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FIEST PEINCIPLES OF 
 CHEMICAL THEOKY 
 
 BY 
 
 C. H. MATHEWSON, PH.D. 
 
 ij 
 
 INSTRUCTOR IN CHEMISTRY AND METALLOGRAPHY AT THE 
 
 SHEFFIELD SCIENTIFIC SCHOOL OF 
 
 YALE UNIVERSITY 
 
 FIRST EDITION 
 
 FIRST THOUSAND 
 
 NEW YORK 
 
 JOHN WILEY & SONS 
 LONDON: CHAPMAN & HALL, LIMITED 
 
 1908 
 
T 
 
 COPYRIGHT, 1S08 
 
 ' ' ' B Y 
 
 Stanhope iprcss 
 
 F. H.GILSON COMPANY 
 BOSTON. U.S.A. 
 
PREFACE. 
 
 THIS small volume has been prepared for the use of first year 
 students at the Sheffield Scientific School, as reference text in 
 connection with a short course of lectures on Chemical Theory. 
 A period of six weeks immediately following the first four months' 
 instruction in General Chemistry is devoted to work of this nature. 
 General principles and theoretical topics are discussed with the 
 utmost simplicity, and in particular view of their continued 
 application. During this time recitations and laboratory exer- 
 cises are adjusted to the particular task of explaining and empha- 
 sizing the lecture subjects. 
 
 It is not the intention to segregate and summarily dispose of 
 much important material by untimely or unduly restricted dis- 
 cussion under the above heading. The purpose is rather to offer 
 very early presentation of leading principles which are of material 
 assistance in teaching the beginner to properly explain and corre- 
 late his experimental results. Such preliminary preparation 
 permits very open class room discussion of the specific chemical 
 phenomena, which are gradually developed in the laboratory. 
 Every opportunity for illustrating and applying these principles 
 is improved as the actual chemical experience of the student 
 increases. 
 
 The advisability of using the Electrolytic Dissociation Theory 
 and the Mass Action Law in first year work is no longer ques- 
 tioned by most teachers. It is rather a question of when and 
 how these subjects should be introduced. As soon as the student 
 has acquired practical familiarity with the molecular and atomic 
 theory and is able to fully comprehend a few of the more general 
 types of chemical change, no particular difficulty will be met in 
 studying the characteristic behavior of electrolytes in aqueous 
 solution, or the effect of enforced concentration changes (forma- 
 tion of gaseous or insoluble products) on the course of a reaction. 
 
 iii 
 
iv PREFACE. 
 
 A fair measure of success has been attained at the Sheffield 
 Scientific School in the early introduction of these subjects along 
 most general lines, preceded by a few months' introductory work 
 and supplemented by continual repetition and illustration in the 
 class room, as additional chemical facts accumulate. 
 
 Before beginning this course, the student should be able to read 
 the introductory chapter with intelligence and a consciousness 
 of familiarity with most of the included material. Incidental 
 remarks on the Kinetic Theory are intended mainly as an aid in 
 picturing a helpful constructive view of matter and more forcibly 
 denning the different states of aggregation. 
 
 The brief discussion of the Periodic System (Chapter II) is also 
 of a preliminary nature. Familiarity with the halogen group 
 alone is assumed. Since the elements are invariably presented 
 for study in some sequence based on the natural classification, 
 an elementary exposition of this arrangement seems desirable at 
 the outset. More detailed consideration of this subject (if, 
 indeed, at all necessary) must be deferred until a large number 
 of elements have been studied. 
 
 Doubtless too little time is available in most elementary 
 courses for any other than cursory consideration of the princi- 
 ples governing equilibrium in heterogeneous mixtures. The 
 fundamental condition that stable contact of different phases 
 must correspond to definitely fixed values of pressure, tempera- 
 ture, and concentration, seems, however, well worth some atten- 
 tion. Brief discussion of the pressure-temperature diagram in a 
 one -component system may at least be offered with propriety, 
 and any thoughtful student cannot fail to welcome the better 
 understanding of sublimation, vapor pressure, critical tempera- 
 ture, allotropic modifications, etc., which is sure to result from 
 a well ordered effort in this direction. Discriminative application 
 of the Phase Rule adds to the effectiveness of the general 
 discussion. 
 
 It may be urged that any text which offers a condensed treat- 
 ment of leading topics, is read by the student with a considerable 
 show of enthusiasm. There is a greater tendency to grasp the 
 essentials of important material appearing consecutively on a 
 few pages, than to locate and assimilate the same information by 
 perusing the mass of material between the covers of some large 
 
PREFACE. V 
 
 book. College teachers who have adopted a similar plan of 
 introducing these topics, may find this little volume of assistance 
 in connection with some one of the general treatises on Inorganic 
 Chemistry, available at the present time. 
 
 For assistance in the preparation of these notes, the author is 
 indebted to Professor Percy T. Walden, who has offered many 
 suggestions emanating from a valuable teaching experience; to 
 Dr. Carl O. Johns, an associate in first year instruction; and to 
 Professor William G. Mixter, under whose active direction this 
 course has been presented at the Sheffield Scientific School. 
 
 C. H. MATHEWSON. 
 JUNE, 1908. 
 
CONTENTS. 
 
 CHAPTER PAGE 
 I. INTRODUCTION OUTLINE OF LEADING PRINCIPLES AND COMMON 
 CONVENTIONS PERTAINING TO THE STUDY OF GENERAL INOR- 
 GANIC CHEMISTRY 1 
 
 II. NATURAL CLASSIFICATION OF THE ELEMENTS 39 
 
 III. DETERMINATION OF MOLECULAR WEIGHTS 47 
 
 IV. DETERMINATION OF ATOMIC WEIGHTS 56 
 
 V. CALCULATION OF FORMULAS 60 
 
 VI. OSMOTIC PRESSURE AND RELATED PHENOMENA WITH PARTICULAR 
 REFERENCE TO DILUTE AQUEOUS SOLUTIONS OF ACIDS, BASES 
 
 AND SALTS 64 
 
 VII. THE ELECTROLYTIC DISSOCIATION THEORY 69 
 
 VIII. THE LAW OF CHEMICAL MASS ACTION 94 
 
 IX. HETEROGENEOUS EQUILIBRIUM 108 
 
 X. THERMOCHEMISTRY 116 
 
 INDEX. . 121 
 
 vii 
 
FIEST PEINCIPLES OF CHEMICAL 
 THEORY 
 
 CHAPTER I. '*' /, ] ] ;;/, 
 INTRODUCTION. 
 
 OUTLINE OF LEADING PRINCIPLES AND COMMON CONVENTIONS 
 
 PERTAINING TO THE STUDY OF GENERAL 
 
 INORGANIC CHEMISTRY. 
 
 THE most casual observer recognizes great diversity in the 
 nature and form of material objects. Natural transformations 
 of matter as the result of varying terrestrial conditions, are 
 phenomena of frequent occurrence. We learn at the outset to 
 distinguish between three common forms in which matter 
 appears, namely, solid, liquid, and gaseous and to realize the 
 potency of certain influences to render these different states 
 interchangeable. Thus, the effect of heating, or adding heat to 
 liquid water is to convert it into water vapor and the effect of 
 adequately cooling, or abstracting heat from liquid water is to 
 produce the solid material called ice. Throughout the course 
 of such transformation, this particular variety of matter, water, 
 has retained its integral composition; it has merely suffered 
 change in its manner of physical appearance. Such alteration 
 is termed physical change. 
 
 The corrosive action of moist air on many metals constitutes 
 a type of alteration in the matter concerned, which produces 
 results of a far more radical nature. The following specific 
 case serves adequately by way of illustration. If the metal 
 sodium is dropped into water, violent agitation begins immedi- 
 ately. An inflammable gas is liberated, heat is evolved and the 
 metal melts and moves rapidly about on the surface of the water, 
 eventually disappearing. In place of the original group, or 
 
 1 
 
2 CHEMICAL THEORY. 
 
 collection of matter consisting of sodium and water, we have, 
 at the close of the transformation, an entirely new system 
 composed of the gas hydrogen (a primary constituent of water), 
 and a substance known as sodium hydroxide (consisting, in 
 part, of sodium and, in part, of elementary particles from water), 
 dissolved in the unchanged remainder, or excess, of water. 
 A deep seated process of this sort affecting the individuality, or 
 ultimate chemical composition of the matter involved, is termed 
 a chemical reaction. The alteration which matter sustains, as 
 ,th6 -insult Qf such Teactiqa, is termed chemical change. 
 
 Aside from the material changes affecting substances concerned 
 in chemical reaction, additional changes of an equally funda- 
 mental character invariably accompany such transformation. 
 These changes are intimately associated with the obvious change 
 in the nature of the materials themselves, and are discussed 
 under the general heading of energy. The relation of energy 
 to matter exercises a most subtle influence over all physical and 
 chemical phenomena. Extended consideration of this subject 
 is fruitful only to those far advanced in the study of both 
 Chemistry and Physics. It is, however, essential, in this connec- 
 tion, to emphasize the general principle that energy associates 
 itself with matter, supplying the inherent capability for trans- 
 formation and the performance of work, which all matter 
 possesses. 
 
 We recognize the existence of different forms of energy 
 generally susceptible to inter-transformation. The copper wire, 
 which transports electrical energy, becomes warm from the 
 continuous change of electrical into heat energy. In the motor, 
 electrical energy is converted into mechanical energy, some 
 of which is, in turn, changed into heat energy by friction of the 
 bearing parts. During the course of a chemical reaction we 
 frequently observe that chemical energy, or energy stored 
 within chemical substances, appears as heat. Other energy 
 manifestations and transformations are familiar to the student 
 of physics. 
 
 The form, or state of aggregation in which a pure substance 
 exists, depends upon the amount of energy which it possesses. 
 For example, the metal copper, in its ordinary solid state, 
 contains less energy than when in the molten state. Addition 
 
INTRODUCTION. 3 
 
 of heat to the solid metal first causes a rise in temperature. 
 When a definite temperature, called the melting point, is 
 reached, further heat addition fails to elevate the temperature, 
 but is absorbed in effecting change from the solid to the liquid 
 state. The analogous change from the liquid to the gaseous 
 state takes place when heat is added at a characteristic 
 temperature, called the boiling point. 
 
 Evidence which has accrued from several centuries of experi- 
 mental work, and which has become more accurate and con- 
 vincing with the progressive refinement of methods and skill in 
 manipulation, leads consistently to the conclusion that matter 
 and energy, although capable of great variety of change, cannot 
 be created or destroyed. These two all-important principles are 
 known as conservation of matter and conservation of energy. 
 
 By means of properly ordered chemical operations, composite 
 matter may be resolved into its simplest forms. In this manner, 
 some 80 forms of matter are recognized at the present day as 
 elements, or elementary substances incapable of further decom- 
 position. Any other form of matter, which retains its integral 
 nature after being subjected to a variety of physical processes 
 tending to isolate it from other associated substances, is complex, 
 containing two or more of these elements in such intimate union 
 that they have apparently lost all physical individuality. Such 
 substances are called chemical compounds and their elementary 
 constituents are said to be chemically combined. The general 
 properties of a chemical compound are thus quite different from 
 those of its constituent elements. 
 
 The characteristic of greatest importance in establishing the 
 individuality of a chemical compound, is the constancy of its com- 
 position. A given chemical compound, whatever its origin, or state 
 of aggregation, invariably contains the same elements in the same 
 proportions. This epoch-making generalization, known as the 
 law of constant composition, or the law of definite proportions, 
 rests on a most satisfactory experimental basis. The possible 
 variation in the composition of certain compounds which have 
 been exhaustively investigated, cannot exceed one part in a 
 million by weight. Hence, the above statement becomes an 
 axiomatic fact as far as human agency can determine. 
 
 While the law of constant composition certifies to the impossi- 
 
CHEMICAL THEORY. 
 
 bility of variation in the composition of a chemical compound, 
 it is a matter of common experience that the same elements 
 may occur combined in more than one definite proportion by 
 weight. In such a case, several individual compounds exist, 
 each conforming to the general law. Closer study of these 
 relations has revealed the following important generalization, 
 known as the law of multiple proportions, which serves to 
 further characterize the combining habits of the elements. 
 When two elements unite to form more than one chemical compound, 
 the different weights of one element, which combine with one and 
 the same weight of the other element, stand to one another in the 
 ratio of simple integers. For example, the five known com- 
 pounds containing only oxygen and nitrogen, have been shown 
 to possess the percentage compositions, by weight, indicated 
 by the accompanying figures: 
 
 
 Nitrogen. 
 
 Oxygen. 
 
 
 
 Nitrous oxide . 
 
 63.65 
 
 36 35 
 
 0.57 
 
 1 
 
 Nitric oxide 
 Nitrogen dioxide 
 Nitrogen trioxide 
 
 46.69 
 36.86 
 30.45 
 
 53.31 
 63.14 
 69.55 
 
 1.14 
 1.71 
 
 2.28 
 
 2 
 3 
 
 4 
 
 Nitrogen pentoxide 
 
 25.94 
 
 74.06 
 
 2.85 
 
 5 
 
 Different weights of oxygen which may combine with one part, 
 by weight, of nitrogen, are given in the third column of figures. 
 It is observed that these numbers are directly proportional to 
 the simple integers in the next column. 
 
 A number of pure chemical compounds may be physically 
 intermixed to an extent dependent on their specific properties 
 and states of aggregation. All gaseous materials are com- 
 pletely miscible, producing a most intimate type of physical 
 mixture. Liquids exhibit all degrees of miscibility , or mutual 
 solubility. Immiscible liquids may be mechanically converted 
 into an emulsion by agitation. Solids may also attain a very 
 intimate state of mutual incorporation, particularly when 
 obtained from a molten liquid mixture by abstraction of heat. 
 The term, solid solution, is used in this connection. In all the 
 above cases, certain physical operations may be devised and 
 used for separation of the co-existent substances. 
 
INTRODUCTION. 5 
 
 The conception that diverse physical and chemical processes 
 may not bring about an infinite division of matter, but that 
 certain finite limits in the masses of the ultimate particles are 
 arbitrarily imposed, had proved attractive to philosophers 
 long before Chemistry had attained the standing of an exact 
 science. The development of earlier ideas which presents a 
 satisfactory conception of material transformations accom- 
 panying physical and chemical processes, embodies three 
 finite stages in the ultimate division of matter. The first 
 division does not alter the chemical nature of the material and 
 may be accomplished by physical agency. More specifically, 
 in terms of the molecular theory of matter, any material, whether 
 of an elementary or compound nature, is composed of a number of 
 finite particles, called molecules, alike among themselves and 
 assembled in certain well defined states of aggregation. We have 
 here, as a further development, the characterization of each 
 different physical aggregation of particles by an essential 
 complement of physical properties. Thus, solids, which con- 
 stitute the most compact form of matter consisting of closely 
 aggregated molecules are rigid and not easily penetrable. 
 In an amorphous, or non-crystalline solid, the closely packed 
 molecules present no regular order of arrangement; hence, the 
 material possesses identical properties in all directions, or is 
 isotropic. A crystalline solid possesses directional properties, 
 i.e., it is anisotropic, owing to the arrangement of its molecules in 
 definite planes of symmetry. The molecules of a liquid are 
 less restricted in their sphere of activity and may easily be dis- 
 placed; hence, great mobility: while those of a gas are widely 
 separated (maximum volume) and prone to fly apart without 
 restriction. 
 
 Beyond this molecular division of matter there is recognized, 
 according to the atomic theory of matter, an arrangement of 
 more elementary particles, called atoms, which may be modified 
 only by processes which we term chemical. Each different kind 
 of atom represents one of the 80 or more elementary substances. 
 Atoms of the same kind are identical, each variety possessing 
 as especial characteristics, definite mass and a certain specific 
 tendency to combine with others of the same kind to form the 
 molecules which constitute, in their aggregate, the physical 
 
6 CHEMICAL THEORY. 
 
 material of this specific variety, and with atoms of other kinds 
 to form the molecules of various chemical compounds. 
 
 Finally, convincing evidence of disintegration of atoms them- 
 selves has accumulated during the past ten or a dozen years. 
 Sub-atomic particles invariably carry electric charges and have 
 been called corpuscles. Atoms of certain kinds (radium, thorium 
 atoms, etc.) disintegrate spontaneously, forming a series of 
 intermediate " atoms " or arrangements of corpuscles, which pos- 
 sess varying stability and continue to break down with greater 
 or less rapidity, forming others, etc. The existence of negative 
 corpuscles, so small that approximately a thousand of them 
 would be required to make up the mass of the hydrogen atom, 
 has been clearly demonstrated. Much investigation bearing on 
 the development of the corpuscular theory of matter is in progress 
 at the present time. While results of a fundamental character 
 have already attended experimental effort in this direction, 
 it should be made evident to the student of Chemistry that no 
 increased perception of chemical phenomena has followed in the 
 wake of these new ideas: the atom still remains the unit of 
 chemical change, and the above mentioned disintegration phe- 
 nomena Constitute an order of alteration in matter entirely 
 apart from that which we shall consider in the following pages. 
 
 * Two classes of phenomena, that accompanying the electric discharge 
 through gases and that associated with so-called radio-active bodies, have 
 constituted the experimental basis for the development of the corpuscular 
 theory. Detailed consideration of intricate physical problems which have 
 arisen in connection with the interpretation of such phenomena is entirely 
 beyond the scope of this text. Nevertheless, in deference to a widespread 
 interest in the unique and startling results which have marked this class of 
 investigation, a brief statement of some generally accepted conclusions may be 
 added at this point. It is not presumed that the student will gain an adequate 
 appreciation of this essentially difficult subject at this juncture, but merely 
 that some better conception of these ideas, in which he may already have 
 acquired a general interest, may result from a reading of the ensuing remarks. 
 
 An enormous electrical force (potential difference) is necessary to cause a 
 visible discharge to pass through a short space enclosing any gas under ordi- 
 nary pressure. If the pressure of the gas is greatly diminished the discharge 
 passes much more readily. At extremely low pressures a greater potential 
 difference is again required. Very ordinary electrical apparatus, however, 
 an influence electric machine, or a voltaic battery in connection with an induc- 
 
 * The author is indebted to Dr. Boltwood for certain criticisms on this part of the 
 manuscript. 
 
INTRODUCTION. 7 
 
 tion coil is capable of supplying electrical energy in satisfactory form and 
 quantity for this purpose. For experiments of this sort, partially evacuated 
 glass tubes with sealed-in metallic conductors (electrodes) are generally used 
 Under properly regulated conditions of gaseous and electrical pressure, the 
 discharge presents features of unusual interest. First of importance in this 
 connection is the production of cathode rays within the vacuum tube. Secon- 
 dary phenomena which are generally attributed to the action of the cathode 
 rays are (1) a characteristic green fluorescence on the anode and the glass 
 opposite the cathode the space in the vicinity of the cathode remaining 
 dark and (2) the Roentgen ray effects. 
 
 The cathode rays are now conceded to consist in rapid flights of negatively 
 charged particles in straight lines directly away from the cathode or negative 
 pole. Many experiments have been devised to prove that this conception is 
 a true one. For example, suitably mounted mica vanes will rotate if placed 
 in the path of the rays. Moreover, by giving that surface of the cathode 
 which is opposite the anode, the proper degree of concavity, the moving par- 
 ticles may be uniformly directed against an anode of small dimensions. In 
 this way the energy of the moving particles is concentrated to such an extent 
 that anodes of the most refractory metals may be fused. Again, cathode 
 rays may be deflected by the application of electrical or magnetic forces, as 
 any stream of charged particles would be. 
 
 Elaborate investigation has shown that these particles, called corpuscles or 
 electrons, may possess a velocity under the most favorable conditions one- 
 third as great as that of light (i.e., they may move at the rate of some 60,000 
 miles per second), that their individual mass is from one to two-thousandths 
 that of the hydrogen atom and that this mass is invariably the same what- 
 ever the gas used in the tube, or the material from which the electrodes are 
 constructed. We believe them, in effect, to constitute the ultimate particles 
 from which all matter is constructed. [The deflection of the charged par- 
 ticles observed directly by the change in position of a spot of fluorescent 
 light caused by their impacts upon a screen coated with a suitable material 
 under the influence of a given electrical force is related to both the velocity of 
 the particles and the ratio of the mass of a particle to the charge which it car- 
 ries, through a known equation. The same quantities constitute the unknown 
 values in an equation defining the deflection in a magnetic instead of an 
 electrical field. Thus, the two quantities are completely defined through two 
 sets of experiments. Velocities of 2 3 X 10* cm/sec, are commonly 
 observed in these experiments (that of light is 3 X 10 10 cm/sec.) The second 
 quantity, which appears as a ratio, is always constant. Several methods 
 have been used with concordant results in fixing the magnitude of the charge 
 carried by a corpuscle (one term of the ratio). This value is also invariably 
 constant and is identical with the charge carried by certain atoms for 
 example, the hydrogen atom when in a condition which will be discussed 
 in the chapter on the Electrolytic Dissociation Theory. But the value ot 
 this ratio for the hydrogen atom, as above, is perhaps a thousand times greater 
 than its value for the corpuscle. Whence, the mass of the corpuscle is some- 
 thing like one -thousandth that of the hydrogen atom. Figures taken 
 
8 CHEMICAL THEORY. 
 
 from J. J. Thomson's "The Corpuscular Theory of Matter" follow: Value 
 of the charge on a corpuscle, or on a charged hydrogen atom, 10~ 20 , in electro- 
 magnetic units; value of the ratio of charge to mass (in grams), 1.7 X 10 7 . 
 
 10~ 20 
 Whence, the mass of the corpuscle is 7 g, or 6 X 10~ 28 g. The mass 
 
 of the hydrogen atom may be placed at 10~ 24 g (cf. p. 12), which is thus some 
 1700 times the mass of the corpuscle.] 
 
 Wherever cathode particles impinge on the metallic anode or glass wall of 
 the vacuum tube a series of etherial waves is produced. These are called 
 Roentgen rays or X-rays. They are supposed to be single pulses traveling 
 through the ether with the velocity of light, as distinguished from the con- 
 tinuous train of waves (thousands of waves succeeding one another in the 
 same path in a fraction of a second) which produce the sensation of light. 
 The thickness of these wave pulses is much less than the wave length of any 
 kind of light, i.e., these waves might travel unimpeded in a much smaller tube 
 than any of the light waves. They possess the power of penetrating many 
 substances which are impervious to light waves, being absorbed by substances 
 in proportion to their density. Thus, in passing through the body, more of 
 the rays are absorbed by the bones than by the flesh, and if they then be 
 allowed to fall upon a sensitized plate a strong contrast will develop. Aside 
 from their action on the photographic plate, these rays cause certain sub- 
 stances to fluoresce or become luminous. A screen covered with such a 
 substance (the fluoriscope) is commonly used in presenting an X-ray picture 
 before the ordinary vision. The Roentgen rays are not deflected by an 
 electrical or magnetic field. They "ionize" gases, or cause them to conduct 
 the current by reason of the formation of corpuscles which carry the electricity. 
 
 In addition to the negative corpuscles discussed above, positive carriers of 
 electricity are found in the vacuum tube. These travel towards the cathode 
 and may be observed and studied in the region back of the cathode by using 
 a cathode through which holes, or canals, have been bored. Hence, they are 
 called canal rays. It has been found that the canal rays are deflected by an 
 electrical or magnetic field in a manner to correspond with their positive 
 charges; that they move much more slowly than the negative corpuscles; 
 that the magnitude of the charge is never smaller than that on the negative 
 corpuscle and that the ratio of mass to charge always possesses a value much 
 smaller than the corresponding value in the case of the negative corpuscle 
 consistently indicating a particle of atomic dimensions. 
 
 Corpuscles are given out by all substances under some condition or other. 
 Metals furnish them when raised to high temperatures. The negative corpus- 
 cles are invariably of the sub-atomic dimensions noted above. The positive 
 particles are never inferior to the lightest known atom the hydrogen atom 
 in point of mass. It is generally supposed that these positive particles are 
 atoms, or groups of atoms, from which one or more negative corpuscles have 
 been detached. 
 
 Of particular interest and importance is the spontaneous emission of charged 
 particles from the atoms of radio-active substances. In this connection we 
 will note primarily that three types of rays are emitted by these substances, 
 
 
INTRODUCTION. 9 
 
 namely, a, ft and y rays ; corresponding to the canal rays, cathode rays and 
 Roentgen rays of the vacuum tube, respectively : and that the study of these 
 phenomena has corroborated and amplified in large measure the conclusions 
 derived from the preliminary study of the phenomena of the cathode tube. 
 All three types of rays "ionize" gases cause. them to conduct the a rays 
 being most efficient (by far) in this respect and the 7 rays least efficient. It 
 is owing to this property that the "activity" of a radio-active substance is 
 easily susceptible to measurement. The substance is brought in the vicinity 
 of a charged electroscope, when the air is rendered conductive and the charge 
 is dissipated from the instrument. This test is extremely sensitive. A 
 radium preparation must be some 150,000 times purer to respond to a test 
 with the spectroscope (and radium is classed among the elements giving the 
 most sensitive spectroscopic reaction) than is required for the electroscope test. 
 (Descriptions of the spectroscope and its use may be read in Holleman- 
 Cooper's "Text Book of Inorganic Chemistry," edition of 1908, p. 386, and 
 Smith's "General Inorganic Chemistry," edition of 1907, p. 561.) On this 
 account, accurate experimental results are obtained with the extremely slight 
 quantities of radio-active substances which are alone available. 
 
 The calculated masses of the a particles are such as to indicate that they 
 may be atoms of a rare gas called helium. This substance has actually been 
 obtained as a disintegration product of radium, whereby we note the first 
 actual realization of a transmutation of the elements. 
 
 Several intermediate disintegration products of the radium atom have been 
 recognized and named (emanation, radium-A, radium-B, etc.). It has been 
 found that the expression, It = 1^^, shows the relation between the initial 
 intensity (7 ) of the radiations (measure of radio-activity) thrown off by one 
 of these disintegrating bodies and the intensity (/<) at the end of a finite 
 time. The letter e denotes the base of the natural logarithms, while X is the 
 disintegration constant for the particular radio-active substance under con- 
 sideration. In other words, >l represents the fraction of substance transformed 
 per unit time and is independent of the temperature and all other physical or 
 chemical conditions. Obviously A may be calculated from observations and 
 the formula used to determine the length of time necessary for a given radio- 
 active substance to disintegrate to any specified extent. Thus, a striking 
 array of figures, giving the times required for successive radium products to 
 become half transformed, has been prepared by Rutherford: 
 Ra-Em. > Ra-A y Ra-B -> Ra-C Ra-D > Ra-E > Ra-F > Ra-G 
 
 4 days 3mins. 21 mins. 28 mins. 40 yrs. 6 days -143 days end product? 
 
 Further calculation leads Rutherford to the conclusion that the life of radium 
 is about 2000 years. 
 
 So far as we know, these disintegration products do not correspond to any 
 previous known chemical elements, nor have we definitely located the end 
 product of the disintegration, in our list of elements. There are only three 
 elements well enough known to appear in the generally accepted list, which 
 are radio-active, namely, radium, thorium and uranium. The parent of 
 radium is thought to be uranium all known uranium ores contain amounts 
 
10 CHEMICAL THEORY. 
 
 of radium strictly in proportion to the amounts of uranium which they con- 
 tain. 
 
 It is particularly to be emphasized that the amounts of energy which are 
 concerned in these remarkable sub-atomic alterations are enormous in com- 
 parison with the corresponding amounts which are associated with ordinary 
 physical and chemical changes. For example, the heat evolved spontaneously 
 by a gram of radium in an hour would be sufficient to raise its own weight of 
 ice from the melting point to the boiling point. The total heat energy given 
 out by a gram of radium during its life would be, according to Rutherford, 
 about half a million times that liberated during the combination of enough 
 hydrogen and oxygen to form a gram of water. 
 
 The ft particles from radio-active bodies move at speeds varying from 
 one-fifth to nine-tenths the velocity of light much faster than the corre- 
 sponding particles developed in the cathode tube. Now, experimental work 
 has shown that, at these high speeds, the ratio of charge to mass is not con- 
 stant. For velocities from zero to one-tenth the velocity of light only is this 
 quantity essentially constant ; at half the velocity of light a perceptible increase 
 has occurred ; while at nine-tenths the velocity of light a nearly two-fold increase 
 is noted. If, then, we consider the charge to be invariable which is in all 
 probability true we have a case in which the mass of a moving particle 
 changes with the velocity. It has been demonstrated mathematically that 
 a moving electric charge concentrated on a sphere of sufficiently small radius 
 possesses inertia by virtue of the electromagnetic field of force created in the 
 surrounding ether, i.e., it possesses apparent (electrical) mass. Further, 
 elaborate calculations have been made, showing that if the mass of the moving 
 particle were to be regarded as wholly electrical, it would increase just as the 
 experiments indicate, with the velocity. This (calculated) increase becomes 
 enormous as the velocity of light is approached, and it is significant, in this 
 connection, that the observed velocities never equal the velocity of light, at 
 which this electrical mass would reach an infinite value. No smaller charges 
 of electricity tlian those associated with (constituting?) the /? particles have 
 ever been indicated by theoretical or experimental efforts. It is possible 
 that these units of energy, apparently ponderable, i.e., possessing the most 
 distinguishing characteristic of matter, in their career of rapid motion, are 
 themselves responsible for the material nature of the atom, which latter may 
 be regarded as a self-contained system of these units in orbital motion around 
 one another under mutual governing influences. A radio-active, or unstable 
 atom, expels a corpuscle or collection of corpuscles and suffers readjustment. 
 Although such definite conceptions are highly speculative and the reader may 
 never learn what matter of energy really is, we may safely say that the question 
 of correlation of the conceptions, matter and energy, no longer appears in a 
 wholly visionary aspect. 
 
 Study of the gaseous state, in which the molecules must be 
 farthest removed from one another (since matter in this form 
 occupies the greatest space per unit mass) and least subject to 
 
INTRODUCTION. 11 
 
 mutual influences, has proved most fruitful in developing our 
 present conceptions of matter. Prior to 1808, when Gay-Lussac 
 (Paris) published the results of experiments showing that gaseous 
 elements combine in simple proportions by volume and the volume 
 of the resulting products, if gaseous, stands in some simple ratio to 
 that of the reacting gases (law of Gay-Lussac), the fundamental 
 conception that an elementary substance is composed of two 
 separate orders of particles was not prevalent among chemists. 
 According to the original theory, most specifically advanced by 
 Dalton (Manchester, Eng.), a few years earlier, indivisible " ele- 
 mentary atoms " were regarded as the ultimate particles of 
 elementary substances, and " compound atoms " as the smallest 
 integral parts of compound substances. It was clearly recog- 
 nized that the numbers of elementary atoms concerned in any 
 combination were never large. 
 
 The simple numerical relations of these " indivisible atoms " 
 when united in the " compound atoms," taken in connection with 
 the equally simple volume relations prevailing in the combination 
 where gases alone were concerned, indicate equally simple rela- 
 tions between the numbers of so-called atoms, whether simple or 
 compound, in equal volumes of the gases under consideration. 
 Boyle's Law : The volume of a gas varies inversely as the pressure 
 if the temperature remains constant; and Charles' Law : The volume 
 of a gas varies directly as the absolute temperature if the pressure 
 remains constant, unite in revealing striking conformity in the 
 behavior of all gases, irrespective of their nature, when subjected 
 to altered physical conditions. This points strongly to a con- 
 clusion that the volume, temperature, and pressure relations of 
 gases are determined solely by the number of particles present 
 in them. The simplest assumption would be that equal voL 
 umes of all gases contain the same number of particles under the 
 same conditions of temperature and pressure. This fundamental 
 conception, which has since been proven in complete harmony 
 with the facts, was most definitely advanced by Avogadro 
 (Turin) in 1811, who showed the necessity of modifying Dalton's 
 original atomic theory by requiring that elementary matter, as 
 well as compound matter, be regarded as divided into two finite 
 orders of particles, of which the particles mentioned above or 
 the molecules previously noted constitute the first order. 
 
12 CHEMICAL THEORY. 
 
 A clearer conception of the foregoing statement may be 
 obtained by considering a typical example of gaseous combina- 
 tion. One volume of oxygen when combined with the requisite 
 amount of hydrogen, furnishes two volumes of water vapor. 
 Since, according to the hypothesis just presented, these two 
 volumes of water vapor must contain twice as many particles 
 (molecules) as the single volume of oxygen, and moreover, since 
 each water particle must contain some oxygen, we are forced to 
 conclude that a division of Dalton's supposedly indivisible oxy- 
 gen particles has preceded combination. 
 
 The terms, atom and molecule, are in constant use among 
 chemists. Whether we believe in the actual existence of either 
 or both orders of particles is of little consequence. The fact of 
 prime importance is, that if matter were so constituted, it would 
 appear as it now does. Moreover, the introduction of such 
 imaginative units aids us to intelligently study and systematize 
 chemical phenomena. For practical purposes, it is necessary 
 to associate with each particular kind of atom, a number which 
 defines its most essential individual characteristic, that of mass. 
 The absolute weight of any atom can only be estimated.* On 
 the other hand, we are quite able to deduce an accurate system 
 of relative weights representing the smallest quantities of each 
 element capable of participating in chemical reaction. These 
 relative numbers are known as atomic weights, and are universally 
 referred to the oxygen standard, which arbitrarily places the 
 oxygen number at 16 times unity, or 16. More extended dis- 
 cussion of this subject follows in Chapter IV. 
 
 With these fundamental principles in mind, we are in a position 
 to consider the complete argument by which experimental results 
 relating to a given case of gaseous combination between the ele- 
 ments may be used to determine the composition of the resulting 
 gaseous compound. 
 
 * According to recent calculations by Lord Kelvin, the number of mole- 
 cules (N) in 1 cubic centimeter of a gas at C., and 760 millimeters pressure, is 
 10 20 . 1 c.c. of hydrogen weighs about 0.00009 gram under these conditions. 
 
 OOOOQ 
 Hence, the weight of a hydrogen molecule is ' ^ , or 9xlO -25 gram, and 
 
 that of q, hydrogen atom (W), 4.5X10" 25 gram, since the hydrogen molecule 
 contains two atoms, as will be shown shortly. According to Van der Waals' 
 calculations, based on the kinetic theory of gases, N=5.4xl0 19 whence, W= 
 
INTRODUCTION. 
 
 13 
 
 One volume of hydrogen combines completely with one volume 
 of chlorine to form two volumes of gaseous hydrochloric acid, 
 if the three gases are measured under the same conditions of 
 temperature and pressure. The accompanying diagram is of 
 service in keeping these relations prominently in view during 
 the discussion. 
 
 By experiment, one volume of chlorine is found to weigh about 
 35.5 times as much as one volume of hydrogen measured under 
 the same conditions. Since the gases combine completely in 
 this ratio, to find the relative numbers of hydrogen and chlorine 
 atoms in the resulting compound it will be necessary to divide 
 
 Hydrogen 
 
 Chlorine 
 
 Hydrochloric Acid 
 
 Two 
 
 Volumes 
 
 Two 
 Mols. 
 
 these ratio numbers by the corresponding relative weights of the 
 atoms. It has already been noted that such relative weights 
 may be readily determined. Without opening a discussion at 
 this time (cf. Chapter IV), of the methods employed to yield these 
 results, we may simply state that the atom of chlorine is known 
 to be about 35.5 times as heavy as the atom of hydrogen. Dividing 
 the ratio representing the combination of hydrogen and chlorine 
 by weight, 1 : 35.5, by the ratio representing the relative weights 
 of hydrogen and chlorine atoms, 1 : 35.5, we obtain a third ratio, 
 1:1, which signifies that there are equal numbers of hydrogen 
 and chlorine atoms in the compound, hydrochloric acid. 
 
 Suppose we start with x grams of hydrogen. The weight of 
 one atom of hydrogen is 1 gram divided by the number of atoms 
 
 (n) making up this weight, or- g-, and the number of atoms in 
 
 x 
 x grams is, I = nx. 
 
 n 
 
 To combine with x grams of hydrogen, 35.5 x grams of chlorine 
 are required. The weight of one atom of chlorine is 35.5 times 
 
14 CHEMICAL THEORY. 
 
 35 5 
 
 the weight of one atom of hydrogen, or a: and the number 
 
 n 
 
 of atoms in 35.5 x grams is, 35.5 = nx, which is identical with 
 
 n 
 the number of hydrogen atoms required for the combination. 
 
