY OF REACTION. CATALYSIS 217 It is important to remember that when one of the reactions is very slow compared with the others, good constants cor- responding with the slow reaction are obtained, but when the rates are not very different, the observed velocity does not correspond with any simple order of reaction. CATALYSIS General We have already met with instances in which the rate of reaction is greatly increased by the presence of a third substance, which itself is unaltered at the end of the reaction. Thus cane sugar is hydrolysed very slowly by water alone, but the change is greatly accelerated by the addition of acids. Such phenomena are termed catalytic^ and the substance which exerts the catalytic or accelerating action is termed a catalysor or catalyst. Ostwald, to whom much of our knowledge of catalytic actions is due, defines a catalyst as " a substance which alters the velocity of a reaction, but does not appear in the end products ". From the point of view of the quantitative treat- ment of reaction velocities, it is important to note that the equa- tions already established remain valid in the presence of catalysts, the only effect of the latter being to alter the value of the velocity constant, k. The acceleration produced by a catalyst is in the majority of cases proportional to the amount of the latter added. 1 Characteristics of Catalytic Actions From the above it will be seen that the term catalysis does not include any explana- tion of the observed phenomena ; it is merely a classification of reactions which have certain features in common. In order to make clear the exact bearing of the term, some characteristics of catalytic actions will now be adduced. (a) The catalyst is usually present in relatively small concen- tration. This is, of course, connected with the fact that it is 1 One or two exceptions to this rule are known ; for example, the ac- celerating influence of iodine monochloride on the rate of reaction between chlorine and benzene is proportional to the square of the concentration of the catalyst (Slator, Zeitsch. physikal. Chem. t 1903, 45, 513). 218 OUTLINES OF PHYSICAL CHEMISTRY not used up during the reaction, so that a relatively small pro- portion of catalyst can effect the transformation of large amounts of the substance acted on. An apparent contradiction to this rule (as regards the small concentration of the catalyst) is the influence of the medium on the rate of reaction (p. 224), but this can scarcely be termed a true catalytic action. (b) The catalyst does not start a reaction, but only accelerates a change which can proceed of itself, though perhaps extremely slowly Although there is some difference of opinion with regard to the general validity of this statement, it is now fairly widely accepted, and seems to derive support from thermodyna- mical considerations. As an illustration, we may consider the combination of hydrogen and oxygen to form water. It is well known that the mixed gases can be kept at the ordinary tem- perature for an almost indefinite time without any apparent combination, but when brought in contact with platinum they combine fairly rapidly. It might at first sight be supposed that the platinum actually initiates the combination. However, when the gases are heated alone at 440, they combine with a measur- able velocity, and at lower temperatures still combination can be observed on long heating. Since the rate of reaction diminishes greatly with fall of temperature (p. 225), it can readily be under- stood that the rate of combination may be so slow at the ordinary temperature as not to be measurable. The alternative view is that the hydrogen and oxygen are not entering into combination at all at the ordinary temperature, that they are in a condition of unstable or false equilibrium and that the catalyst actually initiates the combination. A direct decision between these alternative hypotheses is difficult, but there is some evidence of the existence of false equilibria. For example, oxygen at fairly low pressures acts readily on phosphorus, but when the pressure reaches a certain value, which depends on the temperature, the reaction stops com- pletely, and there is an apparent equilibrium. The conditions determining this curious phenomenon are not well understood. VELOCITY OF REACTION. CATALYSIS 2I g The limit of pressure above which oxidation does not occur depends on the amount of moisture present, and doubtless also on the presence of traces of impurities. (c) The presence of a catalyst does not affect the equilibrium ; it alters the speed of the direct and inverse actions to the same extent The truth of the first part of this statement follows at once from the principle of the conservation of energy ; provided that the catalyst is not combined with any of the products when the reaction is complete, it does not produce any change in the energy content of the system. It has also been proved experi- mentally in many cases. Thus Kiister found that in the reaction represented by the equation 2SO 2 + O 2 = 2SO 3 , the same equi- librium point was reached in the presence of such different catalysts as platinum, ferric oxide and vanadium pentoxide. The second part of the above statement, that the catalyst alters the speed of the direct and inverse actions to the same extent, is a direct consequence of the first part. It has already been shown that the equilibrium constant K = k^k, so that, if k is increased, k must increase in the same ratio in order that K may remain constant. In accordance with this rule, Baker found that in the complete absence of water vapour, neither of the actions represented by the oppositely-directed arrows in the equation NH 4 C1 ^ NH 3 + HC1 took place, but the presence of moisture accelerated the dissociation of ammonium chloride, as well as its formation from its components. Examples of Catalytic Action. Technical Importance of Catalysis There appear to be very few chemical changes which cannot be accelerated by the addition of certain sub- stances, and many catalysts are known. Acids as a class accelerate many chemical changes, more particularly those of hydrolysis, such as the hydrolytic decomposition of cane sugar, of amides, esters, etc., but not of chloroacetic acid. 1 As the catalytic power is in general proportional to the extent to which the acid is split up into its ions, we ascribe the catalytic pro- 1 Senter, Trans. Chem. Society, 1907, 91, 460. 220 OUTLINES OF PHYSICAL CHEMISTRY perty to that which is common to all acids, namely, hydrogen ions. Only in dilute solution is there exact proportionality between hydrogen ion concentration and catalytic power. In stronger solutions, for a reason as yet unexplained, the catalytic activity increases more rapidly than the hydrogen ion concentration. Bases in some cases also exert a catalytic effect, as in the condensation of acetone to diacetonylalcohol, represented by the equation 2 CH 8 COCH 3 - CH 3 COCH 2 C(CH 8 ) 2 OH ; in this case the acceleration is proportional to the OH' ion concentration. Bases have also a powerfully accelerating action in certain isomeric changes of organic compounds. 1 The rare metals, more particularly finely-divided platinum, also accelerate many chemical reactions, especially oxidation reactions. Thus platinum is used commercially in the manu facture of sulphuric acid as a catalyst for the reaction 2SO 2 + O 2 = 2SO 3 , as well as in the oxidation of methyl alcohol to formaldehyde and of ammonia to nitric acid. Hydrogen and oxygen also combine to form water at the ordinary temperature in the presence of finely-divided platinum, and the same catalyst also accelerates the splitting up of hydrogen peroxide into water and oxygen. The latter reaction has been investigated fully by Bredig and his pupils, who used the platinum in so-called " colloidal " solution. The solution was obtained by passing the electric arc between platinum poles immersed in cold water ; under these circumstances the metal was torn from the poles and remained suspended in the water in a very finely- divided condition (p. 232). Another interesting catalyst is water vapour. It has been found, for example, that thoroughly dried carbon monoxide does not burn in thoroughly dried air, but when a trace of moisture is present, combination takes place at once. Reference has 1 Lowry and Magson, Trans. Chem. Society, 1908, 93, 107. VELOCITY OF REACTION. CATALYSIS 221 already been made to the fact that in the complete absence of moisture ammonium chloride can be volatilised without dissociation, and under the same circumstances ammonia and hydrogen chloride do not combine. As the water does not occur in the equation, it acts as a catalytic agent, but its mode of action is quite unknown. The importance of catalysis for technical processes will be clear from the above. Many important technical reactions are very slow, and the mixture has to be kept for a long period at a high temperature to complete them, which adds much to the cost of production. By using a suitable catalyst, the reaction may be completed at a much lower temperature, and in a much shorter time. As an illustration, the oxidation of naphthalene to phthalic acid by means of sulphuric acid an important step in the manufacture of indigo may be referred to. Under ordinary circumstances, the reaction is slow even at high tem- peratures. Owing to the accidental breaking of a thermometer on one occasion when the reagents were being heated together a little mercury fell into the mixture, and the observation that the reaction then proceeded much more rapidly led to the dis- covery that mercury was a catalyst for the reaction, and the whole process was thus rendered commercially successful. 1 The use of copper salts in the Deacon process production of chlorine by oxidation of hydrogen chloride with free oxygen and of oxides of nitrogen in the manufacture of sulphuric acid, are other examples of technical catalysis. Biological Importance of Catalysis. Enzyme Re- actions Catalysis is also of great importance in physiology and allied subjects, as the majority of the changes taking place in the living organism are accelerated by those organic catalysts the enzymes. When Berzelius brought forward the concep- tion of catalysis, he adduced among other illustrations the hydrolysis of cane sugar by invertase, and the hydrolysis of starch in the presence of an extract of malt. It is now generally recognised that these and allied changes, such as 1 Bwichte, 1900, 33, Appendix. 222 OUTLINES OF PHYSICAL CHEMISTRY alcoholic fermentation of certain sugars, are due to the action of catalysts of animal or vegetable origin which can be separated from the living cells without losing their activity, an d which are termed enzymes. In recent years much progress has been made with the investigation of enzyme reactions, and although little or nothing is known as to the nature of the catalysts themselves, no enzyme having so far been isolated in a state of purity, the laws followed by many enzymes have been satisfactorily elucidated. In general it may be said that enzymes behave like inorganic catalysts, but there are certain characteristic differences. Just as in the case of an inorganic catalyst, the acceleration pro- duced by an enzyme is in the first instance proportional to its concentration. The dependence of the speed of the reaction on the concentration of the substance acted on is, however, not so simple. To take a typical illustration, the rate of hydrolysis of cane sugar in the presence of a constant concen- tration of invertase increases with the concentration of the sugar in dilute solution, but beyond a certain concentration of sugar, further addition of the latter has no effect on the rate of the reaction. In contrast to this behaviour, the rate of inversion of cane sugar in the presence of a constant concentration of acid increases with the sugar concentration as far as the reaction has been followed. As in the case of other catalysts, we may expect that the enzyme will accelerate both the direct and inverse actions when the reaction is reversible. The experiments of Croft Hill, Emmerling, Kastle l and others, have shown that this expectation is justified. Mechanism of Catalysis The nature of catalysis becomes 1 Kastle and Loevenhart have shown that the reactions represented by the upper and lower arrows in the equation C 2 H B OH + C 8 H 7 COOH ^ C 8 H 7 COOC 2 H B + H a O (formation and hydrolysis of ethyl butyrate) are both accelerated by lipase, the enzyme which effects the hydrolysis of fats (Amer. Chem. J., 1900, 24, 491). VELOCITY OF REACTION. CATALYSIS 223 somewhat clearer when we represent reaction velocity, in a manner analogous to Ohm's law, by means of the equation Driving force Velocity = -^r r~- Resistance The driving force of a chemical reaction is the same thing as the free energy of the system (p. 149); of the resistance little or nothing is known. It is clear from the above equation that the velocity can be altered in two ways, by increasing the driving force and by lessening the resistance. A catalyst can- not to any extent affect the amount of energy in the system, and we must therefore assume that in some way it increases the velocity by diminishing the resistance. Ostwald compares the action of a catalyst to that of oil on a machine, and it is evident that the analogy is far-reaching. It may be asked whether all catalytic accelerations are due to a common cause. This is very unlikely ; it is much more probable that the mechanism of the acceleration varies with the nature of the catalyst and with that of the reacting sub- stances. The suggestion of Liebig, that the catalyst sets up certain molecular vibrations which lead to chemical changes, has proved quite unfruitful. So-called explanations of this nature, though often employed even at the present day, are bad in principle, as we know very little of the nature of molecular vibrations. It is, however, quite justifiable to inquire into the mechanism of catalytic actions, in so far as it can be elucidated by experimental investigation, and in recent years some light has been thrown on this subject. An explanation of catalytic acceleration which is much favoured is that it depends on the formation of intermediate compounds of the catalyst with the reacting substances. A reaction represented by the equation A -f B = AB may pro- ceed very slowly directly, but in the presence of a catalyst C it may proceed in the following two stages : (a) A + C = AC, (b) AC + B = AB + C, 224 OUTLINES OF PHYSICAL CHEMISTRY much more rapidly to the same final products. For example, it is known that the reaction SO 2 + O = SO 3 is a slow one, and the accelerating effect of nitric oxide on the combination may be represented in the following stages : (a) NO + O - N0 2 ; 0) SO 2 + NO 2 - SO 3 + NO. This explanation of the action of the oxides of nitrogen was suggested more than a century ago by Clement and Desormes, and remains the most plausible one at the present day. It is possible that the finely-divided metals act as catalytic agents mainly in a physical manner. In virtue of their large surface, these metals condense gases and to some extent dissolved sub- stances, and the local increase of concentration thus produced must greatly increase the rate of chemical change. Similar considerations may explain the catalytic effect of certain enzymes. A chemical explanation of the action of finely-divided metals and of enzymes based on the formation of intermediate compounds is, however, to be preferred. Nature of the Medium The rate of a chemical change depends greatly on the nature of the medium in which it takes place, but the way in which the influence is exerted is quite unknown. The most complete data on this subject are due to Menschutkin, who determined the rate of combination of triethylamine and ethyl iodide, represented by the equation (C 2 H 6 ) 8 N + C 2 H 5 I - (C 2 H 6 ) 4 NI in more than twenty solvents at 100 A few typical results are given in the accompanying table, in which , as usual, represents the velocity constant :- Solvent* k. Dielectric Constant. Hexane 0*00018 1-86 (12-3) Ethyl ether 0*000757 4-36 (18) Benzene 0*00584 2-26 (19) Ethyl alcohol 0*0366 2i'7 (i5) Methyl alcohol 0*0516 32-5 (16) Acetone 0*0608 21-8 (15) VELOCITY OF REACTION. CATALYSIS 225 It will be seen that the rate varies enormously with change of medium ; thus the ratio of the velocities in hexane and acetone is approximately i : 340. It is interesting to inquire whether there is any other pro- perty of the different media which is parallel to the effect on the reaction velocity. It was suggested on theoretical grounds by J- J- Thomson, and somewhat later by Nernst, that the " dissociating power of the medium " must be greater the higher its specific inductive capacity or, to use the more modern term, its dielectric constant. The dielectric constants of the media are given in the third column of the table, and it will be seen that there is a distinct parallelism, though not direct proportionality, between dielectric constant and reaction velocity. This question will be again referred to at a later stage. Even a small change in the medium has sometimes a re- markable effect on the rate of reaction. Thus it has recently been shown that the rate of reaction between pure sulphuric acid and oxalic acid is reduced to 1/17 of its original value by the addition of o'i per cent, of water to the reaction mixture. On the other hand, a considerable alteration in the medium may have very little effect on the velocity. Thus the rate of reaction between chloracetic acid and silver nitrate, represented by the equation CH 2 C1CO 2 H + AgNO 3 + H 2 O - CH 2 OHCO 2 H + AgCl + HNO 3 is practically the same in water and in 45 per cent, alcohol. Influence of Temperature on the Rate of Chemical Reaction It is a matter of common experience that the rate of chemical reactions is greatly increased by rise of temperature. Thus the combination of hydrogen and oxygen is so slow at the ordinary temperature that it cannot be detected (p. 218), but at high temperatures it proceeds with explosive rapidity. It has already been pointed out that rise of temperature does not usually affect the form of the velocity equation ; it can be 15 226 OUTLINES OF PHYSICAL CHEMISTRY represented simply as altering the magnitude of the velocity constant. The more important facts in this connection are well illustrated in the following table, which represents the effect of temperature on the magnitude of the velocity constant for the unimolecular reaction between dibromosuccin ic acid and water, represented by the equation C 2 H 2 Br 2 (COOH) 2 =. C 2 HBr(COOH) 2 + HBr. Temperature. k (time in minutes). Temperature, k (time in minutes). 15 0*00000967 70*1 0*00169 40 0*0000863 80*0 0*0046 50 0*000249 89*4 0*0156 60*2 0*000654 101*0 0*0318 The table shows (i) that the velocity increases enormously with rise of temperature ; at 15 and 101 the relative rates are in the ratio 0*00000967: 0*0318 or i : 3300; (2) the ratio for a rise of 10 is approximately the same at different tem- peratures, thus ^0/^70 = 2 '7 2 > ^50/^40 = 2 ' 88 - Ifc is import- ant to remember that the rate of most chemical reactions, as in the above example, is doubled or trebled for a rise of 10, This is shown in the accompanying table, which gives the quo- tient for 10 (kt+tflkt) for a few typical chemical reactions. 1 1 The third column contains the average value of the quotient for 10 be- tween the temperatures of observation. As data are not always available at intervals of 10, the average value of kt+io jkt may be calculated approxi- mately from the equation Iog 10 * 2 - logjA = A (T, - Tj) where k l and k% are the velocity constants at the temperatures Tj and T 2 respectively. (See next section.) This equation gives us the value of A, and the quotient for 10 is given by l gv>(kt+ io)/& = IOA or *L+J_2 = i iOA kt As an example, we will work out the quotient for 10 for the inversion of cane sugar from the data given in the table. Log 10 35-5 - Iog 10 0765 is 1*66657 and as T t - T l = 300 we obtain A <= 0-05555. Hence Iog 10 (kt + io)lkt 0^555 and (kt + io)/fa = 3*60 approximately. VELOCITY OF REACTION. CATALYSIS 227 Reaction. Velocity Constants. Quotient for 10. AsH 3 = As + 3H . ^256 = 0*00035 367 = 0*0034 I-2 3 2 NO = N 2 + O 2 ^689 = 39*63 1347 = 191800 1*17 CH 3 COOC 2 H 5 + NaOH 9.4=2-307 44.90 = 21-648 1*89 CH 2 ClCOONa + NaOH 70 = 0*00089 102 = 0-015 2 '5 CH 2 ClCOONa + H 2 O . 70 = 0*000042 10 = 0*00170 3*2 C 2 H 5 ONa + CH 3 I 0=30-00336 30 = 2*125 3*34 Inversion of cane sugar . 25 = 0-765 ^55=35*5 3*6 H 2 O 2 = H 2 O + O 10 = 0-0180 1-5 Fermentation by yeast . 10-20 3-8 30-40 r6 The quotient for 10 for reactions in solvents other than water is also between 2 and 3 in the majority of cases. According to the molecular theory, rise of temperature ought to increase the rate of chemical change, owing to the accelerating effect on molecular movements. This effect, however, would only increase proportionally to the square root of the absolute tempera- ture (p. 32), and it can easily be calculated on this basis that the quotient for 10 for a bimolecular reaction at the ordinary temperature would be about 1*04, much too small to account for the large temperature coefficient actually observed. Up to the present, no plausible explanation of the great magnitude of the temperature coefficient of chemical reactions has been given. The only other property which appears to increase as rapidly with temperature is the vapour pressure, and it is not improbable that there is a close connection between vapour pressure and chemical reactivity. At moderate temperatures the temperature coefficients of enzyme reactions are approximately the same as those of chemical reactions in general, but at temperatures in the neigh- bourhood of o, the rate of change of k with the temperature is often abnormally high, as the table shows. It is interesting to note that the rate of development of organisms, for example, the rate of growth of yeast cells, the rate of germination of certain seeds, and the rate of develop- 228 OUTLINES OF PHYSICAL CHEMISTRY ment of the eggs of fish, is also doubled or trebled for a rise of temperature of 10, and it has therefore been suggested that these processes are mainly chemical. Formulae connecting Reaction Velocity and Tempera- ture As has already been pointed out (p. 167), the law con- necting the displacement of equilibrium with temperature is known. So far, however, no thoroughly satisfactory formula showing the relationship of rate of reaction and temperature has been established, although many more or less satisfactory empirical formulae have been suggested. If the relationship which has been shown to hold approximately for the rate of de- composition of dibromosuccinic acid that the quotient for 10 is the same at high as at low temperatures holds in general, the equation connecting k and T must be of the form fc)/ those travelling towards the cathode cations. We will now consider the relationship between the amount of chemical action and the quantity of electricity passed through a solution. The amount of chemical action might be estimated by measuring the volume of gas liberated at one of the poles, or by the amount of metal deposited on an electrode. This question was investigated by Faraday, and as a result he established a law which bears his name, and which may be enunciated as follows : For the same electrolyte, the amount of chemical action is proportional to the quantity of electricity which passes. 1 Further, Faraday measured the relative quantities of substances liberated from different solutions by the same quantity of electricity, and was thus led to the discovery of his so-called second law : The quantities of substances liberated at the elec- trodes ivhen the same quantity of electricity is passed through different solutions are proportional to their chemical equivalents. The chemical equivalent of any element (or group of elements) is equal to the atomic weight (or sum of the atomic weights) divided by the valency. The second law, therefore, states that if the same quantity of electricity is passed through solutions of sodium sulphate, cuprous chloride, cupric sulphate, silver nitrate and auric chloride, the relative amounts of hydrogen and the metals liberated are as follows : Electrolyte Na2SO 4 CuCl CuSO 4 AgNO 3 AuCl 3 f ; Cu = *; Cu = 6 -f<; A. - ?; Au=f The above result may also be expressed rather differently as follows : The electrochemical equivalents (the proportions of different elements set free by the same current) are proportional to the chemical equivalents. That quantity of electricity which passes through an electro- lyte when the chemical equivalent of an element (or group of 1 Faraday measured the amount of electricity by its action on a mag- netic needle. 238 OUTLINES OF PHYSICAL CHEMISTRY elements) in grams is being liberated will obviously be a quantity of very considerable importance in electrochemistry. Since i ampere in i second (a coulomb) liberates 0-00001036 grams of hydrogen, it follows that when the chemical equivalent of hydrogen or any other element is liberated, 1/0-00001036 = 96540 coulombs must pass through the electrolyte. It is often designated by the symbol F (faraday). One cou- lomb will liberate 35*45 x 0-00001036 0*000368 grams of chlorine, 127x0*00001036 = 0-001316 grams of iodine, and 108 x 0*00001036 = 0-001118 grams of silver. Mechanism of Electrical Conductivity It has already been pointed out (p. 236) that during the electrolysis of sodium sulphate the products of electrolysis appear only at the poles, the main bulk of solution between the poles being apparently unaffected. This is most readily accounted for on the view that part of the solute is moving towards the positive and part towards the negative pole, these moving parts being termed anions and cations respectively. We now assume further that the cations are charged with positive electricity, and move towards the negatively charged cathode owing to electrical attraction ; similarly, the negatively charged anions are attracted to the cathode. When the ions reach the poles, they give up their charges, which neutralize a corresponding amount of the opposite kinds of electricity on the anode and cathode respec- tively, and then appear as the elements or compounds we are familiar with. The process of electrolysis is illustrated in Fig. 29. Into the vessel containing sodium sulphate solution dip two electrodes (on opposite sides of the vessel) connected with the positive and negative poles of the battery respectively. The direction of motion of the ions to the oppositely-charged poles is illustrated by the arrows. It is not always an easy matter to say what the moving ions are. It is only rarely that they are set free as such, since secondary reactions often take place at the electrodes. When a strong solution of cupric chloride is electrolysed, copper ELECTRICAL CONDUCTIVITY 239 and chlorine are liberated at the cathode and anode respectively, and it is probable that these substances are the ions. In the case of sodium sulphate, however, for which hydrogen and oxygen are the products of electrolysis, secondary reactions must take place. The current is in all probability conveyed through the solution by Na and SO 4 ions. When the former reach the cathode, they give up their charges and form metallic sodium, which immediately reacts with the water, forming sodium hydroxide and hydrogen. In the same way the SO 4 ions, on reaching the anode, give up their charges, and the free SO 4 group then reacts with the water according to the equation SO 4 + H 2 O = H 2 SO 4 + O, oxygen being liberated and sul- phuric acid regener- ated. In this way the phenomena al- ready described are readily accounted for. So far, we have assumed that the material of the elec- trodes is not acted on by the products of electrolysis. This is generally true when the electrodes are made of platinum or other resistant FIG. 29. metal, but in other cases secondary reactions take place between the discharged ions and the poles. Thus when a solution of copper sulphate is electrolysed between copper poles, the SO 4 ions, after losing their charges, react with the anode according to the equation Cu + SO 4 = CuSO 4 , so that the net result of the electrolysis of copper sulphate between copper poles is the transfer of copper from the anode to the cathode. 240 OUTLINES OF PHYSICAL CHEMISTRY We have assumed that in a solution of sodium sulphate the moving ions are Na and SO 4 . As the Na ion moves towards the negative electrode, it must already be positively charged ; this may be indicated thus : Na (Fig. 29), or, more concisely, by a dot, thus : Na*. As neither positive nor negative elec- tricity accumulates in the solution during electrolysis, the amount of positive electricity neutralized on the anode must be equivalent to that neutralized on the cathode. Hence, since two sodium ions are discharged for every SO 4 ion, the latter must carry double the amount of electricity that a sodium ion carries, and this is indicated by the symbols SO 4 or SO 4 " (Fig. 29). According to our present views, the metallic components of salts in solution are positively charged, the number of charges corresponding with the ordinary valencies of the metals. Some important cations are K', Na*, Ag*, NH 4 ', Ca", Hg 2 ", Hg", Fe", Fe"*, etc. The remainder of the salt molecule constitutes the negative ion, which, like the positive ion, may have one, two or more (negative) electric charges. Among the more important anions are Cl', Br', I', NO 3 ', SO 4 ", CO 3 ", PO 4 '", etc. Acids and bases deserve special consideration from this point of view. Since salts are derived from acids by replacing the hydrogen by metals, it is natural to suppose that the positive ion in aqueous solutions of acids is H', and that the remainder of the molecule constitutes the negative ion. On the other hand, aqueous solu- tions of all bases contain the OH' group. These points are dealt with fully at a later stage. Freedom of the Ions before Electrolysis The fact that the ions begin to move towards the respective electrodes im- mediately the current is made appears to indicate that they are electrically charged in the solution before electrolysis is com- menced. The questions therefore arise as to the state of such a salt as sodium chloride in dilute solution, and as to what occurs when the circuit is completed. The view long held was that the atoms are united to form a molecule, NaCl, at least ELECTRICAL CONDUCTIVITY 241 partly owing to the electrical attraction of their contrary charges, and that the current pulls them apart during electrolysis. Careful measurements show, however, that Ohm's law holds for electro- lytes, from which it follows that the electrical energy expended in electrolysis is entirely used up in overcoming the resistance of the electrolyte, so that no work is done in pulling apart the components of the molecule. On the basis of this observation, and in agree- ment with certain views previously enunciated by Williamson as to the kinetic nature of equilibrium in general (cf. p. 160), Clausius showed that the equilibrium condition in electrolytes cannot be such that the ions of contrary charge are firmly bound together ; on the contrary, the equilibrium must be of a kinetic nature, so that the ions are continuously exchanging partners, and must, at least momentarily, be present in solution as free ions. The average fraction of the ions free under definite conditions of temperature and dilution was not estimated by Clausius, but he considered that the fraction was probably very small. Clausius 's theory accounts for the qualitative phenomena of electrolysis, as during their free intervals the ions would be progressing towards the oppositely charged poles, and would finally reach them and be discharged. The views of Clausius were further developed in 1887 by Arrhenius/who first showed how the fraction of the molecules split up into ions could be deduced from electrical conduc- tivity measurements, and independently from osmotic pressure measurements. This constitutes the main feature of the theory of electrolytic dissociation, which is dealt with in detail later (p. 260), and the fact that the two methods for determining the fraction of the molecules present as free ions gave results in very satisfactory agreement contributed much to the general acceptance of the theory. In a normal solution of sodium chlo- ride, then, there is an equilibrium between free ions and non- ionised molecules, represented by the equation NaCl ^ Na- + Cl', in which, according to Arrhenius, about 70 per cent, of the salt is ionised and the remaining 30 per cent, is present as 1 Zeitsch. physikal. Chern., 1887, I, 631. 242 OUTLINES OF PHYSICAL CHEMISTRY NaCl molecules. According to this theory, the electrical con- ductivity is determined exclusively by the free ions, and not at all by the non-ionised molecules or by the solvent. Dependence of the Conductivity on the Number and Nature of the Ions We are now in a position to form a picture of the mechanism of electrical conductivity in a solu- tion. Suppose there are two parallel electrodes i cm. apart (Fig. 29) with the electrolyte between them, and that the differ- ence of potential between the electrodes is kept constant, say at i volt. Before the electrodes are connected with the battery, the ions are moving about in all directions through the solution. When connection is made in other words, when the electrodes are charged they exert a directive force on the charged ions, which move towards the poles with the contrary charges. Those nearest the poles arrive first, give up their charges to the poles, thus neutralising an equivalent amount of electricity on the latter, and then either appear in the ordinary uncharged form (e.g., copper), react with the solvent (e.g., SO 4 when platinum electrodes are used), with the electrodes (e.g., SO 4 with copper electrodes), or with each other. It will be seen that the process does not consist in the direct neutralisation of the electricity on the positive electrode by that on the negative electrode, but part of the charge on the anode is neutralised by the anions, whilst an equivalent amount of charge on the cathode is neutralised by the cations a process which has the same ultimate effect as direct neutralisation. On this basis it is clear that with a constant E.M.F. the rate at which the charges on our two plates are neutralised, in other words, the conductivity of the solution between them, depends on three things : (i) the number of carriers or ions per unit volume ; (2) the load or charge which they carry ; (3) the rate at which they move to the electrodes. Each of these factors will now be briefly considered. (i) The Number of Ions Other things being equal, the conductivity of a solution will clearly be proportional to the ELECTRICAL CONDUCTIVITY 243 number of ions per unit volume. For the same electrolyte, the number of ions can, of course, be varied by varying the concentration of the solution. In general, it may be said that on increasing of concentration the ionic concentration also in- creases, but the exact relationship will be dealt with later. For different electrolytes of the same equivalent concentration, the conductivity will depend on the extent to which the solute is split up into its ions and on their speed. (2) The Charge Carried by the Ions As has already been pointed out, there is a simple relationship between the capacity of different ions for transporting electricity, since the gram- equivalent of any ion (positive or negative) conveys 96,540 coulombs. Thus if in an hour ( = 3600 seconds) a gram-equiva- lent of sodium (23 grams) and of chlorine (35*47 grams) are discharged at the respective electrodes, the current which has passed through the cell is 96 ' 54 - 26-8 amperes. 