 Purely chemical reasoning suffices to show that the molecule 
 of hydrochloric acid contains only one atom of hydrogen (and, 
 consequently, one atom of chlorine); if more than one atom were 
 present, it would be possible to obtain a class of derived com- 
 pounds (acid salts) resulting from partial replacement of the 
 original hydrogen in one molecule of acid by a metal. In the 
 present case, no such derivatives are known. We are thus led 
 to the complete conclusion that a molecule of hydrochloric acid 
 consists of one atom of hydrogen in combination with one atom of 
 chlorine. 
 
 Referring again to the volume relations between these three 
 gases (p. 13), we note that, according to Avogadro's Law, the 
 numbers of molecules in the gases are proportional to the volumes 
 of the gases (see diagram, Fig. 1, p. 13, large and small areas). 
 Therefore, when one molecule of hydrogen loses its identity, one 
 molecule of chlorine participates in the change, and two molecules 
 of hydrochloric acid are formed. Each molecule of acid contains 
 one atom of hydrogen, as developed in the preceding discussion. 
 Therefore, two atoms of hydrogen are contained in the total 
 amount of acid which required one molecule of hydrogen in its 
 formation. We are free to conclude that a single molecule of 
 hydrogen contains two atom,s. 
 
 Similar reasoning may be applied to show that the chlorine 
 molecules are diatomic. All of the common gaseous elements, 
 namely, hydrogen, oxygen, nitrogen, fluorine, chlorine, bromine, 
 and iodine, are likewise composed of diatomic molecules, under 
 the conditions which usually obtain. 
 
 We have already remarked briefly on the different forms of 
 matter determined by the nature of aggregation of the constituent 
 molecules. The kinetic theory carries us a step further in estab- 
 lishing an imaginative mechanical constructive view of matter, 
 by introducing the additional energy factor. According to this 
 
INTRODUCTION. 15 
 
 theory, the heat energy absorbed by substances during tempera- 
 ture elevation, or change of state, is mainly converted into 
 molecular kinetic energy (energy due to motion of the molecules). 
 Molecules constituting a solid are supposed to oscillate around a 
 definite position of equilibrium, which is maintained by the very 
 considerable attractive forces, supposed to operate between 
 them in this close state of aggregation. The (perfectly elastic) 
 molecules, when aggregated to form liquid matter, are capable of 
 much more extended and energetic motion, causing mutual 
 bombardment and a tendency to further separation. They are, 
 nevertheless, closely enough associated to exert mutually attrac- 
 tive forces, sufficient in effect to overcome this disruptive tend- 
 ency and to maintain a limited surface. The constituent 
 molecules of a gas are least subject to mutual attraction and 
 uniformly distribute themselves throughout any inclosing space, 
 irrespective of its size. 
 
 It is easily apparent that such of the molecules within a liquid 
 as reach the surface with a velocity greater than the average, 
 will project themselves out into the space bounding the liquid 
 (evaporate) , and if this space is an enclosed one, will here attain 
 a certain concentration (as vapor) determined by the average 
 rate of mutual exchange across the bounding surface. The 
 effect of heat addition to a liquid is to increase the molecular 
 kinetic energy, causing more evaporation until eventually the 
 liquid disappears. 
 
 The presence of a definite amount of vapor at a given tempera- 
 ture in the closed space above a liquid, determines a certain 
 vapor pressure (pressure due to the molecular impacts against 
 the inclosing walls) within this closed space. A vapor pressure 
 magnitude, in this connection, is often referred directly to the 
 liquid, when it represents the power of the latter to maintain 
 vapor of this pressure, and is called the vapor tension of the 
 liquid. As the temperature of a liquid is raised, its vapor ten- 
 sion increases. If the liquid is open to the air, it boils, or passes 
 rapidly into vapor, when a temperature is attained at which its 
 vapor tension is equal to the opposing atmospheric pressure. 
 
 Transformation of gaseous matter into liquid matter of the 
 same kind is dependent on the temperature and pressure. If 
 effected at some constant pressure, it is always abrupt, 
 
16 CHEMICAL THEORY. 
 
 accompanied by heat evolution, during which the temperature 
 remains constant until complete transformation has occurred. 
 By properly chosen successive variations of temperature and 
 pressure, this change may result without discontinuity, i.e., we 
 may effect a gradual and continuous change from gas to liquid, 
 showing a close inherent relationship between the two states. 
 
 For each substance there always exists a critical temperature, 
 above which it is impossible, no matter how great the compression, 
 to liquefy the gas. This is reasonable, if we reflect that to 
 liquefy a gas it is necessary that the kinetic energy of its mole- 
 cules be adequately decreased and that they be brought closer 
 together. Pressure accomplishes the latter object, but to com- 
 pletely attain the desired end, proper coincidence of the former 
 condition must be secured by sufficient cooling. 
 
 Transformation from the liquid to the crystalline state is 
 invariably discontinuous. It is, indeed, difficult to imagine any 
 change from an isotropic to an anisotropic material other than 
 abrupt. On the other hand, when an amorphous solid is pro- 
 duced by cooling a liquid, the change is gradual and continuous. 
 There is no abrupt change of state. The change is rather one of 
 degree, since the essential difference between an amorphous solid 
 and a liquid lies in the lesser kinetic energy of the molecules when 
 assembled to constitute the former (amorphous solid) material. 
 
 Finally, we recognize the capability of certain elementary 
 substances to exist in more than one solid modification, possi- 
 bilities including, besides the amorphous form, one or more 
 specific crystalline varieties. This property is called allotrop- 
 ism. Such differences in form may be due to varying arrange- 
 ments of the molecules in the solid material, or may be compli- 
 cated by sub-grouping of these component particles resulting 
 in a final aggregation of clusters. 
 
 An elementary or compound substance, which occurs in two, 
 three, or several different crystalline modifications, is called 
 dimorphous, trimorphous, or, in general, polymorphous. Broadly 
 speaking, these related solid modifications are, under specific 
 conditions, interchangeable; energy change always associating 
 itself with the transformation. Thus, the crystalline material, 
 called y iron, which is formed (heat evolution) on cooling pure 
 molten iron when its freezing point, about 1515, is reached, 
 
INTRODUCTION. 17 
 
 undergoes two transformations before it becomes cold. At 
 880, a second modification, called ft iron, is formed spontane- 
 ously (heat evolution), and at 780, a third modification, 
 called a iron, results. The temperatures at which such changes 
 occur, are called transition temperatures. Reverse changes 
 (heat absorption) would occur on heating a iron. The last 
 mentioned variety has no tendency to change its physical form 
 at temperatures below 780 and is the common magnetic 
 modification. At 880, both y and ft iron may remain in contact 
 without predisposition to alteration. If the temperature is 
 raised above this point, all becomes y iron; if lowered, all changes 
 to ft iron. Iron is, thus, trimorphous. 
 
 Again, a single atomic variety of matter, namely, the oxygen 
 atom, exclusively constitutes the material part of two substances, 
 totally different from one another in each of their three states 
 of aggregation and in chemical properties. These substances 
 are ordinary oxygen and ozone, both gases under ordinary 
 conditions. Molecules of the former contain two atoms, while 
 those of the latter contain three. 
 
 Closely similar conditions are presented by such compounds 
 as possess the same percentage composition (contain the same 
 kinds of matter in the same proportions by weight) in connec- 
 tion with different physical and chemical properties. We apply 
 the term isomeric in describing this general condition and dif- 
 ferentiate between two distinguishing cases: (a) those isomeric 
 compounds which possess molecules of different mass, called 
 polymeric; and (b) those isomeric compounds which possess 
 molecules of the same mass and must, in consequence, owe 
 their individuality solely to the configuration of atoms within 
 the molecule. Such compounds are called metameric, or physi- 
 cally isomeric. 
 
 Evidently the gaseous state, in which the effect of attractive 
 forces between the molecules, on account of their great distance 
 from one another, reduces itself from a position of paramount 
 importance to that of a merely modifying influence, presents 
 conditions most favorable to extended development of the 
 kinetic theory. In fact, the Laws of Boyle, Charles, and 
 Avogadro may be deduced with extreme simplicity from this 
 theory, neglecting the effect of such attractive forces. More- 
 
18 CHEMICAL THEORY. 
 
 over, satisfactory mathematical modifications have been made, 
 on the basis of the theory, for the purpose of correcting inac- 
 curacies to which these laws have been shown subject, when 
 applied to highly concentrated, or compressed gases, in which 
 the molecular attractive forces must attain real significance. 
 
 Deduction of the Gas Laws from the Kinetic Theory. (1) Boyle's Law: 
 Consider a quantity of gas containing (n) perfectly elastic molecules of 
 individual mass (m), inclosed in a cubical vessel an edge of which meas- 
 
 ures (I) cm. Let the average velocity of these molecules be (v) -. If 
 
 see. 
 
 one of the molecules strikes a bounding surface at right angles, assuming 
 perfect elasticity of molecule and bounding wall, its direction of motion is 
 reversed, the velocity remaining unchanged. Consequently, its momen- 
 tum has changed from mv to mv. This change in momentum, 
 mv (mv), or 2 mv, is a measure of the force, or pressure, exerted at the 
 point of impact. In reality, the molecules preserve no regularity as to 
 direction of motion, but we may resolve the velocity of each into three 
 components, v 1} v 2 , and v s , directed at right angles towards three sides of 
 the cube. Then, we have the relation, v^ + vj + v 3 2 = v*. The mole- 
 cule suffers a change in momentum of 2 mv 1} due to its component velocity, 
 Vit on striking one side of the cube. The number of impacts per unit of 
 
 time as it travels back and forth between opposite sides, will be y fts 
 
 velocity divided by the number of centimeters traveled before each impact. 
 The total change in momentum, due to motion in this direction is, then, 
 
 r-i-- Similarly, the changes in momentum, due to normal motion 
 between the two remaining pairs of surfaces, are ^ 2 , and ^ 3 . Addi- 
 
 t L 
 
 tion of these three quantities gives, as total pressure effect for each mole- 
 
 cule on all the walls, ... f OT> . To obtain the pres . 
 
 I I 
 
 sure corresponding to impacts of all the molecules on a unit area of sur- 
 face, we must multiply the above expression by (n), the number of mole- 
 cules, and divide by 6P, the total surface area. This operation gives 
 
 the value, , which we may place equal to the gaseous pressure P. 
 Observing that Z 3 is the volume, which we may call V, this equation 
 becomes, P Since none of the values, m, n, and v, can vary if 
 
 the temperature remains constant, the above equation shows that the 
 
INTRODUCTION. 19 
 
 pressure of a gas varies inversely as the volume, at constant temperature. 
 This is one method of stating Boyle's Law. 
 
 (2) Charles' Law: The kinetic theory embraces a primary assumption 
 that the square of the average velocity, with which the molecules of a gas 
 move, is proportional to the absolute temperature. A glance at the trans- 
 posed equation, V = ^ J- (from the final equation in the preceding para- 
 
 O X 
 
 graph) shows that, for a constant value of P (m and n can change only 
 with the nature and amount of gas), the volume varies directly as the 
 square of the velocity. Consequently, the volume at constant pressure 
 varies directly as the absolute temperature, as enunciated by Charles on 
 experimental grounds. 
 
 (3) Avogadro's Law: If we consider identical volumes of two different 
 gases at the same pressure, the PV expressions obtained by transposing 
 the final equation given in (1) must be equal. Expressing the masses, 
 numbers, and velocities of the different molecules by m l , n lt v 1} and m 2 , n 2 , 
 v 2 , respectively, we have the following equality; m 1 n 1 v l = m 2 n 2 v 2 
 There can be no difference in the kinetic energies of molecules composing 
 different gases at the same temperature. Hence, we may write, \ ra^ 2 . 
 
 = \ m 2 v 2 2 . Dividing the first equation by the second, we obtain, f n l % n 2 , 
 or, n l =n. 2 , the relation required by Avogadro's Law. 
 
 Reasoning from the kinetic theory, we would expect gases, 
 irrespective of their nature, to mix completely when brought 
 into contact. The constituent molecules, owing to their great 
 separation and rapid motion, unhampered by mutual attractive 
 forces of appreciable magnitude, could scarcely fail to inter- 
 penetrate. Experiment verifies this conclusion and shows, in 
 addition, that the relative rapidity of such intermixture, or 
 diffusion, of gases is inversely proportional to the square roots 
 of their densities, a result which may itself be significantly 
 deduced from the theory. 
 
 For this purpose, consider the equation, P = --^ derived in the dis- 
 
 o V 
 
 cussion relative to Boyle's Law. Solving for v, we obtain, v = \ - 
 
 V mn ' 
 
 But, is an expression for the density of a gas, i.e., the total mass of 
 
 molecules divided by the volume. Substituting density for this expression 
 
 op 
 
 in the above equation, we have the relation, v=\/- , which shows 
 
 v density 
 
20 CHEMICAL THEORY. 
 
 that v is inversely proportional to the square root of the density. Now, 
 v represents the average velocity of the molecules composing a gas and 
 must determine the rate at which it diffuses. Whence, the rate of 
 diffusion is inversely proportional to the square root of the density. 
 
 The assumption of appreciable attractive forces (cohesion) 
 between the molecules of a substance when in the solid or liquid 
 state, would suggest resistance to any interpenetration by 
 molecules of another kind. On the other hand, the existence of 
 attractive forces between different kinds of molecules (adhesion) 
 would promote such interpenetration. Different liquids, or 
 solids, would, then, intermix until these opposing forces attained 
 equilibrium in the mixture. As a matter of fact, endless 
 variety is observed in the degree of intermixture, or miscibility, 
 between different solids and liquids. Complete miscibility, 
 complete immiscibility, or any intermediate degree of miscibility 
 may occur. The degree of miscibility will vary with the tem- 
 perature, since the relative values of cohesive and adhesive 
 forces depend on the temperature. Thus, molten zinc and 
 molten lead mix completely somewhat above 900, while, at 700, 
 92 parts of zinc will mix with 8 parts of lead, and 81 parts of 
 lead will mix with 19 parts of zinc, both liquids remaining 
 sharply separated when in contact. Molten gold and silver 
 mix completely and, on cooling, form a crystalline solid, likewise 
 characterized by complete intermolecular mixture. The individ- 
 ual crystalline particles composing such a mixture are called 
 mixed crystals. 
 
 When a solid is brought into contact with a liquid, its molecules 
 may mingle to a greater or lesser degree with the molecules of 
 the liquid. The solid is said to dissolve in the liquid, form- 
 ing a solution. We use the term solubility to define the amount 
 of a given solid which a unit amount of liquid, or solvent, will 
 dissolve. Solubility varies with the temperature. 
 
 The concentration of a solution is the amount of dissolved sub- 
 stance contained in a unit volume of solution. A saturated 
 solution contains the maximum amount of material which will 
 dissolve at the given temperature. 
 
 Gases may dissolve in liquids. The extent of such solubility 
 depends primarily on the nature of gas and liquid, but, in any 
 specific case, is directly proportional to the pressure of the gas, 
 
INTRODUCTION. 21 
 
 provided both pressure and solubility are relatively small. The 
 latter generalization, known as Henry's Law, is clear in the light 
 of our theory: Rapidly moving molecules from the gas penetrate 
 the liquid surface, continuing in their motion within the liquid 
 and accumulate here until their rate of reciprocal projection into 
 the gas becomes equal to their rate of entry. The rate at which 
 these molecules enter the liquid is proportional to the number of 
 impacts per unit time, which is, in turn, proportional to the 
 gaseous pressure. Hence, an increase in pressure must require 
 a greater concentration of " gas molecules " in the liquid to 
 determine a rate of expulsion equal to the increased rate of 
 reception. 
 
 Excessive solubility of a gas in a liquid is due to chemical 
 action. One volume of water dissolves more than 1000 volumes 
 of ammonia at C., 760 mm. pressure. In this case, a new sub- 
 stance, called ammonium hydroxide, is formed as the result of 
 such action. 
 
 A liquid dissolves the individual constituents of a gaseous 
 mixture independently (assuming no chemical action in the 
 system). The solubility of each gas is determined exclusively 
 by its own partial pressure (the pressure which it contributes 
 towards the total pressure). 
 
 The student will readily recognize the practical necessity of 
 uniformly adopting some convenient and concise written method 
 of rendering the composition peculiar to each known chemical 
 compound apparent at a glance. The conventional practice 
 employed by all chemists to realize this necessity consists 
 primarily in ascribing to each element a symbol, which abbre- 
 viates its (common or Latin) name to one large letter (or two 
 letters, the first of which is large), and implies an associated 
 atomic weight characteristic of the substance. A list of symbols 
 with atomic weights will be found inside the cover of this book. 
 To indicate the exact composition of a given compound, proper 
 symbols are arranged side by side, with added subscripts, which 
 denote the number of individual atomic weight units (if greater 
 than 1) composing a single molecular weight unit. Such an 
 arrangement of symbols is called a formula. Single molecules 
 of the substances sodium chloride and potassium chlorate, for 
 example, are represented by the formulas, Nad and 
 
22 CHEMICAL THEORY. 
 
 When it is necessary to indicate more than one molecule of a 
 compound, a numerical coefficient is placed before the formula. 
 
 Before proceeding further, it is essential that the true signifi- 
 cance of the terms, atomic weight and molecular weight, be per- 
 fectly clear to the student. As previously noted, we are unable 
 to ascertain the exact weights of individual atoms, but very accu- 
 rate ratios of the weights of these different atoms may be deter- 
 mined. These numbers, consistently referred to the oxygen 
 standard, = 16.00, are the practical units, called atomic weights, 
 which are indispensable to all chemical calculations. Simple 
 addition of the numbers produced by multiplying each individual 
 atomic weight corresponding to the symbols in a formula, by the 
 associated subscript number, gives the molecular weight of the 
 substance. Thus we see that molecular weights are also relative 
 numbers based on the oxygen standard. A formula, to give the 
 actual molecular weight of a substance, must represent not only 
 the relative atomic proportions of each element involved, but 
 the exact number of different atomic quantities in a unit molecu- 
 lar quantity. Thus, the formula KC1O 3 correctly represents 
 the composition and molecular weight of potassium chlorate, 
 while the formula K^C^O,, represents only its composition with 
 accuracy. 
 
 Atomic and molecular weights, as defined above, are quite as 
 valuable for all stochiometrical calculations, as the true weights 
 of atoms and molecules would be. For example, if we know 
 that the material composition of the substance potassium chlorate 
 corresponds to the formula KC1O 3 , and that the relative weights 
 of potassium, chlorine, and oxygen atoms are 39.1, 35.5, and 16 
 (all of which is implied by the symbolic notation), it is clear that 
 39.1 parts (by weight) of potassium, 35.5 parts of chlorine, and 
 48 (3 X 16) parts of oxygen, compose a total of 122.6 parts of 
 potassium chlorate, and we are in a position to calculate the per- 
 centage composition o,f the compound at once. 
 
 By way of further illustration, if all the potassium in 122.6 
 weight units of potassium chlorate, namely, 39.1 units, be brought 
 by direct or indirect chemical operation from its present state 
 of combination into the entirely different chemical relationship 
 expressed by the formula KNO 3 , it is evident that 39.1 4- 14 + 
 (3 X 16), or 101.1 units of this new compound potassium nitrate 
 
INTRODUCTION. 23 
 
 will be formed. In other words, every time one formula weight 
 of potassium chlorate is used, one formula weight of potassium 
 nitrate is produced. Similarly, it would require all the potassium 
 in two formula weights of potassium chlorate, or potassium nitrate, 
 to produce one formula weight of potassium sulphate, K 2 SO 4 . 
 
 We may summarize the results of this reasoning by writing: 
 
 2 KC1O 3 = 2 KN0 3 = K 2 SO 4 , * 
 
 which reads, two molecules (or 2 X 122.6 parts by weight) of 
 potassium chlorate are equivalent to two molecules (or 2 X 101.1 
 parts by weight) of potassium nitrate; are equivalent to one 
 molecule (or 174.2 parts by weight) of potassium sulphate. It 
 should be fully understood that the above equivalents are based 
 on the potassium content of the compounds. 
 
 When sufficient data relating to a given compound are avail- 
 able, its formula may be calculated. Discussion of this subject 
 follows in Chapter V. This constitutes the first step in estab- 
 lishing the nature of the compound. Examination of formulas 
 in general reveals, at a glance, points of similarity in the consti- 
 tution of the different substances along many and varied lines. 
 This, of course, proceeds hand in hand with certain similarities 
 in chemical behavior. In particular, we observe the tendency 
 of well defined groups of atoms, which are incapable of existing 
 alone in such state of combination, to maintain their individ- 
 uality throughout chemical change; that is, to collectively com- 
 bine with different substances. 
 
 Further comparison of formulas forces the conclusion that 
 each atom or group possesses a certain specific capacity for 
 combination, which determines the number of other atoms or 
 groups with which it may unite. It cannot be stated that every 
 elementary substance or group, as defined above, is capable of 
 combining with every other elementary substance or group. 
 In fact, most of the common inorganic compounds represent 
 the union of certain elements or groups, which may constitute 
 a positive list, with certain other elements or groups, which may 
 be assembled in a negative list. In case of combination between 
 positive and negative members, according to this classification, 
 the capacity for combination, or valence, of each assumes a 
 rather definite value; that is, it is seldom modified by the nature 
 * The sign = is used throughout this text in the sense of is or are equivalent to. 
 
24 CHEMICAL THEORY. 
 
 of the combination. For example, on comparison of the 
 formulas H i Cl, Na i Cl, H j NO 3 , Na i NO 3 , H 2 i SO 4 , and Na 2 i SO 4 
 (positive part to the left of dotted line, negative part to the right), 
 we readily observe that hydrogen and sodium possess the same 
 capacity for holding chlorine in combination, also the same 
 capacity for holding the (NO 3 ) group, and finally, the same capac- 
 ity for holding the (804) group. The above phraseology is 
 not intended to suggest that either hydrogen or chlorine plays 
 the aggressive part in determining combination; we know little 
 regarding the nature of forces binding the atoms in chemical 
 combination. 
 
 It is customary to assign a numerical value to the valence of 
 each atom or group, consistently referred to hydrogen as unity. 
 Thus, Cl, (NO 3 ), and Na, each have a valence of 1, and (SO 4 ), 
 a valence of 2. The formula of aluminium chloride is A1C1 3 ; 
 whence, the valence of aluminium is 3. 
 
 Some elementary substances form two well defined series of 
 compounds, corresponding to two separate valence values. In 
 this connection, we may mention monovalent copper, forming cup- 
 rous compounds, such as Cu 2 Cl 2 or Cu 2 SO 4 and bivalent copper, 
 forming the corresponding cupric compounds CuCl 2 and CuSO 4 . 
 Other examples will confront the student from time to time. 
 It is essential to rapid progress in chemical study, that the prin- 
 ciple of valence be used as an aid to the memory in acquiring 
 familiarity with chemical formulas. 
 
 With regard to those compounds formed between two positive or two 
 negative elements, it may be remarked, in general, that no such simple 
 deduction of probable formula types is admissible. The specific nature of 
 such combination appears to greatly modify the combining capacity of 
 each constituent. By way of illustration, univalent sodium and bivalent 
 cadmium form the compound NaCd 2 but fail to unite in the more logical 
 proportions Na 2 Cd. In conclusion, it may be stated that this class of 
 compounds is of comparative unimportance. The general value of the 
 valence principle to the beginner is not seriously impaired by exceptions 
 noted under this category. 
 
 The most comprehensive classification of inorganic chemical 
 compounds, according to related chemical properties and 
 analogous constitution, recognizes three quite distinct types, 
 which are named acids, bases, and salts. 
 
INTRODUCTION. 25 
 
 An acid always contains hydrogen in combination with some 
 non-metal, or characteristic group of elements including oxygen. 
 The term, acid radical, is often applied to such a group. Prop- 
 erties common to all acids are primarily determined by their 
 essential constituent, hydrogen, in its characteristic relationship to 
 the other atoms. In particular, we note that this acid hydrogen 
 is invariably capable of being replaced by a metal. Hence, 
 it is often called replaceable hydrogen. 
 
 A base consists of a metal (or group which may be regarded 
 as equivalent to a metal) in combination with the (OH) group. 
 This group may be replaced by an acid radical. 
 
 The chemical nature of salts is best understood by considering 
 their relationship to acids and bases. Thus, to obtain the 
 typical formula of a salt, we substitute a metal for hydrogen in 
 the typical formula of an acid, or an acid radical for the (OH) 
 group in the typical formula of a base. 
 
 An acid containing one atom of replaceable hydrogen in its 
 molecule is called monobasic.* If the number of replaceable 
 hydrogen atoms is greater than one, the term poly basic (dibasic,* 
 tribasic, etc.) is applied. In addition to the normal salts, derived 
 from an acid by replacing its (acid) hydrogen completely with a 
 metal, a somewhat different type of derivative may be obtained 
 from a polybasic acid by replacing part of its hydrogen by a 
 metal. Such a compound is called an acid salt. Similarly, 
 a base, the molecule of which includes more than one (OH) 
 group, may furnish salt-like derivatives, which still contain this 
 group. A compound of this nature is called a basic salt. It is, 
 perhaps, more common for the composition of a basic salt to 
 indicate combination between one or more molecules of the 
 base and one or more molecules of the normal salt, and for that 
 
 * Indicating that the hydrogen in one molecule of acid may be replaced by 
 the metal in one molecule of the simplest kind of a base, i.e., that containing 
 one (OH) group. Thus, HC1 is a monobasic acid from HC1 and NaOH, 
 we may obtain NaCl. As an example of a dibasic acid, we may cite H 2 SO 4 
 In this case, two molecules of the base NaOH are required for the replace- 
 ment H 2 SO 4 with 2NaCl gives Na^SO^ If the base contains two (OH) 
 groups, only one molecule is required for the latter replacement Ca(OH) 2 
 and H 2 SO 4 give CaSO 4 . The terms, monacid base and diacid base are some- 
 times used to characterize bases with respect to the number of their replace- 
 able (OH) groups. 
 
26 CHEMICAL THEORY. 
 
 of an acid salt to indicate similar combination between the acid 
 and normal salt. 
 
 Simplest among inorganic acids are the binary acids, which 
 contain no oxygen, but consist of one other elementary substance 
 in combination with hydrogen. The termination -ic is used in 
 naming these acids, while the termination -ide is applied in 
 designating their salts. This latter termination is also applied, 
 without reservation, to the names of all other binary compounds, 
 i.e., oxides, nitrides, phosphides, etc. 
 
 The same elementary substance (in combination with hydro- 
 gen and oxygen) often forms two or more oxygen acids. In such 
 cases, the ending -ic is arbitrarily employed in naming one of 
 them, while the ending -ous characterizes another containing 
 relatively less oxygen. The endings -ate and -ite respectively, 
 are used in naming salts derived from these acids. Finally, the 
 prefix hypo- in combination with the ending -ous is employed in 
 naming a possible acid in this series containing still less oxygen, 
 and the prefix per- in connection with the ending -ic in naming 
 a member containing more oxygen than the first. Corresponding 
 salts are named hypo- -ite and per- -ic. 
 
 Two or more salts sometimes combine in definite proportions 
 to form a type of compound, called a double salt, which is rather 
 easily resolved into its constituent salts. Quite different in 
 nature are the mixed salts, in which the constituents of two 
 closely similar salts are found partially replacing one another in 
 equivalent proportions. 
 
 A salt, or double salt, frequently combines with a definite 
 molecular proportion of water on crystallization from aqueous 
 solution. Such compounds are called hydrated salts. Their 
 constituent water is readily removed by heating, in some cases, 
 spontaneously on exposure to the air (efflorescence). 
 
 Oxides of the non-metals usually combine with water to form 
 acids. Such oxides are called acid anhydrides. If the oxide 
 fails to combine directly with water, it is, nevertheless, acidic in 
 character, tending to react with bases, or basic oxides, to form 
 salts. 
 
 Oxides of the metals are basic in character, often combining 
 with water to form metallic hydroxides, or bases. The oxides of 
 certain elements are less definite in their chemical nature- 
 
INTRODUCTION. 
 
 27 
 
 exhibiting basic properties towards strong acids, or acidic oxides, 
 and acidic properties towards strong bases, or basic oxides. 
 
 The following list of examples should be studied in connection 
 with the definitions on the last two pages: 
 
 Acid. 
 
 Formula. 
 
 Base. 
 
 Formula. 
 
 Salt. 
 
 Formula. 
 
 Hydrochloric. . 
 
 HC1 
 
 Calcium hydroxide 
 
 Ca(OH} 2 
 
 Calcium chloride 
 
 CaCL, 
 
 Nitric 
 
 HNO 3 
 
 Ferric hydroxide 
 
 Fe(OH) 3 
 
 Ferric nitrate 
 
 Fe(N0 3 ) 3 
 
 Nitrous 
 
 HNO 2 
 
 Potassium hydrox- 
 
 KOH 
 
 Potassium nitrate 
 
 KN0 2 
 
 
 
 ide 
 
 
 
 
 Sulphuric. . . . 
 
 H 2 SO 4 
 
 Zinc hydroxide 
 
 Zn(OH) 2 
 
 Zinc sulphate 
 
 ZnSO 4 
 
 Sulphurous . . . 
 
 H 2 S0 3 
 
 Barium hydroxide 
 
 Ba(OH) 2 
 
 Barium sulphite 
 
 BaSO, 
 
 Hypochlorous . 
 
 HC1O 
 
 Sodium hydroxide 
 
 NaOH 
 
 Sodium hypo- 
 
 NaCIO 
 
 
 
 
 
 chlorite 
 
 
 Chlorous (hy- 
 
 HC1O 2 
 
 Sodium hydroxide 
 
 NaOH 
 
 Sodium chlorite 
 
 NaClO 2 
 
 pothetical) 
 
 
 
 
 
 
 Chloric 
 
 HC1O 3 
 
 Sodium hydroxide 
 
 NaOH 
 
 Sodium chlorate 
 
 NaClO 3 
 
 Perchloric .... 
 
 HC1O 4 
 
 Sodium hydroxide 
 
 NaOH 
 
 Sodium perchlo- 
 
 NaClO 4 
 
 
 
 
 
 rate 
 
 
 Acetic 
 
 H . C 2 H 3 O 2 
 
 Sodium hydroxide 
 
 NaOH 
 
 Sodium acetate 
 
 NaC 2 H 3 O 2 
 
 
 
 
 
 
 
 Acid Salt. 
 
 Formula. 
 
 Basic Salt. 
 
 Formula. 
 
 Sodium acid sulphate. . . 
 Sodium acid carbonate. . 
 Calcium acid carbonate . 
 
 NaHSO 4 
 NaHCO 3 
 CaC0 3 , H 2 C0 3 
 
 Basic ferric acetate .... 
 Basic lead carbonate. . . 
 Basic bismuth nitrate. . 
 
 Fe(OH) 2 C 2 H 3 O 2 
 2PbCO 3 .Pb(OH) 2 
 Bi(OH) 2 NO 3 
 
 Mixed Salt. 
 
 Formula. 
 
 Sodium-potassium carbonate . 
 
 Calcium chloride-hypochlorite 
 
 Hydrated Salt. 
 
 Copper nitrate 
 
 Zinc sulphate 
 
 Hydrated Double Salt. 
 
 Ferrous ammonium sulphate . . 
 Alum : 
 
 Acid Anhydride. 
 
 Sulphur dioxide, SO 2 
 
 Sulphur trioxide, SO 3 
 
 Phosphorus pentoxide, P 2 O 5 . . . 
 
 NaKCO 3 (The (2) negative valences of CO 3 
 are neutralized by the added (1+1) posi- 
 tive valences of Na and K.) 
 
 Ca(Cl)OCl(Ca<^ cl ) 
 
 Formula. 
 
 Cu(NO 3 ) 2 . 311,0 
 ZnS0 4 . 7H 2 
 
 FeSO 4 . (NH 4 ) 2 SO 4 . 6H 2 O 
 K 2 S0 4 . A1 2 (S0 4 ) 3 . 24H 2 
 
 Corresponding Acid. 
 
 Sulphurous acid, H 2 SO 3 
 
 Sulphuric acid, H 2 SO 4 
 
 Phosphoric acid, H 3 PO 4 , and others 
 
 Silica, SiO 2 , is a common example of an acidic oxide which fails to form an acid on treat- 
 lent with water. 
 
28 CHEMICAL THEORY. 
 
 Basic Oxide. 
 
 Formula. 
 
 Silver oxide 
 
 Calcium oxide (lime) 
 
 Ferric oxide 
 
 Cupric oxide 
 
 Cuprous oxide 
 
 Magnesium oxide (magnesia) 
 Aluminium oxide (alumina) . . 
 
 Ag 2 
 
 CaO 
 
 Fe 2 3 
 
 CuO 
 
 Cu 2 O 
 
 MgO 
 
 A1 2 3 
 
 It is a common practice among chemists to express symbol 
 weights, or atomic weights, and formula weights, or molecular 
 weights, directly in grams, thus introducing the descriptive terms: 
 gram atom, and gram molecule. Amounts of different substances 
 which stand in direct proportion to their atomic, or molecular 
 weights, are called atomic and molecular quantities, respectively. 
 For example, in round numbers, 64 grams of copper, 108 grams of 
 silver and 207 grams of lead constitute one gram atom* of each 
 metal, respectively. One gram molecule of sulphuric acid is 
 about 98 grams, of nitric acid 63 grams. The above amounts 
 are atomic and molecular quantities respectively. 
 
 The result of any chemical reaction is a more or less complete 
 change from one set, or system, of material, to another set, or 
 system, without loss of matter. If the formulas of all substances 
 concerned in the change are known, a chemical equation, repre- 
 senting the change in detail, may be constructed according to the 
 following general outline : Form an expression indicating the sum- 
 mation of different molecules composing the original system, and 
 an analogous expression embracing the different molecules present 
 in the resulting system. Equate these two expressions, by assign- 
 ing such numerical coefficients to each (molecular) formula as 
 will render the sum of all the atoms of each variety equal on 
 both sides of the equation. For example, let it be known that 
 potassium nitrate and sulphuric acid react under conditions which 
 result in the exclusive and complete formation of potassium sul- 
 phate and nitric acid. The systems present before and after chemi- 
 cal reaction are (1) KNO 3 + H 2 SO 4 and (2) K 2 SO 4 + HNO 3 . 
 
 It is at once apparent that two molecular quantities of potas- 
 sium nitrate must be taken to furnish sufficient potassium for one 
 
 * Cf . Table of Atomic Weights inside cover. 
 
 
INTRODUCTION. 29 
 
 molecular quantity of potassium sulphate, and that one molecular 
 quantity of sulphuric acid is required to deliver the complemen- 
 tary amounts of sulphur and oxygen necessary to complete this 
 formula. At the same time, two atomic quantities of nitrogen, 
 six of oxygen, and two of hydrogen, await further disposition. 
 These are, however, the exact amounts needed to form two 
 molecular quantities of nitric acid. 
 
 The properly balanced equation, therefore, reads: 
 2KNO 3 + H 2 SO 4 = K 2 SO 4 + 2HNO 3 . 
 (2X101.19) 98.08 174.36 (2 X 63.05) 
 
 300.46 300.46 
 
 weight units of matter weight units of matter. 
 
 Numbers, representing molecular quantities of the matter 
 involved, are added in order to more clearly demonstrate the 
 quantitative relations. They are, of course, omitted in the 
 general formulation of chemical equations, being implied by 
 the symbols, etc. 
 
 By far the greater number of chemical operations, which 
 form the experimental basis of an introductory course in general 
 chemistry, effect complete transformation of one set of sub- 
 stances, when taken in equivalent proportions indicated by 
 the corresponding equation, into another set of substances, 
 also specifically denned by the equation. Thus, potassium 
 nitrate and sulphuric acid, when taken in the proportions 
 202.38 : 98.08, and heated moderately for a sufficient length 
 of time, will evolve 126.1 units of gaseous nitric acid, and 
 leave a residue of 174.36 units of potassium sulphate. 
 