3600 (3) Migration Velocity of the Ions In this section we will for simplicity consider only univalent ions, but the same considerations apply to all electrolytes. Since positive and negative ions are necessarily discharged in equivalent amount (p. 240), and the number of positive and negative univalent ions discharged in a given time is therefore equal, it might be supposed that the ions must travel at the same rate. This, however, is by no means the case. Our knowledge of this subject is mainly due to Hittorf, who showed that the relative speeds of the ions could be deduced from the changes in concen- tration round the electrodes after electrolysis. The effect of the unequal speeds of the ions on the concen- trations round the poles is made clear by the accompanying scheme (Fig. 30), a modified form of one given by Ostwald. The vertical dark lines represent the anode and cathode respec- tively, and the dotted lines divide the cell into three sections, those in contact with the electrodes being termed the anode 244 OUTLINES OF PHYSICAL CHEMISTRY and cathode compartments respectively. The positive ions are represented by the usual + sign, and the negative ions by the - sign. I. represents the state of affairs in the solution before connection is made ; the number of anions is the same as that of the cations, and the concentration is uniform throughout. The remaining lines represent the state of affairs in the solution after electrolysis on different assumptions as to the relative I. ff. -1- -f -h + + + 4- -t- + t f + +4 4- -h -f- f 4 4- 4- + -f 4- -f -1- 4-f + + f -i- f *- \ + 4- 4- -1- f + + 4- f -f -f FIG. 30. speeds of the ions. Suppose at first that only the negative ions move. The condition of affairs in the solution when all the negative ions have moved two steps to the left is shown in II. Each ion left without a partner is supposed to be dis- charged, and the figure shows that although the positive ions have not moved an equal number of positive ions is discharged. Further, whilst the concentration in the anode compartment has not altered during the electrolysis, the concentration in the cathode compartment has been reduced by half. Suppose now that the positive and negative ions move at the same rate. The state of affairs when each ion, positive or ELECTRICAL CONDUCTIVITY 245 negative, has moved two steps towards the oppositely-charged pole is represented in III. It is evident that four positive and four negative ions have been discharged, and that the con- centration of undecomposed salt has diminished in both com- partments, and to the same extent, namely by two molecules. Finally, let us assume that both ions move, but at unequal rates, so that the positive ions move faster than the negative ions in the ratio 3:2. The state of affairs when the positive ions have moved three steps to the right, and the negative ions two steps to the left, is shown in IV. It is clear that five positive and five negative ions have been discharged, and that whilst there is a fall of concentration of two molecules round the cathode, there is a fall of three round the anode. These results show that the fall of concentration round any one of the electrodes is proportional to the speed of the ion leaving it. In II., for example, there is a fall of concentration round the cathode, but not round the anode, corresponding with the fact that the anion moves, but not the cation. Similarly, in III., the fall of concentration round anode and cathode is equal, corresponding with the fact that the anion and cation move at the same. Finally, in IV., fall round anode : fall round cathode 1:3:2, corresponding with the fact that speed of cation : speed of anion = 3:2. From these examples we obtain the important rule that Fall of concentration round anode _ speed of cation Fall of concentration round cathode speed of anion The student often finds a difficulty in understanding how, as in IV., five ions can be discharged at the anode when only two anions have crossed the partitions. To account for this, it must be assumed that there is always an excess of ions in contact with the electrodes, so that more are discharged than actually arrive by diffusion. The speed of the cations is often represented by u, and that of the anions by v. The total quantity of electricity (say, unit 246 OUTLINES OF PHYSICAL CHEMISTRY quantity) carried is proportional to (u + v), and, of this total n = vj(u + v) is carried by the anions and i - n = uj(u + v) by the cations. , the fraction of the current carried by the anion, is termed the transport number of the anion ; similarly, i - n is the transport number of the cation. It is evident from the figure that there is a central section of the cell between the dotted lines in which no change of con- centration takes place when elec- trolysis is not carried too far. Therefore, in order to investigate the changes in concentration, it is simply necessary to remove the solutions round the electrodes after electrolysis and analyse them, but the experiment will only be successful if the intermediate layer has not altered in strength, Practical Determination of the Relative Migration Velo- cities of the Ions The experi- ment may conveniently be made in the modified form of Hittorf s apparatus used in Ostwald's labo- ratory (Fig. 31). It consists of two glass tubes communicating towards the upper ends ; one of them is closed at the lower end, and the other provided with a stopcock, as shown. The elec- trodes, A and K, are sealed into FIG. 31. glass tubes which pass up through the liquid, and communication with a battery is made in the usual way by means of wires which pass down the interior of the glass tubes. As an illustration, the determination of the transport numbers ELECTRICAL CONDUCTIVITY 247 of the Ag' and NO 3 ' ions in a solution of silver nitrate will be described. The anode A is of silver, and should be covered with finely-divided silver by electrolysis just before the experiment; the cathode is of copper. The electrodes are placed in position, the anode compartment filled up to the connecting tube with 1/20 normal silver nitrate, the cathode compartment up to B with a concentrated solution of copper nitrate, and finally the apparatus is carefully filled up with the silver nitrate solution in such a way that the boundary between the two solutions at B remains fairly sharp. The cell is then connected in series with a high adjust- able resistance, an ammeter, and a sil/er voltameter, and then joined to the terminals of a continuous current lighting circuit (no volts) in such a way that the silver pole becomes the anode. By means of the variable resistance, the current is so adjusted that a current of about o'oi ampere is obtained (to be read off on the ammeter), and the electrolysis continued for about two hours. Finally, a measured amount (about 3/4) of the anode solution is run off and titrated with thiocyanate in the usual way. The strength of the current can be read off on the ammeter, and from this and the time during which the current has passed, the total quantity of electricity passed through the solution can be calculated. It is, however, prefer- able to employ for this purpose the silver voltameter above referred to. It consists of a tube with stopcock similar to the left-hand part of the transport apparatus (Fig. 31), and is provided with a silver electrode (to serve as anode) similar to that in the other apparatus, and placed in a corresponding position (in the lower part of the tube). The tube is filled to 3/4 of its length with a 15-20 per cent, solution of sodium or potassium nitrate, and carefully filled up with dilute nitric acid so that the two solutions do not mix. The cathode, of platinum foil, dips in the nitric acid. During electrolysis, the NO 3 ' ions dissolve silver from the anode, and by titrating the whole of the contents with ammonium thiocyanate after the experiment, the amount of silver in solution can be determined, and from this 248 OUTLINES OF PHYSICAL CHEMISTRY the quantity of electricity which has passed through the solution can readily be calculated (p. 238). We now return to the transport apparatus. For our purpose it will be sufficient to deal only with the change of concentra- tion in the anode compartment. From this the transport number of the cation is obtained, and the transport number of the anion is then at once obtained by difference. During electrolysis, the silver concentration round the anode diminishes owing to migration of silver ions towards the cathode. The process may conveniently be illustrated by III. of Fig. 30 where the fall owing to migration is from 4 to 2. At the same time, however, NO 3 ions reach the anode, and after being discharged dissolve silver from it, the silver concentration in the anode compartment therefore increasing. The latter effect is the same as that taking place simultaneously in the silver volta- meter, as described above, and therefore, if no silver migrated from the anode, the total increase of concentration in this com- partment would be equal to that in the silver voltameter, which, as explained above, is a measure of the total quantity of electricity which passes ; we will term this a. If b is the (unknown) change in concentration due to the migration of the silver ions, the observed change in concentration at the anode will be a b. As a is known, and a b is found by titrating the anode solution after the experiment, b can readily be obtained. In practice, the greater part of the anode solution after electrolysis is run into a beaker, it is then weighed or an aliquot part measured, and titrated. The calculation of the results will be rendered clear from the details of an experiment made in Ostwald's laboratory. Before the experiment 12*31 grams of the silver nitrate solution re- quired 26-56 c.c. of a 1/50 n potassium thiocyanate solution, so that i gram of solution contained 0*00739 grams of silver nitrate. After the experiment, 23-38 grams of the anode solution required 69-47 c.c. of the thiocyanate solution, cor- ELECTRICAL CONDUCTIVITY 249 responding to 0*2361 grams of silver nitrate. The solution, therefore, contained 23*14 grams of water, which before the experiment contained 23*14 x 0*00739 = 0*1710 grams of silver nitrate, hence the increase of concentration at the anode is 0*0651 grams = a b. The contents of the silver volta- meter required 36*16 c.c. of thiocyanate = 0*1229 grams of silver nitrate = a ; the same amount is dissolved at the anode in the transport apparatus. As the actual increase of con- centration was only 0*0651 grams, 0*1229 0*0651 = 0*0578 grams of silver must have left the anode compartment by migra- tion. Hence the transport number for silver is u 0*0578 ! _ n = _ _ = 0*470, u + v 0*1229 and for the NO 3 ' ion v 0*0651 - 0-530. u + v 0*1229 Hence, of the total current 47 per cent, is carried by the silver ions, and 53 per c^nt. by the NO 3 ' ions. It was shown by Hittorf that the transport numbers are practically independent of the E.M.F. between the electrodes, but depend to some extent on the concentration and on the temperature. It is remarkable that at higher temperatures they tend to become equal. Some of the numbers are given in the next section. Specific, Molecular and Equivalent Conductivity Just as in the case of metallic conduction, the resistance of an electro- lyte is proportional to the length, and inversely proportional to the cross-section of the column between the electrodes. Hence we may define the specific resistance of an electrolyte as the resistance in ohms of a cm. cube, and its specific conductivity as i /specific resistance, expressed in reciprocal ohms. Since, however, the conductivity does not depend on the solvent but on the solute, it is much more convenient to deal with solutions containing quantities of solute proportional to the respective molecular weights. The so-called molecular conductivity^ /*, is 250 OUTLINES OF PHYSICAL CHEMISTRY most largely used in this connection ; it is the conductivity, in reciprocal ohms, of a solution containing i mol of the solute when placed between electrodes exactly i cm. apart. It may also be defined as the specific conductivity, *, of a solution, multiplied by #, the volume in c.c. which contain a mol of the solute. Hence we have /JL = KV. As an example, the following values for the specific and mole- cular conductivities of solutions of sodium chloride at 18, as given by Kohlrausch, may be quoted. Sp. Con- Molecular Concentration of Solution. ductivity, Conductivity, K. KV. 1*0 molar (v= 1,000) 0*0744 74-4 o'i molar (#= 10,000) 0^00925 92-5 o'oi molar (v~ 100,000) 0-001028 102*8 0*001 molar (v= 1,000,000) 0*0001078 107*8 0*0001 molar (v= 10,000,000) 0*00001097 109*7 It will be noticed that the molecular conductivity as defined above increases at first with dilution, but beyond a certain point remains practically constant on further dilution. These numbers enable us to illustrate more fully the physical meaning of the molecular conductivity. Imagine a cell of i cm. cross-section and of unlimited height, two opposite walls through- out the whole height acting as electrodes. If a litre of a molar solution of sodium chloride is placed in the cell, it will stand at a height of 1000 cms. We may regard the solution as made up of cm. cubes, 1000 in number, and if the con- ductivity of one of these cubes the specific conductivity is K P the total conductivity (in other words the molecular con- ductivity) is looo/cj. If now another litre of water is added, the height of the solution will be 2000 cms. and its molecular con- ductivity is now 2oooK 2 , where * 2 is the specific conductivity of the half-molar solution. In exactly the same way, the mole- cular conductivity may be determined at still greater dilutions. From the above it is clear that a measure of the conducting ELECTRICAL CONDUCTIVITY 251 power of a mol of the electrolyte in different dilutions is ob- tained by multiplying the volume in c.cs. in which the electrolyte is dissolved by its specific conductivity at that dilution, or in symbols //,= KV as given above. A glance at the last two lines in the table helps us to under- stand the approximately constant value of jm in very dilute solutions. When the solution is diluted from i/iooo to 1/10,000 molar, the specific conductivity is reduced to about i/io, but as the volume is ten times as great, the molecular conductivity is only slightly altered. Besides the molecular conductivity, the term equivalent con- ductivity, A, is sometimes used. As the name implies, it is the specific conductivity of a solution multiplied by the volume in c.c. which contains a gram-equivalent of the solute. Kohlrausch's Law. Ionic Velocities The numbers in the third column of the above table show that the molecular conductivity of sodium chloride increases, at first rapidly and then very slowly, with dilution. This subject was investigated for a number of solutions by Kohlrausch, who found that for solutions of electrolytes of high conductivity (salts, so-called " strong " acids and bases) the molecular conductivity increases with dilution up to about i/ioooo molar solution, and beyond that point remains practically constant on further dilution. Kohlrausch showed further that this limiting value of the mole- cular conductivity, which may be represented by /x,^, is different for different salts, and may be regarded as the sum of two inde- pendent factors one pertaining to the cation or positive part of the molecule, the other to the anion, or negative part of the molecule. This experimental result is termed Kohlrausch's law, and is readily intelligible on the basis of the theory of electrical conductivity developed above. The limiting value of the mole- cular conductivity is reached when the molecule is completely split up into its ions ; under these circumstances the whole of the salt takes part in conveying the current. For simplicity we will consider solutions of binary electrolytes. In very dilute 252 OUTLINES OF PHYSICAL CHEMISTRY equimolar solutions of different electrolytes, the number of the ions and their charges are the same, and the observed differences of /LQQ can only be due to the different speeds of the ions. The limiting molecular conductivities of binary electrolytes are therefore proportional to the sum of the speeds of the ions, and when the units are properly chosen we have /*oo = u + v> where u is the speed of the cation, v that of the anion. This is the mathematical form of Kohlrausch's law, and expresses the very important result that in sufficiently dilute solution the speed of an ion is independent of the other ion present in solution. From the results of conductivity measurements, only the sum of the speeds of the ions can be deduced, but, as has already been shown, the relative values iof u and v can be obtained from the results of migration experiments (p. 246). It was found by Kohlrausch that the value of JUL^ u + v for silver nitrate at 18 is 115*5. The accurate value for the transport number of the anion, NO 3 ', is n = v/(u-+ v) = 0-518. Hence v = 0*518 x 115*5 = 6o % 8 and u = 0-482 x 115*5 = 55*7. The values of u and #, expressed in these units, are termed the ionic velocities^ under the conditions of the experi- ment. The accompanying table gives the ionic velocities, calculated from the results of conductivity and transport measure- ments, for some of the more common ions in infinite dilution x at 1 8, expressed in the same units as the molecular conductivity of sodium chloride (p. 250) : H- -318 Li- =36 OH' =174 K- - 65 NH 4 - - 64 Cl' = 66 Na- = 45 Ag- =56 I' =67 NO 3 '= 6 1 It is interesting to observe that the velocity of the H- ion is relatively very high, about five times as great as that of any of the metallic ions. The ion which comes next to it is the OH' ion, 1 The more concentrated the solution, the smaller are the ionic velocities, owing to the increased resistance to their motion. ELECTRICAL CONDUCTIVITY 253 the speed of which is more than half that of the H* ion, and much greater than that of any of the other ions. Since the conductivity of a solution is, as we have already seen, propor- tional to the speed of the ions, it follows that the solutions of highly ionised acids and bases will have a relatively high con- ductivity. Thus, under conditions otherwise equal as regards concentration, ionisation, temperature, etc., the conductivities of dilute solutions of hydrochloric acid and of sodium chloride will be in the ratio (318 + 66) = 384 to (45 + 66) = in, or about 3*5 : i. Absolute Yelocity of the Ions. Internal Friction The absolute velocity of the ions is proportional to the E.M.F. between the electrodes, and inversely proportional to the re- sistance offered to their passage by the solvent. When the fall of potential is one volt per c.m. (/.*., when the difference of potential between the electrodes is x volts and the distance be- tween them is x cm.) it can be shown (p. 414) that the absolute velocities, in cm. per second, are obtainable from the values for the ionic velocities given above by dividing by 96,540 or, what is the same thing, by multiplying by 1*036 x io~ 5 . Hence the absolute velocity of the hydrogen ion is, under the conditions described, 318 x 1-036 x io~ 6 = 0-00332 cm. per second, and of the potassium ion 0*00067 cm. per second at infinite dilution. The speed of the ions is therefore extremely low ; even the hydrogen ions, under a driving force of i volt per cm., only move about twice as fast as the extremity of the minute hand of an ordinary watch. This very slow motion of the moving particles indicates that the resistance to their passage through the solvent is very great. Kohlrausch has calculated that the force required to drive a gram of sodium ions through a solution at the rate of i cm. per second is 153 x io 6 kilograms weight, or about 150,000 tons weight. The absolute velocity of the ions can also be measured directly by a method the principle of which is due to Lodge, and which may be illustrated by an experiment described by 254 OUTLINES OF PHYSICAL CHEMISTRY Danneel. A U-tube is partly filled with dilute nitric acid, and in the lowest part of the tube a solution of potassium permanganate, the specific gravity of which has been increased as much as possible by the addition of urea, is carefully placed, by means of a pipette, in such a way that the boundary between the acid and the permanganate remains sharp. When platinum electrodes are dipped in the nitric acid in the two limbs, and a current passed through the solution, the violet boundary (due to the coloured MnO 4 ' ion) moves towards the anode. From the observed speed of the boundary and the difference of potential between the poles, the speed of the ion for a fall of potential of i volt/cm, is obtained, and has been found to agree exactly with the value obtained by conductivity and transport measurements. This method is not confined to salts with coloured ions, but the moving boundary can also be observed with colourless solutions when, as is usually the case, the refractive index of the two solutions is different. There are, of course, two boundaries, one due to the positive ions moving towards the cathode, and the other due to the negative ions moving towards the anode. When the conditions are such that both can be observed, the relative speeds give the ratio u/v directly. Measurements of ionic velocities on this principle have been made by Masson, Steele and others, and the results are in entire agreement with those obtained indirectly. Experimental Determination of Conductivity of Elec- trolytes The measurement of the conductivity of conductors of the first class is a very simple operation. Until compara- tively recently, however, no very satisfactory results for the conductivity of electrolytes could be obtained, because when a steady current is passed through a solution between platinum electrodes the products of electrolysis accumulate at the poles and set up a back E.M.F. of uncertain value, a phenomenon known as polarization (p. 373). This difficulty is, however, com- pletely got over by using an alternating instead of a direct ELECTRICAL CONDUCTIVITY 255 current (Kohlrausch, 1880) ; by the rapid reversal of the current the two electrodes are kept in exactly the same condition, and there is no polarization. The arrangement of the apparatus, which in principle amounts to the measurement of resistance by the Wheatstone bridge method, is shown in Fig. 32. R is a resistance box, S a cell with platinum electrodes, between which is the solution the resistance of which is to be measured, ab is a platinum wire of uniform thickness, which may conveniently be a metre long, and is stretched along a board graduated in millimetres, c is a sliding contact. By means of a battery (not shown in the figure) a direct current is sent through a Ruhm- korff coil, K, the latter then gives rise to an alter- nating current, which divides at a into two branches, reach- ing^ by the paths FIQ> adb and acb re- spectively. As a galvanometer is not affected by an alter- nating current, it is in this case replaced by a telephone T, which is silent when the points c and d are at the same potential. The contact-maker, c, is shifted along the wire till the telephone no longer sounds. Under these circumstances, the following relationship holds Length of ac Length of cb ~R~ ~~S~~ and since ac> cb and R are known, S, the resistance of the part of the electrolyte between the electrodes, can ?t once be calculated. As the resistance of electrolytes varies within wide limits, 256 OUTLINES OF PHYSICAL CHEMISTRY different forms of cell are employed according to circum- stances. For solutions of small conductivity, the Arrhenius form represented in Fig. 33. is very suitable. The electrodes, which are stout platinum discs 2-4 cm. in diameter, are fixed (by welding or otherwise) to platinum wires, which are sealed into glass tubes A and B, as shown in the figure. These glass tubes are fixed firmly into the ebonite cover of the cell, so that the distance between the electrodes remains constant, and electri- cal connection is made in the usual way by wires passing down the interior of the glass tubes, in order to expose a larger surface, FIG. 33. FIG. 34. and thus minimise polarization effects, which would interfere with the sharpness of the minimum in the telephone, the elec- trodes are coated with finely-divided platinum by electrolysis of a solution of chlorplatinic acid. For electrolytes of high conductivity, a modified form of conductivity vessel, with smaller electrodes placed further apart, has been found con- venient (Fig. 34). Experimental Determination of Molecular Conduc- tivity It is clear that the observed resistance of the electro- lyte must depend on what is usually termed the capacity of the ELECTRICAL CONDUCTIVITY 257 cell, that is, on the cross-section of the electrodes and the distance between them. The specific conductivity, and hence the specific resistance, of the electrolyte could be calculated if these two magnitudes were known (p. 235); but it is much simpler to determine the " constant " of the vessel, which is proportional to its capacity, by using an electrolyte of known conductivity. For this purpose, a 1/50 molar solution of potas- sium chloride may conveniently be used for cells of the first type. The method of procedure will be clear from an example. Referring to the figure, we have, for the resistance, S, of the electrolytic cell S = ac . . i and conductivity C = ~ S Further, since the specific conductivity, K, must be proportional to the observed conductivity, we have where A is a constant. Since all the other factors, including *, the specific conductivity of potassium chloride, are known, A, the constant of the cell, can be calculated. If, now, with the same distance between the electrodes, a solution of unknown specific conductivity, K lt is put in the cell, and for the resistance R' the new position of the contact is c ', the specific conductiv- ity in question is given by the formula ac "1= A RW' By multiplying KJ by the number of c.c. containing i mol of the solute, the molecular conductivity is obtained. An alternative method of calculating *j without reference to the cell constant is as follows. If S and S x represent the resist- ances of the cell containing N/5oKCl and the solution of specific conductivity K I respectively, then 258 OUTLINES OF PHYSICAL CHEMISTRY From the results of conductivity measurements in different dilutions, /x^ can readily be obtained directly for salts, strong acids and bases ; it is the value to which //, approximates on progressive dilution, yu^ cannot, however, be obtained directly for weak electrolytes, such as acetic acid and ammonia ; before the limiting value of the conductivity is reached with these electrolytes, the solutions would be so dilute as to render accu- rate measurement of the specific conductivity impossible. This difficulty is got over by making use of Kohlrausch's law. The value of /XOQ for acetic acid must be the sum of the velocities of the H- and CH 3 COO' ions. The former is obtained from the results of conductivity and transport measurements with any strong acid, and has the value 318 at 18. In a similar way the velocity of the CH 3 COO' ion can be obtained from ob- servations with an acetate for which the value of /x^ can con- veniently be found, e.g., sodium acetate, /x^ for the latter salt at 1 8 is 78*1, and as the velocity of the Na* ion is 44*4 at infinite dilution, that of the CH 3 COO' ion must be 78*1 -44*4 = 33*7. Hence for acetic acid /**> u + v = 33*7 + 3 l8 = 35 1 '? at l8 - Results of Conductivity Measurements In general, it may be said that the conductivity of pure liquids is bmall. Thus the specific conductivity of fairly pure distilled water is about io~ 6 reciprocal ohms at 18, and even this small con- ductivity is largely due to traces of impurities. It is a remark- able fact that the specific conductivity of a number of other liquids, which have been purified very carefully by Walden, 1 is of the same order as that given above for water. Mixtures of two liquids have in many cases a very small conductivity, not appreciably greater than that of the pure liquids themselves ; this is true of mixtures of glycerine and water, and of alcohol and water. On the other hand, a mixture of two liquids which are practically non-conductors may have a very high conductivity for example, mixtures of sulphuric acid and water. The results obtained for this mix- 1 Ztitsch. Physikal Chem., 1903, 46, 103. ELECTRICAL CONDUCTIVITY 259 ture are represented in Fig. 35, the acid concentration being measured along the horizontal axis, and the specific conductivity along the vertical axis. The figure shows that, on gradually adding sulphuric acid to water, the specific conductivity of the mixture increases till 30 per cent, of acid is present, reaches a maximum value at that point, and on further addition of acid diminishes. When pure sulphuric acid is present (100 per cent, on curve), the conductivity is practically zero, and is increased 07 o'6 o-5 o-4 o'3 C'3 O'l I \ \ c \ 8 o 1 \ a / ^ \ \ / \ H,SO , Cor T icent atior i \ r\ 10 20 30 40 50 60 70 80 90 TOO per cent. FIG. 35. both by the addition of water (left-hand part of curve) and of sulphur trioxide (right-hand part of curve). Further, the curve has a minimum between 84 and 85 per cent, of acid, which, it is interesting to note, exactly corresponds with the composition of the monohydrate H 2 SO 4 , H 2 O. According to the electro- lytic dissociation theory, the conductivity depends on the pres- ence of free ions, and the curve for sulphuric acid and water shows in a very striking way that the condition most favourable for ionisation is the presence of two substances. Why ions are formed in a mixture of sulphuric acid and water, and not appreciably, if at all, in a mixture of alcohol and water, is not well understood (cf. p. 317). Analogous phenomena are met with for solutions of solids 260 OUTLINES OF PHYSICAL CHEMISTRY and of other liquids in liquids. An aqueous solution of sugar has no appreciable conducting power. The so-called " strong " acids and bases form well-conducting liquids with water. The conductivity of most organic acids and bases is small, and in corresponding dilution ammonium hydroxide is a much poorer conductor than potassium hydroxide. On the other hand, all salts, even the salts of organic acids which are themselves weak, have a very high conductivity. The conductivity of substances in solvents other than water is usually small, but solutions in methyl and ethyl alcohols and in liquid ammonia are exceptions. The dependence of electrical conductivity on the nature of the solvent will be discussed later It is interesting to note that many fused salts, such as silver nitrate and lithium chloride, are good conductors, and thus form an exception to the rule that pure substances belonging to the second class of conductors have a very small conductivity. Electrolytic Dissociation It has already been pointed out (p. 124) that solutions of salts, strong acids and bases, have a much higher osmotic pressure in aqueous solution than would be the case if Avogadro's hypothesis was valid for these solu- tions. According to the molecular theory, the solutions behave as if there were more particles of solute present than would be anticipated from the simple molecular formula, and van't Hoff expressed this by a factor /, which represented the ratio between the observed and calculated osmotic pressures. This was the position of the theory of solution in 1885. About that time, Arrhenius pointed out that there is a close connection between electrical conductivity and abnormally high osmotic pressures ; only those solutions which, according to van't Hoff 's theory, have abnormally high osmotic pressures, conduct the electri' current. Kohlrausch had previously shown that the molecular conductivity increases at first with dilution, and for many electrolytes attains a limiting value in a dilution of 10,000 litres (p. 251). Arrhenius accounted for this increase on the assumption that the solute consists of " active " and ELECTRICAL CONDUCTIVITY 261 " inactive " parts, and that only the active parts, the ions, convey the current. The extent to which the solute is split up into ions increases with the dilution until finally (when the molecular conductivity has attained its maximum value) it is completely ionised or completely " active " as far as the conduction of electricity is concerned. The theory of Arrhenius is based upon the views of Clausius on conductivity, as has already been pointed out. Arrhenius, however, went much further, inasmuch as he showed how, from the results of conductivity and of osmotic pressure measure- ments, the degree of dissociation can be calculated, as shown in the following section. Degree of lonisation from Conductivity and Osmotic Pressure Measurements According to the theory of electro- lytic dissociation, the conductivity of a solution depends only on the number of the ions per unit volume, on their charges (which are the same for equivalent amounts of different electrolytes) and on their speed. For the same electrolyte we may assume that the velocities remain practically unaltered on dilution (the friction in a dilute solution being practically the same as that in pure water), therefore the increase of molecular conductivity with dilution must depend almost entirely on an increase in the number of the ions. The molecular conductivity at infinite dilution is given by the formula Moo u + v > where u and v are the speeds of cation and anion respectively and the molecular conductivity at any dilution, v , must therefore be represented by the formula fj. v = a(u + v), where a represents the fraction of the molecules split up into ions. Hence, dividing the second equation by the first, we have Moo 262 OUTLINES OF PHYSICAL CHEMISTRY that is, the degree of dissociation, a, at any dilution, is the ratio of the molecular conductivity at that dilution to the mole- cular conductivity at infinite dilution. For example, /u, y for molar sodium chloride is 74*3 and /x^ = 110-3, hence a = />t t .//x oc = 74-3/110*3 = 0-673. Hence sodium chloride in molar solution is about two-thirds split up into its ions. We have now to consider the deduction of the degree of dissociation from osmotic measurements. The assumption made in this case is that the osmotic pressure is proportional to the number of particles present, the ions acting as separate entities. If a molecule is partially dissociated into n ions and the degree of dissociation the ionised fraction is a, then the number of molecules will be i a, and the number of ions na. Hence the ratio of the number of particles actually present to that deduced according to Avogadro's hypothesis (van't Hoffs factor i) will be / = I - a + na = I + a(n l), or a As an illustration, de Vries obtained for a 0*14 molar solution of potassium chloride / = 1*81, hence, since n = 2, a = o'8i, or the salt is dissociated to the extent of 81 per cent, into its ions, /for a 0*18 molar solution of calcium nitrate is 2'48, therefore, since n = 3, a = = 0*74 in this case. 2 The agreement in the values of / obtained from conductivity and osmotic measurements is strikingly shown in the accom- panying table (van't Hoff and Reicher, 1889). The values of / (osmotic) are from the results of de Vries, those of / (freezing point) mainly from the observations of Arrhenius, and those of / (conductivity) are calculated by means of the formulae a = jjLv/jjiQc and / = i -f- a(n - i) as explained above. It is not certain that the results obtained by the different methods can be expected to agree absolutely (cf. p. 281). ELECTRICAL CONDUCTIVITY 263 Substance. (gram equiv. per litre). pt.). i (osmotic). tivity). KC1 0-14 1-82 r8i r86 LiCl 0-13 i*94 1-92 1-84 Ca(N0 3 ) 2 0*18 2-47 2-48 2-46 MgCl 2 0*19 2-68 2-79 2*48 CaCl 2 0*184 2-67 278 2-42 As regards the mode of ionisation, it is clear that univalent compounds, such as potassium chloride, can ionise only in one way, thus, KCl^tK* 4- Cl'. For more complex molecules, how- ever, there are other possibilities, thus calcium chloride may ionise as follows: CaCl 2 ^ CaCl 1 + Cl' as well as in the normal way CaCl 2 ^tCa** + 2C1'. If ionisation were complete according to the last equation, / would be = 3, as compared with the observed value, 2-67 for 0-184 normal solution, given in the table. Similarly, sulphuric acid may dissociate according to the equation H 2 SO 4 ^H- + HSO 4 ', the latter ion then under- going further ionisation as follows : HSO 4 '^H- + SO 4 ". Effect of Temperature on Conductivity The conduc- tivity of electrolytes increases considerably with rise of tempera- ture. The temperature coefficient for salts is 0*020 to 0*023, for acids and some acid salts 0*009 to 0*016, for caustic alkalis about 0*020, and does not vary much with dilution. Conduc- tivity data are usually given for 18, and the specific conductivity, *, at any other temperature, is given by the formula K t = K 18 [l + C(t - 1 8)] where c is the temperature coefficient. As the conductivity of an electrolyte depends both on the number and velocity of the ions, the question arises as to whether the change of conductivity with temperature is due to the alteration of only one or of both these factors. The matter can be at once decided by calculating the degree of dissociation at the higher temperature from conductivity measurements in the ordinary way, and comparing with that at the lower temperature. For normal sodium chloride at 50, the value of a = ^ v \^^ = 132/203*5 = 0*65, which is 264 OUTLINES OF PHYSICAL CHEMISTRY only slightly less than the value at 18, 0*678. Hence, as the considerable increase of conductivity with temperature cannot be due to an increase in the number of ions, it must be due to an increase in their speed. This increased velocity is doubt- less connected with the diminution in the internal friction of the medium with rise of temperature, and the consequent diminished resistance to the passage of the ions (p. 253). Basicity of Acids from Conductivity Measurements (Empirical) The conductivity of N/32 and N/I024 solutions (equivalent normal) of the sodium salt of the acid is deter- mined. For monobasic acids the difference A 102 4 - A 32 is about 10, for dibasic acids about 20, and so on (Ostwald). Grotthus' Hypothesis of Electrolytic Conductivity- Long before the establishment of the electrolytic dissociation theory, Grotthus put forward a hypothesis to account for the conductivity of electrolytes which is of considerable historical interest. He assumed that under the influence of the charged electrodes the molecules of the salt, e.g., potassium chloride, arrange themselves in lines between the electrodes so that the potassium atoms are all turned to the negative electrode, and the chlorine atoms to the positive electrode. Electrolysis takes place in such a way that the external potassium atom is liberated at the cathode and the chlorine atom at the anode. The potassium atom which is left free at the anode unites with the chlorine atom of the molecule next to it, the chlorine atom of the latter with a potassium atom of the molecule next in the chain, and so on. A similar process takes place starting at the anode, in other words, an exchange of partners takes place right along the chain, from one electrode to the other. Under the influence of the charged electrodes, the new molecules twist round till they are in the former relative position, when the end atoms are again discharged, and so electrolysis proceeds. The fatal objection to this ingenious theory is that a con- siderable E.M.F. would have to be employed before any decomposition whatever takes place, hence Ohm's law would not hold (cf. p. 241). Practical Illustrations The following experiments, which ELECTRICAL CONDUCTIVITY 265 are fully described in the course of the chapter, may readily be performed by the student : (1) Experiment on the migration velocity of the ions (p. 246). (2) Rough determination of the absolute velocity of the MnO 4 ' ion (p. 254). (3) Determination of the constant of conductivity vessel with n /5 potassium chloride. (The specific conductivity, *, of this solution at different temperatures is as follows : 0*001522 at o, 0*001996 at 10, 0*002399 at 18, and 0*002768 at 25.) (4) Determination of the specific and molecular conductivities of solutions of sodium chloride and of succinic acid. As the conductivity of solutions varies greatly with the tem- perature, the conductivity vessel must be partially immersed in a thermostat while measurements are being made. In the case of sodium chloride, measurements may be made with n/i, n/io and n/ioo solutions, and the values obtained for the molecular conductivity compared with those given in Kohlrausch's tables. 1 The results in very dilute solutions are not trustworthy unless great attention is paid to the purification of the water used in making up the solutions. In the case of succinic acid, it is usual to start with a 1/16 vwtar solution; 20 c.c. of this solution is placed in the con- ductivity cell in the thermostat, and when the temperature is constant the resistance is determined. 10 c.c. of the solution is then removed with a pipette, 10 c.c. of water at the same temperature added, the resistance again determined after thoroughly mixing the solution, and so on. Measurements are thus made in dilutions of 16, 32, 64, 128, 256, 512 and 1024 litres. From the values of p. v thus obtained, the degree of dissociation can be calculated by the usual formula a = ^J^^ . /XOQ in this case can only be determined indirectly; its value at 25 is about 381. From the values of a in different dilutions, *, the dissociation constant of the acid may then be calculated ; according to Ostwald, K = 0*000066 at 25. 1 Full details of electrical conductivity measurements and a large amount of conductivity data are given by Kohlrausch and Holborn, Leitvermogen der Elektrolyte, Leipzig, 1898. CHAPTER XI EQUILIBRIUM IN ELECTROLYTES. STRENGTH OF ACIDS AND BASES. HYDROLYSIS The Dilution Law In a previous chapter it has been shown that chemical equilibria, both in gaseous and liquid systems, can be represented satisfactorily by means of the law of mass action. We have now to apply this law to binary electrolytes, on the assumption that the ions are to be re- garded as independent entities. According to the electrolytic dissociation theory, an aqueous solution of acetic acid contains molecules of non-ionised acid in equilibrium with its ions, represented by the equation CH 3 COO' + H-^CH 8 COOH. Suppose in the volume v of solution the total amount of the acid is i, and that a fraction of it, represented by a, is split up into ions. The concentration of the undissociated acid is -, that of each of the ions (since they are neces- sarily present in equivalent amount) -. Hence, from the law of mass action, M 2 r^/ 1 - a \ <* 2 (-) = K( ) or r =. K . . (i) W \ V / (i - a)v where K, as before, is the equilibrium constant. For conduc- tivity measurements, the above formula may be put in a rather different form by substituting pvlp-vs for a It then becomes 266 EQUILIBRIUM IN ELECTROLYTES 267 - K ' It is preferable, however, to remember the dilution formula in the first form, or in the form aV/(i - a) = K. This relationship, which is known as Ostwald's dilution law, may be tested by substituting a value for a (from conductivity or osmotic observations) at any dilution v, and calculating K, the equilibrium constant ; the value of a at any other dilution may then be obtained from the formula and compared with that determined directly. This was done (from conductivity measurements) by van't HorT and Reicher, and the results are given in the accompanying table : Acetic acid: K = 0*0000178 at 14'!; ft^j = 316. v (in litres) . . 0-994 2 ' 2 I 5'9 I ^'i 1500 3010 7480 15000 /*, 1*27 i'94 5'26 5' 6 3 4 6 ' 6 6 4' 8 95* 1 129 iooa (observed) . 0*40 0-614 I>66 1 '7 8 147 20-5 30*1 40-8 looo (calculated) . 0-42 o'6 1-67 178 15-0 20-2 30-5 40-1 The agreement between observed and calculated values is excellent ; it is, in fact, much closer than for any case of ordinary dissociation so far investigated. The table also shows how small is the dissociation of acetic acid solutions under ordinary conditions ; a molar solution is ionised only to the extent of 0-4 per cent, and even a 1/1500 molar solution rather less than 1 5 per cent. The dilution law holds for nearly all organic acids and bases, but does not hold for salts, or for certain mineral acids and bases. The latter point is discussed in a later section. When the deg ree of dissociation is small, as in the case of acetic acid for fairly concentrated solution, a can be neglected in comparison with i, and the dilution law then becomes 9 - K or a - N/Kz> . , (2) v v ' that is, for weak electrolytes the degree of dissociation is approxi- mately proportional to the square root of the dilution. When 268 OUTLINES OF PHYSICAL CHEMISTRY a cannot be neglected in comparison with i, a is given by the equation T7- _ / T7"9_ O (3) obtained by solving equation (i) for a. In order to familiarise himself with the use of the dilution formula, the student should calculate a for acetic acid in different dilutions from the value of K given above both by the approximate and accurate formula. The physical meaning of the constant K will be clear if a in the dilution formula (i) is put = \. Then 2K . = i/v, that is, 2K is the reciprocal of the volume at which the electrolyte is dissociated to the extent of 50 per cent. Acetic acid, for instance, will be half dissociated at a dilution of o* = 2 7777 litres (cf. table). 2 x 0-000018 As the method of deriving it indicates, the dilution law applies only to binary electrolytes, i.e., electrolytes which split up into two ions only, and it is not therefore a priori probable that it will hold for dibasic acids, such as succinic acid, which presumably dissociate according to the equation C 2 H 4 (COOH) 2 ^C 2 H 4 (COO) 2 '' + 2H-. It is, however, an experimental fact that when the concentration of succinic acid is expressed in mols (not in equivalents) per litre, the values of K obtained by substitution in the dilution formula remain constant through a wide range of dilution. This indicates that the acid at first splits up into two ions only, doubtless according to the equation /COO' and that the second possible stage, represented by the equation CH /COO' -* CH / COO "4-H- 2 4 *- U2 *\COO EQUILIBRIUM IN ELECTROLYTES 269 is not appreciable under the conditions of the experiment. In other cases, however, e.g., fumaric acid, the value of K increases with dilution before the dilution has progressed very far, which indicates that the second stage of the dissociation early becomes of importance. Strength of Acids We are accustomed to estimate the strength of acids in a roughly qualitative way by their relative displacing power. Sulphuric acid, for example, is usually re- garded as a strong acid, because it can displace such acids as acetic and hydrocyanic from combination. This principle can be developed to a quantitative method for estimating the rela- tive strengths of acids (and bases) if care is taken to make the comparison under proper conditions. This is sufficiently secured by making the experiments in a homogeneous system under such conditions that all the reacting substances and products of reaction remain in the system. We learn in studying inorganic chemistry that many reactions proceed wholly or partially in a particular direction for two main reasons : (a) because an insoluble (or practically insoluble) product is formed which is thus removed from the reacting system, e.g., Na 2 SO 4 + BaCl 2 - 2NaCl + BaSO 4 (insoluble) ; (b) because a volatile product is formed which under the con- ditions of experiment leaves the reacting system, e.g., 2 NaCl + H 2 SO 4 - Na 2 SO 4 +2HC1 (volatile). Such reactions are obviously unsuitable for determining the relative strengths of the acids concerned. Bearing these considerations in mind, we now proceed to investigate the relative strengths of, say, nitric and dichloracetic acids by bringing them in contact with an amount of base insuffi- cient to saturate both of them, and find how the base distri- butes itself between the two acids. If, for example, the acids are taken in equivalent amount, and sufficient base is taken to saturate one of them, we have to determine the position of equilibrium represented by the equation 270 OUTLINES OF PHYSICAL CHEMISTRY CHCl 2 COOiv + HNO 3 ^CHC1,COOH + KNO 3 . It is evident that no chemical method would answer the purpose, because it would disturb the equilibrium. When, however, a physical property of one of the components, which alters with the concentration, can be measured, the position of equilibrium can be determined. A method used for this purpose by Ostwald, depending on the changes of volume on neutralization, will be readily understood from an example. When a mol of potassium hydroxide is neutralized by nitric acid in dilute solution, there is an increase of volume of about 20 c.c. When, on the other hand, the same quantity of alkali is neutralized by dichloracetic acid, the increase of volume is about 13 c.c. It is therefore clear that the complete displace- ment of dichloracetic acid by nitric acid, according to the equation CHC1 2 COOK + HNO 3 -> CHC1 2 COOH + KNO 3 ,' would give an increase of volume of (20 13) = 7 c.c.; if no displacement took place, there would, of course, be no change of volume. The change actually observed was 5-67 c.c., which means that the reaction represented by the equation has gone from left to right to the extent of = 80 per cent, approxi- mately ; in other words, the nitric acid has taken 80 per cent, of the base, and 20 per cent, has remained combined with the dichloracetic acid. The relative strength, or relative activity, of the acids under these conditions is therefore 80 : 20 or 4 : i. Any other physical property, which is capable of quantitative measurement and differs from the two systems, can be equally well employed for the determination of equilibrium. The heat of neutralization has been used for this purpose by Thomsen, and the measurement of the refractive index by Ostwald ; the principle of the methods is exactly the same as in the example just given. Thomsen's therm ochemical measurements were the first to EQUILIBRIUM IN ELECTROLYTES 271 be made on this subject, and he arranged the different acids in the order of their " avidities " or activities. Ostwald then showed that the same order of the avidities was obtained by the volume and refractivity methods, and, further, that the results were independent of the nature of the base competed for, so that the avidities are specific properties of the acids. The relative strength of acids can also be determined on an entirely different principle, depending on kinetic measurements. It has already been pointed out that acids accelerate, in a catalytic manner, the hydrolysis of cane sugar, of methyl acetate, acetamide, etc. Ostwald made many experiments on this sub- ject and reached the very important conclusion that the order of the activity of acids is the same, whether measured by the distribution method (which is, of course, a static method), or by a kinetic method. This affords further evidence in favour of the conclusion just mentioned, that the activity or affinity is a specific property of the particular acid, independent of the method by which it is measured. Thus far had our knowledge of the subject progressed when in 1884 the first paper of Arrhenius appeared. He showed that the order of the "strengths" of the acids as determined by the methods just described is also that of their electrical conductivities in equivalent solution. This fundamentally im- portant fact is illustrated in the accompanying table, in which the conductivities of the acids in normal solution are quoted, that of hydrochloric acid being taken as unity. Relative Activity. Acid. Thermochemical. Cane Sugar. Conductivity. Hydrochloric 100 100 100 Nitric 100 100 99-6 Sulphuric 49 53-6 65-1 Monochloracetic 9 4-8 4-9 Acetic 0-4 1-4 We have seen that, according to the electric dissociation theory, the electrical conductivity of an acid is mainly deter- 272 OUTLINES OF PHYSICAL CHEMISTRY mined by its degree of dissociation; for example, the con- ductivity of a normal solution of acetic acid is small because it is ionised only to a very small extent. Further, owing to the predominant share taken by the hydrogen ions in conveying the current (p. 252), the relative conductivities of acids will be approximately proportional to their H* ion concentrations. It is therefore natural to suppose that the activity of acids, as illustrated by distribution and catalytic effects, is also due to that which all acids have in common, namely, hydrogen ions. This assumption is in complete accord with the experimental results, as the following illustration shows. The velocity con- stant for the hydrolysis of cane sugar in the presence of 1/80 normal hydrochloric acid is 0*00469 at 54*3 (time in minutes) ; as the acid may be regarded as completely dissociated CH- = 0-0125. CH- for 1/4 normal acetic acid (# = 4, cf. p. 267) may be calculated from the dilution formula or directly from the equilibrium equation as follows : [H-][CH,CO(y] _ [H-] 2 [H-] 2 [CH 3 COOH] " [CHjCOOH] ~ [0-25 - H-]"" whence CH- = 0-002. On the assumption that the catalytic effect of acids is propor- tional to the H- ion concentration, the value of the velocity constant, x, for the hydrolysis of cane sugar by 0-25 normal acetic acid at 54*3 should be 0*0125 : 0*00469 : : 0-002 : #, whence x = 0-00075. This is identical with the result obtained experimentally by Arrhenius, and we have here a very striking confirmation of the electrolytic dissociation theory. From the above considerations, we conclude that the charac- teristic properties which acids have in common, such as sour taste, action on litmus, catalytic activity, property of neutralizing bases, etc., are due to the presence of H' ions. It must be remembered that direct proportionality between H- ion concen- tration and conductivity is neither observed nor to be expected EQUILIBRIUM IN ELECTROLYTES 273 from the theory ; the approximate proportionality is due to the great velocity of the hydrogen ions, and would be altogether absent if the anions were the more rapid. As there is a simple relationship between the H 1 ion con- centration of weak acids and their dissociation constants (p. 267), it is clear that the behaviour of an acid can be to a great extent foretold when its dissociation constant has been measured. Such determinations have been made f, r a great number of weak acids by Ostwald and others, and some of the results are given in the accompanying table, which shows very clearly how greatly the value of K differs for different acids, and the influence of substitution : Acid. Acetic H-CH 3 COO Monochloracetic H'CH 2 C1COO Trichloracetic H C1 3 COO Cyanacetic H'CH 2 CNCOO Formic H HCOO Carbonic H HCO 3 Hydrogen sulphide H SH Hydrocyanic H CN Phenol H-OC 8 H 6 Value of K at 25 (v in litres). o'ooooiS = 180,000 x io~ 10 0*00x55 0-0037 0*000214 3040 x io- 10 570 x io~ 10 13 x io- 10 I '3 x io- lb For a weak acid, a= vKtT, where a is the degree of dis- sociation at the volume v. Hence, for two acids at the same dilution a/a'= \/K/K', or the ratio of the degrees of dissocia- tion is equal to the square root of the ratio of the dissociation constants. From the data given in the table it can readily be calculated that in solutions of monochloracetic and acetic acid of the same concentration the ratio of the H- ion concentrations is approximately 9*3 : i. The effect of replacing one of the hydrogens in acetic acid by chlorine is thus to form a much stronger acid and the CN group has a still greater effect, as the table shows. A further important point is the effect of dilution on the " strength" of an acid. As the degree of dissociation in- creases regularly with dilution, it is evident that the activity of a weak acid will approach nearer and nearer to that of a strong 18 274 OUTLINES OF PHYSICAL CHEMISTRY acid (which is completely active in moderate dilution) until finally, when the weak acid is completely ionised, it will have the same strength as the strong acid in equivalent dilution. It follows that the strength of acids is the more nearly equal the more dilute the solution, and that at " infinite dilution " all acids are equally strong. It can readily be calculated from the conductivity tables that the relative strengths of hydrochloric and acetic acids in different dilutions are as follows : Concentration n/i w/io w/ioo w/iooo w/io,ooo a for HC1 o'8i 0-91 0*97 0-99 i'o a for HC 2 H 3 O 2 0*004 0-013 0*04 0*13 0-4 Ratio HC1/HC 2 H 3 O 2 200 70 24 7-5 2-5 Strength of Bases Just as the strength of acids depends on their concentration in hydrogen ions, so the strength of bases depends on the concentration in hydroxyl ions. On this view, potassium hydroxide is a strong base, because in moderate dilution it is almost completely ionised according to the equa- tion KOH lj K* + OH' ; ammonium hydroxide, on the other hand, is a weak base, because its aqueous solution contains only a relatively small concentration of OH' ions. Since certain organic compounds, including amines and alkaloids, have basic properties, their aqueous solutions must also contain OH' ions. Thus, solutions of pyridine, C 5 H 5 N, contain not only the free base, but a certain concentration of C 5 H 6 N* and OH' ions, in equilibrium with the undissociated hydrate, as represented by the equation C 5 H 6 NOH;C 5 H 6 N- + OH'. The strength of bases may be determined by distribution or catalytic methods, corresponding with those already described for determining the strength of acids, as well as by conductivity methods. A fairly satisfactory catalytic method is the effect on the rate of condensation of acetone to diacetonyl alcohol, 1 represented by the equation 2 CH 3 COCH 3 -> CH 3 COCH 2 C(CH 3 ) 2 OH. 1 Koelichen, Zeitsch. Physikal.Chem., 1900, 33, 129. EQUILIBRIUM IN ELECTROLYTES 275 The order of the strength of bases as determined by this method agrees with the results of conductivity measurements. Another method, which is not purely catalytic, since the base is used up in the process, is the effect on the hydrolysis or saponification of esters (p. 207). This process is usually represented by the typical equation CH 3 COOC 2 H 5 + KOH = CH 3 COOK + C 2 H 5 OH. Experience shows, however, that for the so-called strong bases, which are almost completely ionized in moderate dilution, the rate of hydrolysis is practically independent of the nature of the cation (whether K, Na, Li, etc.), a fact which is readily accounted for on the view that the ions exist free in solution, as the ionic theory postulates, and that the OH' ions are alone active in saponification. The general equation for the hy- drolysis of ethyl acetate by bases may, therefore, be written as follows CH 3 COOC 2 H 5 + OH' = CH 3 COO' + C 2 H 5 OH. The relative strength of bases, as obtained from their efficiency in saponifying esters, is in excellent agreement with their strength as deduced from conductivity measurements. The ionization view of the saponification of esters is further sup- ported by the fact that the reaction between ethyl acetate and barium hydroxide is bimolecular and not trimolecular, as would be anticipated if it proceeded according to the equation 2CH 3 COOC 2 H 5 + Ba(OH) 2 = (CH 3 COO) 2 Ba + 2C 2 H 6 OH. The alkali and alkaline earth hydroxides are very strong bases, being ionized to about the same extent as hydrochloric acid in equivalent dilution. Bases differ as greatly in strength as do acids; the dissociation constants for a few of the more important are given in the table. Base. Ammonia NH 4 *OH Methylamine CH 3 NH 3 'OH Trimethylamine (CH 3 ) 3 NH*OH Pyridine C 5 H 6 N*OH Aniline C 8 H 5 NH 3 *OH Value of K (25) (v in litres) 0*000023 = 230,000 x io~ 10 0*00050 0*000074 23 x io~ lfl 4-6 x io- 10 276 OUTLINES OF PHYSICAL CHEMISTRY Interesting results have been obtained as to the effect of sub- stitution on the strength of bases. Thus the table shows that the basic character is increased by replacing one of the hydrogen atoms in ammonia by the CH 3 group, but is greatly diminished by the C 6 H 5 group. Mixture of two Electrolytes with a Common Ion The dissociation of weak acids and bases is greatly diminished by the addition of a salt with an ion common to the acid or base. For example, the equilibrium in a solution of acetic acid is re- presented by the equation [H-] [CH 3 COO'] = K [CH 3 COOH], and if by adding sodium acetate the CH 3 COO' ion con- centration is greatly increased, the H* ion concentration must correspondingly diminish, since the concentration of the undis- sociated acid cannot be greatly altered (nearly the whole of the acid being present in that form in the original solution) and therefore the right-hand side of the equation is practically constant. The exact equations representing the mutual influence of electrolytes with a common ion are somewhat complicated, but an approximate formula which is often useful can be obtained as follows : If the total concentration of a binary electrolyte is c and its degree of dissociation is a, we have, from the law of mass action, If now an electrolyte with a common ion is added, and the concentration of the latter is c , the above equation becomes (aV)(aV + CQ] _ ^ - 7 - T\ - =* IV . , . 12) (l - a)c This equation is quite accurate. As K, c and c are known, a', where a' is the new degree of dissociation, can be calculated, perhaps most readily by successive approximations. If the degree of dissociation of the first electrolyte is small, i a' can be taken as unity without appreciable error ; further, EQUILIBRIUM IN ELECTROLYTES 277 if the second electrolyte is highly ionised and is added in con- siderable proportion, aV can be neglected in comparison with c oj and equation (2) simplifies to (aV) c, - K, . . . . (3) Otherwise expressed, the concentration of one of the ions of a weak electrolyte is inversely proportional to the ionic concentra- tion of a highly-dissociated salt having an ion in common with the other ion of the weak electrolyte. As an illustration of the application of the last equation, we will consider the effect of the addition of an equivalent amount of sodium acetate on the strength of 0*25 molar acetic acid. In this dilution a for the acid is 0*0085 and cur = 0*0085 x 0>2 5 = 0*002 1 = CH'. I n ' 2 5 niolar solution, sodium acetate is dissociated to the extent of 69*2 per cent., hence c = 0*25 x 0*692 = 0*173. We have, therefore, a! x 0*173 = 0*000018, whence a' = 0*0001. aV is therefore 0*25 x 0*0001 =0*000025= C H . in presence of 0*25 molar sodium acetate, so that the strength of the acid is diminished in the ratio 85 : i. In an exactly similar way, the strength of ammonia as a base is greatly reduced by the addi- tion of ammonium salts. This action of neutral salts on weak bases and acids is largely taken advantage of in analytical chemistry. For example, the concentration of OH' ions in ammonia solution is sufficient to precipitate magnesium hydroxide from solutions of magnesium salts, but in the presence of ammonium chloride the OH' ion concentration is so greatly reduced that precipitation no longer occurs. Similarly, the addition of hydrochloric acid diminishes the concentration of S" ions in hydrogen sulphide to such an extent that zinc salts are no longer precipitated (cf. p. 300). Isohydric Solutions It is of particular interest to inquire what must be the relation between two solutions with a common ion two acids, for example in order that, when mixed, they may exert no mutual influence. This problem was investigated 278 OUTLINES OF PHYSICAL CHEMISTRY both theoretically and practically by Arrhenius, who showed (cf. p. 414) that no alteration in the degree of dissociation of either of the salts (acids or bases) takes place when the con- centration of the common ion in the two solutions before mixing is the same. Such solutions are termed isohydric. The relative dilutions in which two acids or other electrolytes with a common ion are isohydric can readily be calculated from their dissociation constants. The value of K for acetic acid is 0*000018, and for cyanacetic acid 0*0037, both at 25. Since a = \/Kz> approximately, it is clear that the degree of dissocia- tion, a, will be the same for the two acids when the dilutions are inversely as the dissociation constants. The dilution of the cyanacetic acid must therefore be 3700 : 18, or 205 times that of acetic acid for isohydric solutions. Arrhenius has shown that by the principle of isohydric solu- tions the mutual influence of electrolytes with a common ion even of strong acids and their neutral salts, can be calculated with a considerable degree of accuracy, but the methods are somewhat complicated and cannot be given here. Not only is the degree of dissociation of a weak acid greatly influenced by the addition of a strong acid, or other electrolyte with a common ion, but the latter is affected, though to a much smaller extent, by the presence of the former. It can, for instance, be calcu- lated that when a mol of acetic acid and a mol of cyanacetic acid are present in a litre of water, the dissociation of the former is only about 1/14 of its value in aqueous solution, whilst the presence of the acetic acid only diminishes the dissociation of the cyanacetic acid by 0*25 per cent. Mixture of Electrolytes with no Common Ion The equilibrium in a mixture of two electrolytes without a common ion can be calculated when the concentrations and dissociation constants are known, but the calculation is somewhat compli- cated. If solutions of two highly-dissociated salts, such as potassium chloride and sodium bromide, are mixed, small amounts of undissociated sodium chloride and potassium EQUILIBRIUM IN ELECTROLYTES 279 bromide will be formed ; but as the salts are all highly dis- sociated, the mutual effect is very small. If dissociation is complete, the process will be represented by the equation K- + Cl' + Na- + Br' = K- + Cl' + Na- + Br', otherwise expressed, the salts will exert no mutual influence. These considerations account for the observation of Hess (p. 148) that the thermal effect of mixing dilute solutions of two binary salts is very slight. At the time Hess made his observation, it was extremely puzzling, because it was known that the heats of formation of different salts were very different, and therefore heat should either be absorbed or given out as an accompaniment of the double decomposition. On the basis of the electrolytic dissociation theory, however, Hess's results at once become intelligible, since both before and after admixture the solution contains mainly the same free ions. To the question which is very often asked as to what com- pounds are present in a mixed salt solution, it must therefore be answered that all the undissociated salts and ions are present which can be formed by interaction of the components, and that the proportions in which the various molecules and ions are present depend on the concentrations and dissociation constants of the various salts. Dissociation of Strong Electrolytes T It has been pointed out (p. 267) that the law of mass action holds for weak (/.*., slightly ionised) electrolytes, the ions being regarded as inde- pendent units. The proof of the applicability of the law has been brought more particularly by Ostwald from the results of measurements with organic acids. It is a remarkable fact, however, that the dilution formula, a?/(i - a)v K, which is a direct consequence of the law of mass action, does not appear to be valid for the so-called " strong " or highly dissociated electrolytes ; when the values of a, obtained from osmotic or conductivity measurements, are substituted in the above formula, l Cf. Drucker, "Die Anomalie der starken Elektrolyte, " Ahrens 1 Sammlung, Stuttgart, 1905, 2 8o OUTLINES OF PHYSICAL CHEMISTRY K diminishes greatly with dilution. This is well shown in the following table for silver nitrate. The first column contains v, the volume in litres in which i mol of the salt is dissolved, in the second column is given the value of a calculated from con- ductivity measurements at 25, and in the third column are given the values of K calculated by means of the dilution formula. v. 0=^/^05. K. Kj. 16 0*8283 * 2 53 i'n 32 0*8748 0-191 ri6 64 0*8993 0-127 1-06 128 0*9262 0*122 1-07 256 0*9467 0-124 1-08 512 0-9619 0-125 1-09 The deviations from the simple law appear to be fairly regular in character, and van't Hoff has proposed an empirical formula which represents with a fair degree of accuracy the behaviour of the great majority of strong electrolytes. The formula in question is of the form a *l(i - a )*v = Kj which may also be written c;/c; = K, where C/ represents the concentration of the dissociated part (the ions), C tt that of the undissociated part. The application of this formula to solutions of silver nitrate is illustrated in the table, and it will be observed that the values of K x in the fourth column are fairly constant. The slightly different formula suggested by Rudolphi is scarcely as satisfactory as that of van't Hoff. Some observers have suggested a generalised form of van't HofFs formula, 1 as follows : c:-/c H = K 3 l Cf Bancroft, Zeitsch. Physikal Chem., 1899, 31, 188. EQUILIBRIUM IN ELECTROLYTES 281 and experiment shows that in many cases n does not differ much from 1*5. When n is 1*5 the general formula reduces to that of van't Hoff. The reason why the law of mass action does not apply to strong electrolytes, although it holds so accurately for weak electrolytes, has not been satisfactorily elucidated. It was long thought that the values of a obtained from the results of con- ductivity measurements were not the true values of the degree of dissociation, but recent very careful comparison shows that the results obtained by conductivity and freezing-point deter- minations in dilute solution for the best-investigated substances do not, as a rule, differ by more than 2 per cent, on the average, and even these differences may be due largely to experimental error. 1 In a few cases only does there appear to be a real difference between the results obtained by the two methods. As neither of the values for a gives a constant value for K when substituted in the ordinary dilution formula, there can be no doubt that strong electrolytes do behave in an anomalous way. Several disturbing causes might be suggested to account for this behaviour, including (a) the formation of complex ions by combination of the ions with non-ionised molecules; (b) mutual influence of the ions ; (c) interaction of the ions and the solvent, including more particularly hydration of the ions, and one or more of these effects may be operative in any one solution. The existence of complex ions in solutions has been definitely proved by Hittorf and others. In solutions of cadmium iodide, for instance, there is evidence that I' ions unite with CdI 2 molecules to form complex ions of the formula CdI 4 ". The formation of complex ions would diminish the number of non-ionised molecules but not the total number of ions ; it would thus affect the osmotic pressure, but not to any extent the con- ductivity. This disturbing effect will be greatest in fairly concen- trated solutions. In dilute solutions of salts of the alkalis and 1 Drucker, loc. cit. ; Noyes, Technology Quarterly, 1904, 17, 293. 282 OUTLINES OF PHYSICAL CHEMISTRY alkaline earths, the values of a obtained by conductivity and os- motic pressure methods are very nearly equal, and this result appears to show that there is little or no complex ion formation in these solutions. As to the possible effect of the ions on each other, practically nothing can be said with certainty. The fact that weak electro- lytes follow the law of mass action through a very wide range of dilution may be connected with the fact that under all circumstances the ionic concentration is small, a condition which no longer holds in solutions of strong electrolytes. As to how and to what extent the mutual influence is exerted, little or nothing is known. The possibility of the interaction of the ions with the solvent has been much discussed, but as no general agreement has been reached on the matter, a short reference to the subject here will suffice. One way in which this effect might influence the results would be if the ions became associated with a large proportion of water which no longer acted as solvent. The effective con- centrations of an ion would then be the ratio of the amount present to that of the " free " solvent, instead of to the total solvent, as usually calculated. As, however, no satisfactory method of estimating the relative proportions of free and com- bined solvent in the solution of an electrolyte has yet been suggested the question is at present mainly of theoretical interest (P- 3 2 5)' The most logical method so far suggested for dealing with the problem of strong electrolytes is due to Nernst. He considers that, owing to their mutual influence, the activity of the various substances (ions and non-ionised substances) present is not pro- portional to their respective concentrations, but certain correct- ing factors have to be applied depending on the extent of the mutual influence. Among these effects, that of the ions on each other and on the non-ionised part of the molecules, as well as the mutual influence between ions and solvent, seem to be of special importance, but so far comparatively little progress has been EQUILIBRIUM IN ELECTROLYTES 283 made with the determination of the relative magnitudes of the correcting factors. Electrolytic Dissociation of Water. Heat of Neutral- ization So far we have regarded the usual solvent water simply as a medium for dissociation, but there is evidence to show that it is itself split up to a very small extent into ions, according to the equation Applying to this equation the law of mass action, we have, as usual, [H-][OH'] = K[H 2 0], where K is the dissociation constant for water. As the ionic concentrations are extremely small the concentration of the water is practically constant, and therefore the product of the concentration of the ions [H-] [OH'] = K w , a constant. It has been found by different methods, which will be re- ferred to later (p. 293), that the value of the above constant at 25 is about 1*2 x 10 u . In pure water the concentrations of the ions are necessarily equal, hence CH = CbH' = Vi'2 x io~ u = i -i x 10 ~ 7 at 25. Otherwise expressed, this means that pure water contains rather more than i mol of H- and OH' ions, that is, i gram of H' ions and 17 grams of OH' ions, in io 7 or 10,000,000 litres. The ionic product is independent of whether the solution is acid or alkaline, and therefore in a normal solu- tion of a (completely dissociated) acid, since CH- = i, OH' is only io ~ u , and in a solution of a normal alkali CH- is corre- spondingly small. These considerations are of great importance in connection with the process of neutralization. Assuming that the solutes are completely ionised, the neutralization of i mol of sodium hydroxide by hydrochloric acid in dilute solution may be repre- sented as follows : Na + OH' + H + Cl' = Na- + Cl' + H,/). 284 OUTLINES OF PHYSICAL CHEMISTRY Since Na- and Cl' ions occur in equivalent amount on each side, they may be neglected, and the equation reduces to OH' + H--H 2 O, or, otherwise expressed, the combination of hydrogen and hydroxyl ions to form water. The same equation applies to the neutralization of any other strong base by a strong acid ; provided that the solutions are so dilute that dissociation is prac- tically complete, the process in all cases consists in the combination of H' and OH' ions to non-ionised water. It may, therefore, be anticipated that for equivalent amounts of different strong bases and acids the heat of neutralization will be the same, and that this is actually the case is shown in the first part of the table. The magnitudes of the heats of neutralization apply for molar quantities. Heats of Neutralization. Acid and Base. Heat of Neutralization. HC1 and NaOH 13,700 cal. HBr and NaOH 13,700 cal. HNO 3 and NaOH 13,700 cal. HC1 and Ba(OH) 2 13,800 cal. NaOH and CH 3 COOH 13,400 cal. NaOH and HF 16,300 cal. HC1 and ammonia 12,200 cal. HC1 and dimethylamine n, 800 cal. The fact that the heat of neutralization of strong acids and bases is independent of the nature of the acid and base was long a puzzle to chemists, and the simple explanation given above is one of the conspicuous triumphs of the electrolytic dissociation theory. Below the dotted line in the above table are given the heats of neutralization of two weak acids by a strong base and of two weak bases by a strong acid. As the table shows, the heat development in these cases may be more or less than 13,700 cal. for molar quantities," and a little consideration affords a plausible explanation. The neutralization of acetic acid, which EQUILIBRIUM IN ELECTROLYTES 285 is very slightly ionised, by sodium hydroxide, may be repre- sented by the equation CH 3 COOH + Na- + OH' - CH 3 COO + Na- + H 2 O, which may be regarded as taking place in two stages (i) CH 3 COOH = CH 3 COO' + H ; (2) H- + OH' = H 2 O. The heat of neutralization is, therefore, the sum of two effects (i) the heat of dissociation of the acid ; (2) the reaction H' + OH' = H 2 O, which gives out 13,700 cal. Hence, since the observed thermal effect is 13,400 cal. the dissociation of the acid must absorb 300 calories. For hydrofluoric acid, on the other hand, the reaction HF = H* + F' is attended by a heat development of 16,300 13,700 = 2,600 cal. We have thus, an approximate method of determining the heat of ionisation of electrolytes, which may be positive or negative. In the above paragraphs the total heat change has been regarded as the algebraic sum of the heats of neutralization and of ionisation, but it is probable that other phenomena, for example, changes of hydration, also play a part. Hydrolysis It is a well-known fact that salts formed by a weak acid and a strong base, such as potassium cyanide, show an alkaline reaction in aqueous solution, whilst salts formed by the combination of a weak base and a strong acid, for example, ferric chloride, have an acid reaction. In the previous section it has been mentioned that water is slightly ionised, according to the equation H 2 O = H- + OH', and may therefore be re- garded as at the same time a weak acid (since H* ions are present) and a weak base (owing to the presence of OH' ions). It will now be shown that the behaviour of aqueous solutions of such salts as potassium cyanide and ferric chloride are quanti- tatively accounted for on the assumption that water is electro- lytically dissociated. In a previous section (p. 271) it has been pointed out that when two acids are allowed to compete for the same base, the latter distributes itself between the acids in proportion to their 286 OUTLINES OF PHYSICAL CHEMISTRY avidities, and it has also been shown that the ratio of the avidities of two acids is the ratio of the extent to which they are electrolytically dissociated. The same applies to a salt in aqueous solution, water, in virtue of its hydrogen ion concen- tration^ being regarded as one of the competing acids. In the case of a salt of a strong acid, such as sodium chloride, it would not be anticipated that such a weak acid as water would take an appreciable amount of the base, and the available experimental evidence quite bears out this expectation. In other words, an aqueous solution of sodium chloride contains only Na* and Cl' ions and undissociated sodium chloride in appreciable amount, and is therefore neutral. The case is quite different for a salt formed by a strong base and a weak acid, such as potassium cyanide. Here water as an acid is comparable in strength to hydrocyanic acid, and therefore there is a distribution of the base between the acid and the water according to the equation KCN + H 2 ^ KOH + HCN, the proportions of potassium cyanide and potassium hydroxide depending upon the relative strengths of water and hydrocyanic acid. From the equation it is evident that potassium hydroxide and hydrocyanic acid must be present in equivalent amount ; and since the hydroxide is much more highly ionised than hydro- cyanic acid, the solution contains an excess of OH' ions, and must therefore be alkaline, as is actually the case. This process is termed hydrolysis, i.e., decomposition by means of water. Similar considerations apply to the salts formed by combination of weak bases and strong acids, such as aniline hydrochloride. As water is comparable in strength to aniline as a base, an equilibrium is established according to the equation C 6 H 5 NH 3 C1 + HOH ^ C 6 H 5 NH 8 OH + HC1. In this case there is an excess of H* ions, as hydrochloric acid EQUILIBRIUM IN ELECTROLYTES 287 is much more highly ionised than anilinium hydroxide, and therefore the solution has an acid reaction. A salt formed by the combination of a weak acid and a weak base, e.g., aniline acetate, is naturally hydro lysed to a still greater extent. These three types of hydrolytic action will now be considered quantitatively. (a) Hydrolysis of the Salt of a Strong Base and a Weak Acid A typical salt of this type is potassium cyanide, the hydrolytic decomposition of which is represented by the equation KCN + HOH^KOH + HCN, or, according to the electrolytic dissociation theory, K- +'CN' + HOH^K- + OH' + HCN, on the assumption, which is only approximately true, that potassium cyanide is completely ionised and hydrocyanic acid non-ionised. The equilibrium can now be investigated, and the extent of the hydrolysis determined, if a means can be found of deter- mining the equilibrium concentration of one of the reacting substances, for example, the OH' ions. This could not, of course, be done by titrating the free alkali, as the equilibrium would thus be disturbed, but one of the methods given on p.27i may conveniently be used. The method which has been most largely used is to determine the effect of the mixture on the rate of saponifi cation of methyl acetate, which, as has already been pointed out, is proportional to the OH' ion con- centration. The amount of hydrolysis per cent., ioox, for different concentrations, c, of potassium cyanide (mols per litre) at 25, determined by the above method, is as follows: c . 0-947 0-235 '95 ' 2 4 ioox . 0*31 0*72 i'i2 2*34 K n . 0-9 1-2 1*2 1-3x10 6 The table shows that, as is to be expected, the degree of hydrolysis increases with dilution. 288 OUTLINES OF PHYSICAL CHEMISTRY A general equation, by means of which the equilibrium con- dition can be calculated when the acid and base are not neces- sarily present in equivalent proportions, can readily be obtained by applying the law of mass action to the general equation B- + A' + H 2 O^B- + OH' + HA, where B* and A' represent the positive and negative ions respec- tively. As B* occurs on both sides of the above equation, the latter can be simplified to A' + H 2 O ^ OH' + HA. As the salt and the base are practically completely ionised, and the acid is not appreciably ionised, A' and OH' are proportional to the concentrations of salt and base respectively, and HA to that of the acid. Hence, from the law of mass action, [OH'] [HA] [free base] [free acid] = R , } A' [unhydrol. salt] a constant, as the concentration of the water may be regarded as constant. K& is termed the hydrolysis constant, and, like the ordinary equilibrium constant, is independent of the relative concentrations of the substances present at equilibrium, but de- pends on the temperature. In order to illustrate the use of the above formula, the values of Kfc may be calculated from the data for potassium cyanide already quoted. In 0*095 molar solution, potassium cyanide is hydrolysed to the extent of 1*12 per cent., hence O'OCK X I'I2 Cbase = C a dd = ~ Z ^ = 0*001064, and C sa it = 0-095 - 0-001064 = 0-094. (o'ooio64)(o-ooio64) , Hence K h = * -^ -^ = 1-2 x lo" 5 . 0*094 The values of the hydrolysis constant, calculated from the other observations, are given in the table, and are approxi- mately constant, thus confirming the above formula. Con- versely, when from one set of observations the value of EQUILIBRIUM IN ELECTROLYTES 289 Kfc has been obtained, the degree of hydrolysis at any other dilution can be obtained by substitution in the general formula. For convenience of calculation, the simple formula in which the acid and base are present in equivalent proportions, may be written in the form o ? - r- = (i - x) v in which x represents the proportion of acid and base formed by hydrolysis from i mol of the salt and v is the dilution, This form of the equation shows at a glance that the degree of hydrolysis, that is, the value of x, increases with dilution. More* over, from the great similarity of the formula (10) to the dilution formula, it is evident that when the hydrolysis is small it is greatly diminished by the addition of a strong base, just as the degree of dissociation of acetic acid is greatly diminished by the addition of an acetate. The quantitative relation between the hydrolysis constant, K;,, and the dissociation constants for the weak acid and water respectively may be obtained as follows : The electrolytic dis- sociation of the acid, HA, is represented by the equation [H-][A'] = K a [HA] . . . (2) where K a is the dissociation constant of the acid. In the solution there is the other equilibrium [H*] [OH'] = K w (3) where K w is the ionic product for water. Dividing equation (3) by equation (2) we obtain [OH'] [HA] Ka, A' K a (4) The left-hand side of the above equation is simply equation (i) for the hydrolytic equilibrium (p. 288), hence [free base] [free acid] = K = K / q \ [unhydrol. salt] h ~ K a * that is, the hydrolysis constant J?h is the ratio of the ionic product K w for ivaUr to the dissociation constant of the acid, $9 2 9 o OUTLINES OF PHYSICAL CHEMISTRY It has already been deduced from general principles (p. 286) that the hydrolysis is the greater the more nearly the strength of water as an acid approaches that of the competing acid, and the above important result is the mathematical formulation of that statement. In order to illustrate this point more fully, the degree of hydrolysis of a few salts in i/io molar solution at 25 is given in the accompanying table. Salt. Degree of hydrolysis. Sodium carbonate . . . 3*17 per cent. Sodium phenolate . . . 3 05 Potassium cyanide . . . 1*12 Borax ..... 0*05 Sodium acetate .... crooS The numbers illustrate in a very striking way the fact that only the salts of very weak acids are appreciably hydrolysed. Thus although acetic acid is a fairly weak acid (K=r8x io~ 5 ), sodium acetate is only hydrolysed to the extent of 0*008 per cent, at 25, and even potassium cyanide is only hydrolysed to the amount of about i per cent, in i/io normal solution, although the dissociation constant of the acid is only 1*3 x io~ 9 . A com- parison of the above table with the dissociation constants of the acids (p. 273) is very instructive. From the known values of K a and K w for hydrocyanic acid and water respectively at 25, we have Ka, 1*2 X IQ- 14 = = 0-9 x io~ 5 = K h , K a 1-3 x io~ 9 m very satisfactory agreement with the observed value of i'i x 10 " 6 (p. 288). As a matter of fact, however, it is easier to deter- mine the hydrolysis constant than the dissociation constant for a very weak acid, and therefore the latter is often calculated from the observed value of the hydrolysis constant by means of the above formula. EQUILIBRIUM IN ELECTROLYTES 291 (b) Hydrolysis of the Salt of a Weak Base and a Strong Acid The same considerations apply in this case as for the salt of a strong base and a weak acid. The general equation for the equilibrium is of the form B- + A 7 + iH 2 O ^ BOH + H* + A ; which simplifies to B- + H 2 O^BOH + H-. Applying the law of mass action, we obtain [BOH][H-] [free base] [free acid] = K ,, B- [unhydrol. salt] exactly the same equation as is applicable to the hydrolysis of he salt of a strong base and a weak acid. Further, it may be shown, by a method exactly analogous to that employed in the previous section, that in this case that is, the hydrolysis constant Khfor the salt of a weak base and a strong acid is the ratio of the ionic product for water, K,, and the dissociation constant of the base } K&. A typical case is the hydrolysis of urea hydrochloride, 1 which may be represented thus CON 2 HJ + CF + H 2 O^CON 2 H 5 OH + H- + Clf It is clear that the degree of hydrolysis can at once be obtained when the H* ion concentration in the solution has been deter- mined, and for this purpose any of the methods previously described can be employed (p. 275), such as the effect on the rate of hydrolytic decomposition of cane sugar or of methyl acetate or by electrical conductivity measurements. In the experiments quoted in the table, gradually increasing amounts of urea were added to normal hydrochloric acid, and the H* ion concentration deduced from a comparison of the velocity constant for the hydrolysis of cane sugar in the presence of the free acid (k ), and with the addition of urea (k). 