 If the operation is conducted in a closed receptacle of rela- 
 tively small volume, transformation will not be complete. A 
 certain proportion of potassium nitrate and sulphuric acid will 
 have been transformed into potassium sulphate and nitric acid, 
 moreover, in such a way that for every formula weight of 
 potassium sulphate in the mixture, there will be two formula 
 weights of nitric acid, and for every formula weight of sulphuric 
 acid remaining there will be two formula weights of potassium 
 nitrate. In other words, the substances will have reacted 
 according to the above equation, but the final result is a mix- 
 ture of all four, perfectly indifferent in the presence of one 
 
30 CHEMICAL THEORY. 
 
 another, i.e., in equilibrium. If all the material at the start 
 had been in the shape of potassium sulphate and nitric acid, 
 the same identical mixture of four substances would have 
 resulted, under similar working conditions. That is, the reaction 
 may progress in both directions. 
 
 The sign of equality, implying complete transformation 
 towards the right, does not properly apply to a reaction when 
 carried out under conditions which render it incomplete in 
 either direction (i.e., reversible). Two reversed arrows (<=) 
 are used in such cases. 
 
 No feature of chemical study causes the beginner more trouble 
 than equation writing. The erroneous impression often prevails 
 that, once given the left-hand member of an equation, some 
 mechanical-mathematical process of rearranging symbols will 
 suffice to produce the complementary right-hand member. It 
 must be emphasized that the identity of substances formed by 
 chemical action is directly ascertained by experiment, or logi- 
 cally predicted by deference to well recognized chemical princi- 
 ples. The final balancing process alone is independent of such 
 chemical reasoning and observation. Any student who acquires 
 familiarity with the more general types of chemical action 
 and is capable of writing formulas with facility, will find little 
 difficulty in correctly formulating equations. 
 
 Some of these general types of chemical reaction may be 
 briefly outlined at this juncture: 
 
 A single substance is often resolved into simpler substances by 
 heat or other agency. Such change is known as decomposition. 
 Zinc carbonate is decomposed into zinc oxide and carbon 
 dioxide when strongly heated: ZnCOs = ZnO + CCV 
 
 An equally simple chemical change consists in the direct 
 combination of two or more substances when properly handled. 
 Copper and sulphur combine at a temperature approximating 
 low redness: Cu + S = CuS. 
 
 Two salts may react in such a way that the total change 
 would correspond to a primary decomposition of each, followed 
 by an altered recombination of the parts. Change of this sort, 
 called double decomposition, occurs when ammonium sulphate 
 and sodium chloride are moderately heated: 
 
 (NH 4 ) 2 S0 4 + 2NaCl = 2(NH 4 )C1 + NaaSO 4 . 
 
INTRODUCTION. 31 
 
 Double decomposition in solution is frequently indicated by 
 the precipitation, or deposition, of a reaction product (insoluble). 
 The remaining product may usually be obtained in the solid form 
 by subsequent evaporation of the solution. If no precipitation 
 occurs, the. less soluble substance will separate first (as a solid) 
 on evaporation. The nature of such changes is discussed at 
 some length in Chapters VII and VIII. 
 
 Reaction between a compound and an elementary substance 
 frequently results in the replacement, and consequent liberation 
 of some part of this compound by the added material. Metals 
 commonly replace the hydrogen of acids: Zn -f H 2 SO 4 
 
 = ZnSO 4 + H 2 . A halogen displaces any other halogen of 
 greater atomic weight, from its binary compounds: C1 2 + 2KBr 
 
 = Br 2 + 2KC1. 
 Acid and basic substances interact to form salts: CaO + SiO 2 
 
 = CaSiO 3 (at high temperatures), NaOH + HC1 = NaCl + H 2 O 
 (base and acid neutralization), ZnO + 2HC1 = ZnCl 2 + H 2 O 
 (metallic oxide and acid). 
 
 Concentrated sulphuric acid reacts on the salt of a volatile 
 acid, according to the following typical equation : H 2 SO 4 + 2NaCl 
 
 = Na 2 SO 4 + 2HC1. The volatile acid (HC1) escapes from the 
 mixture and a sulphate remains. 
 
 The chemical behavior of oxides towards water has been 
 noted on page 26. 
 
 Particular attention must be directed to the bearing of 
 oxygen on chemical change. Many reactions embody chemical 
 rearrangement of the constituent material, primarily caused by 
 reapportionment of oxygen within the system. Among the 
 great number of oxygen compounds, we readily distinguish 
 between certain ones, which strongly resist any effort to remove 
 their oxygen, wholly or in part, and others which suffer loss 
 of oxygen with greater or less facility. Thus, water (H 2 O), 
 carbon dioxide (CO 2 ), silica (Si0 2 ), alumina (Al 2 Os), magnesia 
 (MgO), etc., represent extremely stable combination of oxygen 
 with other elements, and may be expected to occur liber^ 
 ally as final products (perhaps further combined, according 
 to their individual nature) of diverse chemical action. On the 
 other hand, potassium chlorate (KClOa), mercuric oxide (HgO), 
 silver oxide (Ag 2 O), cupric oxide (CuO), cuprous oxide (Cu 2 O), 
 
32 CHEMICAL THEORY. 
 
 etc., lose oxygen with the greatest ease, and are unlikely to 
 remain intact when subjected to a variety of chemical treatment. 
 
 The process by which oxygen leaves one compound to combine 
 with other substances, is termed oxidation, with respect to the 
 material receiving oxygen, and reduction, with respect to the 
 material losing it. A compound generally capable of effecting 
 the oxidation of other substances is called an oxidizing agent. 
 One which removes oxygen from some moderately stable state of 
 combination is called a reducing agent. 
 
 The reaction Fe 2 O 3 + 2A1 = A1 2 O 3 + 2Fe represents oxida- 
 tion of aluminium by ferric oxide, as well as reduction of ferric 
 oxide by aluminium. 
 
 Certain highly oxidized substances may lose part of their 
 oxygen when treated with a compound susceptible to oxidation, 
 leaving one or more decomposition products which are more 
 stable with respect to their oxygen content. Thus, two molecular 
 quantities of nitric acid, an active oxidizing agent, include three 
 atomic quantities of oxygen, which are available for the oxidation 
 of other material, while the remainder of its oxygen is almost 
 invariably appropriated by its own hydrogen and nitrogen. The 
 following hypothetical reaction illustrates this statement: 
 
 2HNO 3 = H 2 O + 2NO + 30 (available oxygen). 
 
 If charcoal, essentially carbon, is heated with concentrated 
 nitric acid, water, nitric oxide, and carbon dioxide are recognized 
 as final products of the ensuing reaction. An equation descrip- 
 tive of this change may be constructed by using the proper 
 formulas and introducing the numerical coefficients necessary 
 to secure balance between both members: 
 
 4HN0 3 + 3C = 2H 2 O + 4NO + 3CO 2 . 
 
 Only the above set of coefficients (or equal multiples of them) 
 will effect equality between both sides of the equation, and these 
 numbers are best ascertained by the following deductive method, 
 which, at the same time, effectively summarizes the chemical 
 principles involved. 
 
 One atomic quantity of carbon requires two atomic quantities 
 of oxygen for complete oxidation: 
 
 C + 20 = C0 2 . (1) 
 
INTRODUCTION. 33 
 
 Some of the oxygen in nitric acid is available for this purpose, 
 as we have previously noted: 
 
 2HNO 3 = H 2 + 2NO + 3O. (2) 
 
 Since nitric acid, in a reaction of this kind, allows none of its 
 oxygen to escape unused, equality between the amount furnished 
 and the amount used must be established. This is effected by 
 oxidizing three atomic quantities of carbon with the six atomic 
 quantities of oxygen available from four molecular quantities of 
 nitric acid. Thus, each coefficient in equation (1) must be mul- 
 tiplied by three, and each coefficient in equation (2) by two. 
 On addition of both equations, oxygen (which is not a final 
 product) is eliminated by cancellation from both sides, and 
 there results a final (complete) equation, expressing the exact 
 relations between reacting substances and final products: 
 
 3C +^ - 3CO 2 
 4HNO 3 = 2H 2 O + 4NO 
 4HNO 3 + 3C = 2H 2 O + 4NO + 3CO 2 * 
 
 Additional examples will serve to emphasize the practical 
 application of these principles: 
 
 (a) Nitric acid and copper. 
 
 2HNO 3 = H 2 O + 2NO + 3O - Decomposition of nitric acid. 
 
 3Cu + 3O = 3CuO - Oxidation of copper. 
 
 3CuO + 6HNO 3 = 3Cu(NO 3 ) 2 -f 3H 2 O - Reaction between metallic 
 
 oxide and acid. 
 3Cu + 8HNO 3 = 3Cu(NO 3 ) 2 + 4H 2 O + 2NO - Final equation. 
 
 (b) Nitric acid and red phosphorus. 
 
 10HNO 3 = 5H 2 O + 10NO + 15O 
 
 6P + 15O = 3P 2 O 5 
 
 3P 2 O 5 + 9H 2 O = 6H 3 PO 4 General reaction between oxide 
 
 _ of non-metal and water. 
 
 6P + 10HNO 3 = 6H 3 PO 4 + 10NO 
 Dividing by 2, 
 
 3P + 5HNO 3 = 3H 3 PO 4 + 5NO. 
 
 (c) Bromine water and sulphurous acid. 
 
 Br 2 + H 2 O = 2HBr + O General reaction showing oxidizing 
 
 action of halogen in presence of water. 
 H,SO, + O = H g S0 4 
 
34 CHEMICAL THEORY. 
 
 (d) Concentrated sulphuric acid and copper. 
 
 H 2 SO 4 = H 2 O + SO 2 + O - General reaction showing decom- 
 
 position of sulphuric acid. 
 Cu + O = CuO 
 
 CuO + H 2 SO 4 = CuSO 4 + H 2 O 
 
 Cu + 2H 2 SO 4 = CuSO 4 + 2H 2 O + SO a 
 
 (e) Hydrogen peroxide and lead sulphide. 
 
 4H 2 O 2 = 4H 2 O + 4O General reaction showing decom- 
 
 position of hydrogen peroxide. 
 
 PbS + 4O = PbSO 4 
 
 PbS + 4H 2 O 2 = PbSO 4 + 4H 2 O 
 
 (f ) Manganese dioxide and hydrochloric acid. 
 
 MnO 2 + 4HC1 = MnCl 4 + 2H 2 O 
 
 MnCl 4 = MnCL; + C1 2 Change to more stable compound. 
 
 MnO 2 + 4HC1 = MnCl 2 + 2H 2 O + C1 2 
 
 When more than one valence is associated with an element, 
 properly chosen oxidizing agents change the compounds which 
 correspond to its lower valence into those which correspond to 
 its higher valence. Reducing agents accomplish the reverse 
 change. These different valence conditions are often called 
 different (higher and lower) states of oxidation. 
 
 Thus, to represent a transformation of ferrous sulphate (FeS0 4 ) 
 into ferric sulphate (Fe 2 (SO 4 ) 3 ) we require an additional sul- 
 phate group for every two molecules of the former compound 
 taken. This fnay be obtained by oxidizing the hydrogen in one 
 molecule of sulphuric acid: 
 
 Fe SO 4 | 
 
 S0 4 Fe 2 (S0 4 ) 3 . 
 
 . ,. . 
 from oxidizing agent 
 
 H 2 O 
 
 Or, if no free acid were present, part of the iron could be 
 regarded as momentarily relieved from combination, and imme- 
 diately thereafter subjected to complete oxidation: 
 
 6FeSO 4 -> 2Fe 2 (SO 4 ) 3 
 
 from oxidizing agent 
 
INTRODUCTION. 35 
 
 The complete changes follow: 
 
 (1) Oxidation of ferrous sulphate by nitric acid in presence of 
 sulphuric acid. 
 
 2HNO 3 = H 2 O + 2NO + 3O 
 6FeSO 4 + 3H 2 SO 4 + 3O = 3Fe 2 (SO 4 )3 + 3H 2 O 
 6FeSO 4 + 3H 2 SO 4 + 2HNO 3 = 3Fe 2 (SO 4 ) 3 + 4H 2 O + 2NO 
 
 (2) Oxidation of pure ferrous sulphate by nitric acid. 
 
 2HNO 3 = H 2 O + 2NO + 3O 
 6FeSO 4 + 3O = 2Fe 2 (SO 4 ) 3 + Fe 2 O 3 
 
 Fe 2 O 3 + 6HNO 3 = 2Fe(NO 3 ) 3 + 3H 2 O 
 
 6FeSO 4 + 8HNO 3 = 2Fe 2 (SO 4 ) 3 + 2Fe(NO 3 ) 3 + 4H 2 O + 2NO 
 
 Dividing by 2, 
 3FeS0 4 + 4HNO 3 = Fe 2 (S0 4 ) 3 + Fe(NO 3 ) 3 + 2H 2 O + NO. 
 
 Complete oxidation of the iron to the ferric state is effected 
 in (2), part of it forming ferric sulphate, and part,/emc nitrate. 
 
 The successive steps in the above work represent progressive 
 hypothetical chemical change, which leads consistently to a correct 
 final equation. We do not recognize in (2) for example, oxygen 
 and ferric oxide as tangible intermediate products. 
 
 Since a chemical equation defines the relative quantities of 
 all substances involved in a reaction, it is possible, if a definite 
 amount of any one substance is given, to calculate the corre- 
 sponding amounts of any or all the other substances. (Cf. p. 22.) 
 
 Problem: Calculate the amount of cupric nitrate formed when 
 ten grams of copper react with an excess of nitric acid, using the 
 equation: 
 
 3Cu + 8HNO 3 = 3Cu(NO 3 ) 2 + 2NO + 4H 2 O. 
 
 According to this equation, 190.8 weights of copper (3 X atomic 
 weight) require 504 weights of nitric acid (8 X molecular weight) 
 for reaction, thereby forming 562.8 weights of cupric nitrate, 
 60 weights of nitric oxide, and 72 weights of water. If an excess 
 of nitric acid (i.e. more than is needed to react with all the copper) 
 is present, just as much of it will be decomposed as is required by 
 the copper. The total amount of nitric acid, in this case (assum- 
 ing that the above equation applies without reservation as to 
 
36 CHEMICAL THEORY. 
 
 concentration, etc.), will have no bearing on the amount of cupric 
 nitrate, etc., produced. Consequently, in calculating the amount 
 of cupric nitrate produced from a given amount of copper, no 
 attention need be paid to the nitric acid, nor to the nitric oxide 
 and water, which are merely inevitable accessory products. 
 
 To solve a problem of this sort, select the essential formulas 
 from the equation, indicate the proper equivalence between them 
 and between the weights which they represent. Then make a 
 simple proportion between these equivalent weights and the 
 actual weights of the same substances, one of which is unknown 
 (x). 
 
 Thus, in the above case: 
 
 10 g. taken x g. produced 
 3Cu = 3Cu(NO 3 ) 2 
 190.8 562.8 
 
 In substance, if 190.8 parts by weight of copper correspond to 
 562.8 parts of cupric nitrate, 10 grams of copper correspond to 
 how many grams of cupric nitrate? 
 
 The correct proportion is: 
 
 190.8 : 562.8 : : 10 : x. 
 
 Solving, x = 29.5 grams. 
 
 It seems hardly necessary to discuss possible variations in the 
 form of such problems. 
 
 Students frequently fall into the error of using numbers which 
 refer to volumes, and not weights (or to both indiscriminately) 
 directly in these calculations. It is clear that all four terms of 
 the simple proportion must represent weights, since two of them 
 (molecular or atomic weights) do, by primary assumption. If a 
 final result is required in volume units, instead of weight units, 
 the latter must first be calculated, then properly transformed, by 
 using a known relation between weight and volume for the sub- 
 stance in question. 
 
 Suppose we desire to know how much hydrochloric acid must be 
 used to neutralize five grams of sodium hydroxide. The amount is 
 readily calculated from the relation: 
 
 5 g. x g. 
 
 NaOH = HC1 
 40.06 36.45 
 
INTRODUCTION. 37 
 
 which follows from the equation: 
 
 NaOH + HC1 = NaCl + H 2 O. 
 Thus, 40.06 : 36.45 : : 5 : x. Whence, x = 4.55 g. 
 
 But, this is pure hydrochloric acid, a gas under ordinary condi- 
 tions. We seldom handle the pure substance, using by prefer- 
 ence, solutions containing definite amounts of the gas in water. 
 Such a solution, containing 39.1 per cent of the pure acid by 
 weight, has a density of 1.20 and is commonly known as concen- 
 trated hydrochloric- acid (solution). A solution, of density 1.12, 
 containing 23.8 per cent acid, is called dilute hydrochloric acid 
 (solution). 
 
 We would, in all probability, use the dilute acid for neutraliza- 
 tion purposes, measuring, rather than weighing it. The weight of 
 pure acid required in this case is known (4.55 g.). Consequently, 
 it is necessary to know, in addition, the weight of pure hydro- 
 chloric acid in a unit volume of the solution. One cubic centi- 
 meter of this solution weighs 1.120. (Density =1.12 compared 
 to water 1 c.c. water weighs close to 1 g. under laboratory 
 conditions.) But, 23.8 per cent of this weight 0.270.-- is 
 pure hydrochloric acid; the rest is water. That is, 1 c.c. of the 
 solution contains 0.27 g. pure acid. To obtain 4.55 g. acid, 
 
 = 16.8 c.c. dilute hydrochloric acid solution must be taken. 
 
 The volume of concentrated acid necessary for the same pur- 
 
 4.55 
 
 pose is given by the operation, - 
 
 Frequently, we obtain a desired product as the result of several 
 successive reactions, which represent necessary steps in the 
 transformation of our original material. In such cases, we 
 reckon the equivalence between original material and final 
 product by noting each intermediate equivalence and use this 
 as a basis for the single calculation needed to give the weight 
 of final product resulting from a given weight of original sub- 
 stance. 
 
 Thus: How many liters of hydrogen, measured at C., 760 mm. 
 pressure, may be produced by using 100 g. zinc oxide, according to the 
 
38 CHEMICAL THEORY. 
 
 following reactions f One liter of hydrogen weighs approximately 
 0.09 g. under these conditions. 
 
 ZnO + C = Zn + CO. 
 Zn + 2HC1 = ZnCl 2 + H 2 . 
 
 100 g. x g. 
 
 The properly ordered data reads: ZnO = Zn = H 2 , and the 
 
 81.4 2.0 
 
 proportion : 81.4 : 2 :: 100 : x. Whence x = 2.46 (grams hydro- 
 
 2 46 
 gen), and, - = 27.33 (liters hydrogen). 
 
 u.uy 
 
CHAPTER II. 
 NATURAL CLASSIFICATION OF THE ELEMENTS. 
 
 IT becomes apparent early in the course of chemical study 
 that certain of the elements are closely related to one another 
 in their chemical and physical properties. Further experience 
 leads to a division of all the elements into several groups, each 
 embracing a definite quota, the properties of which are broadly 
 similar, but vary more or less gradually from one extreme to 
 another through the several members. 
 
 The first of these natural groups usually presented to the 
 beginner consists of four elements called the halogens; namely, 
 fluorine, chlorine, bromine, and iodine. These elements are 
 characterized by extreme reactivity towards other elements; in 
 consequence, they are not found naturally in the free or 
 uncombined state. All form binary hydrogen compounds, 
 or halogen acids, of the same formula type: H Halogen, 
 stamping them as univalent towards hydrogen. The halogens 
 do not show an equal tendency to combine with a given 
 element, nor are the resulting compounds equally suscep- 
 tible to decomposition, or possessed of the same proper- 
 ties. If such were the case, it would be difficult to recognize 
 them as individual elements. But a marked gradation in any 
 specific property, from fluorine through chlorine, bromine, 
 to iodine, is always apparent. Thus, hydrofluoric acid HF is 
 extremely stable; hydrochloric acid HC1 is very stable; hydro- 
 bromic acid HBr is only moderately stable, its hydrogen rather 
 available for reducing purposes; while hydriodic acid HI is very 
 unstable a valuable reducing agent. 
 
 This gradated behavior is very apparent on considering the 
 oxidation phenomena produced by aqueous solutions of the halo- 
 gens. When substances capable of oxidation are treated with 
 chlorine water, they obtain oxygen as a result of the following 
 decomposition: C1 2 + H 2 O = 2HC1 + O . Chlorine water may 
 
 39 
 
40 CHEMICAL THEORY. 
 
 be kept fairly well without change unless brought into contact 
 with a substance susceptible to oxidation. Fluorine decomposes 
 water instantly. Bromine water and iodine water, in order, are 
 less energetic oxidizing agents than chlorine water. 
 
 A more active halogen displaces a less active one from its binary 
 compounds: C1 2 + 2KBr = Br 2 + 2KC1; Br 2 + 2NaI =I 2 + 2NaBr. 
 The order of decreasing " activity " is Fl, Cl, Br, I. 
 
 Fluorine fails to combine with oxygen. The remaining halo- 
 gens form oxides and oxygen acids, the salts of which are used as 
 oxidizing agents on account of their instability. Towards oxy- 
 gen, somewhat variable valence, never more than seven, must be 
 ascribed to the members of this group. 
 
 The molecules of fluorine and chlorine are diatomic, even at 
 very high temperatures. Those of bromine and iodine are 
 diatomic at temperatures near the boiling points of these 
 substances, but dissociate into monatomic molecules, iodine 
 first, as the temperature increases. 
 
 The variation of physical properties in this group of elements 
 consistently follows the order of chemical gradation. Thus, 
 fluorine is a gas at ordinary temperature and under ordinary 
 pressure, chlorine is a gas more easily liquefied than fluorine, 
 bromine is a low boiling liquid, and iodine is a solid. The 
 melting points, boiling points and other physical properties vary 
 in steps from fluorine to iodine in the above mentioned order. 
 
 Without further extending this argument, we are in a position 
 to .clearly recognize a progressive relationship between these 
 elements, when arranged in the order: Fl, 19.0; Cl, 36.45; 
 Br, 79.96; I, 126.97. This is the order corresponding to 
 the numerical sequence of atomic weights as shown by the 
 associated numbers. 
 
 It remains to more closely examine the relationship between 
 properties and atomic weights. An assumption that the 
 properties of the different elements vary continuously with 
 their atomic weights cannot be entertained, since, between two 
 successive analogues,* there exist a number of dissimilar elements 
 having intermediate atomic weights. It is thus evident that, 
 in a list of the elements arranged in the order of their atomic 
 weights, a halogen will appear at intervals. 
 
 * Substances possessing closely related properties. 
 
NATURAL CLASSIFICATION OF THE ELEMENTS. 41 
 
 At this point it is necessary, for the purpose of rendering the 
 discussion more comprehensive, to anticipate some of the facts 
 which will appear before the student, in greater detail, at a 
 later time. Thus, the eight elements which possess smaller 
 atomic weights than fluorine are: hydrogen, 1.008; helium, 4.0; 
 lithium, 7.03; beryllium, 9.1; boron, 11.0; carbon, 12.00; 
 nitrogen, 14.01; and oxygen, 16.00. All of these, except 
 hydrogen, possess close analogues, which develop at intervals 
 in the complete list of elements arranged according to increasing 
 atomic weight, as we have pointed out relative to fluorine and 
 its analogues. 
 
 It is of particular interest to ascertain how many dissimilar 
 elements follow a given element before its analogue appears. 
 We have remarked that the series of eight elements from 
 helium to fluorine inclusive, are unlike. We now proceed to 
 note that the ninth element, neon, 20, resembles helium; the 
 tenth element, sodium, 23.05, resembles lithium and so on regu- 
 larly until the sixteenth element, chlorine, 35.45, the analogue 
 of fluorine, is reached. Thus, we observe a complete series 
 or period containing eight dissimilar elements which bear an 
 orderly resemblance to the eight dissimilar elements of a second 
 period. 
 
 Continued application of this simple scheme does not result in 
 an equally satisfactory arrangement of all the elements. For 
 example, the eighth element following chlorine, manganese, 54.6, 
 is not a halogen, although it bears some chemical analogy to 
 the halogens. The next three elements, iron, nickel, and cobalt, 
 find no analogues among the elements yet mentioned. Eighteen 
 elements intervene between chlorine and the next halogen, 
 bromine. 
 
 An adequate exposition of the periodic relations of all the 
 elements (Periodic System) was first offered by Mendelejeflf 
 (St. Petersburg) in 1869. The following table closely imitates 
 his classification: 
 
42 
 
 CHEMICAL THEORY. 
 
 tf 
 
 
 ,1 
 
NATURAL CLASSIFICATION OF THE ELEMENTS. 43 
 
 In the table, vertical columns include groups of analogous 
 elements. Periods are arranged horizontally. The groups are 
 numbered 0-8. A general characteristic of each group is the 
 most consistent valence of its members (1) towards hydrogen, 
 or a halogen, and (2) towards oxygen. These valences are 
 given under the group numbers, the symbol R standing for an 
 element of the group in question, O for oxygen and X for 
 hydrogen, or a halogen. 
 
 The first two periods have been discussed above. Reference 
 has been made to additional complexity following these short 
 periods. To secure logical arrangement, elements from argon, 
 39.9, to bromine, 79.96, are included in a long period, which is 
 resolved into two short periods (1) argon-manganese, (2) copper- 
 bromine, and three additional elements, iron, nickel, and cobalt. 
 The members of these two short periods are consistently ordered 
 in groups, 0-7, while the three extra elements constitute the 
 primary members of Group 8. The remaining periods, except 
 the last, are long. 
 
 It is to be observed that sub-grouping is followed after the 
 advent of long periods. Elements composing the first sub- 
 division of the long periods are collectively placed to the left in 
 their corresponding groups; those composing the last sub-division 
 are moved to the right. The members of such a sub-group 
 (elements in vertical alignment), or natural group in the narrower 
 sense, are very closely similar. In some cases, members of the 
 left-hand sub-group are closely related to the two elements which 
 head the group; in other cases members of the right-hand sub- 
 group possess this relationship. Less often the connection is 
 difficult to determine. In this table, the elements which are 
 usually studied in an elementary course, are printed in bold 
 figures. 
 
 Points of interest arise in considering the transition from one 
 group to another in the table. Thus, no valence is associated 
 with the noble gases (Group 0), as they show no tendency what- 
 ever to combine with other elements. The valence towards 
 oxygen increases from one to eight as we pass from Group 1 to 
 Group 8, while the valence towards hydrogen, or a halogen,, 
 increases from one to a maximum of four in Group 4, and then 
 decreases regularly to one in Group 7. The most basic elements 
 
44 CHEMICAL THEORY. 
 
 which we have, the alkali metals, lithium, sodium, potassium, 
 rubidium and caesium, stand next to the most indifferent, helium, 
 neon, argon, krypton and xenon, while the whole table might be 
 rolled vertically around a cylinder in such a manner that the 
 strongly acidic halogens would bound these indifferent noble 
 gases on the other side. All the non-metals (excepting those in 
 Group 0), namely, boron, carbon, silicon, nitrogen, phosphorus, 
 arsenic, oxygen, sulphur, selenium, tellurium, fluorine, chlorine, 
 bromine, and iodine, are rather compactly placed in a triangular 
 area of the table. Groups 3, 4, 5, 6, and 7 each begin with an 
 acid-forming element and end with a base-forming element. As 
 we pass from lower to higher atomic weight in these groups, acid 
 properties become less prominent and basic properties develop. 
 
 The position of hydrogen in the table is uncertain. According 
 to physical properties, as well as numerical relations, it should 
 head Group 7. On the other hand, it shows analogy to the metals 
 of Group 1, by combining in a similar way with negative 
 elements or radicals. 
 
 Examination of the table reveals three inconsistencies in the arrange- 
 ment according to increasing atomic weight: (1) The positions which 
 argon and potassium should naturally assume, must be reversed to place 
 them with their fellows. (2) Cobalt is placed before nickel, although 
 possessing a greater atomic weight. Chemical analogies are more satis- 
 factorily represented by this alteration, which associates cobalt with 
 ruthenium and iridium; nickel with palladium and platinum. (3) Tellu- 
 rium and iodine are transposed for a similar reason. There can be no 
 question of the analogy between iodine and the preceding halogens, nor of 
 that between tellurium and selenium. Careful revision of atomic weight 
 determinations suggested by these abnormalities has failed to reveal error 
 in the original consecutive numerical arrangement. Other apparent 
 exceptions to the general scheme have been relieved from time to time, in 
 this way. The value of the periodic system in criticising atomic weight 
 values is further noted in Chapter IV. 
 
 Although the numerical difference in atomic weight between 
 two successive elements is not uniformly the same, it is always 
 small and not widely divergent. The mean difference for the 
 first ten elements is 2.34, for the ten elements from silver to 
 cerium (well along in the table) it is 3.23, somewhat larger. We 
 note that, in certain cases, two successive elements in a list con- 
 
NATURAL CLASSIFICATION OF THE ELEMENTS. 45 
 
 taining all the known elements arranged in the order of increas- 
 ing atomic weight, show a numerical difference between their 
 atomic weights, which is much greater than the above mean 
 difference. This points to the probable existence of undiscov- 
 ered elements, best evinced by the necessity of leaving blank 
 spaces in the table to secure proper arrangement according to 
 analogies. By way of specific illustration, we may observe the 
 positions of nickel and copper in the table. Copper shows no 
 analogy to the He-Xe family, and is advanced to a more fitting 
 place in Group 1. An unknown rare gas of atomic weight 
 approximating 61 may, however, exist. Again, no known ele- 
 ments are closely related to manganese. Suggestive openings 
 occur between molybdenum and ruthenium (atomic weight 
 difference 5.7) and between tungsten and osmium (atomic weight 
 difference 7), possibly corresponding to unknown elements which,' 
 together with manganese, might constitute a well-defined sub- 
 group. 
 
 A number of elements have been discovered since the first 
 presentation of the periodic table by Mendelejeff. It is a par- 
 ticularly impressive fact that his elaborate predictions concerning 
 the probable nature of several of these elements, based upon 
 a series of interpolations between the properties of adjacent 
 elements, have been since realized with remarkable conformity. 
 
 We have not attempted, in the foregoing discussion, to closely 
 follow the specific nature of analogies, chemical and physical, 
 in each group. It is hoped that the student who has studied 
 chemistry only a few months will find these introductory remarks 
 of value in obtaining some adequate conception of the classifi- 
 cation which he will follow in continuing the subject. Further- 
 more, it seems desirable, as early as possible, to urge that the 
 discovery of the periodic law, which, in brief summation, char- 
 acterizes the properties of all the elements as periodic functions 
 of their atomic weights, constitutes one of the most material 
 advances in chemical science. 
 
 In conclusion, we may state that the exact cause of this unmis- 
 takable natural relationship between certain groups of elements, 
 is, at present, unknown. It is clearly recognized that the atoms 
 themselves are not the ultimate particles of nature, but are more 
 or less intricate aggregations of the much smaller corpuscles. (Cf . 
 
46 CHEMICAL THEORY. 
 
 Introduction, page 6.) Many authorities consider that a periodic 
 similarity in the arrangement of corpuscles in the atom, causing 
 a periodic similarity in properties, develops as the number of 
 corpuscles, or the atomic weight, increases. 
 
 Interesting, in this connection, even to the beginner, are the simpler 
 results of recent investigation on the subject by Professor J. J. Thompson 
 (Cambridge). By considering a number of corpuscles all in one plane, 
 and assuming that their tendency to fly apart due to their negative charges 
 is balanced by an opposite force (positive sphere of electrification) acting 
 everywhere inside the complex with equal intensity, thus constituting a 
 stable arrangement, or atom, he is able to show mathematically that, as 
 more corpuscles are added, there is a periodic similarity in the config- 
 urations which are stable under the influence of these forces. The 
 mathematical development of this idea leads to a system of stable units 
 resembling the periodic system in their relationship. Three dimensional 
 arrangements, corresponding to the natural manifestation of matter, have 
 proven too complicated for mathematical analysis, but there is reason to 
 suppose that equally characteristic periodic relations would obtain. 
 
CHAPTER III. 
 DETERMINATION OF MOLECULAR WEIGHTS. 
 
 IF the correct formula of any compound is known, it is a 
 comparatively simple matter to calculate its molecular weight 
 by adding the constituent atomic weights, or such simple 
 multiples of them as are specified in the formula. We have 
 remarked that these atomic weights are very accurate relative 
 numbers. Consequently, properly calculated molecular weights 
 are very accurate relative numbers; in short, the numbers used 
 in all practical calculations, which the chemist is called upon 
 to perform. 
 
 Now, the approximate molecular weight of a substance may 
 be determined experimentally quite aside from any previous 
 knowledge with regard to its composition, and work of this 
 sort constitutes the first step in developing the aggregate of 
 accurate and indispensable information embodied in the atomic 
 weight numbers and empirical formulas. 
 
 It is often true that the magnitude of a physical effect is deter- 
 mined by the numbers of molecules concerned in producing this 
 effect, irrespective of their specific nature. Hence, the relative 
 masses of different molecules may be deduced by comparative 
 observations. We have already pointed out that equal numbers 
 of molecules determine the same volume for all gases, if the 
 temperature and pressure values are equal (Avogadro's Law). 
 By comparing the masses of equal volumes of different gases 
 under the same conditions of temperature and pressure, we 
 obviously obtain the relation between their molecular masses 
 if one value is known, the other is thereby defined. Suppose 
 hydrogen is adopted as the standard for such comparison. The 
 density of a gas compared to hydrogen is obtained by dividing 
 the weight of one volume of the gas by the weight of one 
 volume of hydrogen, both gases measured under the same 
 conditions: 
 
 47 
 
48 CHEMICAL THEORY. 
 
 Gas density (compared to hydrogen) = 
 
 weight of 1 vol. gas weight of 1 mol. gas 
 weight of 1 vol. hyd. weight of 1 mol. hyd. 
 But, one molecule of hydrogen contains two atoms (cf. 
 Introduction, page 14) and must weigh twice as much as one 
 atom of hydrogen. Therefore, 
 
 weight of 1 mol. gas 
 2 X Gas density m ^ 
 
 weight of 1 atom hyd. 
 
 If the weight of one atom of hydrogen were taken as unity in 
 our system of atomic and molecular weights, the second member 
 of this equation would signify the molecular weight of the gas. 
 However, we prefer to use one sixteenth of the weight of the 
 oxygen atom as the unit standard in fixing these numbers. 
 On this basis, the atomic weight of hydrogen is 1.0076, and the 
 above equation may be altered thus: 
 
 weight of 1 mol. gas 
 
 2 X 1.0076 X Gas density - - - = 
 
 weight of 1 atom ox. -r- 16 
 
 Molecular weight of gas. 
 
 Calculations based on the simple gas laws give only approxi- 
 mate results (cf. Introduction, page 18); hence, the term 1.0076 
 is practically equivalent to unity in this connection, and we may 
 write: The (approximate) molecular weight of a gas is equal to 
 twice its density compared to hydrogen. 
 
 The density of a gas may be calculated from measurement 
 of the volume containing a given weight of substance under 
 carefully noted conditions, referred directly to hydrogen under 
 these conditions, and then multiplied by two to give the 
 molecular weight. In practice, no direct calculation of gas 
 density is customary; the hydrogen comparison is omitted alto- 
 gether, and a fundamental magnitude, called the gram molecular 
 volume, is introduced. By this term, we understand the volume 
 which includes one gram molecule (cf. Introduction, page 28) 
 of a gas at C., 760 mm. pressure. Since weights of different 
 gases, which stand in the same proportion as their molecula'r 
 weights, contain equal numbers of molecules (Relative numbers 
 
 weight of one subst. , weight of other subst. 
 
 of molecules = : : and : 
 
 its mol. weight its mol. weight 
 
 = 1 and 1, if the numerators of these expressions are propor- 
 
DETERMINATION OF MOLECULAR WEIGHTS. 49 
 
 tional to their denominators, as in above case), the volumes 
 occupied by them, or more definitely, by single gram molecules of 
 different gases under like conditions of temperature and pressure, 
 are the same, according to the familiar Law of Avogadro. The 
 value of this magnitude may be ascertained by measuring the 
 volume occupied by 32 g. of oxygen (mol. weight of oxygen = 32, 
 or twice 16, the atomic weight. Cf. Introduction, page 14) 
 under the normal conditions noted above. It is approximately 
 22.4 liters. 
 
 It should be clear, in view of the preceding discussion, that 
 simple calculation of the weight of substance necessary to pro- 
 duce 22.4 liters of gaseous material at C., 760 mm. pressure, 
 results in a number, which can be none other than the molecular 
 weight of the substance. We may, then, summarize the first 
 method of molecular weight determination applying only to 
 substances which may be vaporized without decomposition as 
 follows : Measure the volume occupied by a weighed quantity of the 
 substance in gaseous form under convenient conditions. Reduce 
 this volume to that corresponding to standard conditions by applying 
 the simple gas laws and calculate the weight of material which will 
 occupy 22 .4 liters under these conditions. 
 