1 Walker, Proc. Roy. Soc. (Edin.), 1894, 18, 255. 292 OUTLINES OF PHYSICAL CHEMISTRY Normal hydrochloric acid + c normal urea. k/ko I - k/ko C-I + kjko c. k. free HC1. = salt formed. = free urea. Kh. 0-00315=^ I o*5 0-00237 0'753 0-247 0-253 0-77 I'O 0*00184 0-585 0-4I5 0'535 0*82 2'O 0-00114 0-36 0-64 1-36 0-77 4-0 0*0006 0*19 0-81 3-19 0*75 On the assumption that the rate of hydrolytic decomposition is proportional to the H- ion concentration, kjk represents the concentration of the "free" hydrochloric acid, and (i - kjk ) that of the bound acid, which is, of course, that of the unhydro- lysed salt. The concentration of the free urea, that is, of the hydrolysed salt, is therefore c - (i + kjko). Substituting in the general formula [free base] [free acid] [c - (i + k\kj\\k\k^ = K [unhydrol. salt] i - k\k Q The values of the hydrolysis constant are given in the sixth column of the table, and are approximately constant, as the theory requires. The degree of hydrolysis of a few salts of weak bases and strong acids in i/io molar solution at 25 is given in the table, and the results should be compared with the values for the dissociation constants of weak bases (p. 275) in order to illustrate equation (2). Salt. Degree of hydrolysis. Ammonium chloride . , . 0-005 P er cent - " Aniline hydrochloride . . 1*5 Thiazol hydrochloride . . . 19 Glycocoll hydrochloride . . 20 Hydrolysis of the Salt of a Weak Base and a Weak Acid The hydrolysis of aniline acetate, a typical salt of this class, is represented by the equation C 6 H 5 NH 8 CH 8 COO + HOH^C 6 H 5 NH 3 OH + CH 3 COOH, EQUILIBRIUM IN ELECTROLYTES 293 which, on the assumption that the salt is completely, the base and acid not at all, ionised, may be written as follows C 6 H 5 NH 3 - + CH 3 COO' + HOH^C 6 H 5 NH 3 OH + CH 3 COOH. Applying the law of mass action, and using the former symools, [BOH][HA] [basejacid] K w [B-JA-] ~ [unhydrol. salt] 2 * K*K 6 ' If we express the amounts (in mols) of the base, acid and salt respectively in volume v of the solution by ^, a and 5 respectively, the above equation becomes that is, the degree of hydrolysis of the salt of a weak base and a weak acid is independent of the dilution. Experiment shows that in dilutions of 12*5 and 800 litres, aniline acetate is hydrolysed to the extent of 45-4 and 43*1 per cent, respectively ; the slight deviation from the requirements of the theory is doubtless due to the fact that the assumptions made in deducing the above formula are only approximately true. Determination of the Dissociation Constant for Water It has been shown above that the process of hydrolysis in the case of a salt of a strong base and a weak acid may be looked upon as a distribution of the base between the weak acid and water acting as an acid, and the degree of hydrolysis therefore depends on the relative strengths of the weak acid and water. The relationship between these three factors is expressed by the equation [free acid] [free base] _ _ K, [unhydrol. salt] h " Kj where K/, is the hydrolysis constant, K a the dissociation con- stant (or the acid, and K w the ionic product for water. It is clear that if the degree of hydrolysis of a salt and the dissocia- tion constant of the acid are known, K^, can be calculated, and 294 OUTLINES OF PHYSICAL CHEMISTRY this is one of the most accurate methods for determining the degree of dissociation of water. As an illustration, we may calculate K w from Shields's value for the hydrolysis of sodium acetate 0*008 percent, in 0*1 molar solution at 25 (Arrhenius, Feb., 1893). We have C ac id = Cbase = O'OOOoS X O'l, C sa it = 0*1 (the amount hydrolysed being negligible in comparison). (0-00008 x o*i) 2 Hence v '- = 0-64 x io~ 9 = K h . O'l Now K w = K h K a = (0-64 x lo' 9 ) x (r8 x io- 6 ) = r 16 x lo" 14 . Since [H-][OH'J is thus found to be approximately 1*2 x io~ 14 , the concentration of H' or OH' ions (mols per litre) in water at 25 is 1*1 x io~ 7 . K w can also be calculated from measurements of the hydro- lysis of salts of strong acids and weak bases, and, perhaps with still greater accuracy, from measurements with salts of weak acids and weak bases l by means of the formula K h = K w /K A K b . The degree of dissociation of water has been determined by three other methods at 25 with the following results : E.M.F. of hydrogen-oxygen cell (Ostwald, January, 1893) (corrected value), ro x io ~ 7 at 25. Velocity of hydrolysis of methyl acetate (Van't Hoff- Wijs, March, 1893), 1-2 x io ~ 7 at 25. Conductivity of purest water (Kohlrausch, 1894), 1*05 x io " 7 at 25. When it is borne in mind how small the dissociation is, the close agreement in the values obtained by these four inde- pendent methods is very striking, and forms a strong justifica- tion for the original assumption that water is split up to an extremely small extent into ions. The question can be still further tested by applying van't 1 Lunden, J. Chim. Phys.j 1907, 5, 574 ; Kanolt, J. Amer. Chem. Soc. t 1907, 29, 1402. EQUILIBRIUM IN ELECTROLYTES 295 HofFs equation connecting heat development and displacement of equilibrium to the equilibrium between water and its ions. For the degree of dissociation at different temperatures, the following values were obtained by Kohlrausch from conduc- tivity measurements : Temperature . o 2 10 15 26 34 42 50 Degree of dissociation 0*35 0-39 0^56 0*8 1*09 1*47 1*93 2*48 x io~ 7 From any two of these measurements the heat development, Q, of the reaction, H 2 O ^ H* + OH', can be calculated by sub- stitution in the general formula (p. 167). log loKl - log 10 K 2 = From the values l of K at o and 50, Q = - 13,740 cal., and from that at 2 and 42, Q = - 13,780 cal. In a previous section (p. 284) it has been pointed out that, according to the electrolyte dissociation theory, the neutraliza- tion of a strong base by a strong acid consists essentially in the combination of H* and OH' ions to form water. The heat given out in the reaction is about 13,700 cal. for molar quanti- ties, in excellent agreement with the above value. This sup- ports the assumption that the variation of the conductivity of pure water with temperature is due to the displacement of the equilibrium H- + OH' ^H 2 O, in the direction indicated by the lower arrow. The value of Q, obtained directly as above, may be termed the heat of ionisation of water ; it is the heat given out when i mol of H* and OH' ions combine to form water. The heat of ionisation of any electrolyte can naturally be calculated in the same way from the displacement of the equili- brium with temperature. The effect of increased temperature on the degree of ionisation is almost always slight, and in the majority of cases the ionisation is slightly diminished. As an illustration, the degree of electrolytic dissociation for i/io molar sodium chloride over a wide range of temperature, as deter- 1 K a = (2-48 x io- 7 ) 2 at 50; K a (0-35 x io- 7 ) 2 at o (p. 283). 296 OUTLINES OF PHYSICAL CHEMISTRY mined by Noyes and Coolidge, 1 may be quoted. The values obtained were 84 per cent, at 18, 79 per cent, at 140, 74 per cent, at 218, 67 per cent, at 281, and 60 per cent, at 306. Corresponding with the small variation in the degree of ionisa- tion with temperature, the heat of ionisation is small, and may be positive (as in the present case) or negative. Theory of Indicators The indicators used in acidimetry and alkalimetry have the property of giving different colours depending on whether the solution is acid or alkaline. Ac- cording to Ostwald's theory, which has met with fairly general acceptance, such indicators, including methyl-orange, phenol- phthalein and /-nitrophenol, are weak electrolytes, and their use depends on the fact that the ions and the non-ionised com- pounds have different colours. Since salts are almost always highly ionised, it is clear that only weak acids and bases can be employed as indicators. Phenolphthalein is a very weak acid, the non-ionised acid is colourless, and the negative ion red. In aqueous solution it is ionised according to the equation HP^H'-f- P'(red) (where P' is the negative ion), but so slightly that the solution is practically colourless. If now sodium hydroxide is added, the highly-dissociated sodium salt is formed, and the solution is deeply coloured owing to the presence of the red anion, P'. If, on the other hand, the solution contains a slight excess of acid, the increased H* ion concentration drives back the ioni- sation of the phenolphthalein in the direction indicated by the lower arrow, and the solution becomes colourless (cf. p. 277). Finally, if a weak base, such as ammonium hydroxide, is added, the ammonium salt will be partly hydrolysed, according to the equation NH 4 P + HOH ^ NH 4 OH + HP, and excess of the base will be required in order to drive back l Zeitsch. Physikal Chem., 1904, 46, 323. EQUILIBRIUM IN ELECTROLYTES 297 the hydrolysis (p. 289) ; in other words, there will not be a sharp change of colour when ammonium hydroxide is added. Methyl-orange is an acid of medium strength, the non-ionised acid is red, the negative ion yellow. As the acid is ionised in aqueous solution to some extent, according to the equation HM (red) ^ H- + M' (yellow), the solution shows a mixed colour. The effect of the addition of acids and alkalis is similar to that on phenolphthalein, and only differs in degree. Since the aqueous solution already con- tains a considerable proportion of H* ions, it is evident, from the considerations advanced on p. 276, that a considerable excess will be required to drive back the dissociation in the direction indicated by the lower arrow, so as to turn the solu- tion red. The proportion of H' ions in such a weak acid as acetic acid is not sufficient for this purpose, and therefore methyl-orange should not be employed as an indicator for weak acids. It is, on the other hand, a suitable indicator for weak bases, such as ammonia, as the salt formed is much less hydrolysed than the corresponding phenolphthalein salt, and therefore the change of colour is sharper. Basic indicators are not in use. The considerations to be borne in mind in selecting an indicator, or in choosing a suitable alkali for titrating an acid, or vice versa, may be put concisely as follows (Abegg) : Solutions used. Indicator Examnles Acid. Base. Strong Strong Any Any Strong Weak Weak Strong Strong acid Weak acid Methyl-orange, /-nitrophenol Phenolphthalein, litmus Weak Weak None satisfactory Should be avoided Some investigators maintain that the ionisation theory does not give a satisfactory representation of the behaviour of indi- 298 OUTLINES OF PHYSICAL CHEMISTRY cators, but that the changes of colour are due to changes of constitution, usually from the benzenoid to the quinonoid type and vice versd. 1 In an aqueous solution of phenolphthalein, for instance, there are only traces of the quinonoid (coloured) modifi- cation, and the solution is colourless, but on the addition of alkali the phenolphthalein salt is formed, the negative ions of which, being of the quinonoid type, are strongly coloured. The Solubility Product We have now to consider an equilibrium of rather a different type in which the solution is saturated with regard to the electrolyte. In such a case there is equilibrium between the solid salt and the non-ionised salt in the solution, so that the concentration of the non-ionised salt remains constant at constant temperature. Further, there is equilibrium in the solution between the non-ionised salt and its ions, which may be represented, in the case of silver chloride, for example, by the equation Ag- + Cl'^AgCl. Applying the law of mass action, we have, for the latter equilibrium, [Ag'][Cl'] - K[AgCl] = S, where S is the product of the concentrations of the two ions the so-called solubility product and is constant, since the right-hand side of the above equation is constant. The equi- libria in the heterogeneous system may be represented as follows : Ag + Cr^AgCl(in solution) * t AgCl (solid). As will be shown later, the solubility product for silver chloride at 25 is 1*56 x io~ 10 , when the ionic concentrations are ex- pressed in mols per litre. If the solution has been prepared by dissolving the salt in water, the ions are necessarily present in equivalent proportions, so that a solution of silver chloride, saturated at 25, contains \/i'56 x io~ 10 = 1*25 x io~ 5 mols of Ag* and of Cl' ions. The ions need not, however, be present in equivalent propor- 1 C/. Hewitt, Analyst, 1908, 33, 85. EQUILIBRIUM IN ELECTROLYTES 299 tions ; if by any means the solubility product is exceeded, for example, by adding a salt with an ion in common with the electrolyte, the ions unite to form undissociated salt, which falls out of solution, and this goes on till the normal value of the solubility product is reached. Perhaps the best-known illustra- tion of this is the precipitation of sodium chloride from its saturated solution by passing in gaseous hydrogen chloride. In this case the original equilibrium between equivalent amounts of Na* and Cl' ions is disturbed by the addition of a large excess of Cl' ions, and sodium chloride is precipitated till the original solubility product is regained, when the solution con- tains an excess of Cl' ions and relatively few Na* ions. As already mentioned, the difference between the present form of equilibrium and those previously considered is that the concentration of the non-ionised salt in the solution is constant at constant temperature. If it is diminished in any way, salt is dissolved till the original value is reached ; if it is exceeded, as in the case just mentioned, salt falls out of solution till the original value is reached. Since the equilibrium equation for a binary salt is symmetrical with regard to the two ions, it follows that the solubility of such a salt should be depressed to the same extent by the addition of equivalent amounts of its common ions, whether positive or negative. This consequence of the theory was tested by Noyes, who determined the influence of the addition of equivalent amounts of hydrochloric acid and of thallous nitrate on the solubility of thallous chloride, with the following results : Solubility of thallous chloride at 25 : Concentration of Substance added T1NO S added. HC1 added. (mols per litre). 0*0161 0*0161 0*0283 0-0084 0*0083 0*147 0*0032 0*0033 300 OUTLINES OF PHYSICAL CHEMISTRY The figures in the first column show the amounts of thallous nitrate and of hydrochloric acid added, those in the second and third columns represent the solubility of thallous chloride in mols per litre. The results show that the requirements of the theory are satisfactorily fulfilled. The above results hold independently of the relative amounts of ions and non-ionised salt in the solution. Since in dilute solution all salts are highly ionised, it may, however, be as- sumed that difficultly soluble salts, such as silver chloride, are almost completely ionised in solution ; in other words, the con- centration of non-ionised salt in solution may be regarded as negligible in comparison with that of the ions. This deduction is of great importance in estimating the solubility of difficultly soluble salts (see next page). Applications to Analytical Chemistry The above con- siderations with regard to the solubility product are of the greatest importance for analytical chemistry. A precipitate can only be formed when the product of the ionic concentrations attains the value of the solubility product, which for every salt has a definite value depending only on the temperature. For example, magnesium hydroxide is precipitated from solutions of magnesium salts by ammonia because the solubility product [Mg"] [OH'] 2 is exceeded. When, however, ammonium chloride is previously added in excess to the hydroxide, the OH' ion concentration is diminished to such an extent (p. 277) that the solubility product is not reached, and precipitation no longer occurs. Similarly, zinc sulphide is precipitated when the product [Zn"][S"] exceeds a certain value. In alkaline solu- tion, an extremely small concentration of hydrogen sulphide suffices for this purpose, as the sulphide is considerably ionised, but in acid solution the depression of the ionisation of the hydrogen sulphide, in other words, the diminution in the con- centration of S" ions, is so great that the solubility product is not reached. On the other hand, the solubility product for certain heavy metals, such as lead, copper, and bismuth, is so EQUILIBRIUM IN ELECTROLYTES 301 small that it is reached even in acid solution. It is, however, possible to increase the acid concentration (and therefore to diminish the S" ion concentration) to such an extent that the ionic product is not reached even for some of the above metals, for example, lead sulphide in concentrated hydrochloric acid is not precipitated by a current of hydrogen sulphide. On the same basis, a fact which has long been familiar in quantitative analysis, that precipitation is more complete when excess of the precipitant is added, can readily be accounted for. A saturated aqueous solution of silver chloride contains about 1*25 x io~ 6 gram equivalents of the salt per litre, and the ad- dition of ten times that concentration of Cl' ions (added in the form of sodium chloride) will dimmish the amount of silver in solution to about i/io of its original value (on the assumption that the concentration of the non-ionised salt is negligible in comparison with that of the ions) (cf. p. 277). It is thus evident that in the gravimetric estimation of combined chlorine as silver chloride there might be considerable error owing to the solubility of silver chloride in water, but if a fair excess of the precipitant is used, the error is quite negligible. The concentration in saturated solution at 25, and the solubility product of a few difficultly soluble salts are given in the accompanying table. Salt. Saturation Concentration Solubility Product (mols per litre). (mols per litre). Silver chloride Ag f = 1*25 x io~ 6 1*56 x io~ 10 bromide ,, = 6*6 x io~ 7 4-35 x io~ 13 iodide = 1*0 x io~ 8 i'o x io~ 16 Thallous chloride Tl* r6 x io~ 2 2-6 x io~ 4 Cuprous chloride Cu* = i f i x io~ 3 1*2 xio~ 6 Lead sulphide Pb" = 5'i x io~ 8 2-6 x io- 15 Copper sulphide Cu" = i'i x io~ 21 1-2 x io~ 42 Experimental Determination of the Solubility of Diffi- cultly Soluble Salts When a saturated solution of a rela- 302 OUTLINES OF PHYSICAL CHEMISTRY tively insoluble salt is so dilute that complete ionisation may be assumed (/* = ^ ), the solubility of the salt may readily be obtained from electrical conductivity measurements. The molecular conductivity at infinite dilution, /x^ , can be obtained indirectly (p. 258), the specific conductivity of the saturated solution is determined in the usual way, and, by substitution in the formula /x^ = KV, we obtain the value of 0, that is, the volume in c.c., in which a mol of the substance is dissolved. If the solubility is required in mols per litre, then v = 1000 V, and JUL OQ = IOOO *V, where V is the volume in litres in which a mol of the sub- stance is dissolved. As the specific conductivity of such a solution is small, the conductivity of the water becomes of importance, and it is necessary to subtract from the observed specific conductivity of the solution the conductivity of the water, determined directly. For such measurements, "con- ductivity " water, of a specific resistance not much less than io 6 ohms, should be used. As an example of the determination of solubilities by this method, Bottger found that a solution of silver chloride saturated at 20 had K 1*33 x io~ 6 after subtracting the specific con- ductivity of the water. Hence, as p,^ for silver chloride at 20, determined indirectly (p. 258), is 125-5, we obtain, by substitu- tion in the above formula, 125-5 = 1000 x 1*33 x io~ 6 V, and V = 5_5 04 400, 1-33 x io- that is, 94,400 litres of a solution of silver chloride, saturated at 20, contain i mol of the salt. In one litre of solution there is, therefore, 1/94,400 = 1*06 x io ~ 6 mol, or 0*00152 grams of silver chloride. The values for the solubility of a number of difficultly soluble salts obtained by this method are given in the previous section (p. 301). EQUILIBRIUM IN ELECTROLYTES 303 Complex Ions Complex ions have already been defined as being formed by association of ions with non-ionised molecules It is well known that though silver halogen salts are only slightly soluble in water they are readily soluble in the presence of ammonia. This phenomenon is due to the formation of complex ions (p. 281), in which the Ag* ions are associated with ammonia molecules, forming univalent ions of the type Ag(NH 3 )^. As nearly all the silver is present in this form and very little in the form of Ag' ions, it is evident that a solution may contain a very considerable amount of a silver salt before the solubility product [Ag'] [X'] is reached. The composition of complex ions can be determined by a number of methods, including electrical migration measure- ments, distribution measurements, and solubility determina- tions. Thus the fact that the silver moves towards the anode when an electric current is passed through a solution of potassium silver cyanide shows that the metal in question is a constituent of a complex anion, and from the alteration in the composition of the anode solution caused by the passage of a known quantity of electricity it can be shown that the anion has the formula Ag(CN) 2 '. In certain cases (e.g., solutions of cupric chloride and of cadmium iodide) the metal migrates, for the most part, to the cathode in dilute solution, and to the anode in concentrated solution. This observation is readily accounted for if complex ions are formed which undergo partial dissociation on dilution, e.g. CdI 2 + 2!' ^ Cdl/. Distribution measurements have been used to determine the composition of the azure blue solutions obtained by adding ammonia in excess to solutions of cupric salts. From a com- parison of the partition of ammonia between chloroform and water alone and between chloroform and water containing varying amounts of a cupric salt it was shown that each atom of copper bound four molecules of ammonia, forming complex Cu(NH 3 ) 4 " ions. Similarly, from observations of the effect of potassium iodide (added to the aqueous layer) on the distribu- 304 OUTLINES OF PHYSICAL CHEMISTRY tion of iodine between water and carbon disulphide the con- clusion was formed that complex I 3 ' ions (together with the complex salt KI 3 ) are present in the aqueous solution. Solubility measurements were made use of in determining the composition of ammoniacal solutions of silver salts. The amounts of silver chloride taken up by aqueous solutions of ammonia of various concentrations were determined, and, by application of the law of mass action, it was found that the expression A /XTTT \ was most nearly constant, and, there- fore, that the complex ion present in the solution in largest proportion is Ag(NH 3 )' 2) corresponding with the complex salt Ag(NH 3 ) 2 Cl. It is interesting to note that the only solid complex salt which has been separated from such solutions has the formula 2AgCl, sNH 3 . Influence of Substitution on Degree of lonisation Reference has already been made to the influence of substitu- tion on the strength of acids. As the effect of substitution on the degree of ionisation has been most extensively investigated for this class of compound, a few further examples may be given. In the accompanying table, the affinity or dissociation constants for some mono-substituted acetic acids are given, the value of K holding for 25 (concentrations in mols per litre). Acetic acid CH 3 COO*H .... 0-000018 Propionic acid CH 3 CH 2 COO'H . . 0*000013 Chloroacetic acid CH 2 C1COO'H . . 0-00155 Bromoacetic acid CH 2 BrCOO*H . . 0-00138 Cyanacetic acid CH 2 CNCOO'H . . 0*00370 Glycollic acid CH 2 OHCOO-H . . 0-000152 Phenylacetic acid C 6 H 5 CH 2 COO'H . 0-000056 Amidoacetic acid CH 2 NH 2 COO'H . 3-4 x 10 - 10 As the carboxyl group only is concerned directly in ionisation, the above table affords an excellent illustration of the influence of a group on a neighbouring one. The table shows that when one of the alkyl hydrogens in acetic acid is displaced by Cl, Br, CN or OH or C 6 H 5 an increase in the activity of the EQUILIBRIUM IN ELECTROLYTES 305 acid is brought about ; the effect is least for the phenyl group and greatest for the cyanogen group. On the other hand, the methyl group (in propionic acid) diminishes the activity slightly, and the amido group diminishes it enormously. These observations can readily be accounted for 1 on the assumption that the atoms or groups take their ion-forming character into combination. Thus the Cl, Br, CN and OH groups, which tend to form negative ions, increase the tendency of the groups into which they enter to form negative ions. The " negative favouring " character of the phenyl group is slight but distinct. On the other hand, the so-called basic groups, such as NH 2 , lessen the tendency of the group into which they enter to form negative ions, as is very strikingly shown in the case of amidoacetic acid. The methyl group has also a slight diminishing effect on the tendency of a group to form negative ions. The magnitude of the influence of a substituent on a particu- lar group depends on its distance from that group. This is very well shown by the influence of the hydroxyl group on the affinity constant of propionic acid. Propionic acid CH 3 CH 2 COO'H . . . 0-0000134 Lactic acid CH 3 CHOHCOO'H . . 0-000138 /2-oxypropionic acid CH 2 OHCH 2 COO'H . 0*0000311 When the OH group is in the a (neighbouring) position its effect on the dissociation constant is more than four times as great as when it is in the ft position. It seems plausible to suppose that a comparison of the influence of groups in the ortho, meta and para positions on the carboxyl group of benzoic acid might throw some light ori the question of the relative distances between the groups in the benzene nucleus. The dissociation constants of benzoic acid and the three chlor-substituted acids are as follows: 1 A complete theory of the phenomena in question has recently been worked out by Fliirscheim (Trans. Chem. Soc,, 1909, 95, 718 ; Proc., 1909, 306 OUTLINES OF PHYSICAL CHEMISTRY Benzole acid C 6 H 5 COOH . . . o -000060 o- Chlorobenzoic acid C 6 H 4 C1COOH . . 0-00132 m- 0-000155 /- n . . 0-000093 It will be observed that the presence of the halogen in the ortho position greatly increases the strength of the acid, and it is a general rule that the influence of substituents is always greatest in this position. The effect of substituting groups in the meta and para positions is much smaller, and the order of the two is not always the same. As the table shows, w-chlorobenzoic acid is rather stronger than the para acid, but on the other hand /-nitrobenzoic acid is somewhat stronger than the meta acid. Similar considerations apply to the influence of substituents on the strength of bases, but, as is to be expected, the effect of the various groups is exerted in the opposite direction to that on acids. Thus the displacement of a hydrogen atom in ammonium hydroxide by the methyl group gives a stronger base (methyl amine) but the entrance of a phenyl group gives a much weaker base (aniline) (cf. p. 275). Reactivity of the Ions It is a well-known fact in qualita- tive analysis that in the great majority of cases the positive component of a salt (e.g., the metal) answers certain tests, quite independently of the nature of the acid with which it is combined, and in the same way acids have certain characteristic reactions, independent of the nature of the base present. These facts are plausibly accounted for on the electrolytic dissociation theory by assuming that the positive and negative parts of the salts (the ions) exist to a great extent independently in solution, and that the well-known tests for acids and bases are really tests for the free ions. Thus silver nitrate is not a general test for chlorine in combination, but only for chlorine ions. It is well known that potassium chlorate gives no precipitate with silver nitrate, although it contains chlorine ; this is readily accounted for on the electrolytic dissociation theory because the solution of the salt contains no Cl' ions, but only C1O 8 ' ions, which give EQUILIBRIUM IN ELECTROLYTES 307 their own characteristic reactions. These views appear still more plausible when cases are considered in which the usual tests fail, for example, mercuric cyanide does not give all the ordinary reactions for mercury. This could be accounted foi by supposing that the compound is not appreciably ionised in solution, so that practically no Hg" ions are present, and as a matter of fact the aqueous solution of mercuric cyanide is practically a non-conductor. The chief characteristic of ionic reactions is their great rapidity ; they are for all practical purposes instantaneous, and it is doubt- ful if the speed of a purely ionic reaction has so far been measured. It is well known that silver nitrate reacts with the chlorine in organic compounds such as ethyl chloride and chlor- acetic acid, but very slowly as compared with its action on sodium chloride. There is good reason for supposing that the reactions last mentioned are not ionic actions, but that the changes take place between the silver salt and combined chlorine. The great reactivity of the ions in cases where it is known that they are actually present has led Euler and others to postulate that all reactions are ionic, and that in very slow reactions we are dealing with excessively small ionic concen- trations. 1 This question cannot be adequately considered here, but it may be mentioned that the available experimental evi- dence does not seem to lend any support to Euler's theory. There is good reason to suppose that chemical reactions may take place between non-ionised molecules as well as between ions. Amphoterlc Electrolytes. It is a familiar fact that the hydroxides of certain polyvalent metals show both basic and acidic properties, since they form salts both with acids and bases, e.g.) lead hydroxide, Pb(OH) 2 ; aluminium hydroxide A1(OH) 3 . In terms of the ionisation theory, these compounds must give both hydrogen and hydroxyl ions on dissociation. Substances of this type, which can ionise in more than one way, are termed amphoteric electrolytes. Lead hydroxide, Pb(OH) 2 , can dissociate according to the following equations : 1 Compare Arrhenius, Electrochemistry (English Edition), p. 180. 3 o8 OUTLINES OF PHYSICAL CHEMISTRY (i.a)Pb(OH)jPb(OH)- + OH'; (i.b)Pb(OH)^Pb- + OH' ( 2 .a)Pb(OH) 2 ^PbO(OH)'+H- ; ( 2 .b)PbO(OH)'^PbO 2 "+H- and doubtless all these compounds are present in greater or less concentration in an aqueous solution of lead hydroxide. It will of course be understood that the concentrations of H- and of OH' ions cannot both be considerable in the same solu- tion since the equilibrium [H*] [OH'] = k always holds (p. 283). When an acid is added to the hydroxide, the OH' ions com- bine with the H* ions of the acid to form water, more hydr- oxide dissociates according to equations la and ib, the fresh OH' ions combine with the H- ions to form water, and so on, till ultimately, if sufficient acid is added, the solution contains chiefly Pb" ions and anions derived from the acid. If, on the other hand, alkali is added to the hydroxide, the OH' ions combine with the H* ions derived from the hydroxide and dis- sociation proceeds progressively according to the upper arrows in equations 2a and 2b till ultimately the solution contains chiefly PbO 2 " ions and cations derived from the alkali added. The proof of the above statements is that on electrolysis the lead in acid solution travels to the cathode, in alkaline solution to the anode. Some more complicated compounds can split off both H- and OH' from a single molecule, leaving an uncharged ion or rather an ion which is both positively and negatively charged. For glycine (amidoacetic acid) we have the following equilibrium : + OH-H 3 NCH 2 COOH^H 3 NCH 2 COO + H- + OH'. Ions of this type are termed zwitter ions or hermaphrodite ions. Since they are electrically neutral, they are not affected by an electric current. Practical Illustrations. Dilution Law. Conductivity of Acids and Salts. Many of the results discussed in this chapter can be conveniently illustrated by means of the apparatus J shown in Fig. 36. The glass vessels each contain two circular electrodes of platinized platinum, the lower one is connected with a wire which passes through the bottom of the vessel and is connected through a lamp to the wire E. The upper electrode, which is movable, is connected to a wire which 1 Noyes and Blanchard, J. Amer. Chem. Soc., 1900, 22, 726. EQUILIBRIUM IN ELECTROLYTES 39 passes through the cork loosely closing the vessel, and is connected to the upper wire F. The electrodes in each vessel should be of approximately the same cross-section, and the four lamps of equal resistance. The wires E and F are connected to the terminals of a source of alternating current, and as they are at constant potential throughout, the fall of potential through each of the vessels from E to F must be the same when a current is passing. s B FIG. 36. The use of the arrangement may t>e illustrated by employing it to prove the dilution law in the form a = *Jkv. Solutions of monochloracetic acid containing i mol of the salt in i, 4 and 1 6 litres respectively are prepared, and the vessels A, B and C nearly rilled with them. When connection is made with the alternating current, it will be found that the brightness of the lamps is very different, but the positions of the upper electrodes can be so adjusted that the lamps are equally bright. Under these circumstances it is evident that the resistance of each 310 OUTLINES OF PHYSICAL CHEMISTRY solution is the same. On measuring the distances between the electrodes, it will be found that for the solutions v = i, v = 4, v = 1 6, the distances are in the ratio 4:2:1. Hence, as the conductivities are inversely proportional to the distances between the electrodes, aoc *Jv. Further, it may be shown that, although acids differ very greatly in conductivity, neutral salts, even of weak acids, have a conductivity nearly as great as that of strong acids. The vessels are filled with 1/4 normal solutions of hydrochloric acid, sulphuric acid, monochloracetic acid and acetic acid respectively, and when the distances are altered till the lamps are equally bright, it will be found that the electrodes are very near in the acetic acid solution, far apart in the hydrochloric acid solution, and at intermediate distances for the other two acids. Sufficient sodium hydroxide to neutralize the acid is now added to each vessel, and after stirring and again adjusting to equal brightness of the lamps, it will be found that the distances for all four solutions are approximately equal. Equilibrium Relations as shown by Indicators The equi- librium relations in the case of weak acids and bases may be shown very well by means of indicators. Each of two beakers contains 100 c.c. of water, i c.c. of /i sodium hydroxide, and a few drops of methyl-orange. To the con- tents of one beaker n hydrochloric acid is added drop by drop by means of a pipette, and to the other n acetic acid is added in the same way till both solutions just become red. It will be observed that whereas about i c.c. of hydrochloric acid brings about the change of colour (owing to its relatively high concentration in H- ions), several c.c. of acetic acid are required to produce the same effect, owing to the much smaller H' ion concentration of the latter solution. If now a con- centrated solution of sodium acetate is added to the last solution, the yellow colour of the methyl-orange will be re- stored ; the acetate reduces the strength of the acid to such an extent (p. 277) that the H* ion concentration is no longer sufficient to drive back the ionisation of the methyl-orange. EQUILIBRIUM IN ELECTROLYTES 311 The effect of hydrolysis may be illustrated with indicators as follows: Each of two beakers contains 50 c.c. of 1/2 n hydro- chloric acid and a few drops of methyl-orange and phenol- phthalein respectively. If n ammonium hydroxide is slowly added to the solution containing methyl-orange, the colour will change when about 25 c.c. of ammonia has been added, but a much greater quantity of the same solution will be re- quired to redden the phenolphthalein solution. The explanation of this behaviour has already been given. Owing to the fact that the ammonium salt of phenolphthalein is considerably hydrolysed, it is necessary to add a fair excess of the base before the coloured phenolphthalein ions are produced in considerable amount. The Solubility Product The conception of the solubilitj product may be illustrated by the method employed by Nernst in proving the formula experimentally. A saturated solution of silver acetate is prepared by shaking the finely-powdered salt with water for some time. To a few c.c. of the solution in a test-tube a few c.c. of a fairly concentrated solution of silver nitrate are added, and to another portion of the acetate solution a solution of sodium acetate equivalent in strength to the silver nitrate solution, and the mixtures are well shaken. In each tube a precipitate of silver acetate will be formed. Complex Ions The evidence in favour of the view that in solutions of silver salts in potassium cyanide the silver is mainly present as a constituent of a complex anion, Ag(CN) / 2 , is that the silver migrates towards the anode during electrolysis. The copper in Fehling's solution is also mainly present as a component of a complex anion, as may readily be shown qualitatively by a simple experiment described by Kiister. A U-tube is about half-filled with a dilute solution of copper sulphate, and the two limbs are then nearly filled up with a dilute solution of sodium sulphate in such a way that the boundaries remain sharp. A second U-tube is filled in an exactly similar way with Fehling's solution in the lower part and an alkaline solution of sodium tartrate in the upper part. 312 OUTLINES OF PHYSICAL CHEMISTRY the arrangement being such that the Fehling's solution in the one tube stands at the same level as the copper sulphate solu- tion in the other tube. The U-tubes are then connected by a bent glass tube, filled with sodium sulphate solution, and with the ends dipping in the sulphate and tartrate solutions respectively. A small current is then sent through the U-tubes in series, by means of poles dipping in the outer limbs of the tubes, and after a time it will be observed that the copper sulphate boundary has moved with the positive current, whilst the coloured boundary in the other tube has moved against the positive current towards the anode. It is therefore evident that in the latter case the copper is present in the anion, as stated above. Chemical Activity and lonisation The great difference in chemical and electrical activity produced by ionisation is well shown by comparing the properties of solutions of hydrochloric acid gas in water and in an organic solvent such as toluene. Whilst the former solution conducts the electric current and dissolves calcium carbonate rapidly, the latter solution is a non- conductor, and has little or no effect on calcium carbonate. The same fact is illustrated by the interaction of silver nitrate with potassium bromide, ethyl bromide and phenyl bromide respectively in alcoholic solution. Approximately 5 per cent, solutions of the bromides in ethyl alcohol are prepared, and to each solution is added a few c.c. of a saturated solution of silver nitrate in alcohol. With the potassium bromide there is an immediate precipitate, the action being ionic. With ethyl bromide the reaction is very slow, and there is no apparent reaction with phenyl bromide. The reaction between silver nitrate and ethyl bromide is a good example of a chemical change which is not ionic, as far as one of the reacting substances (the ethyl bromide) is concerned. Non-ionic chemical changes may, however, be very rapid. A solution of copper oleate in perfectly dry benzene reacts immediately with a solution of hydrochloric acid gas in dry benzene, with precipitation of cupric chloride (Kahlenberg). CHAPTER XII COLLOIDAL SOLUTIONS. 1 ADSORPTION Colloidal Solutions. General Up to the present we have dealt with substances which on the basis of their osmotic and electrical behaviour may be classed either as electrolytes or non -electrolytes. In the present chapter we are concerned with a new type of substance which differs in many respects both from typical electrolytes and non -electrolytes. The first discoveries in this field we owe to Thomas Graham (1861) who found that whilst certain substances diffuse rapidly in solution and readily pass through animal and vegetable membranes, other substances diffuse very slowly in solution and are unable to pass through membranes. To the first class of substances, which can readily be obtained in crystalline form, Graham gave the name crystalloids^ whilst the members of the other class, which cannot as a rule be obtained in crystalline form, were termed colloids. Most inorganic acids, bases and salts and many organic compounds, such as acetic acid, cane sugar and urea are crystalloids; starch, gum, gelatine, caramel and pro- teins in general belong to the group of colloids. The dif- ferences in the rates of diffusion in aqueous solution of typical crystalloids and colloids are illustrated in the following numbers, valid for i o, which represent the relative times required for the same amount of diffusion of different substances. 