 Problem: Calculate the molecular weight of a substance, 2 g. 
 of which furnish 395 c.c. of vapor at 100 C., 757 mm. pressure. 
 
 By Charles' Law, 395 : x l :: 373 : 273 
 
 orig. vol. altered vol. orig. temp, (abs.) final temp, (abs.) 
 
 Whence, x = 289.1 c.c. (vol. at C., 757 mm. pressure). 
 By Boyle's Law, 289.1 : x 2 :: 760 : 757 
 
 altered vol. final vol. final press. orig. press. 
 
 Whence, z=287. 9 c.c., or 0. 288 Z (vol. atOC., 760 mm. pressure).* 
 Calculation of weight in gram molecular volume, 
 2 : x :: 0.288 : 22.4 
 
 orig. weight weight in 22.4 I vol. of 2 g 
 
 Whence, x = 155.5, the molecular weight required. 
 
 * Denoting the original values of pressure, volume and abs. temperature by 
 p , v and T Q and the final values by p,, v, and T,, the equation obtained 
 
 by combining both laws reads : ^r-^-^r~- Th e final volume may thus be 
 
 -*o *i 
 obtained by substituting the values given above in this equation and solving 
 
 ,, = 288. 
 o7o 27 o 
 
50 CHEMICAL THEORY. 
 
 The molecular weights of many substances which cannot be 
 converted into gaseous material of the same kind, i.e., which 
 decompose on heating, may be deduced from quantitative 
 observations on characteristic properties evidenced by their 
 solutions in various solvents. In other words, the number .of 
 dissolved particles determine the extent to which a certain 
 property asserts itself. In considering these properties with 
 respect to molecular weight determination, we must exclude 
 aqueous solutions of acids, bases, and salts, since the particles 
 present in such solutions are, in part, more elementary than 
 molecules, and weights derived from reasoning along these 
 lines cannot be correct molecular weights. (Discussion in Chap- 
 ters VI and VII.) 
 
 It has been found that the particles of a substance as they 
 exist dissolved in another substance, exert a pressure susceptible 
 of measurement under certain conditions, which is in many 
 ways to be compared with the pressure which a gas exerts 
 against the walls of the containing vessel. This pressure 
 is called osmotic pressure and will be discussed in a later 
 chapter. For immediate purposes, it is sufficient to point out 
 that the quantitative relations connecting osmotic pressure 
 with the temperature and volume of the solution are precisely 
 those existing between the pressure, temperature, and vol- 
 ume of a gas. Moreover, Avogadro's Law is equally promi- 
 nent in this extended application: Equal volumes of dilute 
 solutions at the same temperature, contain the same numbers of 
 (" dissolved ") molecules, provided they possess the same osmotic 
 pressure. 
 
 Thus, it follows that the same reasoning adopted to ascertain 
 the molecular weight of a substance in the gaseous state, may 
 be applied to dissolved substances. The following procedure 
 for determining the molecular weight of a dissolved substance, 
 based on the application of the gas laws to dilute solution, is, 
 in effect, a reiteration of that outlined above : Measure the 
 volume of solution containing a weighed amount of dissolved 
 substance at the corresponding temperature, and determine the 
 osmotic pressure. Calculate the weight of substance which would 
 produce an osmotic pressure of 760 mm. when present in 22 A 
 liters solution at C. 
 
DETERMINATION OF MOLECULAR WEIGHTS. 
 
 51 
 
 By Charles Law, 246 
 
 orig. vol. 
 
 Problem : One gram of a compound dissolved in 246 c.c. solvent, 
 gives an osmotic pressure o/800 mm. at 18 C. What is its molec- 
 ular weight f 
 
 : x l :: 291 : 273 
 
 altered vol. orig. temp, (abs.) final temp, (abs.) 
 
 Whence, x =230.8 c.c. (vol. at C., 800 mm. osmotic pressure). 
 By Boyle's Law, 230.8 : x 2 :: 760 : 800 
 
 altered vol. final vol. final osm. press. orig. osm. press. 
 
 Whence, x =242.9 c.c. (vol. at C.,760 mm. osmotic pressure).* 
 Calculation of weight in gram molecular volume, 
 
 1 : x 0.243 : 22.4 
 
 orig. weight 
 diss. subst. 
 
 wt. diss. subst. 
 in '22.4 / 
 
 vol. cont'g 1 g. 
 diss. subst. 
 
 Whence, x = 92.2, the molecular weight required. 
 
 A solution freezes at a* lower temperature and boils at a higher 
 temperature, i.e., possesses a lower vapor tension, than the 
 pure solvent. The molecular weight of the dissolved substance 
 may be calculated from measurements of the lowering of the 
 freezing point, elevation of the boiling point, or vapor tension 
 difference between solution and pure solvent. The mutual 
 relationship between these three classes of phenomena is quali- 
 tatively indicated in the accompanying figure: 
 
 The curve ab represents the increase in the vapor tension of the 
 pure solvent with the temperature. When a substance is dis- 
 solved in the solvent, the re- 
 sulting solution has a lower p 
 vapor tension than the pure 
 solvent, at all temperatures. 
 This is indicated by the curve 
 a'6'. Now, the pure solvent 
 or the solution boils as soon 
 as its vapor tension becomes 
 equal to the atmospheric 
 pressure PI. In the case of 
 the pure solvent, this occurs T 4 T 3 
 
 at the temperature TI. At Fi g- 2 - 
 
 this temperature the solution has a lower vapor tension P 2 than 
 the atmospheric pressure PI, hence it must be further heated 
 to the temperature T% before it will boil. Therefore, to a lower- 
 ing in vapor tension, there corresponds an elevation in boiling point. 
 * See note on page 49. 
 
52 CHEMICAL THEORY. 
 
 The curve ca represents the increase in vapor tension of the 
 frozen solvent with the temperature. We may define the 
 freezing point as that temperature at which the vapor tensions 
 of both solid and liquid are equal. Only under this condition 
 could the two states remain in contact with one another without 
 tendency to change, as is the case at the freezing temperature. 
 For the pure solvent, this temperature is T 3 , the abscissa corre- 
 sponding to the point (a) where the vapor tension curves of 
 liquid and solid intersect, i.e., where both solid and liquid have 
 the same vapor tension (P 3 ). When a solution is frozen, it is 
 necessary that the pure solvent should appear as solid material, 
 if the measurements are to be of value in molecular weight 
 determination. This is generally the case, but not invariably 
 so. Now, the curve a'6', representing the vapor tensions of 
 the solution, intersects the curve ca, representing vapor ten- 
 sions of pure frozen solvent, at the point a', the only point at 
 which the vapor tensions (P 4 ) of solid and liquid are equal. This 
 point corresponds to the temperature 7 7 4 (less than T 3 ), which 
 is, consequently, the freezing point. Thus, we see that a depres- 
 sion of the freezing point is determined by a lowering in the vapor 
 tension of the liquid. 
 
 Rigid quantitative connection between such associated prop- 
 erties of dilute solutions as we have cited, may be developed 
 from theoretical considerations. If the osmotic pressure of a 
 solution is known, it is quite possible to calculate the elevated 
 temperature at which this solution will boil, its diminished vapor 
 tension, or the depressed temperature at which it will freeze. 
 
 The method chosen for a specific molecular weight deter- 
 mination will obviously be that which presents the least experi- 
 mental difficulty. Osmotic pressure measurements are difficult 
 to perform, and yield comparatively inaccurate results. The 
 freezing-point method is much more satisfactory in practice, ,and 
 has been used extensively. A few additional remarks will serve 
 to show how molecular weights are calculated from the results 
 of freezing-point experiments. 
 
 As a basis for quantitative developments, in this connection, 
 we have Raoult's Law, which states that molecular quantities of 
 different substances lower the freezing point of the same quantity of 
 given solvent to the same extent. Moreover, experiments show that 
 
DETERMINATION OF MOLECULAR WEIGHTS. 53 
 
 the lowering in any case increases in proportion as the concen- 
 tration of the dissolved substance increases that is, provided 
 only very dilute solutions are considered. If " one gram molecule 
 amounts " of different substances are dissolved separately in like 
 quantities of solvent, the freezing-point depressions must be the 
 same in all cases, according to this law. By adopting a definite 
 amount of solvent to effect such solution we may define a char- 
 acteristic constant applying to the use of this particular solvent. 
 Thus, the depression (in degrees Centigrade) produced by one 
 gram molecule of dissolved substance in 100 g. solvent is often 
 called the molecular depression, or the freezing-point constant of 
 the solvent. If a substance of known molecular weight is dis- 
 solved in this solvent, the constant may be calculated from 
 available experimental data, and applied in calculating the 
 molecular weights of other substances from data correspond- 
 ing to their own solution in the solvent. 
 
 It remains to obtain a mathematical expression connecting 
 the freezing-point constant with such direct experimental data: 
 
 Suppose we obtain a lowering of L C. by dissolving w grams 
 of substance, possessing an (unknown) molecular weight M in 
 W grams of a solvent, the freezing-point constant of which is K. 
 This constant represents the lowering in 100 g. solvent, per gram 
 molecule of dissolved substance, i.e., 
 
 lowering in 100 g. solvent 
 no. gram mols. diss. subst. 
 
 Since the lowering in W grams of solvent is L, the lowering 
 in one gram of solvent produced by the same amount of dis- 
 solved substance will be LW (the concentration is W times as 
 
 great), and the lowering in 100 grams of solvent will be - 
 
 1UU 
 
 (the concentration is as great). 
 1UU 
 
 The actual weight of dissolved substance w divided by its 
 molecular weight M gives the number of gram molecules of 
 
 w 
 
 dissolved substance, viz., : 
 
 M 
 
 LW w 
 
 Substituting the expressions and for the numerator 
 
 100 NL 
 
54 CHEMICAL THEORY. 
 
 and denominator, respectively, in the right-hand member of 
 the above equation, we obtain, 
 
 LW 
 
 w 
 M 
 
 LWM WQKw 
 
 Clearing of fractions, K = , and transposing, M = . 
 
 100 w Li\V 
 
 Problem: Using 18.6 as the freezing-point constant of the 
 solvent, calculate the molecular weight of the dissolved substance 
 from the following data: grams solvent, 50; grams dissolved sub- 
 stance, 0.88; actual lowering, 0.95. 
 
 Substituting the values: TF=50, w = 0.88, L =0.95, and 
 K = 18.6, in the above equation, we obtain, 
 
 .., (100) (18.6) (0.88) 
 M= (0.95) (50) 
 
 The calculation of molecular weights from boiling-point data 
 involves the use of a formula similar to the above. 
 
 Additional methods of molecular weight determination are of 
 relatively less importance than those described in this chapter. 
 
CHAPTER IV. 
 DETERMINATION OF ATOMIC WEIGHTS. 
 
 SUPPOSE it has been found by experiment that about 76 g. of 
 carbon disulphide occupy a volume of 22.4 liters at C., 760 mm. 
 pressure. We know, then, that a molecule of this substance 
 weighs approximately 76 times as much as the unit quantity 
 of material adopted as a basis of comparison for all atomic 
 and molecular weights, namely, the sixteenth part of the 
 oxygen atom. In other words, its molecular weight is approxi- 
 mately 44. 
 
 Now, it is always possible, by some quantitative method of 
 chemical analysis, to determine the exact proportions by weight 
 in which the individual constituents are present in a compound. 
 Thus, we are able to divide the molecular weight unit into parts 
 representing the weights of its several constituents. Such 
 analytical methods are sometimes direct, more often indirect, 
 and involve the use of much cumulative data relative to the 
 composition and particular behavior of certain substances. If 
 a weighed quantity of carbon disulphide could be decomposed 
 into its elements, and these, in turn, weighed, we would possess 
 the results of a direct analysis. By burning a weighed quantity 
 of carbon disulphide and weighing the resulting carbon dioxide, 
 after rendering it suitably pure, we would obtain indirect results 
 leading to the composition of the material. Thus, previous 
 experiment has shown that 27.3 -f per cent of the material in 
 carbon dioxide is carbon by direct synthesis, 27.3 + parts of 
 carbon unite with 72.7 parts of oxygen to form 100 parts car- 
 bon dioxide and it is only necessary to multiply the weight of 
 carbon dioxide obtained from our initial quantity of carbon 
 disulphide by this percentage number, to ascertain how much 
 carbon the latter originally contained. The complementary 
 
 55 
 
56 CHEMICAL THEORY. 
 
 amount of sulphur is obtained by difference original weight 
 of carbon disulphide minus weight of carbon since the com- 
 pound is known to contain no third constituent. 
 
 Analysis of the compound, carbon disulphide, shows that 15.8 
 per cent of its total substance is carbon, while the remainder, 84.2 
 per cent, is sulphur. In the preliminary discussion (cf . Introduc- 
 tion, page 22, in particular) we have already demonstrated that a 
 molecular weight combines the atomic weights, or multiple atomic 
 weights of such elementary substances as compose the compound. 
 Consequently, 15.8 per cent of 76 = 12.0 (that part of the molecu- 
 lar weight of carbon disulphide attributive to carbon) must be 
 the (approximate) simple or multiple atomic weight of carbon; 
 and 84.2 per cent of 76 = 64 (that part of its molecular weight 
 attributive to sulphur) must be the (approximate) simple or 
 multiple atomic weight of sulphur. 
 
 It is clear that an extension of this line of work to a large num- 
 ber of compounds containing carbon, will result in a series of 
 numbers representing either the atomic weight of carbon, or 
 multiples of the same, and furthermore, that the simple number 
 is reasonably certain to develop if the number of compounds 
 investigated is very great; i.e., some one of these compounds will, 
 in all probability, contain a single atom of carbon in its molecule. 
 The determination of other atomic weights is effected by a 
 similar course of procedure. 
 
 The following outlined arrangement serves to briefly summa- 
 rize this argument. 
 
 To Determine the Approximate Atomic Weight of an Element : 
 
 (1) A table of the molecular weights of a large number of com- 
 pounds containing the element is prepared. 
 
 (2) The compounds are analyzed and that portion of the molecu- 
 lar weight consisting of the element under consideration, is tabulated 
 along with the corresponding molecular weight. 
 
 (3) The smallest of these latter numbers is chosen as the atomic 
 weight sought, for larger numbers evidently represent more than one 
 atom, and are consequently multiples of the correct atomic weight. 
 
DETERMINATION OF ATOMIC WEIGHTS. 
 To illustrate: 
 
 57 
 
 Carbon. 
 
 Sulphur. 
 
 
 
 
 Part of 
 
 
 
 
 
 
 
 
 Mol. 
 
 
 
 
 Part of 
 
 Compound. 
 
 Mol. 
 Wt. 
 
 Per cent C. 
 in Comp'd. 
 
 Wt. 
 
 Consist- 
 
 Compound. 
 
 Mol. 
 Wt. 
 
 Per cent S. 
 in Comp'd. 
 
 Mol. Wt. 
 Consisting 
 
 
 
 
 ing 
 
 
 
 
 of 8. 
 
 
 
 
 of C. 
 
 
 
 
 
 Carbon 
 
 
 
 
 Sulphur di- 
 
 
 
 
 monoxide 
 
 28 
 
 42.9 
 
 12 
 
 oxide 
 
 64 
 
 50.0 
 
 32 
 
 Carbon di- 
 
 
 
 
 Sulphur tri- 
 
 
 
 
 oxide .... 
 
 44 
 
 27.3 
 
 12 
 
 oxide 
 
 80 
 
 40.0 
 
 32 
 
 Carbon di- 
 
 
 
 
 Carbon di- 
 
 
 
 
 sulphide . . 
 Methane 
 
 76 
 16 
 
 15.8 
 75.0 
 
 12 
 12 
 
 sulphide 
 Hydrogen 
 
 76 
 
 84.2 
 
 64 
 
 
 
 
 
 sulphide 
 
 34 
 
 94.1 
 
 32 
 
 Acetylene . . 
 
 26 
 
 92.3 
 
 24 
 
 Sulphuryl 
 chloride 
 
 135 
 
 23.7 
 
 32 
 
 Benzene. . . . 
 
 78 
 
 92.3 
 
 72 
 
 Sulphur 
 
 64 
 
 100.0 
 
 64 
 
 etc. 
 
 
 
 
 etc 
 
 
 
 
 
 
 From these two tables, we choose the values 12 and 32 as the 
 atomic weights of carbon and sulphur, respectively. 
 
 It is obviously of great importance to be able to verify an 
 atomic weight number, selected as above, by some independent 
 method. Such a check is offered by the Law of Dulong and 
 Petit (Paris, 1818): 
 
 The products of the atomic weights of the elements into their 
 specific heats are approximately constant. 
 
 The mean value of this product is 6.4. We should note that 
 the specific heat of an element varies with the temperature; in 
 some cases, very emphatically. Moreover, not a few of the ele- 
 ments are polymorphous (cf. Introduction, p. 16), in which case 
 each solid modification has its own characteristic specific heat. 
 Some elements do not follow the law very closely. Nevertheless, 
 deductions from this source are of service, in a broad sense, to 
 indicate whether the atomic weight number resulting from chem- 
 ical reasoning (as above), is a minimum value, or still a multiple 
 of the true value. The fact that conclusions from both sources 
 are quite generally in accord, justifies an increased confidence in 
 their accuracy. 
 
58 CHEMICAL THEORY. 
 
 Additional evidence tending to establish the general accuracy 
 of these numbers, is offered by the Periodic System (Chapter II). 
 The very realization of a comprehensive classification of this sort 
 based on this series of numbers, testifies to their significant nature. 
 Indeed, when sufficiently elaborate chemical data to fully establish 
 the atomic weight of an element are not available, its logical posi- 
 tion in the periodic system may be depended upon to suggest 
 the order of this number. 
 
 We have seen how an approximate number is chosen for the 
 atomic weight of an element. The greater number of atomic 
 weights are now known accurately to one or two places of deci- 
 mals. This refinement is based on very careful analytical work, 
 showing, as accurately as possible, the ratios by weight char- 
 acterizing combination between the different elements and 
 oxygen. It is not necessary to determine the combining ratio 
 between every element and oxygen directly some elements 
 fail to combine with oxygen, or form oxides which are unsuited to 
 analysis since this ratio may be calculated if the data relative 
 to combination with another element, as well as the oxygen ratio 
 of this other element, is known. To obtain a uniform comparison 
 with the arbitrary standard O = 16 the oxygen term of the 
 ratio is altered to exactly 16, and the other term recalculated on 
 this basis. The resulting number may then require to be multi- 
 plied, or divided by some simple integer to furnish the correct 
 atomic weight, already known in approximation. 
 
 It should be clear that the combining ratio between the element and 
 oxygen perhaps ascertained indirectly may represent a relation 
 between any small number of atomic quantities of the element and any 
 small number of atomic quantities of oxygen. In any case, the weight of 
 element is finally referred to one atomic quantity of oxygen, and may, 
 thus, constitute a simple fractional part, or multiple, of the atomic weight. 
 Since we know the approximate atomic weight from previous considera- 
 tions, it is at once apparent how this number must be altered to yield 
 the accurate atomic weight. 
 
 An example will serve to further elucidate these state- 
 ments : 
 
 By the process outlined on page 56, the " round number " 
 atomic weight of hydrogen is fixed at 1. 
 
DETERMINATION OF ATOMIC WEIGHTS. 59 
 
 Unusually elaborate and extended experiments have placed 
 the ratio of hydrogen to oxygen in the compound, water, at 
 0.12595 4:1. Changing the oxygen term to 16, the ratio 
 becomes, 2.0152 : 16. Since the approximate atomic weight of 
 hydrogen is 1, the number 2.0153 divided by 2, gives the refined 
 atomic weight value, 1.0076. The particular significance of 
 the multiple number is that two atoms of hydrogen are combined 
 with one atom of oxygen in the above compound. 
 
 The atomic weight most frequently used in chemical calcu- 
 lations is that of oxygen. It is, therefore, desirable in standard- 
 izing these relative weights that some convenient whole number 
 should be adjusted to oxygen. Berzelius proposed regulation 
 of these numbers on the basis of O = 100. This standard has 
 not met with general approval. On the other hand, hydrogen 
 possesses the smallest atomic weight of any known element and 
 might logically be adopted as unity. In such event, the oxygen 
 number would be a trifle under 16, a rather inconvenient 
 fractional value. It has proven most uniformly satisfactory 
 to make this number exactly 16 (the value which we have used 
 in earlier portions of this text). On this basis, the atomic 
 weight of hydrogen becomes 1.0076 (as shown in the previous 
 paragraph); a number so close to unity that the decimal part 
 need not be considered in practical work. Other atomic weights 
 are invariably referred to this standard, whereby they assume 
 values which are only infrequently expressed by whole numbers. 
 
 We may sum up the essential features of the preceding remarks 
 in the form of a rigid definition of the term atomic weight: An 
 atomic weight is a number expressing the ratio of the mass of 
 the smallest part of an element entering into combination, to 
 yV of the mass of an atom of oxygen. An international com- 
 mission critically examines all new experimental work in this 
 field and revises the list of atomic weights each year. The 1908 
 Table is to be found inside the cover of this book. 
 
CHAPTER V. 
 CALCULATION OF FORMULAS. 
 
 WE have seen that a formula specifies the number of atomic 
 quantities of each elementary substance which together con- 
 stitute one molecular quantity of the compound. Consequently, 
 the composition of a compound must be determined by some 
 process of analysis before any calculation relative to numbers 
 of different atoms in a molecule is possible. The results of 
 chemical analysis are usually presented in such a way that the 
 proportion of each constituent appears as a percentage of the 
 whole. If the analysis is correct, these percentage numbers 
 should total 100, within the limits of experimental accuracy. 
 Thus, a satisfactory analysis of the compound water would be: 
 
 Hydrogen ............. 11.10 per cent (by weight) 
 
 Oxygen ................ 88.82 per cent 
 
 Total .................. 99.92 per cent. 
 
 The analysis might be referred to one part by weight of hydro- 
 gen. Either of the following expressions, in which the figures 
 denote parts by weight, describes the results of this analysis: 
 
 Hydrogen 11<10 + Oxygen^; Hydrogen r-00 + Oxygen 8i00 . 
 
 Now, if we are to use symbols, and assemble our data in the 
 shape of a formula, we must observe that each symbol stands 
 for a certain weight of its particular kind of matter, called the 
 atomic weight. Hence, the relative atomic proportions of 
 hydrogen and oxygen in the compound water obtained by 
 dividing the actual proportions by weight by the respective 
 atomic weights (H = 1, O = 16), may be associated with the 
 symbols, thus: 
 
 HII. IO O 5t55 Hj >00 O 050 
 
 11.10, and 8 ^f - 5.55 } (^ . IM> and 8 _| =0 .5o). 
 
 60 
 
CALCULATION OF FORMULAS. 
 
 61 
 
 At this point, we should reflect that a formula must represent 
 the actual numbers of different atoms which constitute one 
 molecule of the substance. Moreover, these numbers must be 
 simple integers, since one atom is the smallest unit concerned 
 in chemical combination. If, in the above ratio, we assume one 
 atom of oxygen, there will result an integral number of hydrogen 
 atoms, namely, two. But no evidence has been introduced, thus 
 far, to prove that a molecule of water does not contain two 
 atoms of oxygen and four of hydrogen, or some larger total of 
 oxygen and hydrogen atoms, always in the proportion one to two. 
 Therefore, at this stage we may write the simple formula H 2 O with 
 the understanding that it is to a certain extent hypothetical; or 
 the general formula H 2n O n in which n is some simple integer. 
 
 This uncertainty is removed through an actual determination 
 of the molecular weight. The molecular weight of water, if its 
 formula is H 2 O, must be 18, i.e., ((2 X 1) + 16). An experi- 
 mental determination of the molecular weight by the gas density 
 method (cf. Chapter III) presents no difficulty in this case, and 
 results in the above value. Hence, we accept the formula H 2 O 
 without question, as descriptive of the compound water. Had a 
 multiple of 18 been obtained in the molecular weight deter- 
 mination, corresponding alteration of the simple formula would 
 have been necessary, in order to secure the proper agreement. 
 Thus: 
 
 Molecular Weight. 
 
 Formula. 
 
 18 
 
 H 2 O 
 
 36 
 
 ILO, 
 
 54 
 
 HO 
 
 18 n 
 
 H^ 
 
 A working summary of the preceding argument is embodied 
 in the following Rule for the Calculation of Formulas: Divide 
 the numbers which represent the relative weights of each element 
 in the compound, by the corresponding atomic weights. The 
 resulting series of numbers represents the numerical proportionality 
 between the several kinds of atoms in the molecule. Assign the 
 value 1 to the smallest of these numbers and recalculate the others 
 on this basis. Construct a formula using these recalculated num- 
 
62 
 
 CHEMICAL THEORY. 
 
 bers (which should be simple integers) as subscripts, and compare 
 the molecular weight corresponding to this formula with the experi- 
 mentally determined molecular weight. If substantial agreement 
 is apparent, this simplest formula meets all requirements. Other- 
 wise, to obtain a correct formula, divide the experimentally deter- 
 mined molecular weight by the molecular weight calculated from 
 the simplest formula, and multiply each subscript in this formula 
 by the quotient, which must approximate a simple integer. 
 Illustrative calculations : 
 
 Sulphur Dioxide: 
 
 
 Percentage 
 Comp. 
 
 
 At. Wts. 
 
 
 At. Ratio. 
 
 Simplest 
 Ratio. 
 
 Mol. Wt. 
 from 
 Gas. D. 
 
 Sulphur 
 Oxvffen . . 
 
 50.05 
 49 95 
 
 + 
 
 32.06 
 16 00 
 
 = 
 
 1.56 
 3 12 
 
 1.00 
 2 00 
 
 About 
 64 
 
 
 
 
 
 
 
 
 
 
 100.00 
 
 
 
 
 
 
 
 Rational Formula, S0 2 : The simplest formula suggested by 
 the numbers in the fourth column above is SO 2 . The molecular 
 weight corresponding to this formula is 64.06 (32.06 + (2 X 16)), 
 in substantial agreement with the above value, 64. (All the 
 above numbers are ideal, for purposes of illustration.) 
 
 Sometimes it is desirable to express the results of an analysis 
 in terms of characteristic groups of atoms. The analytical data 
 in the following table relates to a very pure sample of the mineral, 
 gypsum.* 
 
 
 Percentage 
 Comp. 
 
 
 Formula Wts. 
 of Constitu- 
 ents. 
 
 
 Ratio. 
 
 Simplest 
 Ratio. 
 
 H 2 O. . 
 
 20.85 
 
 
 18.02 
 
 
 1.16 
 
 2.03 
 
 aO 
 
 so a 
 
 32.84 
 46 07 
 
 4- 
 
 56.1 
 80 06 
 
 = 
 
 0.58 
 0.57 
 
 1.02 
 1.00 
 
 
 
 
 
 
 
 
 
 99.76 
 
 
 
 
 
 
 Simplest Formula, CaSO 4 . 2H 2 O : The simplest formula 
 corresponding to these results is CaO.SO 3 . 2H 2 O, or CaSO 4 . 2H 2 O. 
 
 * Analysis by a student in the Sheffield Scientific School. 
 
CALCULATION OF FORMULAS. 63 
 
 In this case, no molecular weight determination is available for 
 further criticism. 
 
 The reference literature of Chemistry is essentially a collection 
 of definite chemical information relative to all known substances, 
 in which their formulas occupy a prominent position. For the 
 most part, simplest formulas (according to previous interpre- 
 tation) figure in the general enumeration. The simplest for- 
 mula corresponds to the correct molecular weight in the majority 
 of investigated cases. It should be noted, however, that the 
 molecular weights of many compounds have never been deter- 
 mined. Consequently, the simple formulas assigned to them, 
 while certifying to their composition, may or may not represent 
 their molecular weights. 
 
 The ordinary methods of molecular weight determination deal with a 
 substance in the gaseous or dissolved state. There is, perhaps, a general 
 tendency for the same substance to persist in a definite molecular condi- 
 tion throughout change from one to the other of these states. Neverthe- 
 less, many exceptions may be noted indeed, change in molecular 
 complexity in the gaseous state alone, frequently accompanies change of 
 temperature. No method of determining the molecular weight of a 
 solid is known. 
 
 Immediate knowledge of the formulas pertaining to many 
 important compounds is preeminently valuable to the student 
 of Chemistry. Fortunately, a comprehensive array of analogies 
 and relationships underlies the whole scheme of chemical com- 
 bination, rendering a minimum amount of well chosen data 
 directly available for predicting a wealth of detailed information. 
 Any ordinary formula is readily constructed by adjusting its 
 individual constituent parts according to certain well recognized 
 principles of equivalence, which have resulted from the critical 
 examination of many other formulas (cf. Introduction, page 23). 
 This is, in no sense, a rigid determination, or calculation of the 
 formula, but rather an empirical method of rendering our knowl- 
 edge systematic and helpful. 
 
CHAPTER VI. 
 
 OSMOTIC PRESSURE AND RELATED PHENOMENA, WITH PAR- 
 TICULAR REFERENCE TO DILUTE AQUEOUS SOLUTIONS OF 
 ACIDS, BASES, AND SALTS. 
 
 IN a previous chapter, we have noted that the dissolved par- 
 ticles of a solution give rise to a certain pressure effect which 
 obeys the same laws as that due to the particles of a gas. For 
 purposes of comparison, it may be imagined that total elimina- 
 tion of the solvent would convert the dissolved particles into a 
 like number of gaseous particles exerting gaseous pressure equal 
 in magnitude to the osmotic pressure, which they determined 
 when in the dissolved condition. Gaseous pressure is apparent at 
 the bounding surfaces of the gas. On the other hand, the pressure 
 on the walls and bottom of a vessel containing a solution is 
 purely gravitational in nature. The marked difference between 
 the properties of a gas and those of a liquid explains this non- 
 conformity in the manifestation of gaseous pressure and osmotic 
 pressure. Forces of great magnitude are concerned in restraining 
 the particles of a liquid from realizing their inherent disruptive 
 tendency. Outside pressure is not necessary to limit the volume 
 occupied by matter in this state of aggregation, since a self- 
 imposed surface characterizes the liquid state. The forces oper- 
 ating at such a liquid surface determine a pressure effect directed 
 towards the interior of the liquid, at right angles to the surface, 
 i.e., in direct opposition to the osmotic pressure. Experimental 
 study of surface tension phenomena has led to a quantitative 
 estimate of such surface pressures. It appears that they vastly 
 exceed any possible osmotic pressure. Consequently, the latter 
 effect will not appear at a free surface. 
 
 To measure the osmotic pressure of a dissolved substance, we 
 must, therefore, eliminate the free surface. This is accomplished 
 by arranging a boundary between the solution in question and 
 an amount of pure solvent, which shall permit ready passage of 
 
 64 
 
OSMOTIC PRESSURE AND RELATED PHENOMENA. 
 
 65 
 
 the solvent in both directions, but completely enclose the dis- 
 solved particles. Thus, we experiment in a medium of pure sol- 
 vent, which pervades the whole system. Membranes composed 
 of copper ferrocyanide, or certain other gelatinous bodies, are 
 permeable to water and impermeable to most dissolved sub- 
 stances. In this connection, they are called semi-permeable 
 membranes. The cellular tissue of plants and animals is semi- 
 permeable with respect to aqueous solutions of various com- 
 pounds, and osmotic phenomena are prominently concerned in 
 its natural functions. 
 
 Suppose the cylinder represented in Fig. 3 contains a solution 
 of sugar in water, separated from a quantity of pure solvent by a 
 partition, which permits unrestricted passage 
 of the water, but is impervious to the sugar 
 molecules. There is no surface to mark the 
 division between these two compartments, 
 since water is continuous throughout the 
 whole system. Under these conditions, the 
 osmotic pressure due to the sugar molecules 
 contained in the lower compartment will be 
 apparent at the partition, and may be 
 measured indirectly, as we shall see later. 
 If the partition is movable, it will be forced 
 upwards through the pure water until the 
 osmotic pressure of the solution, which 
 decreases as water enters, becomes just equal to the task of 
 supporting its weight. In case no partition had prevented the 
 dissolved particles from escaping, they would have penetrated 
 the pure solvent until the osmotic pressure had become equal 
 throughout the whole solution. In other words, diffusion would 
 have proceeded until a uniform concentration had obtained. 
 
 Owing to the delicate nature of these semi-permeable mem- 
 branes, their practical use in furthering the measurement of 
 osmotic pressure is dependent on some arrangement calculated 
 to render them sufficiently rigid. According to the method 
 commonly used, they are supported by the walls of a porous 
 earthenware vessel. Solutions which will precipitate the mem- 
 brane by interaction, are allowed to penetrate the walls of the 
 vessel from either side, thus meeting in the interior and depositing 
 
 Fig. 3. 
 
66 
 
 CHEMICAL THEORY. 
 
 a thin membrane, which is rigidly secured by the wall substance. 
 Reinforced copper ferrocyanide membranes of this sort are 
 capable of withstanding osmotic pressures of several atmospheres. 
 No membranes of sufficient rigidity to permit accurate work with 
 rather concentrated solutions (in which the osmotic pressure may 
 exceed 100 atmospheres) have been constructed. 
 
 A clear conception of the actual process employed to determine 
 the osmotic pressure of a solution is best obtained with the help 
 of the accompanying diagram (Fig. 4). The porous cup C is 
 prepared for the experiments by depositing a membrane of 
 copper ferrocyanide within its wall substance. It is then 
 fitted with a stopper carrying a long glass 
 tube, and filled to the bottom of the stopper 
 with the solution to be investigated. This 
 apparatus is immersed in a bath of pure 
 solvent S to a depth which brings both liquid 
 surfaces to the same level. The particles of 
 dissolved substance exert a pressure on the 
 membrane. This is held by the cell walls 
 and cannot yield. 
 
 Now, any system invariably tends to such 
 readjustment as will operate against an im- 
 posed deformation. A flow of solvent through 
 the membrane into the solution, whereby 
 the solution becomes diluted and its osmotic 
 pressure diminished, therefore ensues. The 
 resulting increase in the volume of the solution 
 causes it to rise in the tube, and this effect 
 persists until the hydrostatic pressure of the 
 liquid column (h) exactly balances the tendency to inflow. 
 Since the magnitude of this inflow effect is determined by 
 the osmotic pressure of the original solution its cause the 
 resulting hydrostatic pressure, measured by the height of the 
 column (h), is equal to the osmotic pressure. 
 
 We have accounted for gaseous pressure by picturing rapid 
 motion of the constituent molecules, resulting in countless 
 impacts against the walls of the containing vessel. This explains, 
 all facts well and is generally acceptable to the scientific fraternity. 
 To associate osmotic pressure with gas pressure, we have con- 
 
 Fig. 4 
 
OSMOTIC PRESSURE AND RELATED PHENOMENA. 67 
 
 ceived the space between the molecules of a gas to be filled with 
 solvent. But, whether a similar kinetic hypothesis, or some 
 other hypothesis, such as the assumption of attractive forces 
 between dissolved substance and solvent, offers the most rational 
 explanation of osmotic pressure, is an open question. 
 
 In the course of our discussion relative to the determination of 
 molecular weights, we noted the failure of methods employing 
 dilute solutions to yield the correct molecular weight when the 
 dissolved substance is an acid, base, or salt; and the solvent, 
 water. It is just such solutions which merit especial interest 
 on the part of the chemist, by reason of their commonplace 
 occurrence. Consideration of some typical results obtained by 
 the application of these methods to such solutions will be of 
 value in introducing certain fundamental ideas as to the nature 
 of dissolved substances in general. 
 
 For this purpose, we may choose the freezing-point method in 
 preference to the osmotic pressure method, chiefly because it 
 presents less experimental difficulty and has received more 
 attention. The close relationship between these different proper- 
 ties of solutions has already been pointed out (cf. Chapter III). 
 
 From previous considerations, we would expect one gram 
 molecule of sodium chloride to produce the same freezing-point 
 lowering in a liter of water as one gram molecule of sugar, or any 
 other dissolved substance does. That is, as many molecules are 
 dissolved in each case, and we have seen that it is the number of 
 molecules which determines the magnitude of the lowering. In 
 reality, the salt is much more effective in this respect. Thus: 
 
 Lowering in 1000 g. water by 1 g. mol. (342 g.) cane sugar 1.86 
 Lowering in 1000 g. water by 1 g. mol. (58.5 g.) salt 3.46. 
 