1 For fuller details of the subjects treated of in this chapter see Philip, Physical Chemistry : Its Bearing on Biology and Medicine (Arnold, 1910) ; Freundlich, Kapillarchemie (Leipzig, 1909) ; Wolfgang Ostwald, Kolloid- chemie (Dresden, 1911). 313 3 i4 OUTLINES OF PHYSICAL CHEMISTRY Crystalloids. Colloids. Substance . Relative times of equal diffusion . HC1 i NaCl 2-3 Cane Sugar 7 Albumen 49 Caramel 98 As under equivalent conditions the rate of diffusion is pro- portional to the osmotic pressure of the solute, it follows that the osmotic pressure of dissolved colloids is very small and therefore that their molecular weights are very high. This view as to the high molecular weight of colloids was held by Graham, who suggested that the differences in behaviour of the two classes of substance might be connected with the much greater size of colloidal particles as compared with dissolved particles of crystalloids. It may be said at once that later investigation has fully confirmed the view as to the high molecular weight of colloids in solution. As was to be anticipated, the later developments of the subject have led to modifications of Graham's views in some essential respects. In the first place it has been shown that colloids are not a special class of substances ; the colloidal state is a condition into which practically all chemical substances can be brought by suitable methods. For example, metals such as silver and platinum, and even salts such as silver chloride and sodium chloride, all of which are ordinarily met with in crystalline form, can be obtained in colloidal solution. There are, however, great differences in the readiness with which dif- ferent substances can be brought into the colloidal state, and some substances, such as starch and gelatine, are only met with in solution in the colloidal form. A further point, which has been established within the last few years, is that colloidal solutions are not solutions in the ordinary sense of the term. A true solution has been defined as a homogeneous mixture, and therefore consists of a single COLLOIDAL SOLUTIONS. ADSORPTION 315 phase. A colloidal solution, on the other hand, such as col- loidal platinum, can be shown to be heterogeneous ; that is, it consists of two phases at least. As we shall see later, however, all intermediate stages exist between colloidal solutions and true solutions on the one hand, and between colloidal solutions and ordinary suspensions on the other. Within the last few years it has become usual to speak of the phase present in separate particles as the disperse phase and the liquid in which it is distributed as the dispersion medium. The preparation of some typical colloidal solutions, and the properties characteristic of the colloidal state, will now be considered. Preparation of Colloidal Solutions A suitable colloidal solution for demonstration purposes is that of arsenious sul- phide. It is prepared by passing hydrogen sulphide through a cold aqueous solution of arsenious oxide, free from electrolytes, sufficiently long to ensure conversion to arsenious sulphide. Excess of hydrogen sulphide is then removed as far as possible by a stream of hydrogen. The resulting solution, after filtra- tion, is yellowish in colour and clear by transmitted light, but appears turbid by reflected light. The degree of dispersion of the sulphide (that is, the size of the particles) varies greatly with the mode of preparing the solution. Silicic acid is obtained in colloidal solution by slowly add- ing a solution of sodium silicate to excess of hydrochloric acid and then removing the sodium chloride and free hydrochloric acid by dialysis. The simplest form of dialyser is a tube of parchment paper into which the mixture is poured. The tube is then suspended by its ends in water which is continually re- newed, and in course of time the crystalloids are completely removed by diffusion through the membrane, leaving a pure colloidal solution of silicic acid. Ferric hydroxide is obtained in colloidal solution (so called " dialysed iron ") by dissolving the freshly precipitated hydrox- ide in a dilute solution of ferric chloride, and removing the 316 OUTLINES OF PHYSICAL CHEMISTRY ferric chloride by dialysis. Other colloidal hydroxides may be obtained by an analogous method. The preparation of colloidal platinum according to Bredig has already been described (p. 232). Other colloidal metals (e.g. gold, silver, palladium) have been prepared by the same method. Colloidal gold and other metals can also be pre- pared by reducing the corresponding salts in aqueous solution. Gelatine, gum and certain other substances form colloidal systems on simple solution in water. Osmotic Pressure and Molecular Weight of Colloids- It has already been mentioned that, corresponding with their slow rate of diffusion, the osmotic pressure of colloidal solutions is very small. This is fully confirmed by recent investigations, but direct quantitative measurements by different observers have not led to very concordant results. One of the principal sources of error has been the difficulty of freeing colloids com- pletely from electrolytes, which even in very small concentra- tion have considerable osmotic pressure. This difficulty is to some extent overcome by using another colloid, such as parch- ment paper, as semi-permeable membrane ; one colloid, whilst usually permeable for crystalloids, is impermeable to other col- loids. Hence, as parchment paper and other membranes are permeable for dissolved salts, the latter cannot set up a lasting osmotic pressure, and a pressure which persists for a consider- able time may be regarded as due to the colloid only. As illustrating the nature of the results obtained, Lillie, 1 using a collodion membrane, found that a solution of egg albu- men containing 12-5 grams per litre gave an osmotic pressure of 20 mm. of mercury at room temperature. According to Waymouth Reid the osmotic pressure of a i per cent, solution of haemoglobin is about 4 mm. of mercury, but much higher values, indicating a molecular weight of about 16,000, were ob- tained by Roaf (1910). 1 Amer. Journal of Physiology, 1907, 20, 127. COLLOIDAL SOLUTIONS. ADSORPTION 317 Moore and Roaf l observed a pressure of about 70 mm. of mercury for a 10 per cent, solution of gelatine, which remained fairly steady for two months. The effect of electrolytes on the magnitude of the osmotic pressure depends on the nature of the colloid. Neutral salts in many cases lower the osmotic pressure of colloids, a result probably due to partial coagulation of the colloidal particles. Acids and bases often raise the osmotic pressure of colloids, probably in consequence of chemical combination. As the osmotic pressure of colloids is so small when measured by the direct method it will readily be understood that the freezing points and boiling points of colloidal solutions scarcely differ from those of pure water. This is evident when we consider that a solution of osmotic pressure 70 mms. (as observed in the experiments just described) would have a freezing-point less than -j-J^ below that of water. Optical Properties of Colloidal Solutions The majority of colloidal solutions appear homogeneous even under the highest power of the microscope, but their heterogeneous char- acter is established by means of the so-called "Tyndall phe- nomenon ". When a ray of light enters a darkened room its path is recognised by the scattering of the light at the surface of dust particles. Similarly, the path of a beam passed through a colloidal solution can be detected by the scattering of the light at the surface of the ultramicroscopic particles, whereas no indication is afforded of the path of a beam passed through a solution which contains no particles exceeding a certain magnitude. Light which has passed through a colloidal solu- tion is partially or completely polarised. The Tyndall phenomenon has recently been utilised in the construction of the ultramicroscope, by means of which our knowledge of colloidal solutions has been greatly extended. An intense beam of light (the arc light or, better, sunlight) is 1 Moore and Roaf, Biochem. Journ, 1906, 2, 34. 3 i8 OUTLINES OF PHYSICAL CHEMISTRY directed on a very thin layer of the colloid and the latter examined by a microscope at right angles to the direction of the beam, the entrance of light from other sources being pre- vented. When a homogeneous liquid is used the field remains quite dark, but when the liquid contains discrete particles their presence is indicated by the appearance of colourless or (for smaller particles) characteristically coloured luminous moving points on a dark background. It must be emphasised that the ultramicroscope does not render the particles themselves visible, but only shows the light reflected from them, so that such observations afford no information as to the shape, colour, etc., of the particles. The average size of the particles in a colloidal solution can be estimated indirectly by counting the number in a given volume and determining the total amount of substance by analysis. In this way it has been shown that the particles vary greatly in magnitude, depending on the nature and mode of preparation of the colloidal solution, from such as are visible in the ordinary microscope to those not resolvable even by the ultramicroscope. Particles visible in the ordinary microscope (diameter exceeding 250 /A/A, where //, = 0*001 mm. and /A/A == o -ooooo i mm.) are termed by Zsigmondy microns^ those detected only by the ultramicroscope (diameter 6-250 /A/A) are termed submicrons, and those of diameter less than 6 /A/A amicrons. For comparative purposes it may be mentioned that the wave- length of sodium light is 589 /A/A. It has been calculated l that the diameter of an ether molecule is about 0*6 x io~ 6 mm. = 0-6 /A/A, so that the smallest particle which can be detected by the ultramicroscope has a diameter only ten times greater than that of an average chemical molecule. Brownian Movement When a colloidal solution contain- ing microns (e.g. mercuric sulphide, suspension of gum mastic) is examined under the microscope, the particles are seen to be 1 Perrin, loc. cit., p. 50. COLLOIDAL SOLUTIONS. ADSORPTION 319 performing continuous irregular movements (R. Brown, 1827) "They go and come, stop, start again, mount^ descend, remount again, without in the least tending towards immobility " (Perrin). Observations with the ultra-microscope show that the move- ments are the more brisk the smaller the particles and the less the viscosity of the liquid, and they become more rapid with rise of temperature. The phenomenon persists for years ; it is not due to any external cause, such as alterations of temperature or of illumination, and it is now generally agreed that it is a consequence of "the incessant movements of the molecules of the liquid which, striking unceasingly the observed particles, drive them about irregularly through the fluid, except in the case where these impacts exactly counterbalance one another " (Perrin, loc. at.). It has been shown within the last few years, more particularly by Perrin, that the rates of movement of the particles are in entire accord with those deducted on the basis of the molecular-kinetic theory, which amounts to an experi- mental proof of the atomic constitution of matter and of the kinetic nature of heat 1 (cf. p. 32). Electrical Properties of Colloids When two plates are placed at some distance apart in a colloidal solution and con- nected with a source of E.M.F. it will be found as a rule that the particles move slowly towards the anode or cathode ; in other words, they behave as if they are electrically charged. The simplest method of making the experiment is to place the colloidal solution in the lower part of a U-tube, which is filled up on both sides with distilled water in which the electrodes are placed. The latter are then connected with the terminals of the lighting circuit (100-200 volts) and the speed of the moving boundary observed directly. The results show that particles of all kinds move at the rate of 10-40 x io~ B . cm per second for a potential gradient of i volt per cm. As we have seen, this is also the order of the migration velocity of the ions Grundriss der Allg. Chemie., p. iv, 545. 320 OUTLINES OF PHYSICAL CHEMISTRY (p. 253) and we have therefore the remarkable fact that particles of all sizes microns, submicrons, amicrons, ions move with approximately the same speed in the electric field. In the case of the noble metals (gold, platinum, silver, etc.) and the sulphides (arsenic and antimony trisulphides) the particles are negatively charged and move towards the anode, whilst hydroxides (ferric and aluminium hydroxides, etc.) and haemo- globin are positively charged. The charge on some colloids can, however, be altered in sign by certain additions to the medium. Thus Hardy has shown that when acid is added to egg albumen it migrates to the cathode, whilst in alkaline solu- tion it moves towards the anode. The condition in which the colloid is uncharged is known as the isoelectric point, which in the case of egg albumen occurs in approximately neutral solu- tion. Precipitation of Colloids by Electrolytes It is a re- markable fact that many colloidal solutions are readily coagu- lated by the addition of electrolytes. When, for example, a few drops of barium chloride solution are added to a colloidal solution of arsenic sulphide the solution becomes turbid, and in a few minutes the sulphide has completely separated in flocks. The process can be followed under the ultramicroscope, and is seen to consist in a gradual aggregation of the particles (amicrons to submicrons, then to microns and finally to large flocks) the Brownian movement becoming slower and slower and finally ceasing. The efficiency of different electrolytes in the coagulation of arsenic sulphide depends mainly on the valency of the anion and is largely independent of its nature. The molar concen- trations of A1C1 3 , BaCl 2 , and KC1 required to produce same degree of coagulation under conditions otherwise equivalent areas follows: i: 7*4 : 532 (Freundlich). With solutions of ferric hydroxide, on the other hand, the coagulating power of electrolytes is practically independent of the valency of the cation, and is determined chiefly by the valency of the anion. COLLOIDAL SOLUTIONS. ADSORPTION 321 Thus the molar concentrations of K 2 SO 4 and KC1 which pro- duced the same effect are in the ratio i : 45. When it is remembered that the particles of arsenious sul- phide are negatively charged and those of ferric hydroxide positively charged the bearing of these results at once becomes evident. The ion which brings about the coagulation of a colloidal solution is the one carrying a charge of opposite sign to that on the colloidal particles (Hardy). Further investigation has shown that this rule can be extended to the reciprocal action of colloidal particles, inasmuch as two colloidal solu- tions containing particles of contrary sign coagulate on mixing (e.g. colloidal platinum and ferric hydroxide) whilst colloids of the same sign are practically without influence on each other. As regards the nature of the coagulation, it has been shown that in certain cases at least the electrolyte is partially decom- posed, the precipitating ion being carried down along with the precipitate and the inactive ion left in solution in combination with another ion. In order to understand this phenomenon it is necessary to consider rather more fully the question of the stability of a colloidal solution. It has been shown by Hardy, Burton and others that certain colloids reach their point of maxi- mum instability (that is, coagulate most readily) when the charge on the particles (as indicated by their behaviour under the influence of a potential gradient) reaches a minimum. Taking as illustration the coagulation of arsenious sulphide by potassium chloride solution we may assume that some of the salt is taken up by the colloidal particles, the negative charges on the latter are neutralized by the K' ions, with the result that the particles become unstable, aggregate and fall out of solution carrying the K* ions along with them (presumably as a salt). The Cl* ions are left in the solution along with an equivalent of H- ions derived from the hydrogen sulphide always associated with the colloidal sulphide. This is the so-called "adsorp- tion " theory of coagulation. Other theories of the pheno- 21 322 OUTLINES OF PHYSICAL CHEMISTRY menon, notably Billiters "condensation" theory, have also been proposed, but cannot be dealt with here. 1 Suspensions, Suspensoids and Emulsoids All the pro- perties discussed in the previous sections (with the possible exception of the action of electrolytes on the stability) are characteristic of colloidal solutions in general, as well as of suspensions of particles easily visible under the microscope. As typical ' suspensions " may be mentioned clay, finely divided charcoal or gum mastic stirred up with water. They consist of a practically insoluble solid phase, distributed in a liquid, usually water. The particles settle to the bottom of the vessel more or less rapidly, depending on their magnitude, but the system " clears " much more rapidly when electrolytes are added (cf. previous section). From the suspensions we pass through a series of intermediate stages to the suspensoids or suspension colloids, the heterogeneous character of which is only recognised by Tyndall's phenomenon or by the ultramicroscope. Like the suspensions, they consist of a solid phase distributed in a liquid, generally water. " Colloidal solutions " are divided into two fairly well-defined classes, the suspension colloids or sus- pensoids just mentioned and the emulsion colloids or emulsoids. The suspensoids are scarcely more viscous than water, do not gelatinise and are readily precipitated by electrolytes. The emulsoids are viscous, become gelatinous under certain condi- tions and are not readily precipitated by electrolytes. The colloidal metals, sulphides and hydroxides are suspensoids ; silicic acid, gelatine, gum, mucilage of starch and proteins in general are emulsoids. Emulsoids, like suspensoids, are two- phase systems, but consist of two liquid phases, one a honey- comb-like structure, rich in colloid, in the meshes of which the other phase, composed of a dilute solution of the colloid, is distributed. Thus an aqueous solution of gelatine is made up of two phases, one rich in water and containing a 1 Wo. Ostwald, Kolloidchemie, p. 499. COLLOIDAL SOLUTIONS. ADSORPTION 323 little gelatine in true solution, the other rich in gelatine, but containing a little water (Hardy). It is a familiar fact that an emulsoid such as silicic acid can be obtained as a clear, apparently homogeneous solution (p. 315) which on long standing, more rapidly on boiling or on treatment with electrolytes, changes to a semi-solid amorphous mass. The clear solution is termed a sol> the gelatinous mass a gel. The term sol is also applied to suspensoids. When the electrolyte is removed by washing and the gel is again treated with water certain emulsoids, such as the proteins, return to the sol modification (more readily on warming) and are therefore termed reversible colloids. Suspensoids in general and certain emulsoids, such as silicic acid, do not return to the soluble form under these conditions and are therefore known as irre- versible colloids. The coagulation of emulsoids by electrolytes seems to be entirely different to the action on suspensoids, but is by no means well understood. Whether the electrical character of the particles and of the electrolyte plays any part in the process is doubtful ; in fact silicic acid sol seems to be most stable in the electrically neutral condition. The addition of neutral salts in considerable concentration causes the separation of the solid phase, but the ratio of the activities of different electrolytes is quite different from that observed for suspension colloids and resembles the " salting out " observed, for instance, in the effect on the solubility of gases in water (p. 84). Filtration of Colloidal Solutions It has already been pointed out that systems of all degrees of dispersion are met with, from those containing large particles easily visible under the microscope to molecular dispersed systems, which we term true solutions. It is evident, however, that true solutions are only apparently homogenous ; the solute particles are so minute as to escape our present methods of detecting heterogeneity. As already explained, the size of colloidal particles can bo roughly estimated by counting the number in a given volume 3 2 4 OUTLINES OF PHYSICAL CHEMISTRY of solution containing a known weight of the disperse phase. Another method which has recently come into use for this pur- pose is to use filters with pores of different sizes. Bechhold, 1 who has done much work on this subject, uses filter-papers impregnated with gelatine solutions of different concentrations, and finds that a filter with 2 per cent of gelatine retains al\ particles of diameter greater than 44/x/t, one containing 4-4*5 per cent, is required to retain the much smaller particles of serum - albumen, the average molecular weight of which is about 10,000 (3,000-15,000). The permeability of such filters is of course influenced by the pressure under which filtration is carried out. A very early form of the "ultra- filter," introduced by Martin, consists of an ordinary porcelain filter impregnated with gela- tine. Adsorption. General It is a familiar fact that when water containing a colouring matter such as caramel or litmus is shaken up with finely divided charcoal the latter on settling carries down the colouring matter with it, leaving the water practically colourless. Further investigation shows that other substances, including electrolytes and non-electrolytes as well as colloids, are largely taken up by charcoal from aqueous solu- tion, and that other finely divided substances have the same property. Charcoal has also the power of taking up gases, es- pecially those which are easily liquefied, such as ammonia and sulphur dioxide. The nature of this phenomenon will be more readily under- stood in the light of some quantitative observations, and for this purpose the results of a series of experiments carried out by Schmidt 2 on the taking tup of acetic acid from aqueous solution by charcoal are quoted. Animal charcoal (in quan- tities of 5 grams) was shaken up with aqueous solutions of acetic acid (100 ccs. in each case) of different concentrations and the 1 Zeitsch. Chem. Ind. Kolloide, 1907, 2, 3. 2 Zeitsch. physikal Chem., 1910, 74, 689. COLLOIDAL SOLUTIONS. ADSORPTION 325 amount of acid remaining in the water phase determined by titration. In the accompanying table A c represents the amount of acetic acid taken up by the charcoal and A w the amount left in solution at equilibrium. DISTRIBUTION OF ACETIC ACID BETWEEN WATER AND CHARCOAL. A c 0*93 1*15 1-248 i '43 1-62 A w 0*0365 0*084 0-13 0*206 0*350 Q/C W 205 208 180 203 197 As the volume of the solution and the amount of charcoal are kept constant, the amounts given in the table are propor- tional to the respective concentrations, C c and C w , in the two phases. The figures show (i) that in very dilute solution the acid is almost completely taken up by charcoal ; (2) that the con- centration in the charcoal increases much less rapidly than the concentration in the aqueous phase. That we are dealing with true equilibria is shown by the fact that the same results are obtained from either side (starting from concentrated or from dilute solutions of the acid). The question now arises as to how these observations are to be interpreted. In the first instance we will consider whether the process is a physical or a chemical one, and if the former, whether it is mainly a surface condensation or whether solid solutions are formed. It appears highly improbable for several reasons that the phenomena are chemical in nature. In the first place the most various substances, including argon and the other in- active gases, which do not, as far as is known, enter into chemical combination, are taken up by charcoal. Further, a definite chemical compound is constant in composition and, if undissociated, its composition is independent of the concentra- tion in the other phase, whereas, as the table shows, the composi- tion of the carbon-acetic acid system varies continuously 326 OUTLINES OF PHYSICAL CHEMISTRY within wide limits. At first sight it would appear possible to explain the results as being due to the formation of a partially dissociated solid compound in equilibrium with its products of dissociation, but it can easily be shown that this assumption also is incompatible with the facts. Applying the law of mass action to such an equilibrium (in the liquid phase) we have (cf. p. 173) [Absorbent] n * [Substance taken up] ^/[Compound] MS = Const. where the square brackets represent concentrations, and i, 2and s represent the number of molecules of the absorbent (charcoal), the substance taken up (acetic acid) and the compound re- spectively taking part in the equilibrium. Further, since the active masses of the charcoal and the compound are constant [Substance taken up] = Constant (in liquid phase) that is, the concentration of the acetic acid in the solution must be constant as long as both solid phases are present. As a matter of fact, the concentration of acetic acid in the solution increases continuously with the total concentration (compare table), so that no second solid phase (no chemical compound) can be present. The formation of a solid dissociating compound from a solid phase and a substance in solution has been investigated by Walker and Appleyard in the case of diphenylamine and picric acid, which combine to form the slightly soluble brown com- pound diphenylamine picrate. 1 Until the concentration of the acid in the aqueous layer reached 0-06 mols per litre the solid diphenylamine (which is practically insoluble in water) remained colourless, on further addition of picric acid the brown diphenylamine picrate began to form, and finally practically all the diphenylamine was converted into picrate, the concentration of the picric acid in the solution remaining all the time practically constant at 0*06 mols per litre. It is evident that 1 Walker and Appleyard, 1896, 69, 1334. COLLOIDAL SOLUTIONS. ADSORPTION 327 the system exactly corresponds with the calcium carbonate calcium oxide carbon dioxide equilibrium already considered (p. 1 74), except that in the latter case the substance of variable concentration (the carbon dioxide) is in a gaseous and not in a liquid phase. It remains to consider whether the phenomena in question, such as the taking up of acetic acid by charcoal, are due to surface condensation or whether solid solutions are formed. It would seem possible to decide this question at once by observing the rate of establishment of equilibrium, since surface condensation must be a very rapid process, and the formation of a solid solution, whereby (in the case under consideration) one substance has to diffuse into the interior of the other, must be very slow. As a matter of fact the estab- lishment of equilibrium in many cases (but not in all cases, see below) is practically instantaneous, which lends strong support to the surface condensation theory. The strongest evidence in favour of the latter theory, however, is based on a considera- tion of the ratio of the distribution of the substance between the two phases. It has been shown (p. 178) that when a substance distributes itself between two phases the ratio of the distribution is independent of the concentration provided the molecular weight of the solute is the same in both solvents, but if the molecular weight in the solvent A is n times that in the solvent B then \/C A /C B is constant, which may be written more conveniently thus : C^*/C B = Constant. Now the table on p. 325 shows that for the distribution of acetic acid between water and charcoal the formula holds approximately C C 4 /C W = Constant where C e and C w represent the concentrations in charcoal and in water respectively. Comparing this with the distri- bution formula, C A /a yC B ^ Constant, we find that ijx = 4 or x = 1/4; that is % if charcoal and water may be regarded as two solvents 328 OUTLINES OF PHYSICAL CHEMISTRY between which the acetic acid is distributed then the molecular weight of the acid in charcoal is 1/4 that in water. Now it was shown by Raoult that acetic acid exists as single molecules in aqueous solution, so that its molecular weight in charcoal, deduced on the assumption that it is present in solid solution, is an impossible one. Analogous results are obtained with other solutes and other absorbing agents and it follows at once that the " solid solution " explanation of the phenomena under consideration is definitely disproved. There is evidence, however, that in some cases solid solution may play a subsidi- ary part in the phenomena. Thus Davis x found that when iodine is shaken up with charcoal a very rapid action is followed by a slow action, the latter being presumably due to the slow diffusion of the iodine into the interior of the charcoal. Similarly McBain 2 has shown that when hydrogen which has been in contact with charcoal for a long time is pumped out the greater part of it (that condensed on the surface) can be drawn off immediately, but a small residue (presumably present in solid solution) can only be removed very slowly. It has now been established that the phenomenon under consideration is physical in nature and mainly at least due to surface condensation. In order to distinguish it from such a process as the absorption of gases in liquids, an example of true solution, the process is termed Adsorption, and the substance which is condensed on the surface of the solid phase is said to be adsorbed. Adsorption of Gases. Adsorption Formulae. So far we have been concerned mainly with the adsorption of sub- stances from solution. It is now necessary to deal a little more in detail with the fact already mentioned, that porous substances have a considerable adsorptive power for gases, and that those gases which are most easily liquefied are most largely adsorbed. The nature of the results is well shown by the recent accurate 1 Trans. Chem. Soc., 1907, 91, 1666. 2 Phil. Mag., 1909, 18, 816. COLLOIDAL SOLUTIONS. ADSORPTION 329 work of Homfray l and of Titoff 2 on the adsorption of gases by charcoal. The amount of gas adsorbed is proportional to the adsorbing surface and is the greater the lower the temperature and the higher the pressure. Titoff found that the adsorption of hydrogen follows Henry's law, so that the formula CA/CB = Constant applies, where C A represents the concentration in the solid phase, C B that in the gas phase. The other gases at low tem- peratures do not follow Henry's law, but the results are repre- sented fairly satisfactorily by a formula of the type C^/*/C B = Constant. The adsorptive power of charcoal for traces of gas, especially at low temperatures, has been used by Dewar to obtain the highest vacua yet reached; the pressures were too low to be capable of measurement. It has been shown above that a formula of the type C^ ; */C B = Constant an exponential formula affords a fairly satisfactory representation of the adsorption both of gases and dissolved substances. In the literature it is met with in a slightly different form, which will now be given. Instead of writing C^*/G B we may put CA/ C^ = Constant. When for C A we put x/m, where n represents the amount of sub- stance adsorbed by m grams of adsorbent, we obtain, putting p for C B and i/n for x, the formula x/m ftp 1/n where ft and n are constant at constant temperature. When i In = i the adsorption follows Henry's law, but in almost every instance i/n is considerably less than i. This expresses the important fact that adsorption is relatively greatest from dilute solution and falls off rapidly with the concentration (p-325). The Cause of Adsorption Adsorption of gases and liquids occurs more or less at all solid surfaces, a well-known case in point being the adsorption of moisture by glass surfaces, but 1 Proc. Roy Soc., 1910, 84, A, 99. 2 Ztitsch. physikal Chem., 1910, 74, 641. 330 OUTLINES OF PHYSICAL CHEMISTRY it is only when the surface is very large in comparison with the weight of the solid as in the case of porous and finely divided substances that it can readily be measured. We have now to consider why the concentration in the surface layers differs in many cases so greatly from that in the main bulk of the liquid or gas phase. It seems probable at the outset that this must be connected with molecular attraction at the boundary of the phases, in other words with the surface tension (p. 129) and the connection between surface tension and adsorption has been deduced theoretically by Willard Gibbs and by J. J. Thomson. From the general standpoint we must assume that not only increased concentration, but in certain systems a lowering of concentration at the surface, as compared with that in the main bulk of liquid, may occur. Calling an increase of concentration positive adsorption and a diminution negative adsorption, the rule may be expressed as follows : 1 A dissolved substance is positively adsorbed when it lowers the surface tension, negatively adsorbed when it raises the surface tension. The first case is met with in most solutions of organic compounds ; the second in solutions of highly ionised inorganic salts. Further Illustrations of Adsorption One very impor- tant process in which adsorption plays a prominent part is the dyeing of fibres such as wool and silk. Whether dyeing is purely an adsorption phenomenon or whether chemical action also plays a part has given rise to a great deal of discussion, and is by no means finally settled. It has recently been shown that the distribution of crystal violet, new magenta and patent blue between wool, silk and cotton on the one hand and water on the other is satisfactorily represented by the adsorption formula, and the value of the exponent */ is approximately the same as when charcoal is used as absorbent, a result which supports the adsorption theory. On the other hand, Knecht showed some years ago that when the basic dye crystal violet 1 C/. Freundlich, Kapillarchemie. t p. 52. COLLOIDAL SOLUTIONS. ADSORPTION 331 (the hydrochloride of an organic base) is shaken up with wool or silk the dye is decomposed, the cation combining with the fibre and the anion (in this case Cl') remaining in the solution. This result was first described as a case of double decomposi- tion between the dye and the fibre, the dye combining with an organic acid in the fibre to form a salt, and ammonia originally associated with the fibre combining with the chlorine to form ammonium chloride. Freundlich and Neumann l have shown, however, that in certain cases at least the chlorine is not left in the solution as a salt, but in the form of hydrochloric acid. The exact form in which the adsorbed dye occurs on the adsorb- ent does not seem to have been properly established the colour appears to indicate that it is present as a salt and not as the free base. The process just described would at first sight appear to be an ordinary chemical change, but further investigation shows that charcoal and even glass pellets split up dyes in an exactly analogous way, the cation being adsorbed and the anion re- maining in solution. It can scarcely be supposed that the charcoal or the glass enter into chemical action with the dyes. Phenomena of an exactly similar nature have already been met with in connection with the precipitation of colloids by electro- lytes (p. 319), and it has been shown that they are connected with the electrical character of the colloidal particles, that ion being most largely adsorbed which carries a charge of opposite sign to that on the colloid. The splitting of basic dyes de- scribed in the present section might be accounted for on similar lines, as also the well-known fact that an " acid " fibre adsorbs more particularly basic dyes and a " basic '' fibre "acid" dyes. The above is a brief outline of the adsorption theory of dyeing, but the process in any particular case is doubtless complicated by other factors, and at present is far from being understood. It has been suggested by Bayliss and others that adsorption 1 Zeitsch. physikal Chem., 1909, 67, 538. 332 OUTLINES OF PHYSICAL CHEMISTRY plays an important part in enzyme reactions; the substance acted on is first adsorbed by the colloidal enzyme particles and chemical change follows. The interesting fact that colloids such as gelatine increased the stability of suspension colloids such as silver bromide or colloidal gold towards electrolytes, may also be accounted for on the basis of adsorption. In the case under consideration it is assumed that the gelatine is ad- sorbed as a thin film on the surface of the particles, so that the latter do not come directly in contact with the electrolyte. It has quite recently been shown that certain dyes, more parti- cularly erythrosine, also exert a protective action on colloidal silver bromide. Substances acting in this way are termed "protective" colloids. CHAPTER XIII THEORIES OF SOLUTION General The nature of solutions, 1 more particularly as regards the connection between their properties and those of the components, has long been one of the most important problems of chemistry. It was early recognized that the properties of a solution are very seldom indeed the mean of the properties of the components, as must necessarily be the case if solvent and solute exert no mutual influence. Thus we know that when two liquids are mixed either expansion or contraction may occur, the boiling-point of a mixture may be higher or lower than those of either of its components (p. 88), and a mixture of two liquids may have a high conductivity, although the components in the pure condition are practically non-conductors (p. 259). The most obvious way of accounting for observations of this nature is to assume that they are connected with the formation of chemical compounds between the two components of the solution. As a matter of fact, explanations of the observed phenomena on these lines were formerly in great favour. As water was the substance most largely used as a component of solutions (as solvent), the explanation of the properties of aqueous solutions on the basis of formation of chemical com- pounds between water and the solute was termed the hydrate theory of solution. This theory appeared the more plausible 1 For simplicity, only mixtures of two components will be considered in this chapter. 333 334 OUTLINES OF PHYSICAL CHEMISTRY as a very large number of hydrates compounds of substances, more particularly salts, with water are known in the solid state, thus showing that there is undoubtedly considerable chemical affinity between certain solutes and water. In spite of the plausible nature of the hydrate theory, how- ever, it did not prove very successful in representing the properties of aqueous solutions, and some facts were soon discovered in apparent contradiction with it. Thus, as already mentioned, Roscoe showed that the composition of the mixture of hydrochloric acid and water with minimum vapour pressure, alters with the pressure, and therefore could not be connected with the formation of a definite chemical compound of acid and water, as had previously been assumed (p. 90). The development of the electrolytic dissociation theory, which has been discussed in the previous chapters, led to a considerable change of view with regard to the influence of the solvent on the properties of aqueous solutions. The pro- perties of the solvent were to some extent relegated to the background, 1 and it was looked upon simply as the medium in which the molecules and the ions of the solvent the really active things moved about freely. The fact that such great advances in knowledge have been made by working along those lines naturally goes far to justify the method of procedure. Within the last few years, however, mainly as a result of the investigation of solutions in solvents other than water, it has come to be recognized that the solvent may play a more direct part in determining the properties of dilute solutions than some chemists were formerly inclined to suppose. Although the main properties of aqueous solutions can be accounted for without express consideration of affinity between solvent and solute, it appears probable that the latter effect must be taken into con- 1 The properties of the solvent are, of course, all-important in deter- mining whether a substance becomes ionised or not. But it was not found necessary to take the question of affinity into account directly, and the equations representing ionic equilibria did not contain any term referring directly to the solvent. THEORIES OF SOLUTION 335 sideration in order to account for certain secondary phenomena (and possibly also in connection with ionisation) (p. 344). In the previous chapters the evidence in favour of the electrolytic dissociation theory could not be dealt with as a whole, owing to the fact that it belongs to different branches of the subject. In the present chapter a short summary of the more important lines of evidence bearing on the theory will be given, and then a brief account of the investigation of solutions in solvents other than water. Finally, after dealing with the older hydrate theory of solution, the possible mechanism of electrolytic dissociation will be considered. Evidence in Favour of the Electrolytic Dissociation Theory The evidence in favour of the electrolytic dissociation theory is partly electrical and partly noil-electrical. The non- electrical evidence goes to show that there are more particles in dilute solutions of salts, strong acids and bases, than can be accounted for on the basis of their ordinary chemical formulae, and that in dilute solution the positive and negative parts of the molecule behave more or less independently. The electrical evidence goes to show that the particles which result from the splitting up of simple salt molecules are associated with electric charges, either positive or negative. The main points are as follows : (a) If Avogadro's hypothesis applies to dilute solutions, gram-molecular (molar) quantities of different substances, dis- solved in equal volumes of the same solvent, must exert the same osmotic pressure. As a matter of experiment, salts, strong acids and bases exert an osmotic pressure greater than that due to equivalent quantities of organic substances (p. 124). The electrolytic dissociation theory accounts for this on the same lines as the accepted explanation for the abnormally high pressure exerted by ammonium chloride; it postulates that there are actually more particles present than that calculated according to the ordinary molecular formula. (b) Many of the properties of dilute salt solutions are additive, 336 OUTLINES OF PHYSICAL CHEMISTRY that is, they can be represented as the sum of two independent factors, one due to the positive, the other to the negative part of the molecule. This is true of the density, the heat of formation of salts (p. 148), the velocity of the ions (p. 251), the viscosity, and more particularly of the ordinary chemical reactions for the "base" and "acid" as used in analysis (p. 306). A very striking illustration of the independence of the pro- perties of one of the ions in dilute solution on the nature of the other is the colour of certain salt solutions, investigated by Ostwald. He examined the solutions of a large number of metallic permanganates, and found that all had exactly the same absorption spectra. This is exactly what is to be expected according to the electrolytic dissociation theory, the effect being exerted by the permanganate ion. Similarly, salts of rosaniline with a large number of acids in very dilute solution gave identical absorption spectra (due to the rosaniline cation) but rosaniline itself, which is very slightly ionised, gave a quite different spectrum. Too much stress should not be laid on this criterion, how- ever, as certain properties, e.g., molecular volumes of organic compounds (p. 61) and the heat of combustion of hydro- carbons (p. 148), are more or less additive, although nothing in the nature of ionisation is here assumed. (c) The magnitudes of the degree of dissociation, calculated on two entirely independent assumptions (i) that the con- ductivity of solutions is due to the ions alone, and not to the non-ionised molecules or to the solvent; (2) that the abnormal osmotic pressures shown by aqueous solutions of electrolytes are due to the presence of more than the calculated number of particles owing to ionisation show excellent agreement (p. 263). (d) The heat of neutralization of molar solutions of all strong monoacidic bases by strong monobasic acids is 13,700 calories, in excellent agreement with the value for the reaction H- + OH' = H 2 O, calculated by v'an't Hoffs formula from THEORIES OF SOLUTION 337 Kohlrausch's measurements of the change of conductivity of pure water with the temperature (p. 295). (e) The results obtained by four entirely independent methods for the degree of ionisation of water are in striking agreement, in spite of the fact that the assumed ionisation is very minute (p. 294). (/) The formula for the variation of electrical conductivity with dilution, obtained by application of the law of mass action to the assumed equilibrium between ions and non-ionised mole- cules in solution, represents the experimental results in the case of weak electrolytes with the highest accuracy (p. 267). (g) As shown in the next chapter, our present views as to the origin of differences of potential at the junction of two solutions, or at the junction of a metal and a solution of one of its salts, are based on the osmotic and electrolytic dissocia- tion theories, and the good agreement between observed and calculated values goes far to justify the assumptions on which the formulae are based. Many other illustrations of the utility of the electrolytic dissociation theory are mentioned throughout the book. Ionisation in Solvents other than Water 1 In ac- cordance with the mode in which the subject has developed, we have up to the present been mainly concerned with aqueous solutions, and the justification for this order of treatment is that the relationships in aqueous solution are often very simple in character, as shown in detail in the last chapter. The importance of a theory would, however, be much less if it only applied to aqueous solutions, and it is therefore satisfactory that in recent years a very large number of liquids, both organic and inorganic, have been employed as solvents. Although the progress so far made in this branch of know- ledge is not great, the available data appear to show that 1 Carrara, Ahrens' Sammlung, 1908, 12, 404. 338 OUTLINES OF PHYSICAL CHEMISTRY the rules which have been found to hold for aqueous solutions also apply to non-aqueous solutions^ Some solvents, such as ethyl and methyl alcohol, acetic acid, formic acid, hydrocyanic acid and liquefied ammonia, form solu- tions of fairly high conductivity with salts and other substances ; these are termed dissociating solvents (p. 123). Solutions in certain other solvents, such as benzene, chloroform and ether, are practically non-conductors, and the solutes are often present in such solutions in the form of complex molecules. These solvents are therefore often termed associating solvents, but it is not certain whether they actually favour association or polymerization of the solute, or have only a slight effect in simplifying the naturally polymerized solute. It is natural to inquire whether there is any connection between the ionising power of a solvent and any of its other properties. It has been found that as a general rule those solvents with the greatest dissociating power have high dielectric constants (p. 225) (J. J. Thomson, Nernst, 1893). This observation is easily understood when it is remembered that the attraction between contrary electric charges is inversely proportional to the dielectric constant of the medium ; it is evident that the existence of the ions in a free condition must be favoured by diminishing the attraction between the contrary charges. The dielectric constants of a few important solvents (liquids and liquefied gases) at room temperature are given in the table. Solvent. D.C. Solvent. D.C. Hydrocyanic acid . 95 Acetone . . 21 Water . . .81 Pyridine . . 20 Formic acid . . 57 Ammonia . . 16-2 Nitro benzene . 36-5 Sulphur dioxide . 137 Methyl alcohol . . 32-5 Chloroform . . 5*2 Ethyl alcohol . . 21-5 Benzene . . 2-3 *C/. Walden, Zeitsch. phy*ikal.Chem., 1907, 58, 479. THEORIES OF SOLUTION 339 The data are not usually available for an accurate comparison of the dissociating power of a solvent with its dielectric constant, as the values of yu-oo for electrolytes in solvents other than water have been determined in only a few cases. It is important to remember that a comparison of the conductivities of solutions of the same concentration in different solvents is in no sense a measure of the respective ionising powers of the solvents, as the conductivity also depends on the ionic velocity (p. 252). The available data are, however, sufficient to show that although there is parallelism, there is not direct proportionality between dielectric constant and ionising power. There appears also to be some connection between the degree of association of the solvent itself and its ionising power. The examples already given show that water, the alcohols and fatty acids, which are themselves complex, are the best ionising solvents. There are, however, exceptions to this as to all other rules in this section ; liquefied ammonia, though apparently not polymerized, is a good ionising solvent. Briihl has suggested that the ionising power of a solvent depends on what he calls subsidiary valencies (the " free affinity " of Armstrong) ; in other words, the best ionising solvents are those which are unsaturated. It is by no means improbable that the dielectric constant, the degree of poly- merization, and the degree of unsaturation of a solvent are in some way connected. The ionising power of a solvent may be partly of a physical and partly of a chemical nature. The effect of a high dielectric constant would appear to be mainly physical, on the other hand, if the effect of a solvent depends on its unsaturated character, it would most likely be chemical in character. The Old Hydrate Theory of Solution l As already men- tioned, attempts have been made to account for the properties of aqueous solutions of electrolytes on the basis of chemical combination between solvent and solute. Among those who 1 Pickering, Watts's Dictionary of Chemistry, Article " Solution " ; Arrhenius, Thtorits of Chemistry (Longmans, 1907), chap, iii. 340 OUTLINES OF PHYSICAL CHEMISTRY have supported this view of solution, the names of Mendele*eff, Pickering, Kahlenberg l and Armstrong 2 may be mentioned. Mendeleeff made a number of measurements of the densities of mixtures of sulphuric acid and water, and drew the con- clusion that the curve representing the relation between density and composition is made up of a number of straight lines meeting each other at sharp angles, the points of discontinuity corresponding with definite hydrates, for example, H 2 SO 4 , H 2 O ; H 2 SO 4 , 2H 2 O ; H 2 SO 4 , 6H 2 O and H 2 SO 4 , i5oH 2 O. Pickering repeated Mendeleeff s experiments, and found no sudden breaks in the density curve, but only changes in direction at certain points. He also drew the conclusion that these points cor- respond with the composition of definite compounds of the acid and water. In this connection it may be recalled that the curve obtained by plotting the electrical conductivity of mixtures of sulphuric acid and water against the composition (p. 259) shows two dis- tinct minima, at 100 per cent, and 84 per cent, of sulphuric acid respectively, corresponding with the compounds H 2 SO 4 (SO 8 , H 2 O) and H 2 SO 4 , H 2 O respectively. As it is a general rule that the electrical conductivity of pure substances is small, there is little reason to doubt that the 84 per cent, solution consists mainly of the monohydrate H 2 SO 4 , H 2 O. The con- tention of Mendeleeff and Pickering, that aqueous solutions of sulphuric acid contain compounds of the components, is thus partially confirmed by the electrical evidence. There is not much reason to doubt the truth of the first postulate of the hydrate theory, that in many cases hydrates are present in aqueous solution. The hydrates are, however, in all probability more or less dissociated in solution, and it will not usually be possible to determine the presence of definite hydrates from the measurement of physical properties. 1 For a summary of Kahlenberg's views on Solution, see Trans. Faraday Soc., 1905, I, 42. 2 Proc. Roy. Soc., 1908, 81 A, 80-95. THEORIES OF SOLUTION 341 It is probable that in general the equilibria are somewhat com- plicated, and are displaced gradually by dilution in accordance with the law of mass action, which accounts for the experimental fact that in general the properties of aqueous solutions alter continuously with composition. Having proved the existence of hydrates in salt solutions in certain cases, Pickering l attempted to account for the properties of aqueous solutions (osmotic pressure, electrical conductivity, etc.) on the basis of association alone, but as his views have not met with much acceptance, a reference to them will be sufficient for our present purpose. Kahlenberg, 2 who has carried out many interesting experiments in solvents other than water, re gards the electrolytic dissociation theory as unsatisfactory, and considers that the process of solution is one of chemical com- bination between solvent and solute. Armstrong has also attempted to account for the properties of aqueous solutions on the basis of association between solvent and solute. 8 Although, as we have seen, cases are known in which a maximum or minimum or a change in the direction of a curve may correspond more or less completely with the formation of a compound between the two components of a homogeneous solution, this does not by any means always hold. It has already been pointed out that the curve representing the varia- tion of the electrical conductivity of mixtures of sulphuric acid and water with the composition has a maximum at 30 per cent, of acid (p. 259). As the pure liquids are practically non- conductors, whilst the mixtures conduct, there must necessarily be a concentration, between o and 100 per cent, acid, at which the conductivity attains a maximum value. This maximum will clearly have no reference to the formation of a chemical compound between sulphuric acid and water, since this would tend to diminish the conductivity. Similar considerations appear to apply for other physical 1 Loc. cit. *Loc. cit. *Loc. cit., also Encyc. Britannica, xoth Edition, vol. xxvi., p. 741. 342 OUTLINES OF PHYSICAL CHEMISTRY properties which attain a maximum value for binary mixtures. The curve representing the variation of the viscosity (internal friction) of mixtures of alcohol and water with composition shows a maximum at o for a mixture containing 36 per cent, of alcohol, corresponding with the composition (C 2 H 5 OH) 2 , 9H 2 O, and it has therefore been suggested that the solution consists mainly of this hydrate. At 1 7, however, the mixture of maximum viscosity contains 42 per cent., and at 55 rather more than 50 per cent, of alcohol. The last-mentioned mixture corresponds with the composition (C 2 H 5 OH) 2 , 5H 2 O. If we accept the association view of this phenomenon, it must be assumed that at o the solution contains a hydrate (C 2 H 6 OH) 2 , gH 2 O, and at 55 a hydrate (C 2 H 5 OH) 2 , 5H 2 O, and that at intermediate temperatures the hydrates with 6, 7 and 8 H 2 O exist which does not appear very probable. Now, Arrhenius has shown that as a general rule the addition of a non-electrolyte raises the viscosity of water. Therefore, if the viscosity of the non-electrolyte is less than, or only slightly exceeds that of water, the curve obtained by plotting viscosity against the composition of the mixture must necessarily attain a maximum at some intermediate point. Why mixtures of two liquids have often a higher viscosity than either of the pure liquids is not known, no general agreement having yet been reached on this and allied questions. 1 Mechanism of Electrolytic Dissociation. Function of the Solvent The fundamental difference between associa- tion theories of solution, as discussed in the last section, and the electrolytic dissociation theory is that the advocates of association entirely reject the postulate of the independent existence of the ions. As, however, the different theories of association unaccompanied by ionisation have so far proved quite inadequate to account quantitatively for the behaviour of aqueous solutions, whilst the electrolytic dissociation theory not only affords a satisfactory quantitative interpretation of the THEORIES OF SOLUTION 343 more important phenomena observed in solutions of electrolytes (chap, x.), but has led to discoveries of the most fundamental importance for chemistry, it is not surprising that the electro- lytic dissociation theory has now met with practically universal acceptance. It is very likely that as a result of further investi- gation the theory may require modification in some subsidiary respects, but its general validity appears no longer doubtful. We are now in a position to discuss the possible mechanism of electrolytic dissociation, /'. and under definite conditions sugar will enter into or separate from solution according as its solution pressure is greater or less than its osmotic pressure. These considerations, in conjunction with the ionic theory, enable us to express the E.M.F. at a junction metal/solution in terms of solution pressure and osmotic pressure. If a metal is dipped into water it tends to dissolve, in consequence of its solution pressure, P, and as it can only do so in the ionic form, it sends a certain number of positive ions into solution. The solution thus becomes positively charged, and the metal, which was previously neutral, becomes negatively charged in conse- quence of the loss of positive ions. This process will proceed until, by the accumulation of positive electricity in the solution, the latter becomes so strongly positive that it prevents the pas- sage of more positive ions into solution. As the charge on the ions is so great, this process comes to a standstill when the amount of ions gone into solution is still excessively small, too small to be detected by analytical means. The state of affairs is rather different when a metal is dipped into a solution of one of its salts, e.g., zinc in a solution of zinc sulphate. In this case there are already positive metallic ions in the solution, which tend to resist the entrance of further positive ions, and what actually occurs will clearly depend upon the relative values of the solution pressure ', P, of the metal and the osmotic pressure, p, of the ions in solution. There are, in fact, three possible cases, which are represented diagrammatically in the accompanying figure : (a) If P > /, the metal sends ions into the solution until the accumulated electrostatic charges prevent further action ; the metal is then negatively and the solution positively charged. (b] If P < /, the positive ions from the solution deposit on 360 OUTLINES OF PHYSICAL CHEMISTRY the metal until the electrostatic charges prevent further action ; the metal is then positively and the solution negatively charged. (c) If P = /, no change occurs, and there is no difference of potential between metal and solution. As will be shown later, the solution pressures of the different metals are very different. Those of the alkali metals, zinc, iron, etc., are so great that they always exceed the osmotic pressures of their respective solutions (which cannot be increased beyond a certain point owing to the limited solubility of the salts), and these metals are, therefore, always negatively charged with - Metal + * + f + Solution. Metal Solution. Metal - i. . Solution. Pop. P.p. FIG. 38. reference to their solutions. On the other hand, the solution pressure of mercury, silver, copper, etc., is so small that they become positively charged, even in very dilute solutions of their respective salts. Calculation of Electromotive Forces at a Junction Metal/Salt Solution Provided that the changes at the junction of an electrode with a solution are reversible, the E.M.F. at the junction can readily be calculated in terms of the solution pressure, P, of the metal and the osmotic pressure, p, of the solution. This can perhaps be done most simply by calculating the maximum work obtainable when a mol of ELECTROMOTIVE FORCE 361 the electrode metal is brought from the pressure P to the lower pressure /, (i) osmotically, (2) electrically. If a mol of a dissolved substance is brought reversibly from the pressure P to / the work gained (in this case the osmotic work) is (cf. p. 135) ,~. Further, the dissolving of i equivalent of a metal is associated with 96,540 coulombs, and that of a mol of a metal of valency n with 96,540 n coulombs. The work done is the product of the E.M.F. E in volts and the quantity of electricity, 96,540 n coulombs. Equating the osmotic and electrical work, we have n 96,540 E = RT logP// RT . P , . or E =~ - log,- . . (i) 96,540* 5 V In order to obtain E in volts, R must be expressed in electrical units (volt-coulombs). If, at the same time, the change is made to ordinary logarithms (by multiplying by 2-3026) the above equation becomes ^ 2-3026 x 1-99 x 4*183 T P 0-0001983 T P 96,540* loglo / = ~ir logl <7 The numerical values of 2-3026 RT/Fat o, 18, 25 and 30 are as follows : Absolute temperature 273 273 + 18 273 + 25 273 + 30 Value of 2-3026 RT/F 0-0541 0*0577 0*0591 0-0601 At room temperature (15-20) the value of the expression in question is about 0-058, and the general formula becomes which should be remembered. It is clear from the form of the above equation that a tenfold increase or decrease in the osmotic pressure of the ions of the metal will produce a change of E.M.F. of 0*058 volts for a univalent metal, and 0-058/7* volts for a -valent metal, at room temperature. 362 OUTLINES OF PHYSICAL CHEMISTRY Differences of Potential in a Yoltaic Cell Two such electrodes as have just been described may be combined together to form a voltaic cell. This may be done in many ways, but a convenient arrangement is that for the Daniell cell represented in Fig. 39. in which the solutions are separated by a porous partition, A, which prevents convection, but allows the current to pass. When the poles are placed in the respec- tive solutions, the zinc becomes negatively charged, since Pj > p l ; on the other hand, the copper becomes positively charged as/ 2 >P 2 . As already explained, the solution and precipita- tion soon come to a standstill because of the accumulation of electrostatic charges. If, however, the elec- trodes are connected by a wire, the contrary charges neutralize each other through the wire, and in the solution more metal can then be dissolved and de- posited respectively (as there are no longer any opposing forces), the corresponding charges are again neutralized, and so on. The neutralization of charges through a conductor corresponds with the passage of a current. The general question as to the seat of the E.M.F. in such a cell as the Daniell has now to be considered. If the poles of the cell are connected by a wire of metal M, there are no less than five junctions at which there may be contact differences of potential ; two metallic junctions, Zn/M and M/Cu, two metal/ solution junctions, Cu/CuSO 4 and Zn/ZnSO 4 , and one liquid junction, ZnSO 4 /CuSO 4 . The question as to whether there are contact differences of potential at the junction of two metals gave rise to great difference of opinion, and the controversy FIG. 39. ELECTROMOTIVE FORCE 363 lasted the greater part of last century. It is now generally agreed, however, that if there are such differences they are exceedingly small in comparison with those of the junctions metal/salt solution. The difference of potential at the liquid junction is of much more importance and can be calculated by Nernst's theory (p. 384). It also is small in comparison with those at the liquid/metal junctions, and mav therefore, be left out of account for the present. The distribution of differences of potential in the Daniell cell with open circuit is represented in Fig. 40 (a), the ordinate* Fin 40. representing the potentials of the different parts of the circuit. The horizontal lines, AB, CD, DE and FG, illustrate the very important fact that the copper, the zinc and the solutions are each of a definite constant potential, and the ordinates, BC and EF, that there are sudden alterations of potential at the junc- tions metal/solution. For simplicity the solutions of zinc sulphate and copper sulphate are represented as being at the same potential, which is only approximately true. It is as- sumed for the present that the difference of potential be- tween copper and N copper sulphate solution is 0*585 volts, the copper being positive, and that the potential difference, Zn/ZnSO 4 , is 0-52 volts, the metal being negative. The 364 OUTLINES OF PHYSICAL CHEMISTRY total difference of potential between zinc and copper on open circuit is thus 0-585 + 0*52 = 1*105 volts. When the circuit is closed by connecting the copper and zinc by a wire of fairly high resistance, R, the distribution of poten- tial in the cell is as shown in Fig. 40 (b). The sudden changes of potential at the junctions ZnSO 4 /Zn and CuSO 4 /Cu are of the same magnitude as before, but the difference of potential between the zinc and copper, measured by the vertical height, AG, is much less than on open circuit. This is owing to the fall of potential in the cell owing to the resistance of the elec- trolyte, so that the solution in contact with the zinc is at a higher potential than that in contact with the copper, as repre- sented by EDC. If C is the current passing through the cell, and r is the resistance of the electrolyte, the E.M.F. of the cell on closed circuit is given by E = CR + Cr, and CR, the fall of potential in the external wire (represented in the figure by the vertical distance AG), approaches the more nearly to the E.M.F. of the same cell on open circuit the greater R is compared with r (compare p. 355). The E.M.F. of such a combination as the Daniell cell is the algebraic sum of the E.M.F.s at the two junctions, and is represented by the formula Where P x and P 2 are the solution pressures of zinc and copper respectively, p l represents the osmotic pressure of the zinc ions in the solution, and / 2 that of the copper ions. The values of p l and / 2 are therefore known, but the absolute values of the solution pressures P x and P 2 are unknown. The - sign of E 2 is due to the fact that at that junction ions are leaving the solution. In obtaining E as the algebraic sum of the differences of potential E l and E 2 at the two junctions, it is naturally of the utmost importance to take the values of E l and E 2 with their proper sign. Perhaps the best method of avoiding errors in this ELECTROMOTIVE FORCE 3 6 5 connection is to consider the tendency of one kind of electricity, say positive electricity, to pass round the circuit. In going round the circuit in the Daniell cell, starting with the zinc, the different junctions are met with in the order Zn | ZnSO 4 | CuSO 4 | Cu 0-52 0-585 > 1-105 and this is a very convenient method of representing the Daniell or any other cell. Now at the junction Zn/ZnSO 4 positive electricity tends to pass from zinc to solution at a potential (pressure) of 0*52 volts, as indicated by the arrow. Further, as the osmotic pres- sure of Cu- ions in copper sulphate solution is greater than the solution pressure of copper, positive electricity tends to pass across the junction CuSO 4 /Cu, in the direction of the arrow at an E.M.F. of 0-585 volts. It is clear that the forces at the two poles are in the same direction, and therefore positive electricity tends to pass through the solution in the direction indicated by the lower arrow at a total E.M.F. of 0-520 + 0-585 = 1*105 volts. Further illustrations are given at a later stage. Influence of Change of Concentration of Salt Solution on the E.M.P. of a Cell The general equation just given may be written in a slightly different form by substituting for the pressures the corresponding concentrations. Considering first the solution pressure, P v of the zinc, it is theoretically possible to choose a Zn" ion concentration, C v such that its osmotic pressure will just balance the solution pressure of the metal ; this may be substituted for P l in the general equation. Similarly, for p v the osmotic pressure of the zinc ions in the solution, we may substitute the corresponding concentration, c v Dealing in the same way with the copper side of the cell, the equation for the Daniell cell (or any other cell of similar type) becomes 366 OUTLINES OF PHYSICAL CHEMISTRY In this form the general equation may be employed to in- vestigate the question as to how the E.M.F. of the cell is affected by varying the concentration of the salt solutions. For the zinc side, since Q is greater than c lt it is clear that the quotient C^, and therefore E I} is increased by diminish- ing c lt the concentration of the Zn" ions. For the copper side, however, as C 2 is less than c^ (p. 342), the quotient C 2 / and diminishing the concentration of a solution into which new ions are going increases^ the E.M.F. of a cell. It is evident from general principles that the effect must be as described ; in the first case, the tendency to the separation of ions is lessened, and the E.M.F. falls ; in the second case, the entrance of new ions is facilitated, and the E.M.F. increases. If the concentration of the Cu" ions in the solution is pro- gressively diminished, a point must be reached at which the solution pressure of the metal is just balanced by the osmotic pressure of the Cu" ions. If the concentration is still further diminished, the tendency for copper to pass into solution will steadily increase, and ultimately may become greater than the tendency of zinc to pass into solution. It should therefore be theoretically possible to reverse the direction of the current in the Daniell cell by sufficiently diminishing the Cu" ion con- centration, and this state of affairs can be realised experimentally by adding potassium cyanide to the copper sulphate solution. A further important deduction can also be drawn from the general equation. As ^ and c^ stand for the concentration of the positive ions in the solution, the E.M.F. of the cell should be independent of the nature of the negative ion, pro- ELECTROMOTIVE FORCE 367 vided that the salts are equally ionised. This consequence of the theory is completely borne out by experiment. For twenty- one different thallium salts, in N/5o solution, the difference of potential between metal and solution varied only from 0*7040 to 0*7055 volts, the slight variations being readily accounted for by differences in the degree of ionisation. Concentration Cells We have now to consider what are termed " concentration cells," cells in which the E.M.F. de- pends essentially on differences of concentration. In some respects, concentration cells are simpler than those of the Daniell type, which have so far been considered. Concentration cells may be divided into two main classes (a) Those in which the solutions (and therefore the active ions) are of different concentrations. (b) Those in which the electrode materials yielding the ions are of different concentrations. (a) Concentration Cells with Solutions of Different Concen- trations As a type of the elements in question, we will con- sider a cell in which silver electrodes dip in solutions of silver nitrate of different concentrations, ^ and c 2 . The arrange- ment for the practical determination of the total E.M.F. of such a combination is shown in Fig. 41, where A and B repre- sent the cells containing the silver nitrate solutions and the vessel C contains an indifferent electrolyte. As this form of cell is largely employed in measurements of E.M.F., it may be well to describe it fully. It consists of a glass tube 3-4 cm. wide, with a straight side-tube D on one side and a bent side- tube E on the other, the latter being employed for making con- nection with the indifferent electrolyte in C as shown. Into the lower end of a glass tube, F, is cemented a thick rod of silver covered with the finely-divided metal by electrolysis, and the glass tube is held by a cork closing the cell. The cell is filled with a solution of silver nitrate of definite strength through the bent tube by suction through the straight side-tube, D, which is then closed by a clip. The other " half-cell/' B, is prepared 368 OUTLINES OF PHYSICAL CHEMISTRY in exactly the same way, but contains a solution of silver nitrate of different concentration. The ends of the bent tubes are then dipped into an indifferent electrolyte in the vessel, C, as shown, and the total E.M.F. of the combination determined by the potentiometer method in the usual way, connection with the silver electrodes being made by wires passing down the interior of the glass tubes. In this case, the general equation for an electrolytic cell, E simplifies to E FIG. 41. since C, the solution pressure of the metal, is the same on both sides, and is therefore eliminated. A cell of the type Ag AgNO 3 dil AgNO 3 conc | Ag works in such a way that silver is deposited from the more concentrated solution, in which the osmotic pressure is higher, and is dissolved at the pole in contact with the weaker solution, which offers less resistance to the entrance of Ag' ions. The ELECTROMOTIVE FORCE 369 change, therefore, proceeds in such a way that the differences of concentration tend to equalize, and when the solutions have reached the same concentration, the current stops. Positive electricity therefore passes in the element from the weak to the strong solution, as indicated by the arrow, and in the connecting wire from the strong to the weak solution ; the electrode in contact with the strong solution becomes positively charged, the other electrode negatively charged. The equation shows that the E.M.F. of such a concentra- tion cell depends only on the respective concentrations of the positive ions in the two solutions and their valency, and not on the nature of the electrodes or on the nature of the anions, and the experimental results are in full accord with this deduction. Otherwise expressed, the E.M.F. of any element made up of a univalent metal M dipping in solutions of one of its salts of different concentration is of the same absolute value as that of the silver concentration cell, provided that the solutions are of corresponding concentration, and ionised to the same extent. Further, if the solutions are dilute, and electrolytic dissociation therefore fairly complete, the ratio of the ionic concentrations in different dilutions will be approximately the same as the ratio of the concentrations themselves. Thus, in the example under consideration, the ratio cjc^ for i/ioo molar, and i/iooo molar solutions, will be approximately 10 : i ; log^/^ is therefore i, and the value of E for the cell Ag AgN0 3 m/iooo AgN0 3 I Ag m/ioo | is o'058/w = 0*058 volts, since n, the valency of the ions con- cerned, is unity. If, however, the solutions are more concentrated, the fact that ionisation is incomplete must be taken into account in calculating the E.M.F. of a cell. Suppose, for instance, it is required to calculate the E.M.F. of the cell Ag I AgNO 3 ml 100 \ AgNO, mjiol Ag. 24. 370 OUTLINES OF PHYSICAL CHEMISTRY N/io silver nitrate solution is ionised to the extent of 82 per cent, at 18, whence f 2 = 0-082, and N/ioo silver nitrate to the extent of 94 per cent., whence ^ = 0*0094. We have therefore c^c-^ = 0*082/0*0094 = 872, and E = 0-054 volts, in excellent agreement with the experimental value. Strictly speaking, it is not justifiable in cells of this type to neglect the contact difference of potential between the two solutions, which may amount to a considerable fraction of the total E.M.F. The accurate formula for the calculation of the E.M.F. of cells of this type is given in a succeeding section (p. 384). If, however, both solutions contain an indifferent electro- lyte in equivalent concentration great in comparison with those of the active salt, the difference of potential at the liquid junction becomes negligible, and the above formula (i) holds accurately (cf. p. 383). It is evident from the formula that the E.M.F. of a con- centration cell cannot be greatly altered by increasing the con- centration on one side, owing to the limited solubility of the salts used as electrolytes. On the other hand, the E.M.F, may be greatly altered by diminishing the ionic concentra- tion on one side. Conversely, when a cell is made up with a solution of silver nitrate of known Ag* ion concentration, c l9 and one of unknown concentration, c 0t and the E.M.F. of the cell is measured, c can readily be calculated. This principle has been applied more particularly for the determination of very small ion concentrations, and may be illustrated by the determination of the Ag* ion concentration in a saturated solution of silver iodide. When the concentration on one side is very small, it is usual to add some salt, with or without a common ion, to eliminate the potential difference at the liquid junction, and also to increase the conductivity in the cell, so as to render the measurements more accurate. In this case potassium nitrate may conveniently be used. The observed E.M.F. of the cell Ag 1 KNO 8 + Agl | AgNO 3 o-ooiw + KNO 3 | Ag ELECTROMOTIVE FORCE 371 is 0-22 volts. Since ^ = 0*001, we have E = 0-22 = 0-058 Iog 10 (o-ooi/ 2H\ A hydrogen concentration cell is obtained when two hy- drogen electrodes, containing the gas at different pressures, are combined in the usual way. Such cells correspond exactly with those made up with amalgams of different concentrations. The direction of the current is such that the pressures on the two sides tend to become equal, so that hydrogen becomes ionised at the high pressure si4e and is discharged as gas at the low pressure side. 25 386 OUTLINES OF PHYSICAL CHEMISTRY In calculating the E.M.F.'s of such cells by the general formula (p. 371) it has to be remembered that, since the hydrogen molecule contains two atoms, the work gained in bringing a mol of the gas reversibly from the pressure P l to the lower pressure P 2 is RT log e PX/P.J whilst if the same change is carried out electrically, H 2 + 2F~ > 2H t , the energy concerned is 2F coulombs. Hence, since 2F = RT log e P X /P 2 the E.M.F. of the cell is . The same formula applies to gas cells in which chlorine and other divalent gases are used (see also p. 398). On the other hand, since 4F coulombs are associated with the solution of i mol of oxygen (O 2 + 2H 2 O- 4F^4OH') the E.M.F. of an oxygen concentration cell is Another type of hydrogen concentration cell is obtained when the gas concentration in the electrodes is constant and the H- concentration in contact with the two electrodes i? different. An interesting cell of this type is built up as follows : H 2 (Pt) | N/io alkali | N/ioacid | H 2 (Pt) Since the equilibrium H + OH'^H 2 O always holds, there must be a minute concentration of H* even in alkaline solution and therefore the above represents a hydrogen concentration cell. From the E.M.F. of the above cell which, after ap- plying a correction for the contact difference of potential, amounts to 0-6951 volt at 18, the product of the ionic concentration for water, [H-] [OH'] = k can be calculated as follows. From the general equation E = 0*0577 Iog 10 cjc^ we have 0-6951 = 0*0577 Iog 10 ^ 2 f 19 the H- concentration in N/io acid at 18, is p*o88 hence ef^ = 0'0888/- n l for nickel is 2 and c a is 0*06 ; n 2 for silver is i and c 2 is 1-25 x 10 " 5 gram-ions per litre at 25. Hence E=* - 0-25 + 0*029 log 10 (0-06)- 078- 0-058 Iog 10 (i -25 x icr 6 ) - 0*25 <- 0*035 - 0*8 + 0*289 - - 0*796 ELECTROMOTIVE FORCE 391 The total E.M.F. of the cell is - 0796 volts; the P.D. at the silver electrode is + 0-511 volts, and at the nickel electrode - 0*25 '035 = 0*285 v lts. In order to avoid errors of sign, it is well to check results such as the above from the point of view of general principles. Since diminishing the concentration of a solution from which ions are separating lowers, and diminishing the concentration of a solution into which new ions are going increases the E.M.F. at a junction (p. 366) it is evident that the effect on the E.M.F. of alteration of the concentrations of the solutions must be as shown above. From the above considerations it would appear that metals which stand higher than hydrogen in the tension series can liberate hydrogen from acids and that,the numbers in the table afford an approximate measure of the energy of the change On the other hand, hydrogen at atmospheric pressure should displace the metals which stand below it in the tension series. This has been shown to hold in some cases at least with hydrogen occluded in platinized platinum electrodes, the plat- inum presumably acting as a catalyst for reactions which under ordinary conditions are extremely slow. Finally each metal should be able to displace from combination any metal below it in the tension series, the difference of potential between the metals being a measure of the free energy of the change. On the whole these conclusions are borne out by the experi- mental results except in so far as the phenomenon of over- voltage comes into play. This subject is briefly discussed in a later section (p. 403). Cells with Different Gases The simplest example of these cells is the hydrogen-chlorine cell, already referred to, One-half of the cell consists of a hydrogen electrode in acid, the other of a similar electrode saturated with chlorine, and the two electrodes are combined as represented in Fig. 41, the intermediate vessel containing acid of the same strength as that in the cell. The chemical change which takes place in the cell 392 OUTLINES OF PHYSICAL CHEMISTRY is the combination of hydrogen and chlorine to form hydro- chloric acid. Representing the cell as usual H a (Pt) | H- | C1' | Cl 2 (Pt), 1*40 it is clear that positive electricity flows in the cell from hydrogen to chlorine in the direction represented by the arrow, the chlorine becoming the positive and the hydrogen the negative pole. The E.M.F. of the cell in normal acid at the ordinary temperature is about i '40 volts. The most important cell of this type is the hydrogen-oxygen or Grove's cell, the two poles being saturated with hydrogen and oxygen respectively. When connection is made the gases gradually disappear, hydrogen becoming ionized at one pole and oxygen uniting with water to form hydroxyl ions at the other pole. The cell may therefore be represented by the following scheme I (acid, alkali or salt) | 1-23 and positive electricity flows through the cell from hydrogen to oxygen as represented by the arrow, so that hydrogen is the negative pole and oxygen the positive pole. The hydrogen electrode is reversible with regard to hydrogen, as follows : H 2 ^2H-, the reaction taking place at the oxygen electrode is as follows : H 2 O + iO 2 ^2OH'. When employed as indicated above, the change is that represented by the two upper arrows and 2F passes through the wire ; when, on the other hand, 2F is sent through the cell in the opposite direction, the changes at the two poles are represented by the two lower arrows. If absolutely indifferent electrodes were used for absorbing the gases, and the changes at the electrodes were fully rever- ELECTROMOTIVE FORCE 393 sible, the calculated E.M.F. of the cell is 1-23 volts. 