 Since the lowering is proportional to the number of molecules, 
 or concrete particles in general, we reason that the salt solution 
 
 Q A R 
 
 contains 1 or 1.86 times as many particles as the sugar solu- 
 
 1.86 
 
 tion. If we consider the figures given by sugar (and duplicated 
 by other substances which are not acids, bases, or salts) as 
 normal, then we may place the normal freezing-point constant 
 of water at 18.6, i.e., the lowering produced by one gram mole- 
 cule of dissolved substance in 100 grams of solvent (cf. Chapter 
 
68 CHEMICAL THEORY. 
 
 Ill, page 53). Using this value in the formula M = 
 
 LW 
 
 in connection with the actual lowering produced by 58.5 g. salt 
 in 1000 g. water 3.46 we calculate the molecular weight 
 of salt to be 31.4. Now, it is certain that the formula of 
 common salt is NaCl, and its molecular weight, 58.5. Hence, 
 the above result indicates that the (average) formula weight- 
 of the particles present in the aqueous solution of salt 31.4 
 is less than the true molecular weight. We are forced to the 
 general conclusion that the process of solution has caused some 
 sort of disruption, or dissociation (since salt is again formed on 
 evaporation) of the original salt molecules into smaller parts, 
 each of which is comparable with a whole molecule in its power 
 to lower the freezing point of the solvent. 
 
 The following reasoning suffices to show what proportion of 
 the molecules have suffered alteration: At the outset we will 
 make the assumption that each molecule which dissociates, 
 furnishes two particles. Theory concerning the nature of these 
 particles is introduced in the next chapter. At this point, we 
 need only state that a molecule consisting of one atom of sodium 
 and one atom of chlorine could scarcely be expected to furnish 
 more than two concrete chemical particles of any sort. 
 
 Let (ra) equal the fractional part of molecules which dissociate. 
 Then (1 ra) will represent the fractional part of molecules 
 which fail to dissociate, and 2 m + (1 ra), or (1 + ra), the 
 total number of particles (molecules and portions of molecules) 
 present in the solution for every original molecule dissolved. 
 But, we have seen above that the solution contains 1.86 times 
 as many particles as the sugar solution, and we dissolved 
 the same number of molecules in each case. Therefore, 1.86 
 particles are present for every molecule dissolved and we write, 
 (1 + ra) = 1.86. Whence, (ra) = 0.86. This number signifies 
 that 86 per cent of the salt molecules in a solution containing 
 58.5 grams of salt per liter of water, are dissociated into two 
 parts. 
 
CHAPTER VII. 
 
 THE ELECTROLYTIC DISSOCIATION THEORY. 
 
 As a basis for the formulation of a theory which shall explain 
 the condition of substances in solution, we have these funda- 
 mental facts to consider: 
 
 (1) Those substances, and only those, which conduct the 
 galvanic current in aqueous solution, give rise to greater osmotic 
 pressure, etc., in the same aqueous medium, than is calculated 
 from their molecular weights in the usual way (by application of 
 Avogadro's Law). 
 
 (2) These substances do not show this abnormality when dis- 
 solved in most other solvents, and such solutions do not con- 
 duct the current to any great extent. 
 
 (3) Chemical reactions of a particularly significant character 
 are associated with the aqueous solutions of these substances. 
 
 We remarked briefly on the chemical nature of these com- 
 pounds in the earlier discussion of their abnormally pronounced 
 effect in lowering the freezing point of water. Attention is 
 again directed to the fact that they include the three great 
 classes of compounds which are most representative of the whole 
 chemical fabric acids, bases, and salts. The term, electrolyte, 
 is employed to designate all of these substances, with reference 
 to their ability to conduct the galvanic current, when in a 
 suitable condition, such as that of solution in water. 
 
 Substances which do not conduct the galvanic current in 
 aqueous solution, or non-electrolytes, are supposed to disintegrate 
 into molecules when dissolved in any liquid. We have seen 
 (Chapter III) how careful consideration of the properties of their 
 solutions leads consistently to this conclusion. But, the aqueous 
 solution of an electrolyte contains more particles than would 
 correspond to a division into simple molecules. It was sug- 
 gested at the close of the previous chapter, that this condition 
 could be explained by assuming a kind of dissociation in the 
 aqueous solution, whereby some of the molecules of the dis- 
 
70 CHEMICAL THEORY. 
 
 solved substance furnish two or more particles. This reasoning 
 was carried far enough to show how the numerical proportion 
 of molecules which dissociate, could be calculated by comparing 
 the actual freezing-point lowering with the normal lowering in a 
 solution of the same molecular concentration. 
 
 There remains the necessity of placing this theory on a practi- 
 cal footing by introducing some logical conception of the nature 
 of these sub-molecular particles. Reverting to the specific 
 case previously considered, it is not reasonable to suppose that 
 sodium chloride, NaCl, when dissolved in water, dissociates into 
 concrete particles, or atoms, of sodium and chlorine; for we know 
 that both these substances in the atomic state react chemically 
 on water, forming other products. Thus: 
 
 Na + H 2 O = NaOH + H; and Cl + H 2 O = HC1 + O. 
 
 The modified conception, which renders a primary assumption 
 of simple dissociation tenable in the face of all requirements, is 
 embodied in the Electrolytic Dissociation Theory, proposed by 
 Arrhenius (Stockholm, 1887). In effect, each particle is sup- 
 posed to carry a certain quantity of electricity, which thus 
 materially changes its nature. This appears quite reasonable 
 if we reflect that it is the association of matter with energy which 
 determines the nature of chemical, as well as physical change - 
 the association of an electric charge with the sodium atom might 
 well prevent it from reacting with water, as above. Positive 
 and negative electricity cannot appear independently. Conse- 
 quently, the dissociation products from each molecule will be 
 of two kinds, i.e., those carrying positive charges, and those 
 carrying complementary negative charges. 
 
 Electrolytic dissociation follows a plan suggested by general 
 chemical reaction. Thus, the compound potassium chlorate, 
 KClOs, dissociates into positive K particles and negative 
 ClOs particles, and the integrity of the ClOs particle is 
 generally preserved throughout diverse chemical reaction. The 
 name, ion (positive or negative, respectively), is applied to a 
 particle of this sort, and the process by which ions are formed 
 (attending solution of an electrolyte in water for example) is 
 called electrolytic dissociation, or ionization. An ion which corre- 
 sponds to the chemical valence 1 carries a unit charge. This is 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 71 
 
 represented by entering one ( + ) over the symbol, or group of 
 symbols describing its identity. A bivalent atom or group 
 produces an ion of double charge (++), etc. The whole 
 valence scheme serves as a key to the distribution of these ionic 
 charges. A few illustrations will make this matter clear: 
 
 One molecule of sodium chloride NaCl gives one sodium ion 
 
 + 
 
 with unit positive charge, represented Na, and one chloride 
 
 ion with unit negative charge, represented Cl. 
 
 + 
 
 One molecule of sodium sulphate, Na2SO 4 , gives 2Na+ SO 4 . 
 
 + + 
 One molecule of barium chloride, BaC^, gives Ba 4- 2C1. 
 
 + + 
 One molecule of cupric nitrate, Cu(NO3) 2 , gives Cu + 2NOs. 
 
 + + 
 One molecule of fead acetate, Pb(C 2 H 3 O 2 )2, gives Pb +2C 2 H 3 2 . 
 
 i 
 
 One molecule of nitric acid, HNOs, gives H + NO 3 . 
 
 + 
 
 One molecule of sodium hydroxide, NaOH, gives Na + OH. 
 
 While the general idea of dissociation included in our theoreti- 
 cal conceptions relative to aqueous solutions of electrolytes, is 
 definitely suggested by the abnormal behavior of these solutions 
 (as previously shown), consideration of the actual phenomena 
 associated with the conduction of electricity by such solutions 
 has contributed most effectively towards maturing this theory. 
 The prospect of a much clearer insight into the essential asser- 
 tions of the Electrolytic Dissociation Theory, will justify the use 
 of some space for a detailed description of such phenomena, 
 viewed from this standpoint. Before turning to a specific case, 
 it is especially desirable to state with all possible emphasis, that 
 the passage of electricity through an aqueous solution of an 
 electrolyte is accompanied by an alteration in the chemical 
 nature of the material; a transfer of matter differentiates elec- 
 trolytic conduction, or conduction of the second class, from 
 metallic conduction, or conduction of the first class, during which 
 no material change occurs. The process of decomposition, 
 attending the passage of electricity through a substance, or 
 mixture, is called electrolysis. To avoid misconception on the 
 part of the reader, we should note here, that electrolysis is not 
 
72 CHEMICAL THEORY. 
 
 confined to aqueous solutions of electrolytes, although depend- 
 ent on the presence of ions. Some other solvents produce the 
 same ionic condition in an electrolyte. Water is by far most 
 effective in this respect, however. Again, a pure electrolyte 
 may become quite conductive at high temperatures. Thus, we 
 refer to the electrolysis of certain non-aqueous solutions and 
 of fused electrolytes. 
 
 Let us consider the electrolysis of a dilute solution of hydro- 
 chloric acid in water: If no acid were dissolved in the water, the 
 latter would scarcely conduct at all. Likewise, if pure acid were 
 used, very slight conductivity would result. But the solution con- 
 tains particles not present to any appreciable extent in either 
 pure substance, namely, hydrogen ions and chloride ions. These 
 particles are thought to transport electricity from pole to pole. 
 Each dissociating molecule of acid furnishes one hydrogen ion, 
 carrying a unit positive charge, and one chloride ion, carrying 
 a unit negative charge. If the solution is very dilute, most of 
 the acid molecules are dissociated, so that an almost endless 
 number of charged particles are present. It is obvious that no 
 apparent electrification of the solution will result, since there 
 can be no excess of one kind of electricity over the other. The 
 process of dissolving acid in water has, in some obscure manner, 
 caused a readjustment of energy within the system, especially 
 characterized by the appearance of sub-molecular fragments, 
 which are possessed of electrical energy, operating to prevent 
 their complete alienation, i.e., there is a reciprocal attraction 
 between complementary fragments carrying equal and opposite 
 charges of electricity, 
 
 Suppose we follow the process of alteration which a tangible 
 number of these dissociated acid molecules may be expected to 
 sustain when suitable electrodes* connected with some outside 
 source of electricity are introduced into the solution in which 
 they are contained. Four such dissociated molecules are shown 
 underneath the lowest dotted line in Fig. 5. The heavy lines 
 A and C represent platinum plates which are connected with a 
 dynamo, or other apparatus for generating electricity. 
 
 * Platinum electrodes are commonly used in experiments of this sort, owing 
 to their general resistance to corrosion. In this particular case, however, 
 platinum would not remain unattacked and carbon is a more suitable electrode 
 material. 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 
 
 73 
 
 Electrical generators cause a separation of positive from negative elec- 
 tricity by mechanical agency. The positive electricity is accumulated in 
 one part of the apparatus, and the negative electricity in another part. 
 Between these two regions there exists a difference in potential, or electrical 
 pressure, corresponding to the attractive force between positive and 
 negative electricity. If regions of high and low potential are joined by a 
 "metallic conductor, an electric current flows until equalization of the 
 potential is effected. The generator maintains a constant difference of 
 potential, and therefore determines a continuous current. 
 
 For immediate purposes we will assume that the positive pole 
 or electrode, called the anode, is charged with a definite amount of 
 electricity, conveniently measurable in terms of the unit quantity 
 
 Anode 
 
 ++++ 
 
 + 
 
 ? 
 
 
 
 H 
 
 H 
 
 
 
 
 
 Cl 
 
 
 Cl 
 
 
 
 
 ~ 
 
 
 H 
 
 H 
 
 H 
 
 
 
 
 
 Cl 
 
 Cl 
 
 Cl 
 
 
 
 
 
 
 H 
 
 H 
 
 SS 
 
 
 
 
 "* 
 
 Cl 
 
 ci 
 
 ci 
 
 Cl 
 
 
 
 
 + 
 
 ^. 
 
 + 
 
 -)- 
 
 
 
 
 H 
 
 H 
 
 H 
 
 H 
 
 
 
 
 ci 
 
 Cl 
 
 Cl 
 
 ci 
 
 
 Cathode 
 C 
 
 Fig. 5. 
 
 associated with one hydrogen ion, and that the negative pole 
 or cathode is charged with an equal amount of negative 
 electricity. 
 
 The small plus and minus signs arranged along the anode and 
 cathode, respectively, indicate the magnitude of these charges. 
 Now, the relatively large quantity of positive electricity at the 
 anode will exert an attractive force on the nearest negative ion 
 called anion, in this connection and a repulsive force on its 
 positive fellow, sufficient in effect to overcome their mutual 
 attraction. Simultaneously, negative electricity at the cathode 
 attracts the nearest positive ion cation and repels the 
 accompanying negative ion. All the particles are supposed to 
 be moving about in the solvent medium; consequently, the 
 positive ion and negative ion which were repelled towards the 
 interior of the liquid will sooner or later come close enough 
 together so that their reciprocal attraction will determine close 
 
74 CHEMICAL THEORY. 
 
 partnership between them. The negative ion which was attracted 
 by the anode will lose its charge when it reaches this locality, 
 owing to neutralization of the same by an equal amount of posi- 
 tive electricity. After the loss of its negative charge, this chlorine 
 atom possesses the ordinary chemical properties of atomic chlo- 
 rine. According to conditions of concentration, temperature, 
 etc., it may unite with another chlorine atom to form a molecule 
 of gaseous chlorine, which will be liberated, or it may react with 
 water to form oxygen, which will be liberated in the molecular 
 condition: Cl + H 2 O = 2HC1 + O, and O + O = O 2 .* The posi- 
 tive ion which was attracted to the cathode, will lose its charge 
 by neutralization, ultimately appearing as molecular hydrogen. 
 
 Conditions subsequent to the process just described, are 
 represented in that part of the figure immediately above the 
 lower dotted line. There are now three undecomposed molecules 
 of hydrochloric acid, in the ionic form. Symbols printed in bold 
 type indicate the elements in their ordinary atomic condition. 
 Plus and minus signs arranged side by side are to be regarded as 
 extinguishing one another. We see that the production of one 
 atom of hydrogen and one atom of chlorine is identified with the 
 loss of one negative unit of electricity from the cathode and one 
 positive unit from the anode. The continuation of this process 
 is outlined by upward steps in the figure. Ultimately, all four 
 molecules of acid are decomposed at the expense of four units of 
 positive electricity and four units of negative electricity. 
 Instead of the eight units originally present on the anode and 
 the eight originally present on the cathode, four units are 
 finally left at each place. This evidently corresponds to the 
 direct passage of four positive units from the anode to the 
 cathode. In practice, the generating apparatus supplies these 
 amounts of electricity as fast as they are used, i.e., maintains a 
 constant difference of potential, and a measuring instrument 
 inserted anywhere within the circuit shows the quantity of elec- 
 tricity passing. 
 
 By determining the quantity of electricity which flows through 
 the circuit in a definite time interval, as well as the actual 
 weight of hydrogen liberated during the same time, we are 
 
 * Concentrated solutions yield C1 2 for the most part; dilute solutions 
 yield O 2 . 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 75 
 
 in a position to ascertain how much electricity has been carried 
 by an ionic quantity of hydrogen, or by an ionic quantity of 
 chlorine. (The term, ionic quantity, will be understood by 
 comparing the analogous terms, atomic quantity, and molecular 
 quantity.) Thus, experiment shows that one gram ion of hydrogen 
 (formula weight of the ion expressed in grams), or one gram of 
 hydrogen, is liberated every time 96,500 coulombs* of electricity 
 traverse the circuit. It is clear, in view of the above discussion, 
 that the apparent transfer of 96,500 coulombs from A to C (Fig. 5) 
 was brought about by one gram ion of hydrogen (which carried 
 this amount of positive electricity to C), in common with one 
 gram ion of chlorine (which removed this amount of positive 
 electricity from A, in that it carried an equal amount of 
 negative electricity to this region). Hence, we conclude that 
 one gram ion of hydrogen (1 g.) carries a positive charge of 96,500- 
 coulombs, and one gram ion of chlorine (36.45 g.) carries a 
 negative charge equal in amount. 
 
 We have stated (on page 71) as an essential precept of the 
 Electrolytic Dissociation Theory, that the ordinary chemical 
 valence of an atom or group indicates the number of unit elec- 
 trical charges it will carry as an ion. Referring to the table on 
 page 71, we have only to substitute 96,500 coulombs for each 
 single plus or minus to ascertain the magnitude of the charge 
 carried by any one of the ions enumerated. It is equally simple 
 to determine what quantity of a given ion will be liberated during 
 electrolysis. For, obviously, the passage of 96,590 coulombs 
 through the medium in which it is contained, will liberate one 
 gram ion, if it carries a unit charge, but only half as much, if it 
 carries a double charge. To illustrate: The passage of 96,500 
 coulombs through a dilute solution of sodium sulphate will free 
 one gram ion of sodium (or about 23 g.) at the cathode, and one- 
 half of a gram ion of SO* (or about 48 g.) at the anode. In thia 
 case there will be subsequent reactions at both electrodes 
 (cf. p. 74), since neither Na nor S0 are stable in the presence 
 of water. These reactions are as follows: 
 
 (1) 2Na + 2H 2 O = 2NaOH + H 2 , and (2) 2SO 4 
 
 (46) (2) (192) 
 
 + 2H 2 O = 2H 2 SO 4 + O 2 . 
 
 *. (32) 
 
 * The electrical unit of quantity. 
 
76 CHEMICAL THEORY. 
 
 According to these equations, we shall have I g. of hydrogen 
 as a final product in place of 23 g. of sodium, and 8 g. of oxygen 
 in place of 48 g. of SO 4 (cf. Introduction, page 35 et. seq). 
 
 We observe that 1 g. of hydrogen is produced when 96,500 
 coulombs pass through a solution of sodium sulphate, or a 
 solution of hydrochloric acid. If the electrolysis results in hydro- 
 gen at all, irrespective of the nature of the solution electrolyzed, 
 liberation of one gram ion will correspond to the passage of 
 96,500 coulombs. Moreover, this result is not influenced by the 
 temperature of the solution, its concentration, the specific char- 
 acter of the current, etc. 
 
 The quantitative relations connecting the passage of elec- 
 tricity through an electrolyte with the decomposition products 
 at the electrodes, which we have pointed out pursuant to primary 
 assumptions of the Electrolytic Dissociation Theory, were clearly 
 enunciated by Faraday on experimental grounds a half century 
 before this theory was proposed. Obviously, these facts were 
 of fundamental importance in shaping the theory. Faraday's 
 Law may be stated as follows: 
 
 (a) The amount of every substance resulting from decomposition 
 by electrolysis, is directly proportional to the quantity of electricity 
 which has passed through the electrolytic conductor. 
 
 (b) Chemically equivalent amounts of different substances 
 result from all decomposition which is effected by the same quantity 
 of electricity. 
 
 In bringing about chemical decomposition by electrical agency, 
 many specific details, such as current strength, voltage, tem- 
 perature, form of cell, concentration and nature of conducting 
 mixture, must be suitably regulated to secure efficient results, or 
 indeed, any results at all. But, once the process is operative 
 under any conditions, rigid adherence to the above principles 
 obtains. 
 
 Problem: // the passage of a certain quantity of electricity 
 through a solution of copper sulphate deposits 0.3 g. copper, how 
 much silver will the same quantity of electricity deposit from a 
 solution of silver nitrate? 
 
 One atomic quantity of copper is chemically equivalent to two 
 atomic quantities of silver, as is apparent on comparison of the 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 77 
 
 formulas CuSO 4 and AgNO 3 with the formulas H 2 SO 4 and HNO 3 . 
 That is, Cu = 2H, Ag = H, and, consequently, Cu = 2Ag. 
 
 (63.6) (2x107.9) 
 
 Applying Faraday's Law (b): 2 X 107.9 parts by weight of 
 silver will be deposited by the same quantity of electricity which 
 deposits 63.6 parts by weight of copper. A simple proportion 
 shows how much silver corresponds to 0.3 g. copper: 
 
 63.6 : 215.8 : : 0.3 : x. 
 
 x =1.02 (grams of silver deposited). 
 
 We have seen that the Electrolytic Dissociation Theory con- 
 sistently accounts for tho^e associated phenomena peculiar to 
 aqueous solutions of electrolytes, which we cited first of all on the 
 opening page of this chapter, namely, their conduction of the 
 galvanic current, abnormal osmotic pressure, etc. The absence 
 of such phenomena in connection with non-aqueous solutions 
 of electrolytes and aqueous solutions of non-electrolytes (cf. 
 general discussion, page 69) is explained by assuming that no 
 electrolytic dissociation takes place in these cases. 
 
 The chief value of the theory to the student of Chemistry lies 
 in its power to throw light on the nature of chemical processes 
 which take place between solutions of acids, bases, and salts. 
 We have already observed that such reactions possess significant 
 features (page 69), and we may infer, with all propriety, that the 
 ions resulting from electrolytic dissociation are actively con- 
 cerned in producing these results. 
 
 Before proceeding with a detailed description of chemical 
 action, in this connection, it is essential that we obtain some 
 general idea relative to the actual proportion of acid, base, or 
 salt molecules, which are dissociated when the given substance 
 is dissolved in varying amounts of water. First, we shall con- 
 sider how such information may be deduced from experimental 
 evidence. 
 
 For this purpose, the electrical properties of the solution may 
 be investigated, or determination of the osmotic pressure, 
 freezing-point depression, etc., may be chosen. A brief discus- 
 sion of the relation between the freezing-point depression in an 
 aqueous solution of common salt (containing 1 g. mol. NaCl per 
 liter-) and the number of dissolved particles, was presented at 
 
78 CHEMICAL THEORY. 
 
 the close of Chapter VI, by way of introduction to the Electro- 
 lytic Dissociation Theory. It seems expedient at this point, to 
 show by enlarging upon the earlier discussion how the proportion 
 of dissociated molecules, or degree of dissociation may be calcu- 
 lated from freezing-point measurements in any ordinary case. 
 
 At the outset, we assume that the freezing-point depression is 
 proportional to the number of particles of dissolved material, 
 irrespective of their nature, i.e., whether ions or molecules.* 
 
 Suppose half the molecules of a given electrolyte are disso- 
 ciated in an aqueous solution of a certain concentration, and that 
 
 each dissociating molecule furnishes 
 three ions. Then, if four molecules 
 
 O O 
 
 00 00 
 
 O O O O 
 
 were originally introduced, eight par- 
 ticles would result, two whole mole- 
 cules and six ions. In case no disso- 
 ciation had taken place, four molecules 
 would be present in the solution. The 
 relation between the freezing-point 
 depression in these two instances would 
 
 5 be 8 : 4, following the numerical distri- 
 
 Fi g . 6 bution of particles, as shown graphically 
 
 in Fig. 6, a and b. The number of 
 
 particles present in the solution (a) for every original 
 molecule introduced, could be determined by dividing the 
 actual freezing-point depression measured in this solution, by 
 the normal depression which would correspond to the same quan- 
 tity of the dissolved substance, if it did not dissociate. Thus, 
 the depression in (a) divided by the depression in (b) would equal 
 2, indicating that there are twice as many particles in (a) as 
 molecules originally taken. We should note that the actual 
 depression refers to that obtained by experiment, while the 
 normal depression must be calculated by applying the formula 
 
 M = - (cf. Chapter III, pages 53 and 4), in which M, K, w, 
 LW 
 
 and W, are known. The small letter (i) was introduced by 
 van't Hoff (to whom the theory connecting the various proper- 
 
 * According to Raoult's Law, any kind of molecule is equally efficient in 
 lowering the freezing point of a solvent. We attribute the same efficiency to 
 any ion, an assumption which is fully justified by agreement between results 
 resting on this basis, with others furnished by an entirely independent method. 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 79 
 
 ties of dilute solutions is, mainly due) as a coefficient expressing 
 the numerical relation between an actual depression (boiling- 
 point elevation, osmotic pressure, etc.) and the corresponding 
 normal value. 
 
 It is thus clear that the determination of (i) may be realized 
 experimentally from freezing-point measurements, etc., without 
 previous knowledge of the degree of dissociation. 
 
 Now, we may easily obtain an expression for the degree of 
 dissociation, in terms of (i) and one other fundamental quantity, 
 known in any specific instance, namely, the number of ions 
 resulting from one dissociating molecule, which enables us to 
 calculate the degree of dissociation at once. For: 
 
 Let (m) represent the degree of dissociation, and (n) the' 
 number of ions formed when one molecule dissociates. 
 
 Then, from a unit number of molecules originally taken (m) 
 are dissociated and (1 m ) are undissociated. Iii place of 
 each molecule which dissociates, there are (n) ions, making a 
 total of (nm) ions in the solution. Thus, the solution contains 
 (1 m) undissociated molecules and (nm) ions, or (1 m + 
 nm) particles, for every unit number of molecules originally 
 taken. Placing this total equal to (i) which has the same signifi- 
 cance, and solving for (m) we obtain: 
 
 A glance at the diagram (Fig. 6) will serve to fix this relation 
 clearly in mind. In the case represented, i = 2, as previously 
 noted, and n = 3. Whence, m = 0.50, corresponding to our 
 original assumption that half of the molecules were dissociated. 
 
 A far more accurate and convenient method for determining 
 the degree of dissociation is based on (electrical) conductivity 
 measurements. During our discussion of electrolysis, we 
 observed that electricity is carried through the solution by the 
 ions. The ability of a solution to conduct the current, i.e., to 
 effect an apparent transfer of positive electricity from the 
 anode to the cathode, must depend on the number of ions which 
 carry the electricity (since each carries a fixed amount), and their 
 industry in performing the task. We may define the specific 
 conducting power of any solution by measuring the quantity of 
 
80 CHEMICAL THEORY. 
 
 electricity which passes in a unit time between ideal electrodes 
 situated at opposite sides of a unit cube containing the solution 
 at 0C., when a unit electrical force is applied. If the solution 
 in question is further diluted, a lesser amount of dissolved sub- 
 stance is included in the unit volume than before. Consequently, 
 the electricity which would be carried from one electrode to 
 the other by all the ions resulting from the amount of substance 
 previously contained in one cubic centimeter, is equal to the 
 sum of that carried by the ions in every unit volume of the 
 diluted solution. In other words, the total conductivity due 
 to all the ions, is equal to the specific conductivity multiplied by 
 the number of cubic centimeters in which the given amount of 
 substance is dissolved. We commonly refer such measurements 
 to one gram molecule of dissolved substance, and use the term, 
 molecular conductivity, to define the product of specific con- 
 ductivity into the number of cubic centimeters of solution con- 
 taining one gram molecule. 
 
 Now, the rate at which the ions move* under the influence of 
 a given electrical force is known to be practically independent 
 of the concentration, in the case of dilute solutions. Therefore, 
 the respective quantities of electricity which will pass through 
 two unequally concentrated solutions of the same electrolyte 
 at the same temperature f in a definite time interval under the 
 influence of the same electrical force, will be proportional to the 
 other conductivity factor, i.e., the numbers of ions which carry 
 the electricity in each respective solution. Thus, we see that 
 separate determinations of the molecular conductivity at a num- 
 ber of different concentrations serve to show the relative extent 
 to which the dissolved substance is dissociated when dissolved 
 in these different amounts of water or, what amounts to the 
 same thing, the relative numbers of dissociation products, i.e., 
 ions. 
 
 * Substances giving colored ions are used in demonstrating the move- 
 ment of ions visually. Their rate of motion is uniformly slow, but varies 
 considerably with the nature of the ion. Velocities of only a few centimeters 
 per hour are commonly associated with the ordinary ions, even when driven 
 by very considerable electrical forces. The solvent medium evidently offers 
 enormous resistance to the motion of these extremely minute particles. 
 
 t Temperature elevation causes an increase in conductivity by reason of 
 the resulting increase in the velocity of the ions. 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 
 
 81 
 
 To pass from this relative information, to an actual knowledge 
 of the degree of dissociation at any dilution, it is necessary that 
 the molecular conductivity corresponding to complete dissocia- 
 tion be ascertained. It has been found that the molecular con- 
 ductivity invariably increases with the dilution up to a certain 
 point, which may be called infinite dilution, when it remains 
 constant, notwithstanding further dilution. Evidently, the 
 maximum of conductivity has then been attained, owing to the 
 presence of the greatest possible number of ions. We are, 
 therefore, at liberty to assume that the dissolved substance is 
 completely dissociated. 
 
 To obtain the degree of dissociation at any lesser dilution, we 
 divide the molecular conductivity, at this dilution, by the molecular 
 conductivity at infinite dilution. The logic of this process is indi- 
 cated below: 
 
 Mol. Cond. at dilution A 
 
 No. of ions at dilution A 
 
 Mol. Cond. at infinite dilution Greatest poss. no. ions 
 No. of diss'd mols. at dilution A 
 
 Total no. of mols. 
 = Degree of Dissociation at dilution A. 
 
 Conductivity data (taken from Kohlrausch's tables), referring 
 to aqueous solutions of sodium chloride at 18 C., follow: 
 
 Volume in Liters 
 Containing One 
 Gram Mol. NaCl. 
 
 Molecular Conduc- 
 tivity. 
 
 Degree of Dissoci- 
 ation. 
 
 1 
 5 
 10 
 100 
 1000 * 
 
 5000 
 
 10,000 
 Infinite volume 
 
 74.35 
 87.73 
 92.02 
 101.95 
 106.49 
 
 107.82 
 
 108.10 
 108. 99 (calculated) 
 
 74 35 681 
 
 108. 99~ ' 68 
 87-73 
 
 108.99 ' 
 92 2 344 
 
 108.99 
 101 95 035 
 
 108.99 UJ 
 106 ' 49 007" 
 
 108.99 ' 
 
 107 - 82 ooo 
 
 108.99 8 
 Dissociation com- 
 plete. 
 
82 CHEMICAL THEORY. 
 
 It is apparent from these conductivity data that one gram 
 molecule of sodium chloride is completely dissociated into ions 
 when dissolved in 10,000 liters or more of water. Moreover, we 
 see that any ordinary aqueous solution of sodium chloride such 
 as might be used in the laboratory, contains a larger percentage 
 of dissociated, than undissociated molecules. 
 
 Much experimental work has been undertaken to determine 
 whether these different methods for obtaining the degree of 
 dissociation give concordant results, as should be the case if our 
 theory is reliable. Satisfactory agreement between correspond- 
 ing results has always attended such comparative study. 'The 
 superiority of the conductivity method over the freezing point, 
 boiling point, vapor pressure, or osmotic pressure methods, 
 both in point of facility in experimentation and accuracy of 
 results, is responsible for its general adoption in pursuing the 
 study of electrolytic dissociation phenomena. 
 
 We may now proceed to inquire into the characteristic dis- 
 sociation features of the three different chemical varieties of 
 electrolytes, namely, acids, bases, and salts. The degree of 
 dissociation of each invariably increases with the dilution 
 water as the dissociating agent, operates more effectively as its 
 own concentration increases. However, equal molecular quan- 
 tities of different substances are by no means dissociated to the 
 same extent when dissolved in the same quantity of water. 
 Differences in this respect serve as the basis for a detailed 
 theoretical explanation of chemical interaction between aqueous 
 solutions of electrolytes. The very general outline of the com- 
 parative dissociation of different electrolytes, given in the next 
 three paragraphs, will enable us to draw some important con- 
 clusions regarding their tendency to interaction. 
 
 A wide range of variation is observed on comparing the degree 
 of dissociation for different acids in solutions of the same molec- 
 ular concentration. The comparative dissociation of some 
 common acids when dissolved in water to the extent of one- 
 tenth gram molecule per liter is shown by the following very 
 
 approximate percentage numbers: HN0 3 , HC1, HBr, HI 90 
 
 (90 per cent of all the dissolved molecules are dissociated); 
 
 H 2 S0 4 60; H.C 2 H 3 2 1.5; H 2 C0 3 less than 0.2; H 2 S 
 
 less than 0.1 ; H 3 B0 3 0.01. Whatever the acid, its aqueous 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 83 
 
 solution must contain hydrogen ions. We attribute such prop- 
 erties as are common to all aqueous acid solutions, i.e., their 
 sour or " acid" taste, action on litmus, and other general chemical 
 reactions, to these hydrogen ions. In proportion as the solution 
 contains hydrogen ions, these properties will be more marked. 
 Thus, it is logical to say that the strength of the acid depends 
 upon the concentration of hydrogen ions in its solution. From 
 a comparative standpoint, hydrochloric acid is stronger than 
 sulphuric acid, because it furnishes a greater concentration of 
 hydrogen ions when dissolved in water; acetic ac^disweak, while 
 boric acid is extremely weak. 
 
 Similar diversity characterizes the dissociation of bases. The 
 aqueous solution of a base must contain hydroxyl ions. The com- 
 mon strong bases (those yielding hydroxyl ions in quantity when 
 dissolved in water) with their approximate dissociation values, 
 expressed as for acids in the preceding paragraph, are: NaOH, 
 
 KOH 90; Ba(OH) 2 75; and Ca(OH) 2 very highly 
 
 dissociated in a solution containing about one-fiftieth of a gram 
 molecule per liter, which solution represents about the limit of 
 its solubility at ordinary temperature. A large number of weak 
 bases are known, most of them rather insoluble in water. Of 
 these, one is very soluble, and quite indispensable as a labora- 
 tory reagent NH 4 OH 1.5. Others are: Cu(OH) 2 , Cd(OH) 2 , 
 
 Zn(OH) 2 , Mn(OH) 2 , Fe(OH) 2 , Co(OH) 2 , Ni(OH) 2 , Pb(OH) 2 , 
 Sn(OH) 2 , Bi(OH) 3 , Sb(OH) 3 , Fe(OH) 3 , A1(OH) 3 , Cr(OH) 3 , all 
 insoluble, and weakly basic; the last four considerably weaker 
 than those preceding. 
 
 * These very sparingly soluble substances, although commonly re- 
 garded as bases, give hydrogen ions, as well as hydroxyl ions, both in 
 minute concentrations. Thus, they possess weakly basic and acidic prop- 
 erties in common and are called amphoteric electrolytes. From the acid 
 standpoint, we may write their formulas: H 2 ZnO 2 , H 2 Pb0 2 , H 2 SnO a 
 and H 3 A1O 8 , and those of their sodium salts, which are all soluble 
 (i.e., the acids dissolve in sodium hydroxide): Na 2 Zn0 2 (sodium 
 zincate), Na 2 PbO 2 (sodium plumbite), Na 2 SnO 2 (sodium stannite) and 
 Na 3 AlO 3 (sodium aluminate); NaAlO 2 , derived from H 3 A1O 3 - H 2 O, or 
 HA1O 2 , is also known. Chromium hydroxide also dissolves in (cold) 
 sodium hydroxide, giving a salt of the formula, NaCrO 2 . 
 
84 CHEMICAL THEORY. 
 
 In nearly every instance, neutral salts are dissociated to an 
 extent approximating that of strong acids or bases. While a 
 somewhat narrower classification of dissociation values accord- 
 ing to the formula types of salts may be offered, it is of greatest 
 importance to note that seldom less than 50 per cent of a salt is 
 dissociated in an aqueous solution containing 0.1 gram mole- 
 cule per liter. Since some salts are very insoluble, and many 
 relatively so, it is clear that we are not always able to obtain a 
 highly concentrated solution of ions by placing a large quantity 
 of salt in a small volume of water. Neither the positive hydrogen 
 ions, which characterize acid solutions, nor the negative hydroxyl 
 ions, which characterize basic solutions, can be present in neutral 
 salt solutions. 
 
 Pure water is dissociated to a very slight extent. Calcula- 
 tions based on conductivity results, have shown that it takes 
 several hundred million gram molecules of water to furnish one 
 gram ion of hydrogen and one gram ion of hydroxyl its disso- 
 ciation products. 
 
 The process which we have called electrolytic dissociation or 
 ionization stops (in common with other dissociation phenom- 
 ena) when all the changing material has reached a final state of 
 adjustment, according to the dictum of certain ruling conditions. 
 We made use of the term equilibrium in the introductory chapter 
 (page 30), to describe this general condition, and alluded to the 
 conventional use of reversed arrows in an equation to indicate 
 the simultaneous presence of all the reacting constituents and 
 the possibility of displacing the equilibrium in either direction. 
 
 The significance of the following expression for the electrolytic 
 dissociation of hydrochloric acid should, then, be clear: 
 
 HC1^H + C1. (1) 
 
 We have seen that the relative amounts of these different 
 substances are primarily dependent on the dilution; that, the 
 greater the dilution, the more ions produced; and that, for any 
 given dilution, the actual amounts of all three are defined. 
 
 Experience teaches us, furthermore, that this condition of equili- 
 brium is instantly established when the material is dissolved in water. 
 
 Bearing these facts in mind and recalling what has been said 
 on the previous page about the relative dissociation of different 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 85 
 
 electrolytes, let us proceed to consider the effect of mixing certain 
 of them in aqueous solution. 
 
 Suppose one-tenth of a gram molecule of hydrochloric acid is 
 dissolved in a half liter of water and mixed with a solution pre- 
 pared by dissolving one-tenth of a gram molecule of sodium 
 hydroxide in a half liter of water. We now have one-tenth of a 
 gram molecule each of hydrochloric acid and sodium hydroxide 
 in a liter of water unless some chemical reaction has taken place. 
 Equation (1) above shows the three substances present 
 in an aqueous solution of hydrochloric acid; equation (2) below 
 supplies similar information relative to the solution of sodium 
 hydroxide; while we are told on pages 82 and 83 that both 
 (strong) acid and (strong) base are some 90 per cent dissoci- 
 ated in an aqueous solution of this concentration. 
 
 NaOH <=> Na + OH. (2) 
 
 In the light of our present information, should any change 
 
 have occurred on mixing these two solutions? Most assuredly, 
 
 + + 
 
 since two other pairs of ions (Na + Cl) and (H + OH) must 
 attain a proper state of adjustment with the undissociated mole- 
 cules corresponding to their union, i.e., the molecules which 
 would form them, by electrolytic dissociation, on being brought 
 into an aqueous medium. 
 
 Therefore, we write the additional equations (3) and (4): 
 
 Na + Cl <=> NaCl. (3) 
 
 H + OH =i H 2 O. (4) 
 
 Now, a dilute solution of sodium chloride consists mainly of 
 ions. One-tenth of a gram molecule of sodium chloride in one 
 liter of water is about 84 per cent dissociated (cf., page 81) ; hence, 
 there can be no extensive combination of sodium ions with 
 chloride ions in this solution. Reaction (3) will proceed only 
 to a certain slight extent in the right-hand direction. 
 
 On the other hand, water is scarcely dissociated at all, and we 
 
 must expect an almost complete disappearance of hydrogen and 
 
 hydroxyl ions, resulting in the production of undissociated water. 
 
 - Reaction (4) will proceed liberally in the right-hand direction. 
 
 This extensive removal of hydrogen and hydroxyl ions has 
 
86 CHEMICAL THEORY. 
 
 destroyed the balance between undissociated acid and its ions (1), 
 as well as that between undissociated base and its ions (2). Con- 
 sequently, some of the ten per cent more or less of undisso- 
 ciated acid, which was in the solution, will dissociate until 
 readjustment is secured, and the undissociated base will behave in 
 the same way. Hydrogen and hydroxyl ions from this secondary 
 dissociation will combine, as before, to form water, necessitating 
 further dissociation of acid and base. Progressive action of this 
 sort ensues, until practically all of the hydrogen and hydroxyl 
 primarily contained in the acid and base, respectively, have been 
 transformed into undissociated water. Thus, we may use the 
 following equation to express the essential change, neglecting the 
 undissociated acid and base: 
 
 H + Cl + Na + OH = H 2 O + Cl + Na, or, H + OH = H 2 O. 
 
 If the solution is evaporated, the sodium and chloride ions 
 unite to form undissociated sodium chloride. 
 
 The student has, without doubt, recognized the above process 
 as that of neutralization. It should be quite clear that whatever 
 the acid or base used in neutralizing one another, provided both 
 are strong largely dissociated the essential feature of the 
 process is identical, i.e., the formation of water. This theoretical 
 conclusion is substantiated by the fact that, in separate cases of 
 neutralization, the thermal change during the reaction is always 
 the same, if equivalent amounts of acid are used (to guarantee 
 the production of identical amounts of water in all cases). 
 
 No difficulty will be met in adapting the above reasoning to 
 other reactions, in which ions from highly dissociated substances, 
 by their combination, may form much less dissociated substances. 
 Such reactions are generally less complete than the neutraliza- 
 tion process, since the products are much more dissociated than 
 water. Thus, a solution of any common strong acid, such as 
 hydrochloric acid will interact with a solution of sodium acetate 
 (or any salt of a weak acid) to form a certain amount of acetic 
 acid (or the corresponding acid). The essential feature of such 
 a reaction is the union of ions, as follows: 
 
 H + Cl + Na + C 2 H 3 O 2 = H . C 2 H 3 O 2 + Cl + Na, 
 or, H + C 2 H 3 O 2 = H . C 2 H 3 2 . 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 87 
 
 In the same way, a strong base may be used to free a weaker 
 base from its salts: 
 
 Na + OH + NH 4 + NO 3 = NH 4 OH + Na + NO 3 , 
 or, NH 4 + OH = NH 4 OH. 
 
 Of particular interest, is the reaction between solutions of two 
 different salts. We note, here, that there is no great difference 
 in the degree of dissociation, pertaining to different salts, but 
 that there may be great difference in the solubilities of the salts. 
 
 Consider the salt silver chloride which is very insoluble in water. 
 When in contact with water, a certain (very limited) amount 
 dissolves. At any given temperature, the solution must contain 
 a perfectly definite amount, if it is kept in contact with the solid, 
 i.e., if the solution is saturated at the given temperature. Now, 
 another definite relation must exist between the molecules of 
 dissolved silver chloride and the ions which it has formed imme- 
 diately on attaining the dissolved condition. There is, then, a 
 final state of adjustment requiring the presence in the solution 
 
 of a fixed amount of undissociated AgCl maintaining a fixed con- 
 
 + 
 centration of Ag and Cl ions. 
 
 Suppose, in some way, enough silver and chloride ions were 
 brought into a liter of water to represent one-tenth of a gram 
 molecule of silver chloride. Then, if the salt dissociated to about 
 the same extent as sodium chloride, some ten per cent of this total 
 quantity of ions would unite to form undissociated AgCl, which 
 would have to remain in solution to keep the remaining ions 
 inactive. This would, however, be an amount most overwhelm- 
 ingly in excess of that which can actually dissolve; hence, it would 
 almost completely precipitate, and the ions would continue to 
 furnish undissociated material, likewise precipitating, until their 
 concentrations became reduced to the values normally consistent 
 with the final concentration of dissolved silver chloride molecules. 
 
 Now, whenever solutions of a soluble silver salt and a soluble 
 chloride are mixed, the general condition just considered is 
 realized. That is, appreciable concentrations of silver ions and 
 chloride ions are brought within range of one another. Precipi- 
 tation of silver chloride will therefore result until practically all 
 
88 CHEMICAL THEORY. 
 
 the silver and chlorine in the initial substances is deposited in 
 this form. 
 
 Such characteristic formation of insoluble products is of service 
 in identifying the materials which participate in the change. We 
 must, however, fully appreciate the limitations of any one pre- 
 cipitation test, it reveals the identity of only part of each 
 reacting substance in the above case, silver from the dissolved 
 silver salt and chlorine from the dissolved chloride. It is, there- 
 fore, most consistent to refer the whole process to the Electrolytic 
 Dissociation Theory by defining each test in terms of its critical 
 factors, the ions. Thus, the silver ion is a test for the chloride ion : 
 
 Ag + NO 3 + Na + Cl = AgCl + NO 3 + Na, 
 2Ag + S0 4 + Zn + 2C1 = 2AgCl + SO 4 + Zn, etc. 
 And, the barium ion is a test for the sulphate ion: 
 
 Ba + 2C1 + 2Na + S0 4 = BaSO 4 + 2C1 + 2Na, 
 
 Ba + 2N0 3 + Mg + SO 4 = BaSO 4 + 2NO 3 + Mg, etc. 
 
 If we mix solutions of two soluble salts, the ions of which by 
 altered recombination form two other soluble salts, there will, of 
 course, be no precipitation. On continued evaporation of the 
 solution, that salt, of the four, which first reaches saturation, 
 will be the first to deposit. There is, in general, no appreciable 
 thermal change on mixing different dilute salt solutions, since no 
 extensive formation of undissociated molecules results. A solu- 
 tion containing one-fifth of a gram molecule of sodium nitrate 
 per liter when mixed with an equal volume of a solution contain- 
 ing one-fifth of a gram molecule of potassium chloride per liter, 
 contains the same material, disposed in the same manner, as a 
 mixture made from one-fifth of a gram molecule of sodium chloride 
 and one-fifth of a gram molecule of potassium nitrate in the same 
 volume. All four salts will be present to about the same slight 
 extent in the undissociated condition, and about 80 per cent of 
 the total material will be in the form of ions. 
 
 An adequate perception of the varied possibilities of chemical 
 change due to " crosswise " combination between two pairs of 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 89 
 
 ions, should follow a careful reading of the last few pages. The 
 quantitative aspect of such change will be made the subject for 
 some additional discussion at the close of the chapter on Mass 
 Action. Before proceeding to this special subject, however, some 
 further remarks relative to the general bearing of ion formation 
 on chemical change, will be introduced: 
 
 No great amount of experience in the chemical laboratory is 
 required to teach us that the precipitated compounds of certain 
 metals are more or less soluble in ammonia. To the beginner, 
 silver and copper are most prominent in this connection. While 
 a detailed consideration of the solution process in such cases is 
 beyond the scope of this text, it may be stated, in general terms, 
 that the addition of ammonia to such a body, results in the 
 formation of a soluble compound yielding complex cations 
 containing ammonia, in place of the simple metal cations. Thus, 
 
 silver chloride dissolves in ammonia, and the resulting solution 
 
 + + 
 
 contains, Ag.2NH 3 ions and Cl ions the original Ag ions have 
 combined with NH 3 to form complex silver-ammonia particles, 
 
 each carrying the single positive charge originally carried by the 
 
 + + 
 
 silver alone. The complex copper-ammonia cation, Cu.4NH 3 , is 
 deep blue in color, hence the use of ammonia in testing for the 
 presence of copper. 
 
 The solvent effect of solutions of the alkali cyanides (KCN, 
 or NaCN) on many metallic compounds, is likewise due to the 
 formation of complex ions. In such cases we have complex 
 anions instead of complex cations. Thus, silver cyanide is 
 
 soluble in a solution of potassium cyanide, the CN ions having 
 
 + 
 
 united with AgCN to form Ag(CN) 2 ions, which, with K ions, 
 constitute the dissociation products of the soluble salt, KAg(CN)2- 
 The individuality of any complex ion is reflected in its chemical 
 behavior. Its reactions are quite different from those of the ion 
 or ions from which it was generated. For example, solutions 
 containing the complex silver-ammonia ion, mentioned above, 
 do not precipitate silver chloride on the addition of chloride ions, 
 i.e., an ammoniacal solution of silver nitrate fails to precipitate 
 silver chloride when mixed with a solution of sodium chloride. 
 Usually, however, such an ion is very unstable, tending to pass 
 
90 CHEMICAL THEORY. 
 
 into the simpler state, unless conditions most favorable to its 
 non-alteration are maintained. Invariably, the solution con- 
 taining any complex ion also contains a very inconsiderable 
 complement of simple ions, which have resulted from its dis- 
 sociation. Hence, the introduction of another ion, which may 
 give a sufficiently undissociated in effect, sufficiently insoluble 
 compound with the simple ion to actually reduce its normal 
 concentration in the solution, will cause the complex ion to 
 supply this deficiency which becomes progressive by breaking 
 up, and we shall have, as a final result, the characteristic reaction 
 of the simple ion. Thus, hydrogen sulphide precipitates the 
 
 copper from an ammoniacal solution of any copper salt, which must 
 
 + + 
 
 contain Cu.4NH 3 ions, to the almost complete exclusion of 
 + + 
 Cu ions, just as it would from an acid solution (which could con- 
 
 + + 
 
 tain only Cu ions), because the compound copper sulphide 
 + + 
 (Cu + S = CuS) is extremely insoluble, maintaining a lesser 
 
 + + 
 concentration of Cu ions than does the complex ion itself. 
 
 There is a wide difference between a salt which gives a com- 
 plex ion when dissolved in water, and a double salt (cf . Intro- 
 duction, page 26). The latter dissolves in water to give the 
 simple ions of its constituent salts. By way of illustration, 
 contrast : 
 
 KAg (CN) 2 ^ K + Ag(CN) 2 , with: 
 CsBr.2PbBr 2 <= Cs + Br + 2Pb + 4Br. 
 
 We have made early note of that general type of reaction in 
 which one elementary kind of matter drives another kind out 
 of its state of combination with another or other elements, 
 usurping its place (cf. Introduction, page 31). Reactions of this 
 sort, or replacements, as we have named them, may be very 
 easily brought into harmony with the general scheme of ionic 
 disposition and transfer of material, which we have been con- 
 sidering. Let us first turn to the replacement of one positive 
 element by another in a reaction such as the following: 
 
 Zn + 2AgNO 3 = 2Ag + Zn(NO 3 ) 2 . 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 91 
 
 Study of many reactions like the above has led to an empirical 
 arrangement of the positive elements, i.e., the metals and hydro- 
 gen, in an order representing their successive ability to replace 
 one another. Each metal in the accompanying list will replace 
 those metals which follow. The metals preceding hydrogen will 
 replace it in an acid they dissolve in acid with evolution of 
 hydrogen.* 
 
 Mg Zn Fe Sn Pb H Cu Hg Ag Au 
 
 Writing the reaction between zinc and silver nitrate in the 
 ionic form: 
 
 Zn + 2Ag + 2NO 3 = 2Ag + Zn + 2NO 3 
 
 it appears that the zinc, which had no charge at the outset, has 
 assumed the charges previously held by two silver ions, releasing 
 these atoms of silver from the ionic condition. Evidently the 
 zinc has a greater tendency to enter this condition than silver. 
 To describe this general tendency of metals to enter solution, 
 implying, of course, the formation of ions,f we use the words, 
 electrolytic solution tension. The metals are arranged in the 
 above list, according to their decreasing electrolytic solution 
 tension. 
 
 A better understanding of the replacement process is obtained 
 By picturing the sequence of changes which would logically follow 
 a difference in electrolytic solution tension between the two 
 metals. 
 
 Suppose a zinc strip to be suspended in a vessel of pure water. 
 The expansive force tending to send zinc ions out into the liquid 
 immediately becomes operative. Every zinc ion carries two unit 
 positive charges of electricity, and since the zinc particle has 
 assumed this positive electrification on leaving the strip, the 
 latter must have assumed an equivalent negative electrification. 
 When a number of ions have been projected into the liquid, they 
 
 * Lead fails to dissolve in the ordinary dilute acids, owing to the insolu- 
 bility of its salts as soon as an appreciable amount of salt is formed, this 
 acts as a protective coating to prevent further action. 
 
 t The metals dissolve only in the ionic condition. 
 
92 CHEMICAL THEORY. 
 
 will forcibly repel one another, owing to their like charges and 
 the absence of partners carrying opposite charges. Conse- 
 quently, they will be continually projected within the immediate 
 sphere of attraction of the strip and will tend to reattach 
 themselves to it. On the other hand, it becomes increasingly 
 difficult, as ions enter the liquid, for others to leave the strip 
 in the face of its constantly accumulating negative charge. 
 The magnitude of this electrostatic force opposing the accu- 
 mulation of ions in the solution is very great, even when only 
 a few ions are concerned, since each ion carries a very consider- 
 able charge. We therefore assume that, before a measurable 
 quantity of ions has entered the solution, successful opposition 
 to- the electrolytic solution tension of the metal has been set 
 up, so that a condition of balance is maintained. 
 
 Although the electrolytic solution tension of zinc causes a 
 number of zinc ions to remain in solution in the face of this 
 opposing force, ions from a metal of lesser electrolytic solution 
 tension would be driven by its agency to the zinc strip. Action 
 of this sort ensues when the strip is immersed in a solution of 
 silver nitrate. When two silver ions reach the strip, two of its 
 negative charges are used in neutralizing their two positive 
 charges. The solution has now lost two positive charges and 
 the strip has lost two negative charges; hence, the electrical 
 force operating against the electrolytic solution tension of zinc, 
 is reduced sufficiently to permit one more zinc ion to enter the 
 solution, Whereby this force is restored to its former value. 
 Thus, we see that two atoms of silver have been deposited, 
 one atom of zinc has entered the solution as an ion, and the 
 system is again in position to repeat the process. 
 
 Closely related to the electrolytic solution tension of a metal is 
 the electrical pressure (electromotive force) required to drive the 
 metal out of solution (during electrolysis) . As would be expected, 
 the order which the metals assume, according to their decreasing 
 electrolytic solution tension, is preserved when the respective 
 values for the electromotive force necessary to decompose 
 equally concentrated (in molecular quantities) solutions of their 
 salts are made the basis for gradated arrangement. 
 
 The negative elements are equally characterized by a specific 
 tendency to enter the ionic condition. Here, we are dealing with 
 
THE ELECTROLYTIC DISSOCIATION THEORY. 93 
 
 soluble substances, for the most part. One of the familiar 
 halogen replacements is represented by the following reaction: 
 
 C1 2 + 2K + 2Br = Br 2 + 2C1 + 2K, 
 
 which may be interpreted in the same general way as the 
 Zn-Ag replacement. 
 
CHAPTER VIII. 
 
 THE LAW OF CHEMICAL MASS ACTION. 
 
 The reversible nature of chemical action has been pointed 
 out and emphasized in earlier portions of this book. The 
 phenomena of electrolytic dissociation, considered in the last 
 chapter, offer abundant illustration of this principle. Reactions 
 in general between substances, however disposed, whether 
 gaseous, liquid, solid, ionic, etc., proceed more or less completely 
 in either direction, in measure determined by the prevailing 
 physical conditions, i.e., temperature, pressure, concentration, 
 nature of solvent, etc. 
 
 The electrolytic dissociation of an acid, base, or salt in aqueous 
 solution is very little influenced by the temperature or pressure, 
 but varies from to infinity with the concentration. Many 
 gaseous substances dissociate into simpler gaseous substances. 
 The extent of such dissociation is primarily dependent on the 
 temperature and pressure. In any specific case, concentrations 
 of the initial substance and its dissociation products will be 
 perfectly defined for any given temperature and pressure. If 
 the temperature is raised (at constant pressure), more gas dis- 
 sociates; if lowered, some of its dissociation products recombine. 
 
 In the laboratory, we are accustomed to work under rather 
 constant conditions of temperature and pressure. To be sure, 
 'reaction mixtures are heated, cooled, enclosed in sealed tubes 
 so that the pressure may rise, or placed in connection with a 
 vacuum pump, to bring about desired results, but withal, certain 
 approximately defined temperatures and pressures such as, 
 " room temperature," " low redness," " ordinary pressure," 
 "diminished pressure," etc. are commonly maintained, and 
 it is the concentration factor which is subjected to wide variation. 
 
 The term, dissociation implies reversibility, or a reciprocal 
 tendency of the dissociation products to reunite. While other 
 processes, involving more than one initial substance are equally 
 
 94 
 
THE LAW OF CHEMICAL MASS ACTION. 95 
 
 important as examples of reversible reaction, attention is first 
 drawn to this particular class of phenomena on account of its 
 simplicity. 
 
 The case of gaseous dissociation represented by the equation : 
 
 N 2 4 * 2NO 2 , 
 
 is frequently chosen to illustrate the subject in hand, since both 
 changes may be brought about with ease and a marked difference 
 in color between the two varieties of molecules renders the gen- 
 eral state of the mixture apparent at a glance. 
 
 Undissociated nitrogen tetroxide molecules (N 2 C>4) are 
 colorless, while the simpler molecules (NO 2 ) are reddish brown. 
 Under ordinary conditions, the gas is distinctly colored, con- 
 sisting of both N 2 (>4 and NO 2 molecules. Each variety consti- 
 tutes a certain definite proportion of the mixture. If more N0 2 
 molecules could be added and the temperature and pressure kept 
 constant, the color of the mixture would not deepen, but the re- 
 action would proceed towards the left until a sufficient number 
 of N 2 (>4 molecules had been formed to restore the proportion of 
 each variety to its original value. At a lower temperature the 
 mixture contains fewer NO 2 molecules. This may be shown by 
 immersing a sealed tube containing the gas in a vessel of 
 ice water, when the color practically disappears. On gently 
 warming the tube, the color returns and becomes more pro- 
 nounced as NO 2 molecules continue to be formed as the 
 reaction proceeds towards the right. 
 
 Gaseous hydriodic acid dissociates into hydrogen and iodine 
 at temperatures above some 200: 
 
 2HI <= H 2 + I 2 . 
 
 If the acid is enclosed in a sealed tube at room temperature 
 and atmospheric pressure and then heated to about 500, 
 approximately 20 per cent will be dissociated. A mixture of 
 hydriodic acid, hydrogen, and iodine in any proportions whatever, 
 if brought under the same condition of temperature and pressure 
 as in the above case, will readjust itself by reaction towards 
 the right or left as needs be to attain a final composition 
 identical with the above. 
 
96 CHEMICAL THEORY. 
 
 At some higher temperature, approximating 800, the dia- 
 tomic iodine molecules begin to dissociate: 
 
 I 2 <=* 21. 
 
 This dissociation becomes complete at about 1500. 
 
 We conceive that the two reactions corresponding to any 
 reversible change take place simultaneously. When both pro- 
 gress at an equal rate, the actual amounts of all the reacting 
 substances remain unaltered, i.e., a condition of equilibrium 
 results. A brief outline of the imaginative working of such a 
 process from the standpoint of the kinetic theory, will serve to 
 bring about a better understanding of these relations. 
 
 For this purpose, we will consider the substances A and B 
 enclosed in a suitable receptacle and elevated to a temperature 
 at which reaction occurs, with formation of the new substances 
 C and D, according to the equation: 
 
 A + 2B = C + D. 
 
 We may reason that the impacts of the rapidly moving A 
 and B molecules are responsible for their chemical alteration 
 breaking apart and reuniting in the form C + D. One molecule 
 of A must meet two molecules of B to determine change as pre- 
 scribed by the above equation. But it is not necessary to assume 
 that every impact of this sort results in chemical change. The 
 A and B molecules move with a certain average velocity depend- 
 ent on the temperature. Of two individual molecules chosen at 
 random, however, one may move faster than the other. Conse- 
 quently, some of the A-2B impacts will be more forcible than 
 others, or more likely to cause alteration. The number of 
 impacts which are effective in this respect must, in any event, 
 be proportional to the total number of impacts. In other words, 
 the rate at which the substances A and B combine to form the 
 substances C and D is proportional to the rate at which one A 
 molecule meets two B molecules. 
 
 In the same manner, we reason that the rate at which the 
 substances C and D combine to form the substances A and B is 
 proportional to the rate at which one C molecule meets one D 
 molecule. 
 
THE LAW OF CHEMICAL MASS ACTION. 97 
 
 For a time, the rate at which A and B combine will be greater 
 than the rate at which C and D combine, since the A and B 
 molecules are in position to impact frequently, being relatively 
 numerous and closely packed at the start, while the C and D 
 molecules are absent in the original mixture and collide infre- 
 quently following their initial appearance. As the reaction 
 proceeds towards the right, A and B molecules disappear, their 
 collisions become less frequent and the rate of reaction diminishes. 
 On the other hand, as the molecules of C and D increase in num- 
 ber, their collisions become more frequent and the rate of reaction 
 towards the left increases. Obviously, there will come a time 
 when the rates of both reactions will be equal. Then, as much 
 A and B as C and D will be produced in a unit time and the 
 quantities of all four substances will remain unchanged. 
 
 Let us consider the relation between the concentration of each 
 variety of molecules and the rate of reaction in greater detail. 
 (We ordinarily express the molecular concentrations of different 
 substances in gram molecules per liter. Such concentration 
 values are proportional to the actual numbers of molecules 
 involved.) 
 
 The number of impacts between a single chosen molecule of the 
 substance A and any of the B molecules in a time unit is evi- 
 dently proportional to the concentration of the latter. During 
 this time, the number of impacts between a single B molecule 
 and others of its kind is also proportional to their concentration. 
 But every other B molecule has the same opportunity to collide 
 with its fellows, and this aggregate of B molecules is represented 
 by proportional to the number which expresses their molec- 
 ular concentration. Therefore, the total number of individual 
 impacts between B molecules in a unit time is proportional to 
 the square of their concentration (concentration of B X concen- 
 tration of B). Now, we have seen that the rate of the reaction 
 towards the right is proportional to the number of A-2B impacts. 
 Since the number of 2B impacts is proportional to the square of 
 the concentration of B molecules, the number of times one chosen 
 A molecule will meet two B molecules at once is proportional to 
 the same value; or, the total number of A-2B impacts due to the 
 motion of all A and B molecules and consequently, the rate of 
 reaction towards the right, is proportional to the concentration 
 
98 CHEMICAL THEORY. 
 
 of A molecules, multiplied by the square of the concentration of 
 B molecules. 
 
 Applying the same reasoning to the reaction towards the left, 
 we conclude that the rate of this reaction is proportional to the 
 concentration of C molecules multiplied by the concentration 
 of D molecules. 
 
 In general, the rate of any reaction is proportional to the con- 
 centration of each reacting substance multiplied by itself as many 
 times as its coefficient in the equation for the reaction indicates. 
 
 The simple Law of Chemical Mass Action announced by 
 Guldberg and Wange (Christiania) in 1867, will now appear in 
 a satisfactory light. It may be stated in the following words: 
 
 The rate of chemical action is proportional to the active mass of 
 each reacting substance. 
 
 From the preceding discussion, it is clear that the mass of any 
 substance concerned in a reaction where all the material is evenly 
 and equally distributed, is active (or efficient in promoting the 
 reaction) in direct proportion to the number of molecular units in 
 a given volume, which it represents, if only one molecule of the 
 particular substance enters into the equation. Otherwise, the 
 coefficient representing the number of molecules of the sub- 
 stance required by the equation, must be used as an exponent 
 in connection with this molecular measure, or concentration, to 
 correctly define the relation of the mass of the substance to the 
 change. 
 
 This law is of particular service in showing the quantitative 
 relations between different substances in equilibrium with one 
 another, as the result of reversible change. 
 
 Suppose the four substances A, B, C, and D are concerned in 
 such change, according to the reaction: 
 
 mA + nB <= pC + qD, 
 
 where the letters m, n, p, and q represent ordinary numeri- 
 cal coefficients. Let the small letters a, b, c, and d denote the 
 respective concentrations of each substance; the term, concen- 
 tration, is used throughout this chapter in the sense of molecular 
 concentration. 
 
 Then the rate of the reaction: 
 
 mA + nB = pC + qD, (1) 
 
THE LAW OF CHEMICAL MASS ACTION. 99 
 
 is proportional to a m and to b n , according to the above law. Or, 
 it is equal to a constant quantity multiplied by a m and b n . 
 Denoting this rate, or velocity, by V and the constant by KI we 
 have : 
 
 From the transformed equation K l = -7- we see that K l defines the 
 
 a b 
 
 rate of the reaction when the concentration of each reacting substance is 1. 
 That is, when both a and b possess the value 1, another rate, just equal to 
 K 1} will replace F t . As the reaction proceeds, the concentrations a and 6 
 diminish, but the Mass Action Law continues to hold, and the constant KI 
 preserves its former significance. To illustrate: At the end of a finite 
 time (t) let us assume that the concentration of A has diminished by an 
 amount (m) (x) gram molecules per liter. Then the concentration of 
 B will have diminished by an amount (n) (x), since, according to the equa- 
 tion, every time (m) molecules of A react, (n) molecules of B are con- 
 cerned in the change ; and their respective concentrations will have become 
 (a mx) and (b nx) . The rate of the reaction will now be equal to K^ 
 (amx) m (b nx) n , where K v denotes, as before, the rate corresponding to 
 unit concentrations of A and B. 
 
 By strictly analogous reasoning, we place the rate of the re- 
 action : 
 
 pC + qD = mA + nB, (2) 
 
 which may be indicated by V 2 equal to a characteristic constant 
 K<2 multiplied by the active masses of the substances C and D. 
 Thus: 
 
 V 2 = K 2 cW. 
 
 For the special case of equilibrium, the rates of both reactions 
 are equal, and we write: 
 
 V l = V 2 , or 
 Whence, 
 
 which becomes, 
 
 K 
 
 rr 
 
 on substituting a new constant K for the quotient 
 
 A- 
 
100 CHEMICAL THEORY. 
 
 We have seen, in the note above, that the constant KI repre- 
 sents the rate of reaction (1) when unit concentrations of the 
 substances A and B are allowed to react. Hence, it is called the 
 velocity coefficient of this reaction. The second constant K 2 is, 
 then, the velocity coefficient of reaction (2). 
 
 TT 
 
 The ratio of both velocity coefficients - , or K bears the name, 
 
 K 2 
 
 equilibrium coefficient. Its physicial significance is as follows: 
 
 When the several substances participating in reversible chemical 
 change have reached a state of equilibrium (whereby no further 
 alteration in their respective concentrations occurs) the product of 
 the active masses of all the substances constituting one set of changing 
 material, divided by the product of the active masses of all the sub- 
 stances constituting the other set of changing material, is equal to a 
 quantity, called the equilibrium coefficient, which possesses the 
 same value for this particular process, at a given temperature, what- 
 ever the actual amounts of any or all the substances used at the 
 start. 
 
 In the laboratory, new substances are frequently evolved in 
 the gaseous state by heating a mixture of two salts, a salt and an 
 acid, or a salt and a base. These compounds are always capable 
 of double decomposition or crosswise recombination among them- 
 selves, and to determine whether a given pair will proceed to 
 produce the complementary pair on being heated in an open 
 vessel, or will themselves constitute the end products of reaction 
 between the (our under these conditions, we have only to apply 
 the principle of mass action, in connection with our general 
 information relative to the physical properties of each substance. 
 
 By way of general illustration, let us suppose that the sub- 
 stances A B and CD are mixed and heated at first in a closed 
 space. Then we may write the following reversible reaction, 
 indicating that all four compounds A B, CD, AD, and BC are 
 present in certain fixed proportions at any given temperature: 
 
 AB + CD<= AD + BC. 
 
 For the sake of simplicity, it is assumed that only one molecule 
 of each substance enters into the equation. 
 
 If we denote the equilibrium concentrations of these four sub- 
 
THE LAW OF CHEMICAL MASS A-Ctl)N; / /'1Q1 
 
 stances by C AB , C CD , C AD , and C BC the/state ?f t/he, mixture, i? 
 defined by the expression, --/'", :,, J J i'^/'J** '"- 
 
 r' v r* 
 
 ^.4D A r cr 
 
 where K is the equilibrium coefficient. 
 
 We should note, however, that this implies an even distribution of all 
 the substances in some form so that no boundary separates one from 
 another. In practice, reaction mixtures are most often heterogeneous, 
 consisting of gaseous, liquid, or solid material without reservation. The 
 reaction may then take place in the liquid phase, as well as in the gaseous 
 phase, and separate equilibrium constants, defined as above, will apply to 
 each. There is, however, a definite numerical relation between these two 
 constants, since the concentration of any gas as dissolved in a liquid, is 
 proportional to the pressure, or concentration, of the gas itself (cf. Intro- 
 duction, page 20). If a liquid constituting one of the reacting substances 
 plays the part of solvent for the other substances, its active mass as regards 
 this reaction within its own substance is considered constant its own 
 concentration is bound to be infinitely great in proportion to the concen- 
 trations of dissolved material. When solid material participates in equi- 
 librium, its active mass is assumed to be constant. 
 
 Suppose the substance AB is a liquid at the temperature in 
 question; CD and AD, solids; and EC a gas. Further, we will 
 assume the use of an excess of A B as solvent, and consider the 
 above equation as applied to the reaction taking place in this 
 liquid medium. 
 
 Then C AB , being very great in comparison to the other concen- 
 trations, will not change appreciably during the course of the 
 reaction in either direction; C CD represents the concentration 
 of (solid) CD dissolved in AB, C AD the concentration of (solid) 
 AD dissolved in AB, and C BC the concentration of gaseous BC 
 dissolved in AB. The latter concentration gaseous BC dis- 
 solved in A B is maintained by the pressure, or enforced con- 
 centration of the gas in the closed space above the liquid. 
 
 If, now, the mixture is opened to the air, there is nothing to 
 prevent the gas from escaping. It leaves the liquid, as well as 
 the open space above, since the former cannot hold as much under 
 the diminished pressure of gas above. 
 
 C X C 
 Turning to the relation AD [ BC = K, we see that to restore 
 
102 CHEMICAL THEORY. 
 
 the quotient to Hs constant value after C BC has been diminished, 
 it :i& 'necessary yGr *C AD to increase, or C AB X C CD to diminish. 
 Readjustment along these lines is accomplished by reaction 
 between AB and CD to form AD and BC anew. But, the 
 formation of more BC is attended by its further escape, so that 
 equilibrium is again disturbed; the same process again ensues, 
 and becomes progressive as long as both AB and CD remain in 
 the mixture. 
 
 The action of sulphuric acid on salts of less volatile acids may 
 be cited as a very common reversible change which results in 
 continuous formation of the volatile substance in this case, 
 the less volatile acid unless checked by a retaining (closed) 
 vessel. 
 
 Thus, nitric acid and hydrochloric acid are made commercially 
 by treating their salts with concentrated sulphuric acid: 
 
 H 2 S0 4 + 2NaN0 3 = N^SC^ + 2HNO 3 . (1) 
 
 H 2 SO 4 + 2NaCl = Na^CU + 2HC1. (2) 
 
 Applying the mass action principle for equilibrium: 
 
 (1) , 4 X HN0 3 -K, and (2) ** ' * - K.. 
 
 OH 2 SO 4 X C/NaNOg OH 2 SO 4 X 
 
 In (1) or (2) the second term of the numerator becomes 
 smaller when the equilibrium mixture is opened, owing to escape 
 of nitric acid or hydrochloric acid respectively. Nitric acid is a 
 liquid at ordinary temperature and pressure, but very volatile 
 at a temperature which causes no appreciable volatilization of 
 sulphuric acid, also a liquid. Hydrochloric acid is a gas under 
 ordinary conditions. The other materials are solids, non- 
 volatile, except at high temperatures. 
 
 As explained above, these reactions will proceed towards the 
 right in a continuous attempt to restore equilibrium by 
 increasing the numerator product and decreasing the denomi- 
 nator product; always ineffectual, however, owing to the escape 
 of one component material as soon as it is formed. 
 
 Towards the close of Chapter VII (on page 87 and succeeding 
 pages) it was pointed out that precipitation occurs on mixing 
 aqueous solutions of different acids, bases, or salts, when such 
 mixture brings appreciable concentrations of certain ions into 
 
THE LAW OF CHEMICAL MASS ACTION. 103 
 
 the presence of one another. Application of the Mass Action 
 Law to the electrolytic dissociation of these substances leads us 
 to a clearer perception of precipitation phenomena. 
 
 According to this law, equilibrium between any electrolyte 
 and its ions is defined in terms of the several concentrations 
 involved, i.e., those of the undissociated substance, and of the 
 different ions. For example, an aqueous solution of sodium 
 chloride contains undissociated salt, sodium ions and chloride ions 
 in such proportions that a certain definite and characteristic 
 
 C + X C~ 
 value is reached by the expression ^ - corresponding to 
 
 ^ 
 
 the reversible action: 
 
 NaCl^Na + Cl. 
 P + v P 
 
 That is, 
 
 and K, the equilibrium coefficient, in such a case, may be more 
 appropriately termed, the dissociation coefficient. 
 
 If the solution contains as much sodium chloride as will dis- 
 solve at the given temperature, i.e., if it is saturated, the term 
 CN & CI possesses a constant value, and the above expression 
 reduces to, 
 
 const. 
 which may be re-formed thus, 
 
 where k represents a third constant called the solubility product. 
 
 A saturated solution of sodium chloride must, then, contain ions 
 in sufficient quantity so that the product of their concentrations 
 equals a certain definite value. If additional ions (of the same 
 kinds) were introduced, in some way, they would be forced to 
 combine, and the resulting sodium chloride would precipitate, 
 since the solution can hold no more of it. 
 