1 The values actually observed are smaller, probably owing to the formation of an oxide of platinum, which has an oxygen potential different from that of free oxygen. Theoretically, only pure water is necessary as electrolyte, but, in order to increase the conductivity, dilute acid or alkali or a dilute salt solution is employed as electrolyte. The E.M.F. of the cell is independent of the nature of the electro- lyte since the product [H*][OH'] is the same in acid, alkaline, or neutral salt solution, but this is not the case for the single potential differences at the electrodes. Oxidation-Reduction Cells The gas cell just described is a typical oxidation-reduction cell, as when working hydrogen is being oxidized at the negative pole and oxygen reduced at the positive pole. As may be anticipated, corresponding cells can be con- structed in which instead of hydrogen another reducing agent is used, and instead of gaseous oxygen another oxidizing agent. Indifferent metals, such as platinum or iridium, are used as electrodes in all cases. We will first consider a cell built up of a hydrogen electrode on one side and a platinized platinum electrode dipping in a solution of a ferrous and a ferric salt on the other. When the two electrodes are connected up, a current flows in the cell from the hydrogen to the other electrode. Hence at the hydrogen electrode gaseous hydrogen is going into solution as hydrogen ions according to the equation H 2 + 2F = 2H', 2 and at the other electrode Fe*" ions are being reduced to Fe*- ions according to the equation 2Fe*" - 2F = 2Fe", the charges neutralizing each other through the wire and thus producing 1 Corresponding with the free energy of formation of water from its elements. The calculation is rather complicated. (Compare Nernst and von Wartenberg, Zeitsch. physikal. Chem., 1906, 56, 544.) *2F or 2 x 96,540 coulombs converts a mol of hydrogen to H i ions. 394 OUTLINES OP PHYSICAL CHEMISTRY a current. When the same quantity of electricity is passed through the cell in the opposite direction, Fe~ ions are con- verted to Fe*" ions, and hydrogen gas is liberated at the other pole ; the cell therefore works reversibly, and the measurement of the E.M.F. gives a measure of the free energy or affinity of the reaction. The total change is, of course, expressed by the equation 2Fe*" + H 2 = 2Fe* + 2H*. Other oxidizing agents can be measured in the same way against the hydrogen electrode, and from the results a table of various solutions, arranged in the order of their oxidizing potentials, can be obtained. Some of the values obtained in this way may be given. SnCl 2 in HC1 0-23 volts FeCl 3 in HC1 0-98 volts NH 2 OH in HC1 0-38 volts KMnO in H 2 SO 4 i -50 volts The above are only meant to indicate the order of the results, as the accurate values depend greatly on the concentration and composition of the solutions. The four solutions mentioned, even stannous chloride, in acid solution exert an oxidizing action on gaseous hydrogen, and therefore the direction of the current is the same as in the ferric chloride cell. As might be anticipated, potassium per- manganate has the highest oxidation potential. When, on the other hand, a platinum electrode dipping into a solution of stannous chloride in potassium hydroxide is con- nected with a hydrogen electrode so as to form a cell Sn" in H 2 (Pt) I H OH' (Pt) 0*560 hydrogen ions are discharged and the stannous salt becomes oxidized, positive electricity, therefore, flowing in the cell in the direction of the arrow. The change which takes place in the cell may be represented by the equation 2H- + Sn- = Sn-" + H 2 , the hydrogen acting as the oxidizing agent. In this case we ELECTROMOTIVE FORCE 395 may say that the stannous chloride solution has a certain reduc- tion potential. The above considerations are sufficient to show that the terms " oxidizing agent " and " reducing agent " are relative and not absolute ; whether a substance acts as an oxidizing or a reducing agent depends on the substance with which it is brought in contact. The hydrogen electrode may be replaced by a platinum electrode dipping in a solution of a reducing agent, an oxida- tion-reduction cell containing only liquids being obtained. One well-known cell of this type consists of platinum electrodes dipping in solutions of ferric chloride and stannous chloride respectively. The changes at the electrodes may be represented by the equations (i) 2Fe- - 2F - 2Fe- (2) Sn- + 2F = Sn and the total change as follows 2Fe- + Sn- 2Fe" + Sir- It is now easy to understand what at first sight appears very puzzling, that a ferric salt can oxidize a stannous salt at a dis- tance, the solutions being in separate cells and possibly con- nected by an indifferent solution. The above equations show that the essential feature of the phenomenon is the transference of two positive charges from the iron to the tin ions through the wire. As a definite potential may be ascribed to every substance acting as an oxidizing or reducing agent, it is clear that the E.M.F. of an oxidation-reduction cell may be represented as the algebraic sum of the differences of potential at the two junc- tions. When a strong oxidizing solution is combined with a still stronger oxidizing solution to form a cell, the former will be oxidized at the expense of the latter, but the E.M.F. of the cell will be small, as the solutions are acting against each other. The further apart two solutions are in the oxidation- reduction potential series, the greater will be the E.M.F. of the cell formed by their combination. 396 OUTLINES OF PHYSICAL CHEMISTRY We are now in a position to give a clear definition of oxida- tion and reduction in dilute salt solutions. An increase in the number of positive charges or a diminution in the number of negative charges on an ion denotes oxidation ; decrease in the number of positive charges or increase in ttie number of negative charges on an fan denotes reduction. The usual definition of oxidation as consisting in an addition of oxygen to a compound or the abstraction of hydrogen from it, is clearly inapplicable to salt solutions, but the older definition retains its value for changes in which organic compounds are concerned, and for solid compounds ; these have so far been very little investigated from an electro-chemical standpoint. According to the above definition, all reactions which take place electromotively are oxidation - reduction reactions, oxidation taking place at one electrode and reduction at the other. In the Daniell cell, for instance, oxidation takes place at the cathode, Zn + 2F-Zn", and reduction at the cathode Or- - 2F =a Cu. It follows that the displacement of one metal by another is to be regarded as an oxidation-reduction process. Elements which can only give positively charged ions, e.g. the typical metals, can only act as reducing agents, whilst elements such as chlorine, which only yield negatively charged ions, invariably exert an oxidizing action. Solutions, on the other hand, may behave according to the conditions either as oxidizing or reducing agents, since one or the other ion may react. Cupric bromide solution, for instance, acts as an oxidizing agent towards zinc and as a reducing agent towards copper. Moreover, a single ion, e.g. ferrous ion, Fe" may act either as an oxidizing or as a reducing agent since it can be changed into uncharged Fe or into Fe ". Electromotive Force and Chemical Equilibrium. In the previous section, we have considered oxidation-reduction cells from the qualitative standpoint only. Just as in the case of the Daniell cell, which indeed is a special type of oxidation- ELECTROMOTIVE FORCE 39 > reduction cell, the E.M.F. at an electrode depends upon the concentration of all the ions taking part in the change. Thus the E.M.F. at a platinized platinum electrode immersed in a solution of a ferric salt is only definite when a certain proportion of Fe" ions are also present, and the E.M.F. depends on the concentrations of both ferric and ferrous salt. The general equation representing the dependence of the E.M.F. of such cells on the concentrations of the substances taking part in the reaction will now be given. The reversible reaction n 1 A 1 + n 2 A 2 + . . . ^n/A^ + n/A/ ... (p. 159), when it proceeds in one direction in an electrolytic cell, may be represented by the equation n^ 4- n 2 A 2 + . . . + nF-Mi/A/ + n 2 'A 2 ' + . . . which indicates that n l mols of A 1 and n 2 mols of A 2 . . . are converted into n/ mols of A/ and n 2 ' mols of A 2 ' by taking up n faradays. The maximum work obtainable when the substances on one side of the equation at definite concentrations are transformed isothermally and reversibly into the substances on the other side of the equation also in definite concentrations may be derived by a n on -electrical method or by carrying out the reaction in a galvanic cell. In the former case the maximum work may be stated in the form where the square brackets represent concentrations and K represents the equilibrium constant. When the process is carried out in a galvanic cell the maximum work obtained is A = nFE (p. 352) hence E - RT (lo* K - log g ' ' nF ' ' [A Jn, [A 2 ]n 2 When both the initial substances and the final products are in unit concentration the maximum work obtainable non- electrically is A = RT lo ge K 398 OUTLINES OF PHYSICAL CHEMISTRY and in a galvanic cell nFe , where e is the normal potential. Hence the general equation representing the dependence of the E.M.F. of the cell on the concentrations of the reacting substances is - nF [AJih [A 2 ]n 2 The concentrations of the more highly oxidized substances (i.e. those formed by taking up positive charges) occur in the denominator. For the change Fe- + the above expression has the form For the chlorine electrode 2C1' + 2F^C1 2 TT* E = to _ log.[dT/[Cl 2 ]. As regards the permanganate electrode, for which the equation MnO 4 ' + 8H* 5F^t Mn" + 4H 2 O represents the probable chemical change, the expression for the E.M.F. is as follows : _ RT [Mn]- [H.OF 5 F =>' [MnOJ [H-] It is clear from the above equations that the effect on the E.M.F. of the cell of systematic variation in the concentrations of the reacting substances throw light on the nature of the chemical change taking place in the cell and also on the number of faradays associated with the change in question. Electrolysis and Polarization If an external E.M.F. of i volt is applied to two platinum electrodes dipping in a con- centrated solution of hydrochloric acid, it will be found that the large current which at first passes when connection is made rapidly diminishes and finally falls practically to zero. The ex- planation of this behaviour is that while the current is passing hydrogen accumulates on the cathode and chlorine on the ELECTROMOTIVE FORCE 399 anode, thus setting up an E.M.F. which acts against the E.M.F. applied to the poles of the cell. This phenomenon is termed polarization. In the above case the gases go on accumulat- ing in the electrodes till the back E.M.F., which we will term then the external circuit is broken and the E.M.F. of polarization measured at once. This method depends upon the fact already indicated, that the de- composition potential is that E.M.F. which is just sufficient to overcome the E.M.F. of polarization. As has just been pointed out, the potential required to dis- charge an ion such as Zn** must just exceed the difference of potential at the junction Zn/Zn**, and is, therefore, the same as the potential of the metal in volts in the tension series (p. 389). Further, the E.M.F. required to decompose an electrolyte is clearly the sum of the separate differences of potential required to discharge the anion and cation respectively, and is, there- fore, obtained bv adding the values for the two ions in the tension series. The matter becomes clearer when we consider that the potential difference between an element and its ions may conveniently.be regarded as a measure of the affinity of the element for electricity. Thus the affinity of zinc for positive electricity is equivalent to 0*770 volts, and that of chlorine for negative electricity to 1*40 volts. To convert zinc ions to metallic zinc we must, therefore, apply a contrary E.M.F. which just exceeds the affinity of zinc for positive electricity, in other words, the decomposition potential of zinc ions is 0*770 volts. On this basis, the decomposition potential of zinc chloride should be 0-770 + 1*40 = 2*170 volts, of hydrochloric acid 1-40 volts, and of copper chloride ( - 0*329 + i'4) = 1*071 volts respectively. This is fully confirmed by the experimental determinations of Le Blanc, who obtained the following values : ZnCl 2 = 2-15 volts, HC1 = 1*31 volts, CuCl 2 =* 1*05 volts, an agreement within the limits of experimental error. Separation of Ions (particularly Metals) by Electro* lysis The results just mentioned are well illustrated by the phenomena observed when a mixture of electrolytes is electro- lysed at different values of the applied E.M.F. The foregoing ELECTROMOTIVE FORCE 401 considerations show that on gradually raising the E.M.F. that chemical change takes place most readily for which the least difference of potential is required, and this may be taken advantage of for the electrolytic separation of metals which are discharged at different potentials. Suppose, for example, a mixture of hydrochloric acid, zinc and copper chlorides is subjected to electrolysis. Below i volt practically no change will occur, but at n volts, a little above the decomposition potential for copper chloride, copper will be deposited on the cathode. When it has been almost completely removed, and the potential is raised to 1*4 volts, hydrogen will be liberated at the cathode. Finally, the attempt may be made to remove zinc by raising the external E.M.F. above 2*2 volts, but this cannot be effected in acid solution, as there is a large excess of hydrogen ions, which are more easily discharged than zinc. In an exactly corresponding way, almost all the bromine may be electrolytically separated from a solution containing zinc chloride and zinc bromide before the chlorine appears. It is, therefore, clear that it is the value of the E.M.F., and not the strength of the current, which is of primary importance for the separation of metals, and in recent years methods based on this principle have become of great commercial importance. Besides the value of the applied E.M.F., the concentration of the ions in contact with the cathode is of great importance, as the decomposition potential necessarily depends on the ionic concentration, and hence great attention is now paid to the efficient stirring of the electrolyte. 1 The Electrolysis of Water. OverYoltage (Super- tension) at Electrodes. When aqueous solutions of many salts and strong acids and bases are electrolysed with smooth platinum electrodes only hydrogen and oxygen are liberated as products of electrolysis and the decomposition potential is in 1 The electrolytic separation of metals on this principle is described in recent papers by Sand (Journal of the Chemical Society, 1907, 91, 373, 1908, 93, 1572), and others, 26 402 OUTLINES OF PHYSICAL CHEMISTRY all cases about 1*66 volts. It was formerly supposed that one or both of these gases were formed by the action of the primary products of electrolysis on the solvent, but this does not account for the fact that the decomposition potential is in general the same for different acids and bases. It is now accepted, for reasons given below, that the gases are products of the primary decomposition of water. If such is the case, and the decomposition of water proceeds reversibly at the electrodes, we would expect the decomposi- tion potential to be about 1-2 volts, in agreement with the E.M.F. of the hydrogen-oxygen cell, whereas it is considerably higher. When, however, platinized platinum electrodes are used and the current is plotted against the applied E.M.F., the latter being gradually increased, it is found that there is a sudden increase in the current at 1*1 volts (so that water can be continuously decomposed at the latter potential), but a much more rapid increase at i -66 volts. Two possible explanations of these remarkable facts might be suggested. Nernst was formerly of opinion that at the lower potential H* and O" ions are being discharged the current being veiy small because of the exceedingly minute concentration of the O" ions. The more rapid decomposition at 1*66 volts is due to the discharge of H' and OH' ions the latter combining to form water and oxygen according to the equation 4.OH ->2H 2 O + O2. Another mode of explaining the results is that the decom- position potential depends on the nature and condition of the electrode material ; at many electrodes the potential must be raised above that theoretically required for reversible decom- position in order to reach the point of decomposition. Thus assuming that the decomposition of N/i sulphuric acid takes place reversibly at a platinum cathode, the following values for the cathodic decomposition potential with other metals were obtained: Pd + 0-26, Pt o, Fe - 0-03, Cu - 0-19, Al - 0-27, Pb - 0*36, Hg - 0-44. Thus hydrogen is eliminated more easily at a palladium than at a platinum electrode, per- ELECTROMOTIVE FORCE 403 haps owing to the formation of an alloy with the former metal ; in all other cases a greater or less excess of E.M.F. is required in order to liberate the gas. Overvoltage phenomena also oc- cur at the anode when oxygen is being liberated, but in this case the order of the metals is not the same as with hydrogen. The magnitude of the overvoltage increases considerably with increase of current-density. There is no doubt as to the great importance of overvoltage phenomena, although they are not ye} fully understood. They appear to depend, in part at least, on supersaturation with the gas. Thus when hydrogen is liberated at a platinized platinum anode, the latter dissolves a large amount of the gas and facili- tates its escape in bubbles, thus bringing about equilibrium between the gas in solution and in the gas space. On the other hand smooth platinum, and such metals as lead and mercury, have very little solvent power for hydrogen, and a much higher pressure is required in order to force in sufficient of the gas to admit of the formation of bubbles (Nernst). Ac- cording to Forster, the liberated substance forms some com- pound with the electrode material, and the supertension h determined by the concentration of the gas thus dissolved in some form in the electrode. By making use of the high concentration of hydrogen obtainable at electrodes showing considerable supertension, reductions not readily effected by other methods can be performed. Supertension phenomena have an important bearing on the dissolving of metals in acids. Pure zinc should liberate hydro- gen from acids at a potential of 0*770 volts but the superten- sion is so great as almost to reach this value and the reaction therefore proceeds very slowly. The overvoltage at impure zinc is much less and therefore the metal dissolves much more readily in acids. In the latter case local differences of potential doubtless also play a part. The main evidence in favour of the view that water under- 404 OUTLINES OF PHYSICAL CHEMISTRY goes primary decomposition during electrolysis is that the de- composition potential is largely independent of the electrolyte, whether acid, base or salt ; and further, that of the possible changes which can take place at the electrodes the decomposi- tion of water is usually that which can take place at the lowest potential (compare previous section). In the case of hydro- chloric acid the relationships are more complicated. In con- centrated solution the decomposition potential is lower than that of water (p. 400) and the main products are hydrogen and chlorine; with progressive dilution the decomposition potential rises and ultimately a mixture of oxygen and chlorine is liber- ated at the anode. The decomposition potential curve of sulphuric acid shows two further points of rapid increase of current, at 1*95 and 2-6 volts respectively. It seems probable that the former value is connected with the discharge of SO/' and the latter with the discharge of HSO 4 ' ions. Electrolysis and Polarization (continued). The E.M.F. required to bring about decomposition of an electrolyte is not determined solely by the magnitude of the polarization due to the products of electrolysis. The current also causes concen- tration changes at the electrodes and these changes always act in opposition to the E.M.F. driving current through the cell. This effect is known as concentration polarization and is mini- mised by stirring the electrolyte. Any substance which tends to diminish the polarization in a cell is termed a depolarizer. It may act as a catalyst in ac- celerating the changes at the electrodes, e.g., platinized platinum in the liberation of hydrogen, or it may alter the change taking place at the electrodes to one that takes place more easily, e.g., the use of potassium dichromate in the so- called Bichromate cell. The " insoluble " salt in an electrode of the second kind acts as a depolarizer. Recent investigations have shown that polarization occurs in ELECTROMOTIVE FORCE 405 many cases where it would not be anticipated, and this fact has raised the question as to the exact nature of the changes taking place at the electrodes during electrolysis. When, for in- stance, a current is passed through the cell Cu | CuSO 4 | Cu it would be anticipated according to the accepted views re- garding electrolysis that Cu" ions would be discharged at the cathode as metallic copper, that SO 4 " ions after discharge at the anode would immediately attach the latter forming copper sulphate. As a matter of fact Le Blanc * has shown that under these circumstances considerable polarization occurs both at anode and cathode, so that the changes taking place at the poles can scarcely be as simple as those just assumed. A still more striking case occurs in the electrolysis of solid silver salts between silver electrodes. With silver sulphate, for in- stance, a polarization E.M.F. of 0-312 volts was observed two minutes after breaking the circuit and at - 80 an E.M.F. of no less than 1*562 volts one minute after breaking the circuit. 2 The cause of these remarkable observations is still by no means understood. Aooumulators As is well known, accumulators are em- ployed for the storage of electrical energy. An accumulator is a reversible element ; when a current is passed through it in one direction the electrodes become polarized, and when the polar- izing E.M.F. is removed and the poles of the accumulator are connected by a wire, the products of electrolysis recombine with production of a current and the cell slowly returns to its original condition. It will be clear from the above that the Grove's gas cell is a typical accumulator or secondary element; when a current is passed through it in one direction the electrodes become charged with hydrogen and oxygen, and these gases can be 1 M. Le Blanc, Abhandlungen der Bunsen-Gesellschaft, No. 3, 1910. 2 Haber and Zawidzki, Zeitsch. physikal. Ghent., 1911, 78, 228. Com- pare Annual Reports Chemical Society for 1912, p. 19. 406 OUTLINES OF PHYSICAL CHEMISTRY made to recombine with production of a current. From a technical point of view, however, a satisfactory accumulator must retain its strength unaltered for a long time when the poles are not connected, and must be easily transported. A gas accumulator would be in many respects un suited for commercial purposes. The apparatus most largely used for the storage of electricity is the lead accumulator^ the electrodes of which in the un- charged condition contain a large amount of lead sulphate (obtained by the action of sulphuric acid on the porous lead of which the electrodes largely consist at first) and dip in dilute sulphuric acid. The accumulator is charge by sending an electric current through it. At the cathode, the lead sulphate is reduced by the hydrogen ions (or rather by the discharged hydrogen) to metallic lead according to the equation PbSO 4 + 2H- - 2 F - Pb + 2H- + SO 4 " or more simply, PbSO 4 - 2F Pb + SO 4 " On the other hand, the SO 4 " ions wander towards the anode and react with it according to the equation PbSO 4 + SO 4 " + 2H 2 O + 2F - PbO 2 + 4H' + 2SO 4 " so that the anode and cathode consist mainly of lead peroxide and metallic lead respectively. On connecting up to obtain a current (discharging), SO 4 " ions are discharged at the new anode (the lead pole), and reconvert it to lead sulphate, according to the equation Pb + SO/ 7 + 2F - PbSO 4 , and simultaneously H' ions are discharged at the new cathode (the peroxide pole), the peroxide being reduced to the oxide, and acted on by sulphuric acid to reform the sulphate, according to the equation PbO 3 + 2H- + H 2 SO 4 - 2F - PbSO 4 + 2H 2 0. ELECTROMOTIVE FORCE 4> The chemical changes taking place on charging and discharging are summarized in the equation Pb + PbO 2 + 2H 2 SO 4 ^ 2PbSO 4 + 2H 2 O ; the upper arrow represents discharging, and the lower arrow charging. The E.M.F. of the lead accumulator is about 2 volts. It is not strictly reversible, but under ordinary conditions of working about 90 per cent, of the energy supplied and stored up in it can again be obtained in the form of work. The only other accumulator of commercial importance is that developed more particularly by Edison and his co-workers, and known as the Edison accumulator. In the charged condition the positive plate consists of hydrated nickelic oxide, Ni 2 O 3 , x H 2 O and the negative plate of finely divided iron, the electro- lyte being about 4 N alkali. On discharging the nickelic oxide is reduced to nickelous hydroxide Ni(OH) 2 and the iron is oxidized to ferrous hydroxide Fe(OH) 2 . According to Forster the changes taking place on charging and discharging are re- presented approximately by the equations : Fe + Ni 2 3 , i-2H 2 + i-8H 2 0^Fe(OH) 2 + Ni(OH) 2 . Both the anode and cathode consist of steel flames provided with a large number of pockets (made of nickel-plated steel) in which the active electrode materials are packed. The potential during discharge is about 1*34 volts, and, as the above equation shows, is independent (in practice only very slightly dependent) on the alkali concentration. One advantage possessed by the Edison accumulator is its comparative lightness. The Electron Theory l In the previous chapters we have learnt that certain atoms (or groups of atoms) can become associated with definite quantities of electricity, and that certain other atoms can take up twice as much, three times as much, and so on. No atom is associated with less positive electricity 1 Nernst, Theoretical Chemistry, chap. ix. ; Rutherford, R dio- Activity ; Ramsay, Presidential Address, 2Yo?w, Cham. Svc., 1908, 93, 774. 4 o8 OUTLINES OF PHYSICAL CHEMISTRY than a hydrogen atom, and we may therefore state that a hydrogen atom unites with unit quantity of electricity to form an ion. A barium ion has twice as rrmch positive electricity, and a ferric ion three times as much positive electricity as a hydrogen ion. Further, since quantities of hydrogen and chlorine ions in the proportion of their atomic weights are electrically equivalent, it follows that Cl' (and other univalent negative ions) contain unit quantity of negative electricity. This increase by steps in the amount of electricity associated with atoms at once recalls the law of multiple proportions, and it appears plausible to ascribe an atomistic structure to electricity ; in other words, to postulate the existence of positive and negative electrical particles, which under ordinary cir- cumstances are associated with matter. On this view, the number of dots or dashes ascribed to positive and negative ions respectively indicates the number of electrical particles (positive or negative) with which the atoms become associated to form ions. These views 1 (Helmholtz, 1882) have received powerful support during the last few years from the results of experi- ments on the passage of electricity through vacuum tubes, the so-called Hittorf s or Crookes' tubes. When a current at very high potential is sent through a highly evacuated tube, rays from the cathode the so-called cathode rays stream across the tube with great velocity, and it has been shown that these rays consist of negative electricity. The speed of the particles depends on the E.M.F. between the poles of the tube, but at a difference of potential of 10,000 volts is about one-fifth of the velocity of light. The mass of these particles is about i/i ooo of that of the hydrogen atom. They are usually termed negative electrons. More recently, it has been dis- covered that the fi rays given off from disintegrating radium at a speed approaching that of light also consist of negative electrons. 1 Helmholtz, Faraday Lecture, Trans. Ghent. Soc., 1882. ELECTROMOTIVE FORCE 409 As negative electrons have thus been found to exist separate from matter, it is natural to expect that free positive electrons may also be isolated. So far, however, this has not been found possible, and opinions differ somewhat as to the reason. Nernst, following Helmholtz, considers that there is no ground for doubting the existence of positive electrons ; the reason why it has not yet been found possible to isolate them is due to their great affinity for matter. Further, Nernst and others assume that positive and negative electrons unite to form neutral atoms or neutrons^ and that these neutrons constitute the ether which is assumed to pervade all space. Other investigators regard a positive ion as an atom minus one or more negative electrons ; the loss of a negative electron would leave the previously neutral atom positively charged. 1 From observations on the effect of a magnetic field on the cathode discharge, it has been calculated that the actual charge carried by a univalent ion (positive or negative) is about 4 x 10 ~ 10 electrostatic units. The application of the electron theory to ordinary chemical changes yields interesting results. For simplicity we will assume the existence of positive electrons, and designate them by the symbol , negative electrons by the symbol 0. When hydro- gen arid chlorine unite to form hydrochloric acid, we assume that under ordinary conditions the valency of the hydrogen is satisfied by that of the chlorine. We may, however, dis- place a chlorine atom by a positive electron, and thus obtain the saturated chemical compound H or H ; in an exactly similar way, the hydrogen may be displaced by a negative electron, forming the saturated compound Cl. In the same way, a dilute solution of copper sulphate contains the saturated compounds Cu/^ or Cu and SO 4 ^ or SO 4 ". ^ vt/ fe/ The electrons, therefore, behave exactly as univalent atoms, 1 Ramsay, loc. cit. 4 io OUTLINES OF PHYSICAL CHEMISTRY the positive electrons enter into combination with positive elements such as H, K, Na, Ba, etc,, the negative electrons enter into combination with negative elements or groups, such as Cl, Br, I, NO 3 , SO 4 . Nothing is known as to the constitution of a non-ionised salt molecule in solution. The formula for non-ionised sodium chloride may perhaps be Na 0C1, the molecule being held together at least partly by electrical forces. Just as there are great differences in the affinity of the elements for each other, so the elements have very different affinity for electrons. Zinc and the other metals have a great affinity for positive electrons, the so-called non-metallic ele- ments have in many cases considerable affinity for negative electrons. The order of the elements in the tension series may be regarded as the order of their affinity for electricity. On this view the potential required to discharge the ions is simply the equal and opposite E.M.F. required to overcome the attraction of the element and the electron (p. 375). Practical Illustrations. Dependence of Direction of Current in Cell on Concentration of Electrolyte It has already been pointed out (p. 346) that the current in a Daniell cell may be reversed in direction by enormously reducing the Cu" ion con- centration by the addition of potassium cyanide. The two chief methods for diminishing ionic concentration are (i) the forma- tion of complex ions (as in the above instance) ; (2) the forma- tion of insoluble salts. When a cell of the type Cd CdSO 4 dilute KNO CuSO 4 dilute Cu is set up, and the poles are connected through an electroscope, it will be found that positive electricity passes in the cell in the direction of the arrow. If some ammonium sulphide solution is then added to the copper sulphate solution, "insoluble" copper sulphide is formed, and the concentration of the Or* ELECTROMOTIVE FORCE 411 ions is reduced to such an extent that the current flows in the reverse direction. If the Daniel! cell Zn ZnSO 4 I KNO 8 CuSO 4 dilute dilute Cu is built up in the same way, it will not be. found possible to re- verse the current by the addition of ammonium sulphide, owing to the greater solution pressure of the zinc as compared with cadmium ; but if potassium cyanide is added, the current changes in direction, owing to the fact that the Or* ion con- centration in a strong solution of potassium cyanide (in which the copper is mainly present in the complex anion Cu(CN) 4 ") is considerably less than in a solution of copper sulphide. The following experiments, which are described in consider- able detail in the course of the chapter, should if possible be performed by the student. For further details text-books on practical physical chemistry should be consulted. (a) Preparation of a standard cadmium cell (p. 357). (b) Measurement of the E.M.F. of a cell by the compensation method (p. 355). (c) Preparation and use of a calomel "half-cell " (p. 375). (d) Preparation and use of a capillary electrometer (p. 380). (e) Measurement of the E.M.F. of a concentration cell (p. 368). (/) Measurement of the E.M.F. of the hydrogen-oxygen cell (p. 392). (g) Determination of the solubility of a difficultly soluble salt, e.g., silver chloride, by E.M.F. measurements (p. 370). PROBLEMS AND QUESTIONS (i) Formulce for Equilibria in Gaseous Systems. When one molecule of a gas yields n molecules on dissociation (e.g., PC1 6 , N 2 O 4 , COC1 2 ), the relationship between density and degree of dissociation, a, at constant pressure is as follows : If d l is the density and v 1 the volume of the undis- sociated gas, d% the density and v 2 the volume of the partially dissociated gas (in which the number of molecules is (i a + no) = i + a(n - i)), we have v *d J . . J ; _i = __ 2 whence a = -. x *- = , -. i + a(n- 1) z> 2 d 1 (n - i)d 2 When the total pressure, P, varies, the equilibrium constant, K^, when concentrations are expressed in terms of partial pressures, is as follows. When one molecule of the gas gives two molecules on dissociation : Kn = 7 ~ (i - a)P (I - a 2 ) I + a (2) Correction for the Change of Volume of Gases taking part in Chemical Reactions. It has been pointed put (p. 144) that when gases are involved in chemical changes the heat given out or absorbed may differ considerably according as the reaction is carried out at constant pressure or at constant volume. When a mol. of gas is generated at the absolute temperature T, work is done by the system and RT calories is absorbed ; when, on the other hand, a mol. of gas disappears RT calories is given out. A little consideration will show that if Q is the heat of reaction in calories at constant volume (when no external work is done) and Q p the heat of reaction at constant pressure (when external work may be done) the relationship between Q tt and Q p is given by the formula QP = Q, + K - 2 ) RT where w x and 2 represent the number of mols. of gas in the initial and final stages of the reaction respectively. For example, the reaction 2H 2 + O 2 - H 2 O (liquid) gives 2 x 68,400 calories at constant pressure, and therefore the heat of reaction at constant volume at 17 is 68,400 = Q, + i x 580, whence Q v *= 67,530 cal. for 1 8 grams of water. (3) Formula Connecting Latent Heat of Vaporisation and Change of Vapour Pressure with Temperature. The formula in question can readily be obtained by means of a reversible cyclic process applied to va- porisation. According to the second law of thermodynamics, in a revers- ible cycle work done change of temperature heat absorbed temperature of absorption* The work done is (V 2 - Vj) dp where V 1 is the volume of a mol. of substance in the form of liquid, V 2 the corresponding volume in the vapour form and dp is the change of vapour pressure for a small change of temperature dT. Substituting in the above equation, we obtain ffk^l*-" (I) where q is the latent heat of vaporisation of i mol. of liquid at the absolute temperature T. 412 PROBLEMS AND QUESTIONS 413 As the volume of a definite quantity of a substance is so much greater in the vapour than in the liquid form, no great error will be made by neg- lecting Vj in comparison with V 2 . Further, according to the gas laws (p. 26) p V 2 = R T. Substituting the value of V 2 from this equation in the formula V^dp/q =dT/T we obtain i dp_*= q or ~p ' dT RT 2 __ dT RT 2 v ; * The above relationship can be obtained in more convenient form by integration, on the assumption that q remains constant for the small interval of temperature concerned. Integrating between the absolute temperatures T 1 and T a (the corresponding pressures being p l and/ 2 ) we obtain (cf. p. 166) . log 10 , a - 10^ = ^^ (3). As an illustration of the use of formula (3) the value of q for benzene may be calculated from the observation that the vapour pressures at 20 and 3oC. amount to 75*0 mm. and 118 mm. respectively. Hence 0-19682 . -V( } 4-581 \293 x 303 ) and q = 8004 calories. An approximate relationship between latent heat of vaporisation and the absolute temperature at which vaporisation takes place the so-called Trouton's rule states that the quotient of the molecular heat of vaporisa- tion by the absolute temperature, is constant in symbols qjT = constant. The rule is approximately valid for non-associated liquids, but associ- ated liquids, such as water and alcohol, show very considerable deviations. Formula (i) applies also to other changes of state, for example from solid to liquid. As an illustration the effect of a change of pressure of one atmosphere on the melting-point of ice will be calculated. In all such calculations, care must be taken to state the factors concerned in corresponding units. The available data are that the latent heat of fusion of ice is 80 calories or 80 x 42,650 gram-cms., that the specific volume of ice is 1-087 when that of water is taken as unit, and that dp is 1033 grams/cm. 8 Substituting in the equation (a - v,) dp dT . UL_ - i; ^ we have <1 T o'oS7 x 1033 dT 80 x 42*650 273 whence dT = 0-0072 (cf. p. 181) It can readily be deduced from the formula that if *>,, is greater than v l dp and dT must have the same sign, in other words increased pressure will raise the melting-point, when, on the other hand, v 2 is less than v lt as 4H OUTLINES OF PHYSICAL CHEMISTRY in the case of water, dp and dT are of opposite sign and increase of pressure will lower the temperature at which the transformation occurs. (3) Mathematical Formulation of the Relationship between Electri- cal Conductivity and the Nature of the Electrolyte. Consider the transport of electric current through a cm. cube of electrolyte. As already pointed out, the strength of the current depends upon the number of ions, on their speed and on the charge which they carry. If c is the concentration of the electrolyte in gram-equivalents per c.c. a is the degree of dissociation and U 1 and V x the speed of the cation and anion re- spectively, in cm. per sec., the current passing through the cm. cube is 96,540 ac (\J 1 + V^ amperes, 96,540 coulombs being the charge carried by i gram equivalent of electrolyte. The current may also be re- presented as the product of the specific conductivity k and the difference of potential, E, between the two sides of the cube. Therefore Ek = 96540 ac (Uj + VJ. Now k/c or kv is the equivalent conductivity of the solution, which we will term A. If further, the potential gradient is i volt per cm. E = i and the above equation simplifies to \ = 96540 o (U + V) where U and V represent the speed of the ions, in cm. per second, when the potential gradient is i volt per cm. When dissociation is complete o = i and the above formula, in the case of a binary uni-univalent electrolyte, for which AQQ = ^t^ becomes (cf. p. 252) /*oo = u + v = 96540 (U + V). From this equation it follows that, as already pointed out (p. 253), the speed of the ions in cm. per sec. are obtainable from the velocities ex pressed in the ordinary units by dividing by 96,540. (4) Proof of Conditions under which Two Solutions are Isohydric (cf* p. 278). Suppose the electrolytes with a common ion are two monobasic acids, HA and HA', both of which obey Ostwald's dilution law, and that in isohydric solutions of the two acids the dilutions are v and v' and the degrees of dissociation a and a' respectively. For the acid HA, according to the law of mass action, the equation holds and for the acid HA' the corresponding equation (I - a>' = K ' (2> When the solutions are mixed, the volume becomes v + v l and the pro- portion of H' ions a + a'. For the acid HA we now have (I - a )(v + V) ' Dividing equation (3) by equation (i) we obtain (a + a')v a + a' V + v' T TIT- = i or sx (v + v')a a v whence a v a a = or = . a v v v PROBLEMS AND QUESTIONS 415 Nov, mlv and a/v' are the respective concentrations of H' ions in the isohydric solutions of the acids, and have now been shown to be equal in other words, the condition for isohydry is that the concentration of the common ion in the two solutions before mixing must be the same. (5) Measurement of Chemical Affinity. We have seen that there are two principal methods of measuring chemical affinity (i) by means of E.M.F. measurements in a galvanic cell (p. 351) and (2) by measurements of the position of equilibrium in the system under definite conditions. The first method has already been fully described. A proof of the for- mula used in the equilibrium method and one or two examples will now be given. It will be sufficient for our present purpose to derive the affinity formula for a reaction in which gases only are concerned; the same formula applies to reactions in heterogeneous systems. A vessel contains hydrogen, oxygen, and water vapour of the respec- tive concentrations Cn 2 , Co 2 > and Ce 2 at the constant temperature T. It is assumed that one of the walls of the vessel is permeable for hydro- gen only, another for oxygen only, and a third for water vapour only, and that the walls can be displaced without friction. Outside each of these walls is the particular gas for which it is permeable, at the same tempera- ture and concentration as the corresponding gas inside, and the amounts both outside and inside are so great that no appreciable change in con- centration is caused by the passage of a mol of gas into or out of the vessel. The wall permeable for hydrogen is now moved inwards so that 2 mols of hydrogen are removed from the vessel, and similarly, by moving in- wards the wall permeable for oxygen, i mol of the latter gas is brought outside. In these processes no work is done, as no alterations of pressure are set up. The hydrogen and oxygen are now allowed to expand rever- sibly at constant temperature T until they attain any desired smaller concentrations Cn 2 and Co 2 . The work done by a mol of a perfect gas in expanding from the volume v to v- is A = RT log e 0J/* = RT log e C/C' and therefore (assuming that both hydrogen and oxygen behave as perfect gases) the total work gained in the above processes is A, - 2 RT log e ^ + RT log, ^. C H 2 C 2 The 2 mols of hydrogen (concentration Cn 2 ) and the mol of oxygen (concentration Co 2 ) are now combined to form 2 mols of water vapour of concentration Cji 9 0, the latter concentration being so chosen that the water vapour is in equilibrium with hydrogen and oxygen of the respec- tive concentrations Cn 2 and Co 2 . No work is done in this combination, which is carried out under equilibrium conditions. Finally the 2 mols of water vapour of concentration CH 2 o are brought isothermally and rever- sibly to the initial concentration Cn 2 o and added to the contents of the vessel through the wall permeable for the vapour. In the latter process the work gained is The result of these processes is that in the interior of the vessel 2 mols of hydrogen of the concentration Cjj 2 and i mol of oxygen of the poncentra- tinn Cf\~ have disatmeared and 2 mols of water vaoour of the concentration 4 i6 OUTLINES OF PHYSICAL CHEMISTRY Cn 2 o have been formed without any alteration of temperature or concei. tration inside the system. The total work gained is A = Aj + A 2 * 2RT log. ^ + RT log. ^ + 2RT log. ^-^ which is a measure of the affinity of hydrogen and oxygen at the tempera- ture and concentration in question. The above equation may be written in the form Now A depends only on the initial and final states of the system and is therefore independent of the arbitrarily chosen concentrations Cn 2 an d Co 2 to which the gases were brought after removal from the vessel. It follows that the expression ., 2 . = constant = K, in other words, CH 2 Co 2 whatever be the concentrations Cn 2 and Co 2 , the concentration Cn 2 of water vapour in equilibrium with Cn 2 and Co 2 is such that the above equation holds. We have here a thermodynamical proof of the law of mass action, first established by Guldberg and Waage from kinetic considerations. The affinity of hydrogen to oxygen is therefore represented by the formula A RT log, K - RT log. and can be obtained for any concentration C of the reacting substances when the equilibrium constant of the action has been determined. It can easily be shown that a formula of this type applies both to homogeneous and heterogeneous reactions. The general formula is as follows (p. 297) : [AJh [AJ'V- which, when the initial substances and the products are in unit concen- tration, simplifies to A =* RT log, K. For the combination of hydrogen and iodine the general formula becomes At the temperature of boiling sulphur (T = 273 + 445 = 718) K = JL 50. 