 A substance, which is commonly called insoluble, produces 
 very few ions when placed in water. That is, its solubility 
 product is small. If highly dissociated soluble substances, which 
 
104 CHEMICAL THEORY. 
 
 together yield the pair of ions corresponding to this insoluble 
 substance, are dissolved in water and poured together, a pre- 
 cipitate will result, because the solubility product of the latter 
 substance is sure to be exceeded at once. 
 
 If a substance yielding sodium or chloride ions is dissolved in a 
 saturated solution of sodium chloride, precipitation of the latter 
 is caused. This illustrates the common ion effect, which may be 
 understood in its general aspect by noting the following expla- 
 nation of the case in point. 
 
 Suppose sodium nitrate is dissolved in a saturated solution of 
 sodium chloride. The relation C^ a X CQ = k which especially 
 characterizes this latter solution, will, then, be disturbed by the 
 increase in the concentration of sodium ions following solution 
 of the former salt. To restore the product to its normal value, 
 sodium ions will unite with chloride ions to form undissociated 
 sodium chloride. In other words, the reaction (page 103) will pro- 
 ceed towards the left. Since the solution is already saturated, 
 any undissociated sodium chloride formed in this way cannot 
 remain in solution, but must precipitate. Potassium chloride 
 would produce the same effect by increasing the concentration 
 of the chloride ions. Substances giving no common ion would 
 dissolve in the saturated solution of sodium chloride as though no 
 sodium chloride were present. 
 
 Thus far, in describing the interaction between ions in an 
 aqueous medium, we have taken no account of the presence of 
 hydrogen and hydroxyl ions from the dissociation of water itself. 
 The extremely slight dissociation of water was, however, men- 
 tioned in the previous chapter (page 84) . If we are dealing with 
 a substance which, when brought under the influence of " water 
 ions " when dissolved in water could give rise to a product 
 by the ordinary " crosswise recombination " between ions of the 
 substance and the ions from water, itself slightly dissociated in 
 measure comparable with that of water, then the dissociation of 
 water acquires some significance. Since water gives hydrogen 
 and hydroxyl ions, only salts are in a position to produce new 
 undissociated substances by interaction with water, and these 
 new substances must be acids or bases. 
 
 Now, there is a great difference in the degree to which different 
 acids and bases are dissociated (cf. pages 82 and 83), and certain 
 
THE LAW OF CHEMICAL MASS ACTION. 105 
 
 of them very weak ones are so little dissociated that the 
 above effect becomes noticeable when one of their salts is dis- 
 solved in water. This type of chemical action involving water 
 is called hydrolysis. 
 
 To supplement the above statements by a more detailed 
 argument, let us start with a dilute solution of sodium chloride 
 in pure water: 
 
 The primary reaction involved is, 
 
 Na + Cl, (1) 
 
 such that, Na = K. 
 
 To describe the dissociation of water we write, 
 
 and, 
 
 H 2 O <= H + OH, (2) 
 
 OSXC6H 
 
 For the crosswise reactions: 
 
 HC1 <=> H + Cl, (3) and, NaOH + Na 4- OH, (4) 
 
 H X C5i , CNS X CQ"H 
 
 - K 3 , and, = K 
 
 the relations: 
 
 must obtain. 
 
 Now, the dissociation coefficient K of sodium chloride, a salt, 
 is large, that is, in the expression following equation (1), the 
 terms C^ and CQ are large, while the term C NaC1 is small. 
 On the other hand, the coefficient for water K 2 is extremely small, 
 or the terms CH and C O ~H i* 1 ^ ne expression following equation 
 (2) are extremely small. 
 
 Consider to what extent undissociated hydrochloric acid or 
 undissociated sodium hydroxide would be formed by the union of 
 their ions present as specified above until the relations 
 following equations (3) and (4) are satisfied. Both of these 
 substances are highly dissociated HC1 a strong acid and NaOH 
 
106 CHEMICAL THEORY. 
 
 a strong base therefore the coefficients K 3 and K 4 will be 
 large. On comparing the equilibrium relations corresponding to 
 reactions (1) and (3), bearing in mind that the two expressions 
 
 C + X C~ C + X C~ 
 
 -~ - and -^** - are not far different in value, and 
 
 that C^j is the same in both, we see that, since C NaC1 is small in 
 the first expression where CJ a is large, the corresponding term 
 C HC i in the second expression, where CH is extremely small, 
 must possess a trifling value. The same conclusion regarding 
 the concentration of undissociated sodium hydroxide follows from 
 a comparison of the equilibrium relations corresponding to 
 reactions (1) and (4). Thus, no appreciable quantities of 
 hydrochloric acid or sodium hydroxide are formed by hydrolysis 
 when sodium chloride is dissolved in water. 
 
 If, however, we replace the strong acid HC1 by a very weak 
 acid, for example, HCN, the corresponding salt NaCN will be 
 largely dissociated, as was NaCl. But this acid is very slightly 
 
 C + X C ~~ 
 dissociated comparable to water and the expression H 
 
 must reach a very small value to represent equilibrium between 
 the acid and its ionization products. The numerator product 
 CH X CCN even though CJ is very small, will here be much 
 larger than this equilibrium value, and a considerable amount of 
 undissociated HCN will be formed, according to the reaction: 
 
 H + CN = HCN. 
 
 As hydrogen ions are used up in this change, the equilibrium 
 between water and its ions is disturbed and more water will 
 dissociate reaction (2) will proceed towards the right 
 until complete readjustment is effected. This production of 
 additional hydrogen ions is, of course, accompanied by an equiva- 
 lent production of hydroxyl ions, which have no tendency to 
 unite with sodium ions, as we have previously noted. Hence, 
 they accumulate in the solution giving it alkaline properties. 
 
 When the salt corresponds to a weak base and a strong acid, 
 hydrolysis occurs, and is explained in the same general way as 
 above. In such a case, undissociated base is formed and the 
 solution possesses acid properties. 
 
THE LAW OF CHEMICAL MASS ACTION. 107 
 
 The following reactions illustrate both cases: 
 
 NaCN + H 2 O <= NaOH + HCN 
 
 (chiefly diss'd) (chiefly undiss'd) (chiefly diss'd) (chiefly undiss'd) 
 
 FeCl 3 + 3H 2 O <= Fe(OH) 3 4- 3HC1 
 
 (chiefly diis'd) (chiefly undiss'd) (chiefly undiss'd) (chiefly diss'd) 
 
 If both acid and base are very weak, hydrolysis of the corre- 
 sponding salt may be so nearly complete that the latter cannot 
 exist appreciably in the presence of water. Sulphides and car- 
 bonates of aluminium, chromium, and iron (Fe +H " + ), are, thus, 
 stable only in the dry state. When reagents, calculated to form 
 one of these substances, are mixed, the products of its hydrolysis 
 result instead. For example, the addition of sodium carbonate 
 to aluminium chloride, in solution, causes precipitation of alumi- 
 nium hydroxide, and evolution of carbon dioxide. We may write 
 the reaction in steps, as follows: 
 
 (1) SNaaCOs + 2A1C1 3 = A1 2 (CO 3 ) 3 + GNaCl (Hypothetical 
 formation of aluminium carbonate). 
 
 (2) A1 2 (CO 3 ) 3 + 6H 2 O =2A1(OH) 3 + 3H 2 C0 3 (Hydrolysis 
 of this salt with formation of free acid unstable and free base 
 insoluble). 
 
 (3) H 2 C0 3 = H 2 O 4- CO 2 (Ordinary decomposition of car- 
 bonic acid). The final reaction is: 
 
 (4) SNaaCOg + 2A1C1 3 + 3H 2 O = 2A1(OH) 3 + 6NaCl + 3C0 2 . 
 
CHAPTER IX. 
 HETEROGENEOUS EQUILIBRIUM. 
 
 ANY single variety of material may assume a number of dif- 
 ferent physical forms, according to the physical influences which 
 are brought to bear upon it. The three most apparent differ- 
 ences in this respect are defined by the terms, gas, liquid, and 
 solid. Solid material, in particular, is subject to further classi- 
 fication, as previously noted (Introduction, page 16), whereby we 
 speak of amorphous, or specific crystalline modifications. When 
 different substances are brought into close association with one 
 another, the matter occurring in any one of these three forms 
 may consist of mixed material, each respective form being 
 homogeneous in its own makeup and presenting the same 
 general appearance as if pertaining to a simple substance. 
 Thus, we are familiar with mixed gases or liquids, and some- 
 what less so with mixed solids, in the sense that they are 
 completely " dissolved " in one another (cf. Introduction, 
 pages 4 and 20) . On the other hand, it is not necessary that the 
 liquid corresponding to one kind of material, should completely 
 mix with that corresponding to another kind of material, when 
 both are placed in contact. The two liquids may remain 
 in contact with one another, separated by their own surfaces 
 (cf. Introduction, page 20). Two different solids most fre- 
 quently fail to mix, except mechanically, when rubbed together. 
 Gases invariably merge into one another. Thus, we see that a 
 system of associated material may consist of several separately 
 homogeneous fractions in mechanical contact. 
 
 These individual physical modifications comprising the sys- 
 tem are called phases. 
 
 The different chemical substances taken at will to produce 
 a collection of phases, are called components. 
 
 The nature of the phases appearing in a given system, as well 
 
 108 
 
HETEROGENEOUS EQUILIBRIUM. 109 
 
 as the number of phases which may remain in contact without 
 tendency to alteration, is primarily dependent on the physical 
 conditions, i.e., temperature, pressure, and concentration (of the 
 several components), under which the system is required to exist. 
 For example, it is the solid form of iodine which we handle in the 
 laboratory, because this is the stable form under ordinary con- 
 ditions. If we elevate the temperature of this solid substance 
 at atmospheric pressure, it changes into vapor, i.e., it sublimes, 
 when a certain temperature is reached, because, at this point, 
 the latter form becomes capable of existence, and is, therefore, 
 formed when heat is added to the solid. If, when part of the 
 solid is transformed into vapor, the heating is made merely suf- 
 ficient to keep the temperature constant to prevent subsequent 
 cooling both solid and vapor will continue to coexist. Had 
 we increased the pressure sufficiently before heating the solid, 
 liquid, instead of vapor, would have resulted the solid iodine 
 would have melted. 
 
 When a number of substances are placed in contact, great 
 variety in the configuration of the system is possible, as the tem- 
 perature, pressure, and concentrations are altered. Owing to the 
 discovery by Gibbs (Yale, 1874-8), of a simple numerical relation 
 between the number of phases, the number of components, and 
 the number of physical conditions which may be varied inde- 
 pendently of one another within certain limits without causing 
 the disappearance of any current phase, or the appearance of 
 any new phase, in any system, chemical or physical we are 
 in a position to impose a well ordered classification upon what 
 at first appears to be a bewildering diversity of equilibrium 
 phenomena. 
 
 Denoting the number of variable conditions, in the above con- 
 nection, by V, the number of components by C and the number 
 of phases by P, we have, according to Gibbs' Phase Rule, 
 
 V = C + 2 - P, 
 
 or, in words, When the different phases, composing a given system, 
 are in a state of equilibrium, the number of physical conditions 
 which may be independently varied without disturbing this equi-. 
 librium, is equal to the number of components increased by 2, less 
 the number of phases. 
 
110 CHEMICAL THEORY. 
 
 The following special cases may be noted : 
 
 (1) If the system shows two more phases than components, 
 no one of the obtaining conditions may be varied without sub- 
 jecting the whole system to readjustment resulting in a different 
 number of phases (C P 2, and V = 0). The system 
 is then said to be nonvariant. 
 
 (2) If the system shows one more phase than components, 
 one condition may be varied at will to a certain limited extent 
 
 - without disturbing the equilibrium (C P = 1, and 
 V = 1). The system is monovariant. 
 
 (3) If the system shows the same number of components 
 as phases, two conditions may be varied independently without 
 disturbing the equilibrium (C P = 0, and V = 2). The 
 system is divariant. 
 
 In a phase system generated from a single component, the 
 variable conditions are the temperature and the pressure. 
 When two components replace the one, there obtains the addi- 
 tional factor of concentration, which may be varied at will, 
 thereby constituting a third variable condition. 
 
 A simple one -component system, in which equilibrium is deter- 
 mined by the temperature and pressure alone, will be chosen, on 
 account of simplicity, to illustrate the general application of the 
 phase rule. The disposition of each of the three possible phases, 
 gaseous, liquid, and solid (leaving out the possibility of more than 
 one solid phase) with respect to the pressure and temperature, 
 may be represented graphically on a plane surface. We have 
 already made use of such a pressure temperature diagram 
 (page 51 ) to represent the different vapor tensions of a solid 
 corresponding to different temperatures (sublimation curve of 
 the solid), as well as the different vapor tensions of a liquid 
 corresponding to different temperatures (vaporization curve of 
 the liquid). In the accompanying diagram (Fig. 7), similar 
 curves, numbered 1 and 2, are drawn. Any point on the sub- 
 limation curve 1, represents a temperature and pressure at 
 which solid and vapor can coexist, i.e., 'are in equilibrium. Any 
 point on the vaporization curve represents a temperature and 
 pressure at which liquid and vapor can coexist. The point 
 where both curves meet represents the temperature and pressure 
 at which solid, liquid, and vapor can coexist (cf. Chapter III, 
 
HETEROGENEOUS EQUILIBRIUM. 
 
 Ill 
 
 page 52). Solid and liquid, which are in equilibrium (with 
 vapor) at 0, continue in equilibrium when the temperature and 
 pressure are altered, as shown by the curve numbered 3 which 
 meets curves 1 and 2 at 0. In other words, this curve indicates 
 the change in the melting point of the substance with the pressure. 
 
 Vapor 
 
 Temperature 
 Fig. 7. 
 
 As drawn in the diagram, it corresponds to a decrease in melting 
 point with an increase in pressure, a condition illustrated by the 
 familiar solid phase of water, namely, ice. 
 
 Consider the physical change which occurs when we pass from 
 any point on the sublimation curve directly towards the right, 
 i.e., increase the temperature at constant pressure. Solid and 
 vapor, which are in equilibrium at the temperature and pressure 
 corresponding to this point, will no longer continue to coexist, 
 but the solid will become completely transformed into the vapor. 
 That is, the temperature cannot rise until the solid has absorbed 
 heat enough to convert it into vapor. In like manner, passing 
 from a point on the vaporization curve directly towards the 
 temperature axis, i.e., decreasing the pressure at constant tem- 
 perature, we note a disappearance of the liquid phase, corre- 
 sponding to complete change of the material into vapor. The 
 points x and y with attached dotted lines, serve to suggest the 
 above changes. It should be clear that the whole field in which 
 
112 CHEMICAL THEORY. 
 
 these points are situated, bounded by curves 1 and 2, represents 
 concurrent temperature and pressure values, at which the sub- 
 stance must exist completely in the form of vapor. This field is, 
 therefore, defined on the diagram by the word, Vapor. The 
 remaining space is divided between a Liquid field, bounded by 
 curves 2 and 3, and a Solid field, bounded by curves 1 and 3. In 
 passing from one field to another across a boundary line, dis- 
 continuity occurs there is a time when both phases are in 
 contact. It is, however, possible to pass around the vaporiza- 
 tion curve (2) from the vapor field into the liquid field, or vice 
 versa, by suitably altering the temperature and pressure, since 
 this curve possesses a determinate end point. There would be 
 no discontinuity in such transformation. The end point C is 
 called the critical point. We have already noted the existence 
 of a critical temperature, above which, no matter how great the 
 compression, the vapor cannot be converted into liquid. In other 
 words, liquid does not exist above this temperature, and the 
 vaporization curve (giving its vapor tension) must end here. 
 At the point C, then, we have reached the critical temperature 
 and pressure of the liquid. 
 
 The diagram which we have discussed above may be regarded 
 as a map showing the configuration of a one component system, 
 with respect to the temperature and pressure. The fundamental 
 curves 1, 2, and 3 are determined by experiment. Hence we 
 have here an arrangement of experimental results, which should 
 be of assistance in the interpretation of the phase rule. 
 
 Referring again to the diagram, it is clear that, in any one of the 
 three fields, solid, liquid, or vapor, a great variety of temperature 
 and pressure values may be chosen quite independently of one 
 another to represent the conditions under which the correspond- 
 ing phase is existent. To make the illustration concrete, ice, at 
 atmospheric pressure, may be subjected to a number of different 
 temperatures (limited by its melting point) without sustaining 
 any physical change. Stars on the upper dotted line in the 
 diagram, represent such different temperatures. At any of 
 these temperatures, for example that represented by the second 
 star, the pressure may be diminished at will indicated by the 
 perpendicular dotted line with stars provided it does not fall 
 below the sublimation pressure at this temperature, without 
 
HETEROGENEOUS EQUILIBRIUM. 113 
 
 causing the solid phase to change. Thus, on experimental 
 grounds, we conclude that the one component system, embracing 
 a single phase, is divariant. 
 
 According to the phase rule, such a system should be divariant. 
 For, C =.1, and P = 1. Whence, V = 1 + 2 - 1, or 2. 
 
 It has been pointed out that each of the curves 1, 2, and 3 
 defines the temperatures and pressures under which a certain pair 
 of phases may coexist. The temperature corresponding to a 
 point on one of these curves may be altered without causing 
 either phase to disappear, provided the pressure sustains a per- 
 fectly definite alteration at the same time, whereby a new point 
 on the same curve results. In order that the same equilibrium 
 continue, variation of one condition must be accompanied by 
 (dependent) variation of the other condition. Both may not be 
 varied independently. Since only one condition at a time may be 
 varied arbitrarily, the equlibrium is termed monovariant. Turn- 
 ing again to the system H 2 O for a concrete illustration, we 
 note that the point A on curve 3 corresponds to the melting 
 temperature of ice under atmospheric pressure. At this tem- 
 perature C. and under atmospheric pressure, ice and liquid 
 water are in equilibrium. Both phases remain in equilibrium 
 at temperature-pressure values along the curve AO. Thus, on 
 decreasing the pressure from 760 mm. (A) to about 4 mm. (0), a 
 temperature slightly less than 0.01 above C., must correspond 
 to the latter pressure value, if no change in the equilibrium is to 
 occur. Greater elevation of the temperature at this pressure 
 will bring about complete transformation of solid into vapor, i.e., 
 we pass into the vapor field on leaving the curve at 0, as specified. 
 
 The phase rule requires this system to be monovariant, in 
 agreement with the experimental conclusion. For, here, C = 1, 
 and P = 2. Whence, V = 1 + 2 - 2, or 1. 
 
 At the point all three phases are in equilibrium. This point 
 is called a triple point. Obviously, no change of either tempera- 
 ture or pressure is possible without passing into one of the three 
 adjacent fields. The system, in this condition, is, therefore, 
 nonvariant. 
 
 In this case, the expression, V = C + 2 P, becomes, 
 V =1 + 2 3, or 7=0, a result in complete agreement with 
 the above. 
 
114 CHEMICAL THEORY. 
 
 We have seen that the coexistence of two or more phases is 
 rendered possible under properly chosen conditions of tempera- 
 ture, pressure and concentration. The general state of coexist- 
 ence, in this connection, is defined by the expression heterogeneous 
 equilibrium. That equilibrium of this sort differs in the degree 
 of its flexibility in the face of changing conditions, has been 
 shown in the last few paragraphs. If the phases concerned are 
 capable of coexisting at one temperature alone when the pressure 
 is arbitrarily chosen, a most complete and satisfactory regula- 
 tion of their equilibrium must be conceded. The phrase com- 
 plete heterogeneous equilibrium is applied in defining this 
 condition. The equilibrium along each curve in the diagram is 
 complete in this sense. Thus, ice and liquid water are in a con- 
 dition of complete heterogeneous equilibrium at 0, under 
 760 mm. pressure; such that any alteration of the temperature 
 or pressure, without corresponding alteration of the pressure 
 or temperature, respectively, is accompanied by the complete 
 disappearance of one phase. 
 
 Obviously the phase rule is chiefly important as an instrument 
 for indicating the numerical relation between the number of 
 components and the number of phases, which must characterize 
 this preeminently definite condition of equilibrium. The rule 
 tells us that complete heterogeneous equilibrium results when the 
 system shows a number of phases which is one greater than the 
 number of components. 
 
 If a relatively smaller number of phases is present, the equi- 
 librium is incomplete. 
 
 Consider, for example, the system composed of water vapor 
 and an unsaturated solution of common salt in water. Here 
 C = 2 (H 2 O and NaCl) and P = 2, or, P is less than C + 1. We 
 have seen in Chapter III that solution of salt in water lowers the 
 vapor tension of the latter. At the same temperature, then, 
 unequally concentrated solutions will possess different vapor 
 tensions (cf. Fig. 2, Chapter III, page 51, and discussion). 
 Hence, at a given temperature, many different pressures may 
 correspond to equilibrium between the vapor and liquid phases 
 (the latter possessing definite concentration NaCl in H 2 O - 
 for each definite pressure). If, in any specific case, the external 
 pressure is increased, the vapor phase will not completely dis- 
 
HETEROGENEOUS EQUILIBRIUM. 115 
 
 appear, but some vapor will be converted into liquid, whereby 
 the solution becomes more dilute, reaching equilibrium with the 
 vapor under another definite pressure. When an excess of salt 
 is added to the solution, the equilibrium becomes complete. 
 There are now three phases, solid NaCl, saturated solution, and 
 water vapor, i.e., one in excess of the number of components. 
 At a given temperature, a single vapor pressure corresponds 
 to the (saturated) solution. If the external pressure is increased, 
 vapor condenses, but the solution cannot become less concen- 
 trated, on account of the presence of solid NaCl; therefore no new 
 equilibrium is reached, and the vapor continues to condense until 
 it is no longer present. 
 
 The addition of ice to the last mentioned mixture, increases 
 the number of phases to four. According to the phase rule, 
 V = 2 -f 2 4, or 0. There will be a single temperature and 
 pressure at which the saturated solution is in equilibrium with 
 solid H 2 O, solid NaCl, and vapor. If the mixture is opened to 
 the air, the latter phase is not concerned in the equilibrium, since 
 vapor may escape freely. Neglecting this phase, then, we have, 
 V =2 + 2 3, or 1. Under atmospheric pressure, these three 
 phases require a certain definite temperature to determine their 
 coexistence. This temperature is considerably below the freez- 
 ing temperature of water. If the temperature of the mixture 
 were above this equilibrium value at the outset, ice would melt, 
 thereby absorbing heat, until the proper lowering had resulted. 
 Corresponding to the dilution of the solution due to this process, 
 solid salt would dissolve, keeping the solution saturated. The 
 final state of equilibrium would be maintained without change 
 in the amount of any phase, provided no change in the external 
 conditions were imposed. If, as is frequently the case, such a 
 mixture were used to cool some foreign substance, ice would 
 continue to melt absorb heat in the endeavor to maintain 
 the equilibrium temperature within the system. 
 
CHAPTER X. 
 THERMOCHEMISTRY. 
 
 IT is a matter of common experience that chemical change 
 is accompanied by heat evolution or heat absorption aside 
 from the recombination of matter on an altered plan, which 
 especially characterises such change, there is a redistribution of 
 energy effected in such a way that either previously bound 
 (chemical) energy is set free in the form of heat, or available 
 heat energy (supplied from without to carry on the reaction) 
 is appropriated and properly disposed as chemical energy in 
 the new system. 
 
 Our ordinary chemical equations do not represent these 
 associated heat changes, but it should be well understood that 
 the quantity of heat evolved or absorbed during any given 
 chemical change, under definite conditions, is quite as specific 
 and definite as is the nature of the substances formed 
 specified in the equation. 
 
 To properly record the heat effect corresponding to any given 
 reaction, we must adopt some system of measuring heat, and then 
 specify certain fixed amounts of the reacting substances. The 
 first of these requirements is realized by referring quantities of 
 heat to a unit quantity, called the calorie, sufficient to elevate the 
 temperature of one gram of water one degree centigrade; the 
 second, by uniformly choosing gram molecules of the different 
 substances in the proportions defined by the equation as a basis 
 for the thermal data. In place of the gram calorie, defined above, 
 the kilogram calorie, or the heat quantity required to elevate 
 1000 g. of water one degree centigrade, is frequently used as a 
 more convenient measure when the heat effects are consider- 
 able. These terms are commonly abbreviated to cal. and CaL 
 respectively. 
 
 The direct measurement of a heat effect attending a given 
 chemical reaction is effected by enclosing the reaction mixture 
 in a suitable vessel, placing the latter in a calorimeter, and then 
 
 116 
 
THERMOCHEMISTRY. 117 
 
 starting the process, perhaps by an electric spark. The calo- 
 rimeter is usually a receptacle containing a weighed quantity of 
 water (water calorimeter) which is kept in agitation by a stirring 
 apparatus to insure an even distribution of heat, supplied with 
 an apparatus thermometer for measuring the temperature. 
 Heat from the reaction, raises the temperature of the water in the 
 calorimeter, and observation of the temperature difference before 
 and after the reaction, coupled with knowledge of the amount 
 of water involved, enables us to calculate the total heat quantity 
 concerned in changing the temperature of the water. Some 
 heat is used in raising the temperature of the containing vessel. 
 Suppose this vessel is made from some definite kind of material. 
 Then, a well-defined amount of heat will be required to raise the 
 temperature of one gram of this substance one degree. This 
 amount expressed in calories is called the specific heat of the 
 material. The weight of the vessel (in grams) multiplied by its 
 specific heat gives the heat quantity required to raise it one 
 degree. This value multiplied by the temperature difference 
 noted above gives the heat quantity used to produce its eleva- 
 tion to the final temperature of the experiment, which must be 
 added to the value calculated from the change in temperature 
 of the water. Other corrections are necessary, according to 
 the general method of procedure. 
 
 The heat effect accompanying a reaction is called, in general, 
 the heat of reaction. Owing to the existence of distinct varieties 
 of chemical action, we may substitute more descriptive terms 
 for this general term. Thus, the student will readily appreciate 
 the logic of designating the heat of reaction when 12 g. of carbon 
 are completely burned to carbon dioxide, according to the 
 equation: 
 
 C + O 2 = CO 2 , 
 
 as the heat of combustion, or the heat of oxidation of carbon. 
 This heat effect is very considerable, amounting to about 100 CaL 
 Again, the heat evolved or absorbed when one gram molecule 
 of a compound is formed from its elements, is called its heat of 
 formation. If heat is evolved during such formation, the com- 
 pound or reaction is said to be exothermic ; if absorbed, the term 
 endothermic is applied. 
 
118 CHEMICAL THEORY. 
 
 When 1 g. of hydrogen combines with 35.5 g. of chlorine: 
 }(H 2 + C1 2 = 2HC1), 
 
 about 22 Cal. of heat are liberated. The heat of formation 
 of the exothermic compound, hydrochloric acid, is, therefore, 
 22 Cal. 
 
 Most compounds are exothermic. As an example of the other, 
 or less common type, we may mention Acetylene C 2 H 2 , one gram 
 molecule of which is formed from its elements under a heat 
 absorption of about 53 Cal. When this endothermic compound 
 is burned, in addition to the heat of combustion due to the 
 carbon and hydrogen which it contains, there is an evolution 
 of 53 Cal. corresponding to the decomposition itself. 
 
 The descriptive terms, (latent) heat of fusion and (latent) 
 heat of vaporization, commonly signify in physics, the heat 
 quantity required to completely melt, or vaporize one gram of the 
 substance at its melting point, or boiling point respectively. 
 Such values must be multiplied by the molecular weights of the 
 substances to which they refer, if they are to be used in a chemi- 
 cal connection. 
 
 Obviously, the heat evolved by a given reaction will depend 
 upon the states of aggregation of the substances in general. 
 Thus, the heat of formation of liquid water at 100 is about 
 68 Cal. Some of this heat, however, will go to vaporize the 
 water, so that in practice, water vapor, instead of liquid water, 
 will be formed. The heat quantity necessary to convert one 
 gram molecule of liquid water at 100 into water vapor, at the 
 same temperature, is about 9.5 Cal. Hence, the difference, 
 689.5, or 58.5 Cal. will be evolved when one gram molecule of 
 water vapor is formed. In the above case, passing directly 
 from the gases, hydrogen and oxygen to water vapor, at the 
 constant temperature, 100, we have a heat evolution of 58.5 Cal.: 
 
 2H + O = H 2 * + 58.5 Cal. (1) 
 
 vapor 
 
 * In order that the equation may show one molecule of water, atoms 
 instead of molecules of hydrogen are represented. In general, equations 
 should show molecules, when the volume relations (in the case of gases) are at 
 once apparent (by Avogadro's Law). Thus: 
 
 2H 2 + 2 = 2H 2 0. 
 
 2 mols 1 mol 2 mols 
 2 vols 1 vol 2 vols 
 
 Cf. pages 14 and 28. 
 
THERMOCHEMISTRY 119 
 
 Considering this as a dual process: 
 
 2H + O = H 2 O + 68 CaL, (2) 
 
 liquid 
 
 and, 
 
 H 2 + 9.5 CaL = H 2 O, (3) 
 
 liquid vapor 
 
 we obtain by summation, 58.5 CaL (68 4- - 9.5), the final heat 
 effect to be written as a positive value in the right hand 
 member of equation (1). 
 
 In this way, we may pass from one system to another through 
 many individual physical and chemical processes, or directly 
 in one operation, but the final heat effect representing the sum of 
 all heat effects concerned in the entire series of constituent 
 changes, will invariably be the same. This principle known as 
 the Law of Hess, may be concisely stated as follows: 
 
 The total calorific effect which accompanies the transformation 
 of one chemical system into another is independent of the steps 
 passed through. 
 
 The thermal behavior of acids, bases, and salts in aqueous 
 solution was not well understood until the advent of the elec- 
 trolytic dissociation theory. When solutions of electrolytes in 
 the dissociated condition are mixed and no marked combination 
 between the ions occurs, there will be no marked heat effect. 
 Thus, we refer to the thermo-neutrality of salt solutions. Since 
 salts are dissociated to the same general extent, which we may 
 regard as practically complete in ordinarily dilute solution, no 
 appreciable change takes place when dilute solutions of different 
 salts are mixed. When a salt is dissolved in water, there is a 
 heat effect, corresponding to the dissociation of its molecules 
 into ions. 
 
 The reaction which alone occurs to any extent when a dilute 
 solution of any strong acid is mixed with a dilute solution of any 
 strong base, is: 
 
 H 4- OH = H 2 O. 
 
 Hence, the same heat effect accompanies all neutralization 
 reactions in dilute solution, where strong acids and bases are 
 concerned. 
 
INDEX. 
 
 Acid, 25; monobasic, diabasic, poly- 
 basic, 25; binary, 26; oxygen, 26. 
 
 Acid anhydrides, 26. 
 
 Acidic substances, 27, 31. 
 
 Acid radical, 25. 
 
 Acids, nomenclature of, 26. 
 
 Active mass, 98. 
 
 Adhesion, 20. 
 
 Allot ropism, 16. 
 
 Ammonia, solubility in water, 21. 
 
 Amorphous solids, 5, 16. 
 
 Anion, 73. 
 
 Anisotropic substances, 5, 16. 
 
 Anode, 73. 
 
 Atoms, 5, 11, 12; weight of hydrogen, 
 12 ; groups of, 23. 
 
 Atomic quantity, 28. 
 
 Atomic theory, 5. 
 
 Atomic weight determination, out- 
 line of method, 56; refinement of, 
 58. 
 
 Atomic weight of carbon, 57; of 
 hydrogen, 59; of oxygen, 59; of 
 sulphur, 57. 
 
 Atomic weights, 12, 22, 28. 
 
 Base, 25. 
 
 Basic substances, 27, 31. 
 Boiling point, 3. 
 Boiling point elevation, 51. 
 Bromine, number of atoms in mole- 
 cule, 14, 40. 
 
 Calculation of formulas, rule for, 61. 
 
 Calculations based on chemical equa- 
 tions, 35. 
 
 Calorie, 116; gram, 116; kilogram, 116. 
 
 Calorimeter, 116. 
 
 Canal rays, 8. 
 
 Cathode, 73; rays, 7. 
 
 Cation, 73. 
 
 Chemical analysis, bearing on atomic 
 weight determination, 55; bearing 
 on calculation of formulas, 60. 
 
 Chemical change, 2. 
 
 Chemical compounds, 3. 
 
 Chemical equations, calculations based 
 on, 35; construction of, 28. 
 
 Chemical reaction, 2 ; types of, 30. 
 
 Chlorine, number of atoms in mole- 
 cule, 14, 40. 
 
 Cohesion, 20. 
 
 Common ion effect, 104. 
 
 Combination, 30. 
 
 Complex amions and cations, 89. 
 
 Components, in a phase system, 108. 
 
 Concentration, of a solution, 20. 
 
 Conduction, electrolytic, 71 ; metallic, 
 71. 
 
 Conservation of energy, 3. 
 
 Conservation of matter, 3. 
 
 Corpuscular theory, 6. 
 
 Critical phenomena, 16, 112. 
 
 Crystalline solids, 5, 16. 
 
 Dalton's theory, 11; modification of, 
 by Avogadro, 11. 
 
 Decomposition, 30; double, 30. 
 
 Degree of dissociation, calculation of, 
 from freezing point measurements, 
 77-9; calculation of, from conduc- 
 tivity measurements, 79-81. 
 
 Diffusion, gaseous, 19; liquid, 65. 
 
 Dimorphous substances, 16. 
 
 Dissociation, 94; of N 2 O 4 , 95; of 
 HI, 95; of I 2 , 96. 
 
 Dissociation coefficient, 103. 
 
 Divisibility of oxygen molecule, 12. 
 
 Electrical conductivity, specific, 80; 
 
 molecular, 80. 
 
 Electrolysis, 71 ; of HC1, 72. 
 Electrolytes, 69; non-, 69; reaction 
 
 between solutions of, 84. 
 Electrolytic dissociation, 70, 84; of 
 
 acids, bases, salts, and water, 82-84. 
 Electrolytic solution tension, 91. 
 Elements, 3; natural groups of, 39, 
 
 43; periods of, 41, 43. 
 Endothermic substances, 117. 
 Energy transformations, 2. 
 Equation writing, 30. 
 Equilibrium, 30, 84, 100; between an 
 
 electrolyte and its ions, 103; in 
 
 system H 2 O, 111; in system H,O- 
 
 NaCl, 114. 
 
 121 
 
122 
 
 INDEX. 
 
 Equilibrium coefficient of a reversible 
 
 reaction, 100. 
 Equivalents, 23. 
 Exothermic substances, 117. 
 
 Fluorine, number of atoms in mole- 
 cule, 14, 40. 
 
 Formula, 21, 60; construction of a, 63 ; 
 weights, 28. 
 
 Formulas, method of calculating, 61; 
 simplest, 62. 
 
 Freezing point constant of a solvent, 
 53; mathematical expression for, 
 53, 54. 
 
 Freezing point lowering, 51 ; by acids, 
 bases, and salts, 67. 
 
 Gas, molecular condition of, 15. 
 
 Gas density, 47, 48; method of molec- 
 ular weight determination, 47. 
 
 Gases, electric discharge through, 6. 
 
 Gas laws, 17; applied to dilute solu- 
 tion, 42; deduction of, from kinetic 
 theory, 18. 
 
 Gold and silver, miscibility of, 20. 
 
 Gram atom, 28. 
 
 Gram ion, 75. 
 
 Gram molecular volume, 48. 
 
 Gram molecule, 28. 
 
 Groups of atoms, 23; of elements, 39. 
 
 Halogens, 39. 
 
 Heat, of combustion, 117; of for- 
 mation, 117; of fusion, 118; of 
 oxidation, 117; of reaction, 117; of 
 vaporization, 118; specific, 117. 
 
 Heterogeneous equilibrium, 1 14 ; com- 
 plete, 114; incomplete, 114. 
 
 Hydrochloric acid, composition of, 
 14 ; concentrated, 37 ; dilute, 37. 
 
 Hydrogen, number of atoms in mole- 
 cule, 14 ; position of, in periodic sys- 
 tem, 44; replaceable, 25; weight 
 of one atom, 12; weight of one 
 liter, 38. 
 
 Hydrogen standard, of atomic weights 
 of, 59 ; of gas density measurements, 
 47. 
 
 Hydrolysis, 105. 
 
 Iodine, number of atoms in molecule, 
 
 14, 40. 
 Ion, 70. 
 
 Ionic quantity, 75. 
 lonization, 70, 84. 
 Ions, complex, 89. 
 Iron, polymorphic modifications of, 
 
 16. 
 