0-02 D The work obtained by the combination of i mol of iodine and r mol of hydrogen, each at unit concentration, to 2 mols of hydrogen iodide, also at unit concentration, is therefore A = 1-985 x 718 x 2-303 Iog 1() 50 :* + 5575 calories. We have here a case where the affinity of a reaction and the heat of reaction are of opposite sign - the latter is about - 6000 cal. The general formula will now be used to calculate the chemical affinity of a heterogeneous reaction, namely, the maximum work obtain- able in the combination of i mol of carbon dioxide with calcium oxide at PROBLEMS AND QUESTIONS 417 a definite temperature to form calcium carbonate. It is usual to denote the affinity of a gas as that shown towards the solid substances at atmo- spheric pressure. We proceed to calculate the affinity of carbon dioxide for calcium oxide at 671 C. = 944 abs., the equilibrium pressure at this temperature being 13-5 mm. In this case (p. 174) __ - [CaO] [COJ />co 2 and A= - RTlog e /. therefore A = - 1-985 x 944 x 2-303 Iog 10 13-5/760 = 7540 calories. The value of A obtained is the same whether concentrations or partial pressures are used for calculations in which gases are concerned. In the above calculation the pressure of the atmosphere is taken as unit. (6) Deduction of the Formula Connecting Displacement of Equilibrium with Change of Temperature. Van't Hoff's formula (p. 166) which is usually written in the form d(\oge K) - Q dT RT 2 can easily be deduced from the expression A - Q = T(dA/dT) for the second law of thermodynamics (p. 151) and the affinity formula A = RT log e K given in the last section. From the latter formula we obtain by differentiation and A - Q = T = RT log. K + whence - Q d(\og e K) _ - Q ~~~dT RT*' 1. A certain quantity of a gas measures 100 c.c. at 25 and 700 mm. pressure. What pressure will be required to change the volume to 50 c.c. at - 10 C. ? Ans. 1236 mm. 2. What volume is occupied by (a) i gram of nitrogen, (b) i gram of carbon dioxide at 20 and a pressure of 72 cm. of mercury ? Ans. (a) 906-3 c.c. ; (b) 576-8 c.c. 3. An open vessel is heated till one-third of the air it contains at 20 is expelled. What is the temperature of the vessel ? Ans. 117-6 C. 4. If 0*5 grams of a gas measure 65 c.c. at 10 and 500 mm. pressure, what is its molecular weight ? Ans. 271-5. 5. If i gram of nitrogen, i gram of oxygen and 0*2 gram of hydrogen are mixed in a volume of 2*24 litres at o, calculate the respective partial pressures of the gases in the mixture, in grams per sq. cm. Ans. 369, 323, and 1025 grams /cm. 2 6. The density of benzyl alcohol, C 6 H <5 CH 2 OH, at its boiling-point is 1-145. Compare the observed and calculated values of the molecular volume (p. 61). Ans. Obs. 123-7. Calc. 128-8. 7. The density of a solution containing 4*1375 grams of iodine in 100 grams of nitrobenzene is 1*2389 at 18, the density of the solvent at the same temperature being 1*20547. From these data calculate the molecu- lar solution volume of iodine. Ans. 67*2 c.c. 8. The density of formic acid at 20 is 1*2205 and n D at the same tem- perature is 1*3717. Calculate the molecular refractivity of formic acid by 27 418 OUTLINES OF PHYSICAL CHEMISTRY the Lorentz formula and compare it with the value calculated from the atomic refractivities (cf. p. 65). Ans. Obs. 8-56. Calc. 8-35. 9. The value of n D for a mixture of formic acid and water containing 62*7 per cent, of the latter was found to be 1*3625 at 19-5, and the density at the same temperature 1*1462. Calculate the refraction constant by the Lorentz formula and compare it with that calculated on the assumption that the components exert their effects independently. [D 19 for water 0-9984 N D = 1*3333-] Ans. Obs. 0-1937. Calc. 0-1936. 10. Find the relationship between the solubility, s, of a gas and its absorption coefficient, a, in a liquid at t (cf. p. 83). Ans. s/a = (273 + *)/ 2 73- 11. Calculate the gas constant, R, in litre-atmosphtres from the obser- vation that a solution containing 34-2 grams of cane sugar in i litre of water has an osmotic pressure of 2*522 atmospheres at 20. Ans. 0-0860. 12. The osmotic pressure of a 2 per cent, solution of acetone in water is equal to 590 cm. of mercury at 10. What is the molecular weight of acetone? Ans. 60 (found), 58*0 (theor.). 13. What is the molecular concentration of an aqueous solution of urea which at 20 exerts an osmotic pressure of 4*6 atmospheres ? Ans. 0-19 molar. 14. The vapour pressure of ether (mol. wt. 74) is lowered from 38-30 cm. to 36-01 cm. by the addition of 11*346 grams of turpentine to 100 grams of ether. Calculate the molecular weight of turpentine. Ans. 132 (theor. 138). 15. The vapour pressure of water at 50 is 92 mm. How much urea (mol. wt. 60) must be added to 100 grams of water to reduce the vapour pressure by 5 mm. ? Ans. 18-1 grams. 16. A current of dry air was passed in succession through a bulb con- taining a solution of 30 cane sugar in 160 grams of water, through a bulb, at the same temperature, containing water, and finally through a tube containing concentrated sulphuric acid. The loss of weight in the water bulb was 0*0315 grams and the gain in weight in the sulphuric acid bulb 3-02 grams. Calculate the molecular weight of cane sugar in the solution. Ans. 339. 17. The addition of 1*065 grams of iodine to 30*14 grams of ether raises the boiling-point of the latter by 0*296. What is the molecular weight of iodine in ether? Ans. 251. 18. The vapour pressure of ether at o is 183-4 mm., at 20 433*3 mm. Calculate the latent heat of vaporisation per mol. of ether at 10. Ans. 6840 cal. 19. The vapour pressure of water over a mixture of CuSO 4 , 5H 2 O and CuSO 4 , 3HoO is 2*933 mm. at 13*95 and 21*701 mm. at 39*7. Calculate the heat given out when i mol. of water combines with CuSO 4 , 3H 2 O to form CuSO 4 , sH ? O. Ans. - 13,73 cal. 20. 0-3 grams of camphor, C 10 H 16 O, added to 25*2 grams of chloroform raise the boiling-point of the solvent by 0*299. Calculate the molecular elevation constant for chloroform. Ans. 38*2. 21. From the data in the previous question calculate the heat of vapo- risation of chloroform (boiling-point 61). Ans. 6931 cal. 22. 1-2 grams of a substance dissolved in 24*5 grams of water (K = PROBLEMS AND QUESTIONS 419 18-5) caused a depression of the freezing-point of 1-05. Find the mole- cular weight of the substance. Ans. 86. 23. Beckmann found that 0-0458 grams of benzoic acid in 15 grams oi nitrobenzene (K = 80) caused a depression of the freezing-point of 0-099. What conclusion can be drawn from this observation as to the molecular condition of benzoic acid in nitro benzene ? Ans. Acid is associated. 24. At 343 the vapour pressure of ammonium bromide is 195 mm. and at 356 it is 289 mm. Calculate the heat of vaporisation of ammonium bromide, assuming dissociation complete. Ans. 45,000 cal. 25. From formula (i) p. 137, deduce the expression and hence calculate the osmotic pressure of an ethereal solution the boil- ing-point of which is 35-2. (Boiling-point of ether, 34*8; latent heat of vaporisation per gram 84-5 cal. Ans. 6-5 atmos. 26. At 21 the surface tension, % of diethyl sulphate in 28-28 dynes/cm. 2 and at 62-6 y is 24*00 dynes/cm. 2 Find the value of c, the temperature coefficient of the molecular surface energy (D 21 = 1*0748 ; D 62.6 = j-0278). Ans. 2*17. 27. For rronochlorhydrin y at 17 is 47*61 dynes/cm. 2 (D = 1*3254) and at 57*8 4372 dynes/cm. 2 (D = 1*2883). What conclusions can be drawn from these data as to the molecular complexity of the liquid ? Ans. c = 1*44, liquid is associated. 28. Calculate the heats of formation of ethane, ethylene and acety- lene respectively from their elements at 17 (a) at constant pressure, (b) at constant volume from the following data. Heats of combustion : ethane 370,440 cal., ethylene 333,350 cal., acetylene 310,100 cal. Heats of formation: carbon dioxide 94,300 cal., liquid water 68,400 cal., all at constant pressure. Ans. Ethane: C.P. 23,360 cal., C.V. 22,200 cal. Ethylene: C.P. - 7950 cal., C.V. - 8530 cal. Acetylene: C.P. - 53,100 cal., C.V. - 53,100 cal. 29. Find the heat of formation of anhydrous aluminium chloride from the following data (Thomsen). 2A1 + 6HClAq = 2AlC! 3 Aq + 3H 2 -f 239,760 cal. H 2 + C1 2 = 2HC1 + 44,000 cal. HC1 + Aq = HClAq + 17,315 cal. A1C1 3 + Aq = AlCl 3 Aq + 76,845 cal. Ans. 321,960 cal. (for Al.^Cy. 30. The heat of solution of anhydrous strontium chloride is 11,000 cal., that of the hexahydrate - 7300 cal. What is the heat of hydra- tion of the anhydrous salt to hexahydrate. Ans. 18,300 cal. 31. The specific heats of diamond and graphite in the neighbourhood of 10 (o-i7) are 0-1128 and 0*1604 calories per gram respectively. The heats of combustion are 94,310 and 94,810 calories per 12 grams respec- tively. Find the heat evolved in the transformation of graphite to diamond at o C. Ans. 490 cal. 32. In the synthesis of nitric acid and of ammonia the primary reac- tions are N 2 + 2 J2NO - 43,200 cal. N a + 3H 2 r^2NH 3 -f 24,000 cal. 420 OUTLINES OF PHYSICAL CHEMISTRY Discuss fully the effect of temperature and pressure on these reactions and refer, for illustration, to the manufacturing processes : why is it that in these processes an elevated temperature is used, although one reaction is endothermic and the oiher exothermic ? At 2000 abs. K = [NO]/[N 2 ]*[OJi = 0-0153. Assuming the heat of reaction independent of temperature, calculate the equilibrium constant at 2500 abs. (Birmingham Univ.) 33. The vapour density of phosphorus pentachloride referred to air as unity was found to be 5-08 at 182, 4-00 at 250, and 3-65 at 300, calcu- late the degrees of dissociation at these temperatures. Ans. 41-7 per cent. ; 80 per cent. ; 97-3 per cent. 34. From the following data for the equilibrium N 2 O 4 ^2NO 2 at 49-7 calculate the degree of dissociation at each pressure and show, by finding the dissociation constant, that the law of mass action applies: Pressure in mm. Hg 26*80 93*75 182*69 261-37 49775 Density (air = i) 1*663 1788 1*894 I 'Q63 2 * I 44 The vapour density of N 2 O 4 is to be taken as 3-20 (air = i). Ans. 0*93; 0-789; 0*69; 0*63 ; 0*493. 35. Bodenstein found that the degree of dissociation of carbonyl chloride, according to the equation COC1 2 ^> CO + C1 2 , is 67 per cent, at 503, 80 per cent, at 553, and 91 per cent, at 603. From these results calculate the heat of dissociation of carbonyl chloride. Ans. 19,210 cal. from 5O3-553; 26,550 cal. from 553-6o3. 36. The ratio of distribution of aniline between benzene and water is io- 1 : i. When a litre of aniline hydrochloride solution, containing 0*0997 mols. of the salt, was shaken with 59 c.c. of benzene at 25 it was found that 50 c.c. of benzene had taken up 0*0648 grams of aniline. Find the amount of hydrolysis of aniline hydrochloride in the solution and calculate the dissociation-constant of aniline as a base (cf. p. 291). Ans. 1*56 per cent., 4*6 x io J 37. When heated in aqueous solution at 52*4 the concentration of sodium bromoacetate in solution was 11*0, 9*4, 7*9 and 6*9 at times o, 26, 52 and 74 hours respectively from the commencement of the reaction, the decomposition being ultimately complete. Find the order of the reaction and calculate the times required to complete (a) one-third, (b) two-thirds of the change. Ans. Unimolecular. 65*2 hours, 177 hours. 38. In an experiment on the rate of reaction between sodium thiosul- phate and ethyl bromoacetate (cf. p. 232) 50 c.c. of the reaction mixture required the following amounts of o'oiio N iodine at the times from the commencement of the reaction indicated in the table. t (min.) o 5 io 15 25 40 ^ cc.s. iodine solution 37' 2 5 2 4'7 l8 '75 I 5'3 I]C ' 6 8<8 5 4*4 Show that the reaction is of the second order and find the velocity constant for concentrations of i mol. per litre. Ans. 14*6. 39. From the electrolysis of hydrochloric acid in a cell with a cadmium anode the following results were obtained : change in concen- tration of chlorine at anode and cathode respectively + 0*00545 gram silver deposited in voltameter connected in series with the cell 0*0986 gram. Calculate the transport numbers of hydrogen and chlorine (Cl = 35*46; Ag = 107*9). Ans. H = 0*832; Cl = c-i68. PROBLEMS AND QUESTIONS 421 40. The transport number of the cation in potassium chloride was found to be 0*497 and \ x = 130*1. What is the absolute velocity of K* in cm. per second, under unit potential gradient ? Ans. 0-00067 cm. /sec. 41. At 18 the velocity of migration of the Ag' ion is 0*00057 cm. /sec. and of the NO 3 ion 0-00063 cm./sec. What is the value of p.^ for silver nitrate at 18 ?' Ans. /* ^ = 115-8. 42. Find the degree of ionisation of lactic acid at different dilutions and calculate the ionisation constant from the following data, valid for 25:- v (litres) 64 128 256 512 oo pv 34-3 47'4 64-2 87-6 381 Ans. 0-000138. 43. If the velocity coefficient for catalysis by N/4 acetic acid is 0*00075 what will be the coefficient when the solution is also N/4O with respect to sodium acetate, assuming that the latter is dissociated to the extent of 86 per cent. ? Ans. 0-000075. 44. If an amount of base insufficient for complete saturation is added to an equimolecular mixture of acetic and glycollic acid, in what propor- tion will the salts be formed? (Dissociation constants at 25. Acetic acid o'ooooiS, glycollic acid 0-00015.) Ans. i : 2-9. 45. A N/io solution of sodium acetate is ionised to the extent of 80 per cent, at 18. What is the osmotic pressure of the solution at this temperature ? Ans. 4*28 atmos. 46. Sodium chloride in 0*2 molar solution is dissociated to the extent of 80 per cent, at 18. What will be the concentration of a urea solution which is isotonic with the salt solution ? Ans. 21*6 grams per litre. 47. Calculate the E. M. F. of an oxyhydrogen cell from the facts that 2H 3 + O 2 = 2H 3 O + 2 x 6S,4oo cal. and that the temperature coefficient of the E. M. F. of the cell is - 0*00085 volts at room temperature (17). Ans. 1*23 volts. 48. Find the E. M. F. at each electrode and the total E. M. F. of the cell Fe I FeSO 4 o*iN | CuSO 4 o-oi N | Cu at 25, assuming that the iron salt is 40 per cent, ionised and the copper salt 60 per cent, ionised at the dilutions in question, and that the P. D. at the liquid contact is eliminated. [Use the general formula on p. 390.] Ans. Fe electrode - 0*46 - 0*041 = 0-501 volts. Cu + 0-329 - 0*064 = + 0-265 volts. Total E. M. F. of cell - 0-776 volts. 49. Discuss the influence of temperature and pressure on the equilibrium 2SO 2 -f O 2 ^2SO 3 + 45,200 cal. and show how the change of the equilibrium constant with temperature can be calculated. (University Coll., London.) 50. Criticise the various theories which have been advanced to explain the mechanism of electrolytic conduction. 51. Criticise Berthelot's principle of maximum work. 52. What do you understand by the solubility product ? Discuss the question of the simultaneous solubility of two salts possess>g a common ion. (St, Andrews Univ.) 53. Explain carefully why the ratio of the specific heats of a gas de- pends on the number of atoms in the molecule. 422 OUTLINES OF PHYSICAL CHEMISTRY Briefly describe the method by which for physico-chemical purposes this ratio is determined. (Sheffield Univ.) 54. Define the terms "absorption coefficient," '* critical solution tem- perature," "solid solution" and " eutectic alloy," giving examples. (Sheffield Univ.) 55. "Every chemical reaction is reversible." Discuss the statement carefully so as to reveal the extent to which it is true, quoting examples. (Sheffield Univ.) 56. Write a brief account of the developments in electro-chemistry associated with the names of Daniell, Faraday, Hittorf and Arrhenius. (Sheffield Univ.) 57. How would you determine, either directly or indirectly, the critical temperature, pressure and volume (or density) of a pure substance ? (Dublin Univ.) 58. Discuss the conditions on which the possibility of completely separating a mixture of two miscible liquids by fractional distillation de- pends. (St. Andrews Univ.) 59. Discuss the associating and dissociating properties of solvents. (St. Andrews Univ.) 60. Describe some experiments in support of the view that ions migrate during electrolysis. How are the transport numbers of ions determined ? (St. Andrews Univ.) 61. Describe the preparation and properties of some colloidal solutions. What is the present view as to the nature of such solutions ? (St. Andrews Univ.) 62. Explain why (a) a higher potential is necessary to electrolyse a decinormal solution of hydrochloric acid than is necessary for a normal solution, (b) why an E.M.F. is usually set up at the surface of contact of dilute and concentrated solutions of the same electrolyte, (c) why magnesium displaces hydrogen slowly from water but rapidly from hydrochloric acid. (St. Andrews Univ.) 63. Describe an experiment to illustrate the migration of ions during electrolysis. How would you show that the cation and anion in a solu- tion of copper sulphate move with different velocities, and how would you determine the relative velocities ? (Birmingham Univ.) 64. State the phase rule and explain the terms involved. Apply the mle to explain the fact that the extent of dissociation of calcium car- bonate depends only on the temperature. (Sheffield Univ.) 65. What class of substance have in solution molecules of larger size than that calculated from the formula, and how does the phenomenon depend on (a) the constitution of the solute, (b) the nature of the solvent ? (Sheffield Univ.) APPENDIX. EQUIVALENT CONDUCTIVITY AT 18. TABLE la. Normal Concentr'n. KC1. NaCl. KNOg. AgN0 3 . NaC 2 H 3 2 . K 2 SO 4 . Na 2 CO 3 . BaCl 2 . 0*0001 129-5 109*7 124-7 115*5 76-8 I33'5 _ 20 "5 0*0002 129'! 109*2 124*3 115*2 76-4 1327 19-8 0*0005 128*3 108*5 123-6 TI 4*5 75*8 130*8 18-3 O'OOI 127-6 107 '8 122-9 114*0 75 '2 129*0 II2'O i6'9 O'OO2 1 26 '6 106*7 122*0 113-0 74 '3 126-3 108-5 15-0 0*005 i24'6 104*8 120*1 III'O 72-4 121*9 IO2'5 11-3 O'OI 122*5 I02'8 118-1 108*7 70*2 117*4 96*2 107-7 0*02 I2O'O 100*2 115-2 105*6 67-9 111*8 89-5 I0 3*3 0*05 MS'9 95 '9 110*0 100*1 64*2 102-5 80*3 96-8 0*1 m'9 92'5 104*4 947 6n 95 '9 72*9 Q2'2 0'2 1077 88*2 98-6 88*1 57'i 88*9 65*6 86-7 0'5 102-3 80-9 89*7 77'8 49'4 787 54*5 77'6 I 98*2 74 '4 80-4 67-8 41*2 71-8 45*5 70 '3 2 92-6 64*8 69-4 55'8 30*0 34*5 60*3 TABLE U. Normal Concentr'n. CuS0 4 . KOH. NaOH. NH 4 OH. HC1. HNO 3 . HjS0 4 . HC 2 H 3 O O'OOOI 113*3 66 107 0*0003 111*1 53 80 0*0005 106*8 38*0 368 57 0*001 101*6 234 208 28*0 377 375 36i 4i 0*002 93 '4 233 206 20 '6 376 374 351 30-2 0*005 81*5 230 203 13-2 373 37i 330 20*0 0*01 72*2 228 200 9-6 370 368 308 i4'3 0'02 63*0 225 197 7'i 367 3 6 4 286 10*4 '5 5i'4 219 190 4'6 360 357 253 6*48 O'l 45' 213 I8 3 3'3 35i 350 225 4*60 0'2 39*2 206 I 7 8 2-3 342 340 214 3*24 *5 30*8 197 I 7 2 *'35 327 324 205 2"OI I 2 25-8 20*1 184 160*8 160 131*4 0-89 o'532 301 254 310 258 198 183 1*32 0-80 From Kohlrausch and Holborn, Leitvermo%en der Elektrolyte. 423 424 OUTLINES OF PHYSICAL CHEMISTRY IONIC MOBILITIES (VELOCITIES) IN AQUEOUS SOLUTION AT 18. TABLE lla. Normal Concentr'n. K. Na. Li. NH 4 . Ag. Ba. jSr, Ca. 4 M e- Zn. o'oooo 65-3 44*4 35'5 64*2 557 57*3 54 'o 53'o 49 47'5 0*0001 64*7 43 '8 34 '9 63*6 55'4 55' 5i7 50*6 47 45' 1 0*0002 64*4 43 ' 6 347 63'4 55'i 54*3 5 I>0 50*0 46 44 '5 0*0005 64*1 43'3 34*4 63-0 54*9 53'3 r;c*o 48*9 45 43 '5 O'OOI 637 42*9 34'o 62*7 547 52*2 48-9 47'8 43 42'3 0'CO2 63*2 42*4 33*5 62'2 54 '2 507 47 '4 46*4 42 40-9 0*005 62*3 41-4 32*6 6l*2 53 <2 48*2 44*9 43*9 40 38-4 0*01 61-3 4'5 31-6 6o*2 5i'9 457 42-4 41-4 37 35'9 0*02 60 'o 39 '2 30-3 59'o 5' 427 39'4 38-3 34 32 '9 0'03 59 '2 38-3 29*4 58*1 48-6 40 '5 37*2 36-1 32 307 0-05 57 '9 37 'o 28*2 56*8 46*6 377 34 '4 33 '4 29 27*9 0*1 55'8 35*o 26*1 54-8 43 '3 33'8 30'5 29-4 25 24*0 TABLE Normal Concentr'n. H. Cl. I. N0 3 . C10 3 . C 2 H 3 2 . S0 4 . JC 2 4 . JC0 8 . OH. 0*0000 3i8 65-9 66*7 60*8 56*2 337 69*7 63 174 O'OOOI 3i8 6 5'3 66*1 60 '2 55*5 33-1 67 '2 61 172 0*0002 316 65-1 65-9 60'0 5 5 '2 33 'o 66*6 60 172 0*0005 315 64*8 6.T5 59 '6 54 '6 32*8 65*4 59 171 O'OOI 3*4 64-4 65*1 59'3 54'i 32*6 64*0 58 69 171 0*002 3 T 3 63'9 64*6 58-8 53*4 32-4 62-3 56 66 170 0*005 3 11 63-0 637 57'8 52*4 31*6 59*2 54 60 168 O'OI 310 62*0 62*7 56-8 Si '3 30*8 56-i 5i 55 167 0*02 307 60*7 6i'5 55'6 497 29-8 52'3 48 50 165 0*03 305 59'8 60*6 547 48*4 29-0 497 46 47 163 0*05 302 58'6 59*3 53'4 46-4 28 'o 46*1 43 43 161 O'l 296 S6'5 57 '3 5i'4 43'2 26*4 41*9 39 38 157 From Kohlrausch and Holborn, Leitvermogen der Elektrolyte. APPENDIX TRANSPORT NUMBERS OF ANIONS. TABLE III. = gram equivalents per litre. 425 n = O'OI. 0-02. 0*05. 0*1. 0*2. 0-5- i. 2. KC1 ^ KBr 1 KI f 0*506 0-507 0-507 0*508 0-509 0-513 0-514 0-5I5 NH 4 ClJ NaCl _ O*6l4 0*617 0-620 0*626 0*637 0-642 KN0 3 NaNO 3 ~ 0*497 0*615 0-496 O'6l4 0-492 O'6l2 0*487 o'6n 0*479 0-608 . AgNO, 0*528 0-528 0*528 0*528 0-527 0-519 0*501 0*476 KC 2 H 3 2 o'33 0-33 0-33 0*331 0-33 2 KOH 735 0-736 0-738 0-740 NaOH o'8i 0*82 0*82 0-82 0*825 HC1 0*172 0-172 0-I72 0-173 0*176 0*185 JBaCl 2 0*56 0-565 0-575 0-585 0-595 0-615 0*640 0-657 ^CaCl 2 0*58 0'59 0-61 0-64 0-66 0-675 0*686 0*700 |K 2 CO 3 0*39 0*40 0-41 0-435 '434 0*413 A Na 2 CO 3 0*52 0-53 0-^3 0-54 0-548 0-542 J-MgS0 4 o'6o 0-64 0*66 0*70 0*74 0*76 |CuS0 4 0*62 0*626 0*632 0*643 0*668 0-696 0*720 iH SO 4 ~ _ 0-193 0*191 0*188 0-182 0*174 0-168 POTENTIAL SERIES OF THE ELEMENTS. 1 TABLE IV. fhe numbers in the following table give the potentials of the substances in question in contact with normal ionic solutions of their salts, referred to three different standards The numbers under e oA are referred to the potential of the hydrogen electrode as o'o volts, those under oc are referred to the normal calomel electrode as zero, and those under to the calomel electrode = + 0*560 volts. - oc. " Absolute e oc. " Absolute Potentials." Potentials." Manganese -1*07 -I- 3 6 0*80 Hg/Hg 2 " 0775 0-492 1*052 Zinc -0*770 ~ I '53 -0-493 Hg/Hg" 0-835 '55 2 I'II2 Iron 0*46 -0*74 0*18 Silver 25 0*798 0-515 1*075 Cadmium 0*42 -0703 -0-143 Platinum 0*86 0-58 I-I4 Thallium 0*32 - 0*603 -0-043 Gold i -08 0-80 1-36 Cobalt -0*30 -0*58 0*02 Fluorine 2'0 i '7 2-26 Nickel 0*25 -o'53 + 0-03 Oxygen 2 1-2(1-66) 0-9 1*46 Lead 0*119 0-402 + 0-158 Chlorine^j 1*400 I '120 1-68 Hydrogen Copper + O'OOO + 0*329 -0-283 +0*277 + 0-046J +0-606 Bromine ^25 Iodine J 1*095 0-628 0*812 0-345 1-372 0*905 1 From Le Blanc, Lehrbuch der Elektrochemie. 2 Cf. p. 400. These values apply to a solution of normal H* concentration. In order to liberate oxygen from a solution of normal OH' concentration 0*8 volts less are re- quired, and to liberate hydrogen from the same solution o'8 volts more are required than in the case of a normal solution of acid. INDEX. ABNORMAL molecular weights in solu- tion, 123. vapour densities, 40-42. "Absolute" potentials, 375, 378. Absorption of light, 69-73. spectra and chemical constitution, 73- Accumulators, 405. Acetic acid, adsorption of, 325. atomic volume of, 61. density of vapour, 41. dissociation of, 267. Acids, catalytic action of, 205, 219, 272. effect of substitution on strength of, 304. strength of, 269-274. Active mass, 156. of solids, 173. Additive properties, 62, 251, 335. Adsorption, 324. and enzyme action, 332. and surface tension, 330. by charcoal, 324. . formulae, 328. -- theories of, 324-328. Affinity, chemical, 148, 154, 271, 415. constant, 157, 273, 275. Amalgams, cells with, 351. Amicrons, 318. Ammonium chloride, dissociation of, 42, 219. hydrosulphide, dissociation of, 176. Amphoteric electrolytes, 307. Argon, position in periodic table, 23. Associated solvents, ionising power of, 339- Associating solvents, 123. Association in gases, 41. in solution, 124, 338-342. Atomic heat, 21. hypothesis, 5. 427 Atomic refractions, values of, 65. volumes, 60. weights, determination of, 8-15. standard for, 17. table of, 19. Attraction, molecular, 34, 58. Available energy, 104, 150, 352. Avidity of acids, 269-274. Avogadro's hypothesis, 10, 36. deduction of, from kinetic theory of gases, 32. valid for solutions, 103, 109. BASES, catalytic action of, 220. strength of, 274-276, 292. Beckmann's methods, 116, 120. Benzoic acid, distribution between solvents, 178, 198. Beryllium (glucinum), atomic weight of, 10, n. Bimolecular reactions, 207, 230. Binary mixtures of liquids, 84-91. distillation of, 87. vapour pressure of, 87. Blood, catalysis by, 202, 229. Boiling-point, elevation of, 114, 118. Boron, atomic heat of, 12. Brownian movement, 318. CADMIUM standard cell, 356. Calomel electrode, 373. Calorimeter, 146, 147, 153. Capillary electrometer, 380. Cane sugar, hydrolysis of, 205. Carbon, atomic heat of, 12. dioxide, critical phenomena of, 49. Catalysis, 217-224. mechanism of, 222. technical importance of, 219. Cathode rays, 399. Chemical affinity, 148, 154, 271. Chemical equilibrium and E.M.F., 396. 428 OUTLINES OF PHYSICAL CHEMISTRY Chemical equilibrium and pressure, 169. and temperature, 166, 169. Clark cell, 358. Coagulation of colloids, 320. adsorption theory of, 323. Colligative properties, 62. Colloidal particles, charged, 319. size of, 318, 323. platinum, 220, 232, 316. solutions, 313. coagulation of, 319. filtration of, 323. optical properties ot, 317. preparation of, 315. Colloids, 313. diffusion of, 313. electrical properties of, 319. irreversible, 323. precipitation by electrolytes, 319. reversible, 323. Combining proportions, law of, 4. volumes of gases, law of, 9, Combustion, heat of, 145. Complexions, 281, 303, 310. Components, definition of, 181. Concentration cells, 367-373. Conductivity, electrical, effect of tem- perature on, 263. equivalent, 251. of pure substances, 258. measurement of, 254-258. molecular, 249, 257, 265. specific, 235, 249. Conservation of energy, law of, 140. of mass, law of, 3. Constant boiling mixtures, 89. Constitutive properties, 62. Continuity of gaseous and IFquid states, 53. 55- Copper sulphate, hydrates of, 174. Corresponding states, law of, 56. temperatures, 57. Critical constants, 51, 56. phenomena, 49-58, 69. solution temperature, 86. temperature, determination of, 77. Carbohydrates, 188. Crystallisation interval, 192. Crystalloids, 313. " Cyclic" processes, 133, 136. DANIELL cell, 348, 362, 366. reversal of current in, 366, 401. Decomposition potential of electrolytes, 399- Deliquescence, 175. Density of gases and vapours, 36, 43. determination of, 37, 41, 48. Dialysed iron, 315. Dialysis, 315. Dielectric constant, 225, 338. and ionisation, 338. Diffusion of gases, 33. in solution, 108. and osmotic pressure, 98, 108. Dispersed system, 315. Dispersion, 315. Dissociating solvents, 123. Dissociation constant, 266, 273, 275. electrolytic, 260-263. 335'337- degree of, 261. evidence for, 335-337. mechanism of, 342. of water, 283, 293. of salt hydrates, 174. in gases, 42, 125, 163. solution, 125, 260-263 thermal, 163. Distillation of binary mixtures, 87, g. steam, 90. Distribution coefficient, 95, 178, 197, 327- Dulong and Petit's law, IT. Dyeing, adsorption theory of, 330-331. EDISON accumulator, 407. Efflorescence, 175. Electro-affinity, 410. Electrode, calomel, 373. hydrogen, 376, 385. mercuric oxide, 378. Electrodes, normal, 375, 376 Electrolysis, 236-238, 393. of water, 401. separation of metals, etc., by, 395. Electrolytes, strong, 279-282. Electrolytic dissociation. See Dis- sociation, electrolytic. Electrometer, capillary, 380. Electromotive force and chemical equilibrium, 396. Electromotive force and concentration of solutions, 365. measurement of, 354. standards of, 356. Electrons, 407. and light adsorption, 72. INDEX 429 Electrons and valency, 409. Elements, i. disintegration of, 2. periodic classification of, 20. potential series of, 386. table of, 21. Emulsoids, 322. Enantiotropic substances, 197. Endothermic and exothermic com- pounds, 144. Energy, available, 104. 150, 332. chemical, 140, 351-354- conservation of, 140. free, 104, 150, 352. internal, of gases, 46. intrinsic, 143. kinds of, 139. Enzyme action and adsorption, 332. reactions, 221. reversibility of, 222. Equilibrium, effect of pressure on, 169. of temperature on, 166-170. false, 218. in gaseous systems, 161-164. in clectrolyt s, 266-312. in non-electrolytes, 164-166. kinetic nature of, 158, 160, 241. Equivalents, chemical, 8, 15, 237. electrochemical, 237. Ester equilib ium, 156, 164. Esters, hydrolysis of, 206. -- sapouification of, 207, 275. Eutectic point, 187, 191. Exothermic nnd endothermic com- pounds, 144. Expansion of gases, work done in, 27. FARADAY'S laws, 237. Ferric chloride, hydrates of, 194. Filtration of colloidal solutions, 323. Fluidity, 74. Formation of compounds, heat of, 143. Freedom, degrees of, 179, 182. Freezing-point, lowering of, 119-121, 194. Friction, internal. See Viscosity. GAS cells, 364. constant, R, 26, 102. laws, 25-26. deduction of, 31-33. deviations from, 28, 33-35. Gases, 25-48. adsorption of, 328. Gases, behaviour of, on compression, 51. kinetic theory of, 29-35, 4^- liquefaction of, 58. solubility of, in liquids, 82. specific heat of, 43-48. Gay-Lussac's law of gaseous volumes, 9- of expansion of gases, 25. Gel (hydrogel), 323. Gladstone- Dale formula, 64. Grot thus' hypothesis, 264. HAEMOGLOBIN, osmotic pressure of, 316. Heat of combustion, 145. additive character of, 148. of ionisation, 285, 295, 344. of solution, 146, 153. Helium, liquefaction of, 59. critical constants of, 51. Helmholtz formula, 351-354, 373. views on valency, 399. Henry's law, 82, 95, 178. Hess's law, 125. Heterogeneous equilibrium, 172 199. Hydrate theory, 333, 339. Hydrated ions, 346. Hydrates, dissociation of, 174. in solution, 340. Hydration in solution, 345-347. Hydrogel, 323. Hydrogen, adsorption of, 329. electrode, 375, 385. iodide, decomposition of, 159, 161. Hydrogen -oxygen cell, 392. peroxide, decomposition of, 202, 229. Hydrogen sulphide, dissociation of, 167. INDICATORS, theory of, 296, 309. Intermediate compounds in catalysis, 223. Ionic and non-ionic reactions, 307. Ionisation and chemical activity, 311. degree of, 261, 281. energy relations in, 343. heat of, 285, 295, 344. mechanism of, 342, 345. role of solvent in, 314, 338, 342- 345- Ionising power of solvents, 338, 339. and free affinity, 339. Ions, 236. 430 OUTLINES OF PHYSICAL CHEMISTRY Ions, complex, 281, 303. 310, migration of, 236, 243-249. reactivity of, 306, 311. velocity or mobility of, 252-254. Irreversible electro-chemical processes, 354- Isoelectric point, 320. Isohydric solutions, 277, 414. Isomorphism, 13, 14. Isosmotic solutions, 105. Isotonic coefficients, 106. solutions, 105. JOULE-THOMSON effect, 58. KINETIC energy, 32, 46, 140. and temperature, 32, 319, of gas molecules, 46. theory of gases, 29-35, 46. Kohlrausch's law, 251. LEAD accumulator, 405. Le Chatelier's theorem, 169. Light, absorption of, 69-73. Liquefaction of gases, 58. Liquids, molecular weight of, 125. miscibility of, 84, 95. properties of, 49-79. Lorenz-Lorentz formula, 64. MASS action, law of, 155-160, 173. and strong electrolytes, 279- 283. in heterogeneous systems 172. proof of, 1 60. Maxima and minima on curves, 76, 88, 339-342. " Maximum work " and chemical af- finity, 150. Medium, influence of, on reaction velocity, 224. Metastable phases, 184. Microns, 318. Migration of the ions, 236, 243-249. Miscibility of liquids, 84. Mixed crystals, 13, 95, 190, 192. Molecular attraction, 34, 58. surface energy, 125. volume, 60, 78. in solution, 62. weight of colloids, 316. abnormal, 40, 123. of dissolved substances, 109- 125- Molecular weight of gases, 36-43. of liquids, 125-127. Molecules, velocity of gaseous, 33. Monotropic substances, 197. Morse and Frazer's measurements of osmotic pressure, 104. Movement, Brownian, 318. Multiple proportions, law of, 4. NATURAL law, definition of terms, 6, 7 Neumann's law, 13. " Neutal salt action," 84. Neutralization as ionic reaction, 284. heat of, 148, 283-285, 336. Neutrons, 409. Normal electrodes, 374, 375. potentials, 388. OCTAVES, law of, 20. Optical activity, 66-69, 229. van't Hoff-Le Bel theory of, 67, Order of a reaction, 213. Osmotic pressure, 97-109. and diffusion, 98, 108. and elevation of boiling-point, 109, 138. and gas pressure, 102, 103. and lowering of freezing-point, 109, 136. and lowering of vapour pres- sure, 109, 131. measurement of, 99, 105. mec anism of, 106. of colloids, 316. Ostwald's dilution law, 266, 307, Overvoltage, 401. Oxidation, definition of, 396. Oxidation-reduction cells, 393. Ozone-oxygen equilibrium, 168. PARTIAL pressures, law of, 81. Periodic law, 23. system, 20-24. table, 21. Phase, definition of term, 172. rule, 179. Phosphorus pentachlori 'e, dissociation of, 163. Plasmolysis, 105. Polarisation, concentration, 404. electrolytic, 350, 355, 398, 404. of light, 66. Potential differences at liquid junctions, 382. INDEX 43 * Potential differences, origin of, 362. single, 375, 379, 381. series of the elements, 387. Potentials, "absolute," 375, 378. normal, 388. Protective colloids, 332. Prout's hypothesis, 17. QUADRUPLE point, 196. R, value of, for gases, 27. for solutes, 102. Radium, 2, 379. Raoult's formula, 112. Reactio i, orJer of, 213. Reactions, consecutive, 216. counter, 216. side, 215. Reduction, definition of, 395. Refraction formulae, 64. Refractivity, 63-66. Reversibility in cells, 354. Reversible reactions, 151, 156 222. Rotatory power, 66, 229. magnetic, 69. SALT solutions, solubility of gases in, 84. Semi-permeable membranes, 81, 97, 105, 107, 130. Silicic acid, colloidal, 315, 323. Sodium sulphate, solubility of, 93. Sol (hydrosol), 323. Solubilities, determination of small, 300-302, 370. Solubility, coefficient of, 83. curves, 86, 93, 196. effect of temp-T ture on, 93, 96. of guises in liquids, 82. of liquids in liquids, 84. of solids in liquids, 91-94. product, 298. Solution, heat of, 146, 153. Solutions, boiling-point of, 114. colioi lal, 127-129. freezing-point of, 11-9. isotonic, 105. solid, 94, 192. supersaturated, 92. Solvent, influence of, on ionisation, 338, 342-345- Solvents, associating, 123, 338. dissociating, 123, 338. Specific heat of gases, 43-47. solids, 11-13. Spectrum, absorption, 70. effect of dilution on, 71. Strong electrolytes, ionisation of, 279. Submicrons, 318. Substituti m, effect of, on ionisation, 273. 276, 304. Sulphur, equilibrium between phases, 183- vapour density of, 41. Supersaturated solutions, 92. Super tension at electrodes, 401. Surface tension and adsorption, 330. and molecular weight of, liquids, 125-127. nature of, 129. Suspensions, 322. Suspensoids, 322. TELLURIUM, atomic weight of, 24. position in periodic table, 23. Temperature coefficient of chemical reactions, 225-229. of conductivity, 263. Theory, definition of term, 7. Thermoneutrality, law of, 148, 279, Transition curves, 184. points, 183, 197. determination of, 198, 199. Transport numbers, 246-249. Trimolecular reactions, 209. Triple point, 181. Tyndall phenomenon, 317. ULTRAFILTER, 324. Ultramicroscope, 317. Unimolecular reactions, 202, 229. VALENCY, 15. Van der Waal's equation, 33-35, 53-57. Van't Hoff-Raoult formula, 112. Hoff s factor, i, 125, 262. theory of solutions, 101. Vapour densities, 36-41. at high temperatures, 40, 41. pressure of binary mixtures, 87, 91. of solids, 173. lowering of, in. measurement, 113. Velocity of reaction, 200-233. Victor Meyer's method of determining vapour densities, 37. 432 OUTLINES OF PHYSICAL CHEMISTRY Viscosity and electrical conductivity, 253, 261, 347. of liquids, 73-77, 322. measurement of, 75. absolute values of, 76. of binary mixtures of, liquids, 76, 342. WATER, catalytic action of, 219, 220, 2 33- decomposition by, 285-293. dissociation constant of, 283, 293, 387- electrolysis of, 401-404. equilibrium between phases, 179. ionisation of, 283, 293. PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS, ABERDEEN 3 enter- ^453 ... .34 1921 An 1*1 T Y} & c 3 f} > T"^ Vl T"*" Cf "1 ft \J u. U J. Hit? > Ui. JUIl^oJ-C;^ i en em. /I^^J I AUG14 IS iCT * MR 29*56 UNIVERSITY OF CALIFORNIA LIBRARY