 Isomeric substances, 17. 
 Isotropic substances, 5, 16. 
 
 Kinetic theory, 14, 17, 18, 19, 96. 
 
 Law of Avogadro, 11, 14, 19, 47, 49, 
 50, 69; of Boyle, 11, 18; of Charles, 
 11, 19; of chemical mass action, 98; 
 same applied to electrolytic dissocia- 
 tion, 103 ; mathematical expression 
 for same, 99 ; of constant composi- 
 tion, 3; of definite proportions, 3; of 
 Dulong and Petit, 57; of Faraday, 
 76; of Gay Lussac, 11; of Henry, 
 20; of Hess, 119; of multiple pro- 
 portions, 4 ; of Raoult, 52. 
 
 Lead and zinc, miscibility of, 20. 
 
 Liquid, molecular condition of, 15. 
 
 Melting point, 3. 
 
 Membrane, semipermeable, 65. 
 
 Metals, solution of, in acids, 91. 
 
 Metallic hydroxides, 26. 
 
 Metameric substances, 17. 
 
 Miscibility, of gases, 4, 19 ; of liquids, 
 4, 20; of solids, 4, 20. 
 
 Mixed crystals, 20. 
 
 Molecular depression of the freezing 
 point, 53. 
 
 Molecular quantity, 28. 
 
 Molecular theory, 5. 
 
 Molecular weights, 22, 28, 47; from 
 freezing point measurements, 51 ; 
 from gas density, 48 ; from osmotic 
 pressure, 50; of dissolved sub- 
 stances, 50. 
 
 Molecules, 5, 11, 12, 15; number in 
 1 c.c. gas, 12. 
 
 Natural group of elements, 39, 43. 
 
 Neutralization, 31, 86, 119. 
 
 Nitrogen, number of atoms in mole- 
 cule, 14. 
 
 Nomenclature of acids and salts, 26. 
 
 Non-metals, enumeration of and 
 place in periodic table, 44. 
 
 Osmotic pressure, 50, 64; measure- 
 ment of, 64 ; molecular weight deter- 
 mination by measurement of, 50. 
 
 Oxidation, 32 ; states of, 34. 
 
 Oxidizing agent, 32. 
 
 Oxides, 26, 31. 
 
 Oxygen, available, 32; bearing on 
 chemical change, 31; divisibility of 
 molecule, 12: number of atoms in 
 molecule, 14, 17. 
 
 Oxygen standard of atomic weights, 
 12, 22, 48, 59. 
 
 Ozone, number of atoms in molecule, 
 17. 
 
 Partial pressure of a gas, 21. 
 Periodic law, 45. 
 
INDEX 
 
 123 
 
 Periodic system, 41; table, 42; use in 
 defining atomic weight values, 58. 
 
 Phases, 108. 
 
 Phase rule, 109. 
 
 Physical change, 1. 
 
 Physical mixture, 4. 
 
 Polymeric substances, 17. 
 
 Polymorphous substances, 16. 
 
 Potential, electrical, 73. 
 
 Precipitation, 31; discussion of, 87, 
 104. 
 
 Radio-active bodies, 8, 9. 
 
 Rays; a, /?, y, canal, cathode, Roent- 
 gen, X-, 6-10. 
 
 Reaction, at electrodes during elec- 
 trolysis, 74, 75 ; between acidic and 
 basic substances, 31; of cone, sul- 
 phuric acid on a salt, 31, 102; re- 
 versible, 30, 94. 
 
 Reducing agent, 32. 
 
 Reduction, 32. 
 
 Replacement, 31, 90. 
 
 Reversible reaction, 30, 94. 
 
 Roentgen rays, 8. 
 
 Salt, 25; acid, basic, normal, 25; 
 double, 26, 90. 
 
 Salts, hydrated, 26; mixed, 26; nom- 
 enclature of, 26 ; reactions between 
 dissolved, 87. 
 
 Saturated solution, 20. 
 
 Silver and gold, miscibility of, 20. 
 
 Sodium chloride, proportion of mole- 
 cules dissociated in an aqueous 
 solution of, 68, 81. 
 
 Solid, molecular condition of, 15; var- 
 ious modifications of, 5, 16. 
 
 Solid solution, 4. 
 
 Solubility, 20. 
 
 Solubility product, 103. 
 
 Solution, 20 ; concentration of a, 20 ; 
 of a gas in a liquid, 20, 21; satu- 
 rated, 20. 
 
 Solution tension, electrolytic, 91. 
 
 Solvent, 20. 
 
 State of aggregation, 2, 5. 
 
 Stochiometrical calculations, 22, 35. 
 
 Sulphuric acid, reaction of (cone.) on 
 a salt of a volatile acid, 31, 102. 
 
 Symbol, 21 ; weights, 28. 
 
 System, diyariant, 103, 106; equi- 
 librium in one-component, 103; 
 monovariant, 103, 106 ; nonvariant, 
 103, 107. 
 
 Table of the elements, 42. 
 
 Tests, 88. 
 
 Thermoneutrality of salt solutions, 
 
 119. 
 
 Transition temperatures, 17. 
 Trimorphous substances, 16. 
 Triple point, 113. 
 
 Valence, 23; increase or decrease in, 
 
 34. 
 Vapor tension lowering by dissolved 
 
 substances, 51. 
 Vapor pressure, 15. 
 Vapor tension of a liquid, 15. 
 Velocity coefficient of a reaction, 100. 
 Volume, gram molecular, 48. 
 
 Water, composition and formula of, 
 60, 61. 
 
 Weights, atomic, 12, 22, 28; mole- 
 cular, 22, 28, 47. 
 
 X-rays, 8. 
 
 Zinc and lead, miscibility of, 20. 
 
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 * Burr's Ancient and Modern Engineering and the Isthmian Canal 8vo, 3 50 
 
 Comstock's Field Astronomy for Engineers 8vo, 
 
 * Corthell's Allowable Pressures on Deep Foundations I2mo, 
 
 Crandall's Text-book on Geodesy and Least Squares 8vo, 
 
 Davis's Elevation and Stadia Tables 8vo, 
 
 Elliott's Engineering for Land Drainage i2mo, 
 
 Practical Farm Drainage i2mo, 
 
 *Fiebeger's Treatise on Civil Engineering 8vo, 5 oo 
 
 Flemer's Phototopographic Methods and Instruments 8vo, 5 oo 
 
 Folwell's Sewerage. (Designing and Maintenance.) 8vo, 3 oo 
 
 Freitag's Architectural Engineering 8vo, 3 50 
 
 French and Ives's Stereotomy 8vo, 2 50 
 
 Goodhue's Municipal Improvements I2mo, i 50 
 
 Gore's Elements of Geodesy 8vo, 2 50 
 
 * Hauch and Rice's Tables of Quantities for Preliminary Estimates I2mo, i 25 
 
 Hayford's Text-book of Geodetic Astronomy 8vo, 3 oo 
 
 Bering's Ready Reference Tables (Conversion Factors) i6mo, mor. 2 50 
 
 Howe's Retaining Walls for Earth i2mo, i 25 
 
 6 
 
* Ives's Adjustments of the Engineer's Transit and Level i6mo, Eds. 25 
 
 Ives and Hilts's Problems in Surveying i6mo, mor. i 50 
 
 Johnson's (J. B.) Theory and Practice of Surveying Small 8vo, 4 oo 
 
 Johnson's (L. J.) Statics by Algebraic and Graphic Methods 8vo, 2 oo 
 
 Kinnicutt, Winslow and Pratt's Purification of Sewage. (In Preparation). 
 Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) 
 
 i2mo, 2 oo 
 
 Mahan's Descriptive Geometry 8vo, i 50 
 
 Treatise on Civil Engineering. (1873.) (Wood.) 8vo, 5 oo 
 
 Merriman's Elements of Precise Surveying and Geodesy 8vo, 2 50 
 
 Merriman and Brooks's Handbook for Surveyors i6mo, mor. 2 oo 
 
 Morrison's Elements of Highway Engineering. (In Press.) 
 
 Nugent's Plane Surveying 8vo, 3 50 
 
 Ogden's Sewer Design I2mo, 2 oo 
 
 Parsons's Disposal of Municipal Refuse 8vo, 2 oo 
 
 Patton's Treatise on Civil Engineering 8vo, half leather, 7 50 
 
 Reed's Topographical Drawing and Sketching 4to, 5 oo 
 
 Rideal's Sewage and the Bacterial Purification of Sewage 8vo, 4 oo 
 
 Riemer's Shaft-sinking under Difficult Conditions. (Corning and Peele.) . .8vo, 3 oo 
 
 Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, I 50 
 
 Smith's Manual of Topographical Drawing. (McMillan.) 8vo, 2 50 
 
 Soper's Air and Ventilation of Subways. (In Press.) 
 
 Tracy's Plane Surveying 16mo, mor. 3 oo 
 
 * Trautwine's Civil Engineer's Pocket-book i6mo, mor. 5 oo 
 
 Venable's Garbage Crematories in America 8vo, 2 oo 
 
 Methods and Devices for Bacterial Treatment of Sewage 8vo, 3 oo 
 
 Wait's Engineering and Architectural Jurisprudence 8vo, 6 oo 
 
 Sheep, 6 50 
 
 Law of Contracts 8vo, 3 oo 
 
 Law of Operations Preliminary to Construction in Engineering and Archi- 
 tecture 8vo, 5 oo 
 
 Sheep, 5 50 
 
 Warren's Stereotomy Problems in Stone-cutting 8vo, 2 50 
 
 * Waterbury's Vest-Pocket Hand-book of Mathematics for Engineers. 
 
 2lXsl inches, mor.* i oo 
 Webb's Problems in the Use and Adjustment of Engineering Instruments. 
 
 i6mo, mor. i 25 
 
 Wilson's Topographic Surveying 8vo, 3 50 
 
 BRIDGES AND ROOFS. 
 
 Boiler's Practical Treatise on the Construction of Iron Highway Bridges. .8vo, 2 oo 
 
 Burr and Falk's Design and Construction of Metallic Bridges 8vo, 5 oo 
 
 Influence Lines for Bridge and Roof Computations 8vo, 3 oo 
 
 Du Bois's Mechanics of Engineering. Vol. II Small 4to, 10 oo 
 
 Foster's Treatise on Wooden Trestle Bridges 4to, 5 oo 
 
 Fowler's Ordinary Foundations 8vo, 3 50 
 
 French and Ives's Stereotomy 8vo, 2 50 
 
 Greene's Arches in Wood, Iron, and Stone , 8vo, 2 50 
 
 Bridge Trusses 8vo, 2 50 
 
 Roof Trusses. 8vo, i 25 
 
 Grimm's Secondary Stresses in Bridge Trusses 8vo, 2 50 
 
 Heller's Stresses in Structures arid the Accompany in Deformations 8vo, 
 
 Howe's Design of Simple Roof -trusses in Wood and Steel 8vo, 2 oo 
 
 Symmetrical Masonry Arches 8vo, 2 50 
 
 Treatise on Arches 8vo, 4 oo 
 
 Johnson, Bryan, and Turneaure's Theory and Practice in the Designing of 
 
 Modern Framed Structures Small 4to, 10 oo 
 
 7 
 
Merriman and Jacoby's Text-book on Roofs and Bridges : 
 
 Part I. Stresses in Simple Trusses 8vo, 2 50 
 
 Part II. Graphic Statics 8vo, 2 50 
 
 Part III. Bridge Design 8vo, 2 50 
 
 Part IV. Higher Structures 8vo, 2 50 
 
 Morison's Memphis Bridge Oblong 4to, 10 oo 
 
 Sondericker's Graphic Statics, with Applications to Trusses, Beams, and Arches. 
 
 8vo, 2 oo 
 
 Waddell's De Pontibus, Pocket-book for Bridge Engineers i6mo, mor, 2 oo 
 
 * Specifications for Steel Bridges i2mo, 50 
 
 Waddell and Harrington's Bridge Engineering. (In Preparation.) 
 
 Wright's Designing of Draw-spans. Two parts in one volume 8vo, 3 50 
 
 HYDRAULICS. 
 
 Barnes's Ice Formation 8vo, 3 oo 
 
 Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from 
 
 an Orifice. (Trautwine.) 8vo, 2 oo 
 
 Bovey's Treatise on Hydraulics 8vo, 5 oo 
 
 Church's Diagrams of Mean Velocity of Water in Open Channels. 
 
 Oblong 4to, paper, i 50 
 
 Hydraulic Motors 8vo, 2 oo 
 
 Mechanics of Engineering 8vo, 6 oo 
 
 Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50 
 
 Flather's Dynamometers, and the Measurement of Power i2mo, 3 oo 
 
 Folwell's Water-supply Engineering 8vo, 4 oo 
 
 Frizell's Water-power 8vo, 5 oo 
 
 Fuertes's Water and Public Health i2mb, i 50 
 
 Water-filtration Works i2mo, 2 50 
 
 Ganguillet and Kutter's General Formula for the Uniform Flow of Water in 
 
 Rivers and Other Channels. (Bering and Trautwine.) 8vo, 4 oo 
 
 Hazen's Clean Water and How to Get It Large I2mo, i 5o 
 
 * Filtration of Public Water-supplies 8vo, 3 oo 
 
 Hazlehurst's Towers and Tanks for Water- works 8vo, 2 50 
 
 Herschel's 115 Experiments on the Carrying Capacity of Large, Riveted, Metal 
 
 Conduits 8vo, 2 oo 
 
 Hoyt and Grover's River Discharge 8vo, 2 oo 
 
 Hubbard and Kiersted's Water- works Management and Maintenance 8vo, 4 oo 
 
 * Lyndon's Development and Electrical Distribution of Water Power. . . .8vo, 3 oo 
 Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 
 
 8vo, 4 oo 
 
 Merriman's Treatise on Hydraulics 8vo, 5 oo 
 
 * Michie's Elements of Analytical Mechanics 8vo, 4 oo 
 
 Mo liter's Hydraulics of Rivers, Weirs and Sluices. (In Press.) 
 
 Schuyler's Reservoirs for Irrigation, Water-power, and Domestic Water- 
 supply Large 8vo, 5 oo 
 
 * Thomas and Watt's Improvement of Rivers 4to, 6 oo 
 
 Turneaure and Russell's Public Water-supplies 8vo, 5 oo 
 
 Wegmann's Design and Construction of Dams. 5th Ed., enlarged 4to, 6 oo 
 
 Water-supply of the City of New York from 1658 to 1895 4to, 10 oo 
 
 Whipple's Value of Pure Water Large i2mo, i oo 
 
 Williams and Hazen's Hydraulic Tables 8vo, i 50 
 
 Wilson's Irrigation Engineering Small 8vo, 4 oo 
 
 Wolff's Windmill as a Prime Mover 8vo, 3 oo 
 
 Wood's Elements of Analytical Mechanics 8vo, 3 oo 
 
 Turbines 8vo, 2 50 
 
 8 
 
MATERIALS OF ENGINEERING. 
 
 Baker's Roads and Pavements 8vo, 5 oo 
 
 Treatise on Masonry Construction 8vo, 5 oo 
 
 Birkmire's Architectural Iron and Steel 8vo, 3 50 
 
 Compound Riveted Girders as Applied in Buildings 8vo, 2 oo 
 
 Black's United States Public Works Oblong 4to, 5 oo 
 
 Bleininger's Manufacture of Hydraulic Cement. (In Preparation.) 
 
 * Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 
 
 Burr's Elasticity and Resistance of the Materials of Engineering 8vo, 7 50 
 
 Byrne's Highway Construction 8vo, 5 oo 
 
 Inspection of the Materials and Workmanship Employed in Construction. 
 
 i6mo, 3 oo 
 
 Church's Mechanics of Engineering 8vo, 6 oo 
 
 Du Bois's Mechanics of Engineering. 
 
 Vol. I. Kinematics, Statics, Kinetics Small 4to, 7 50 
 
 Vol. II. The Stresses in Framed Structures, Strength of Materials and 
 
 Theory of Flexures .' Small 4to, 10 oo 
 
 *Eckel's Cements, Limes, and Plasters 8vo, 6 oo 
 
 Stone and Clay Products used in Engineering. (In Preparation.) 
 
 Fowler's Ordinary Foundations 8vo, 3 50 
 
 Graves's Forest Mensuration 8vo, 4 oo 
 
 Green's Principles of American Forestry i2mo, I 50 
 
 * Greene's Structural Mechanics 8vo, 2 50 
 
 Holly and Ladd's Analysis of Mixed Paints, Color Pigments and Varnishes 
 
 Large izmo, 2 50 
 
 Johnson's Materials of Construction Large 8vo, 6 oo 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Kidder's Architects and Builders' Pocket-book i6mo, 5 oo 
 
 Lanza's Applied Mechanics 8vo, 7 50 
 
 Maire's Modern Pigments and their Vehicles i2mo, 2 oo 
 
 Martens's Handbook on Testing Materials. (Henning.) 2 vols 8vo, 7 50 
 
 Maurer's Technical Mechanics 8vo, 4 oo 
 
 Merrill's Stones for Building and Decoration 8vo, 5 oo 
 
 Merriman's Mechanics of Materials 8vo, 5 oo 
 
 * Strength of Materials i2mof i oo 
 
 Metcalf's Steel. A Manual for Steel-users i2mo, 2 oo 
 
 Patton's Practical Treatise on Foundations 8vo, 5 oo 
 
 Rice's Concrete Block Manufacture 8vo, 2 oo 
 
 Richardson's Modern Asphalt Pavements 8vo, 3 oo 
 
 Richey's Handbook for Superintendents of Construction i6mo, mor., 4 oo 
 
 * Ries's Clays: Their Occurrence, Properties, and Uses 8vo, 5 oo 
 
 Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo 
 
 *Schwarz'sLongleafPinein Virgin Forest iamo, i 25 
 
 Snow's Principal Species of Wood 8vo, 3 So 
 
 Spalding's Hydraulic Cement i2mo, 2 oo 
 
 Text-book on Roads and Pavements i2mo, 2 oo 
 
 Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo 
 
 Thurston's Materials of Engineering. In Three Parts 8vo, 8 oo 
 
 Part I. Non-metallic Materials of Engineering and Metallurgy 8vo, 2 oo 
 
 Part II. Iron and Steel 8vo, 3 5<> 
 
 Part in. A Treatise on Brasses, Bronzes, and Other Alloys and their 
 
 Constituents 8vo, 2 50 
 
 Tillson's Street Pavements and Paving Materials 8vo, 4 oo 
 
 Turneaure and Maurer's Principles of Reinforced Concrete Construction.. .8vo, 3 oo 
 Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on 
 
 the Preservation of Timber 8vo, 2 oo 
 
 Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 
 
 Steel 8vo, 4 OO 
 
 9 
 
RAILWAY ENGINEERING. 
 
 Andrews's Handbook for Street Railway Engineers 3x5 inches, mor. i 25 
 
 Berg's Buildings and Structures of American Railroads 4to, 5 oo 
 
 Brooks 's Handbook of Street Railroad Location i6mo, mor. 
 
 Butt's Civil Engineer's Field-book i6mo, mor. 
 
 Crandall's Railway and Other Earthwork Tables 8vo, 
 
 Transition Curve i6mo, mor. 
 
 * Crockett's Methods for Earthwork Computations 8vo, 
 
 Dawson's "Engineering" and Electric Traction Pocket-book i6mo. mor. 5 oo 
 
 Dredge's History of the Pennsylvania Railroad: (1879) Paper, 5 oo 
 
 Fisher's Table of Cubic Yards Cardboard, 25 
 
 Godwin's Railroad Engineers' Field-book and Explorers' Guide. . . i6mo, mor. 2 50 
 Hudson's Tables for Calculating the Cubic Contents of Excavations and Em- 
 bankments 8vo, i oo 
 
 Ives and Hilts's Problems in Surveying, Railroad Surveying and Geodesy 
 
 i6mo, mor. i 50 
 
 Molitor and Beard's Manual for Resident Engineers i6mo, i oo 
 
 Nagle's Field Manual for Railroad Engineers i6mo, mor. 3 oo 
 
 Philbrick's Field Manual for Engineers i6mo, mor. 3 oo 
 
 Raymond's Railroad Engineering. 3 volumes. 
 
 Vol. I. Railroad Field Geometry. (In Preparation.) 
 
 Vol. II. Elements of Railroad Engineering 8vo, 3 50 
 
 Vol. III. Railroad Engineer's Field Book. (In Preparation.) 
 
 Searles's Field Engineering i6mo, mor. 3 oo 
 
 Railroad Spiral i6mo, mor. i 50 
 
 Taylor's Prismoidal Formulae and Earthwork 8vo, i 50 
 
 *Trautwine's Field Practice of Laying Out Circular Curves for Railroads. 
 
 i2mo. mor, 2 50 
 
 * Method of Calculating the Cubic Contents of Excavations and Embank- 
 
 ments by the Aid of Diagrams 8vo, 2 oo 
 
 Webb's Economics of Railroad Construction Large i2mo, 2 50 
 
 Railroad Construction i6mo, mor. 5 oo 
 
 Wellington's Economic Theory of the Location of Railways Small 8vo, 5 oo 
 
 DRAWING. 
 
 Barr's Kinematics of Machinery 8vo, 2 50 
 
 * Bartlett's Mechanical Drawing 8vo, 3 oo 
 
 * " " " Abridged Ed 8vo, 150 
 
 Coolidge's Manual of Drawing 8vo, paper, i oo 
 
 Coolidge and Freeman's Elements of General Drafting for Mechanical Engi- 
 neers Oblong 4to, 2 50 
 
 Durley's Kinematics of Machines 8vo, 4 oo 
 
 Emch's Introduction to Projective Geometry and its Applications 8vo, 2 50 
 
 Hill's Text-book on Shades and Shadows, and Perspective 8vo, 2 oo 
 
 Jamison's Advanced Mechanical Drawing 8vo, 2 oo 
 
 Elements of Mechanical Drawing 8vo, 2 50 
 
 Jones's Machine Design: 
 
 Part I. Kinematics of Machinery 8vo, i 50 
 
 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo 
 
 MacCord's Elements of Descriptive Geometry 8vo, 3 oc 
 
 Kinematics ; or, Practical Mechanism 8vo, 5 oo 
 
 Mechanical Drawing 4to, 4 oo 
 
 Velocity Diagrams 8vo, i 50 
 
 McLeod's Descriptive Geometry Large i2mo, i 50 
 
 * Mahan's Descriptive Geometry and Stone-cutting 8vo, i 50 
 
 Industrial Drawing. (Thompson.) 8vo, 3 50 
 
 10 
 
Meyer's Descriptive Geometry 8vo, 2 oo 
 
 Reed's Topographical Drawing and Sketching 4:0, 5 oo 
 
 Reid's Course in Mechanical Drawing 8vo, 2 oo 
 
 Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo 
 
 Robinson's Principles of Mechanism 8vo, 3 oo 
 
 Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo 
 
 Smith's (R. S.) Manual of Topographical Drawing. (McMillan.) 8vo, 2 50 
 
 Smith (A. W.) and Marx's Machine Design 8vo, 3 oo 
 
 * Titsworth's Elements of Mechanical Drawing Oblong 8vo, i 25 
 
 Warren's Drafting Instruments and Operations I2mo, i 25 
 
 Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50 
 
 Elements of Machine Construction and Drawing 8vo, 7 50 
 
 Elements of Plane and Solid Free-hand Geometrical Drawing. . . . i . 2010, i oo 
 
 General Problems of Shades and Shadows 8vo, 3 oo 
 
 Manual of Elementary Problems in the Linear Perspective of Form and 
 
 Shadow i2mo, i oo 
 
 Manual of Elementary Projection Drawing I2mo, i 50 
 
 Plane Problems in Elementary Geometry I2mo, i 25 
 
 Problems, Theorems, and Examples in Descriptive Geometry 8vo, 2 50 
 
 Weisbach's Kinematics and Power of Transmission. (Hermann and 
 
 Klein.) : 8vo, 5 oo 
 
 Wilson's (H. M.) Topographic Surveying 8vo, 3 50 
 
 Wilson's (V. T.) Free-hand Lettering 8vo, i oo 
 
 Free-hand Perspective 8vo, 2 50 
 
 Woolf's Elementary Course in Descriptive Geometry .Large 8vo, 3 oo 
 
 ELECTRICITY AND PHYSICS. 
 
 * Abegg's Theory of Electrolytic Dissociation, (von Ende.) i2mo, i 25 
 
 Andrews's Hand-Book for Street Railway Engineering 3X5 inches, mor., i 25 
 
 Anthony and Brackett's Text-book of Physics. (Magie.) Large i2mo, 3 oo 
 
 Anthony's Lecture-notes on the Theory of Electrical Measurements. . . .i2mo, i oo 
 
 Benjamin's History of Electricity 8vo, 3 oo 
 
 Voltaic Cell 8vo, 3 oo 
 
 Betts's Lead Refining and Electrolysis 8vo, 4 oo 
 
 Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.).8vo, 3 oo 
 
 * Collins's Manual of Wireless Telegraphy i2mo, i 50 
 
 Mor. 2 oo 
 
 Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 oo 
 
 * Danneel's Electrochemistry. (Merriam.) I2mo, i 25 
 
 Dawson's "Engineering" and Electric Traction Pocket-book i6mo, mor 5 oo 
 
 Dolezalek's Theory of the Lead Accumulator (Storage Battery), (von Ende.) 
 
 i2mo, 2 50 
 
 Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 4 oo 
 
 Flather's Dynamometers, and the Measurement of Power i2mo, 3 oo 
 
 Gilbert's De Magnete. (Mottelay.) 8vo, 2 50 
 
 * Hanchett's Alternating Currents I2mo, i oo 
 
 Bering's Ready Reference Tables (Conversion Factors) i6mo, mor. 2 50 
 
 Hobart and Ellis 's High-speed Dynamo Electric Machinery. (In Press.) 
 
 Holman's Precision of Measurements 8vo, 2 oo 
 
 Telescopic Mirror-scale Method, Adjustments, and Tests. .. .Large 8vo, 75 
 
 * Karapetoff 's Experimental Electrical Engineering 8vo, 6 oo 
 
 Kinzbrunner's Testing of Continuous-current Machines 8vo, 2 oo 
 
 Landauer's Spectrum Analysis. (Tingle.) 8vo, 3 oo 
 
 Le Chatelier's High-temperature Measurements. (Boudouard Burgess.) 12010, 3 oo 
 
 Lob's Electrochemistry of Organic Compounds. (Lorenz.) 8vo, 3 oo 
 
 * Lyndon's Development and Electrical Distribntion of Water Power 8vo, 3 oo 
 
 * Lyons'? Treatise on Electromagnetic Phenomena. Vols. I. and II. 8vo, each, 6 oo 
 
 * Michie's Elements of Wave Motion Relating to Sound and Light 8vo, 4 oo 
 
 11 
 
Morgan's Outline of the Theory of Solution and its Results i2mo, i oo 
 
 * Physical Chemistry for Electrical Engineers I2mo, i 50 
 
 Niaudet's Elementary Treatise on Electric Batteries. (Fishback). . . . i2mo, a 50 
 
 * Norris's Introduction to the Study of Electrical Engineering 8vo, 2 50 
 
 * Parshall and Hobart's Electric Machine Design 4to, half morocco, 12 50 
 
 Reagan's Locomotives: Simple, Compound, and Electric. New Edition. 
 
 Large I2mo, 3 50 
 
 * Rosenberg's Electrical Engineering. (Haldane Gee Kinzbrunner.). . .8vo, 2 oo 
 
 Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50 
 
 Swapper's Laboratory Guide for Students in Physical Chemistry i2mo, i oo 
 
 Thurston's Stationary Steam-engines , 8vo, 2 50 
 
 * Tillman's Elementary Lessons in Heat 8vo, i 50 
 
 Tory and Pitcher's Manual of Laboratory Physics Large i2mo, 2 oo 
 
 Ulke's Modern Electrolytic Copper Refining 8vo, 3 oo 
 
 LAW. 
 
 * Davis's Elements of Law 8vo, 2 50 
 
 * Treatise on the Military Law of United States 8vo, 7 oo 
 
 Sheep, 7 50 
 
 * Dudley's Military Law and the Procedure of Courts-martial . . . .Large i2mo, 2 50 
 
 Manual for Courts-martial i6mo, mor. i 50 
 
 Wait's Engineering and Architectural Jurisprudence 8vo, 6 oo 
 
 Sheep, 6 50 
 
 Law of Contracts 8vo, 3 oo 
 
 Law of Operations Preliminary to Construction in Engineering and Archi- 
 tecture 8vo 5 oo 
 
 Sheep, 5 50 
 MATHEMATICS. 
 
 Baker's Elliptic Functions 8vo, 50 
 
 Briggs's Elements of Plane Analytic Geometry. (Bocher) i2mo, oo 
 
 * Buchanan's Plane and Spherical Trigonometry 8vo, oo 
 
 Byerley's Harmonic Functions 8vo, oo 
 
 Chandler's Elements of the Infinitesimal Calculus i2mo, oo 
 
 Compton's Manual of Logarithmic Computations i2mo, 50 
 
 Davis's Introduction to the Logic of Algebra 8vo, 50 
 
 * Dickson's College Algebra Large i2mo, 50 
 
 * Introduction to the Theory of Algebraic Equations Large i2mo, 25 
 
 Emch's Introduction to Projective Geometry and its Applications 8vo, 50 
 
 Fiske's Functions of a Complex Variable . 8vo, oo 
 
 Halsted's Elementary Synthetic Geometry 8vo, 50 
 
 Elements of Geometry 8vo, 75 
 
 * Rational Geometry I2mo, 50 
 
 Hyde's Grassmann's Space Analysis 8vo, oo 
 
 * Jonnson's (J- B.) Three-place Logarithmic Tables: Vest-pocket size, paper, 15 
 
 100 copies, 5 oo 
 
 * Mounted on heavy cardboard, 8 X 10 inches, 25 
 
 10 copies, 2 oo 
 Johnson's (W. W.) Abridged Editions ot Differential and Integral Calculus 
 
 Large i2mo, i vol. 2 50 
 
 Curve Tracing in Cartesian Co-ordinates i2mo, i oo 
 
 Differential Equations 8vo, i oo 
 
 Elementary Treatise on Differential Calculus. (In Press.) 
 
 Elementary Treatise on the Integral Calculus Large I2mo, I 50 
 
 * Theoretical Mechanics , i2mo, 3 oo 
 
 Theory of Errors and the Method of Least Squares ramo, i 50 
 
 Treatise on Differential Calculus Large i2mo, 3 oo 
 
 Treatise on the Integral Calculus Large i2mo, 3 oo 
 
 Treatise on Ordinary and Partial Differential Equations. . Large 12 mo, 3 50 
 
 12 
 
Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.). i2mo, 2 oo 
 
 * Ludlow and Bass's Elements of Trigonometry and Logarithmic and Other 
 
 Tables 8vo, 3 oo 
 
 Trigonometry and Tables published separately Each, 2 oo 
 
 * Ludlow's Logarithmic and Trigonometric Tables 8vo, i oo 
 
 Macfarlane's Vector Analysis and Quaternions .8vo, i oo 
 
 McMahon's Hyperbolic Functions 8vo, i oo 
 
 Manning's IrrationalNumbers and their Representation bySequences and Series 
 
 i2mo, i 25 
 Mathematical Monographs. Edited by Mansfield Merriman and Robert 
 
 S. Woodward Octavo, each i oo 
 
 No. i. History of Modern Mathematics, by David Eugene Smith. 
 No. 2. Synthetic Projective Geometry, by George Bruce Halsted. 
 No. 3. Determinants, by Laenas Gifford Weld. No. 4. Hyper- 
 bolic Functions, by James McMahon. Ko. $. Harmonic Func- 
 tions, by William E. Byerly. No. 6. Grassmann's Space Analysis, 
 by Edward W. Hyde. No. 7. Probability and Theory of Errors, 
 by Robert S. Woodward. No. 8. Vector Analysis and Quaternions, 
 by Alexander Macfarlane. No. 9. Differential Equations, by 
 William Woolsey Johnson. No. 10. The Solution of Equations, 
 by Mansfield Merriman. No. n. Functions of a Complex Variable, 
 by Thomas S. Fiske. 
 
 Maurer's Technical Mechanics 8vo, 4 oo 
 
 Merilman's Method of Least Squares 8vo, 2 oo 
 
 Solution of Equations 8vo, i oo 
 
 Rice and Johnson's Differential and Integral Calculus. 2 vols. in one. 
 
 Large i2mo, i 50 
 
 Elementary Treatise on the Differential Calculus Large i2mo, 3 oo 
 
 Smith's History of Modern Mathematics 8vo, i oo 
 
 * Veblen and Lennes's Introduction to the Real Infinitesimal Analysis of One 
 
 Variable 8vo, 2 oo 
 
 * Waterbury's Vest Pocket Hand-Book of Mathematics for Engineers. 
 
 2&X5t inches, mor., i oo 
 
 Weld's Determinations 8vo, i oo 
 
 Wood's Elements of Co-ordinate Geometry 8vo, 2 oo 
 
 Woodward's Probability and Theory of Errors 8vo, I oo 
 
 MECHANICAL ENGINEERING. 
 
 MATERIALS OF ENGINEERING, STEAM-ENGINES AND BOILERS. 
 
 Bacon's Forge Practice lamo, 50 
 
 Baldwin's Steam Heating for Buildings i2mo, 50 
 
 Bair's Kinematics of Machinery 8vo, 50 
 
 * Bartlett's Mechanical Drawing 8vo, oo 
 
 * " " Abridged Ed 8vo, 50 
 
 Benjamin's Wrinkles and Recipes i2mo, oo 
 
 * Burr's Ancient and Modern Engineering and the Isthmian Canal 8vo, 3 50 
 
 Carpenter's Experimental Engineering 8vo, 6 oo 
 
 Heating and Ventilating Buildings 8vo, 4 oo 
 
 Clerk's Gas and Oil Engine Large i2mo, 4 oo 
 
 Compton's First Lessons in Metal Working I2mo, i 50 
 
 Compton and De Groodt's Speed Lathe 12mo, i 50 
 
 Coolidge's Manual of Drawing 8vo, paper, i oo 
 
 Coolidge and Freeman's Elements of General Drafting for Mechanical En- 
 gineers Oblong 4to, 2 50 
 
 Cromwell's Treatise on Belts and Pulleys i2mo, i 50 
 
 Treatise on Toothed Gearing I2mo, i 50 
 
 Durley's Kinematics of Machines 8vo, 4 oo 
 
 13 
 
Flather's Dynamometers and the Measurement of Power i2mo, 3 oo 
 
 Rope Driving i2mo, 2* o 
 
 Gill's Gas and Fuel Analysis for Engineers i2mo, i 25 
 
 Goss'n Locomotive Sparks 8vo, 2 oo 
 
 Hall's Car Lubrication I2mo, i oo 
 
 Bering's Ready Reference Tables (Conversion Factors) i6mo, mor. f 2 50 
 
 Hobart and Eliis's High Speed Dynamo Electric Machinery. (In Press.) 
 
 Button's Gas Engine 8vo, 5 oo 
 
 Jamison's Advanced Mechanical Drawing 8vo, 2 oo 
 
 Elements of Mechanical Drawing 8vo, 2 50 
 
 Jones's Machine Design: 
 
 Part I. Kinematics of Machinery 8vo, i 50 
 
 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo 
 
 Kent's Mechanical Engineers' Pocket-book i6mo, mor., 5 oo 
 
 Kerr's Power and Power Transmission 8vo, 2 oo 
 
 Leonard's Machine Shop Tools and Methods! 8vo, 4 oo 
 
 * Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.) . . 8vo, 4 oo 
 MacCord's Kinematics; or, Practical Mechanism 8vo, 5 oo 
 
 Mechanical Drawing 4to, 4 oo 
 
 Velocity Diagrams 8vo, i 50 
 
 MacFar land's Standard Reduction Factors for Gases. 8vo, i 50 
 
 Mahan's Industrial Drawing. (Thompson.) 8vo, 3 50 
 
 * Parshall and Hobart's Electric Machine Design . . . .Small 4to, half leather, 12 50 
 Peele's Compressed Air Plant for Mines. (In Press.) 
 
 Poole's Calorific Power of Fuels 8vo, 3 oo 
 
 * Porter's Engineering Reminiscences, 1855 to 1882 8vo, 3 oo 
 
 Reid's Course in Mechanical Drawing 8vo, 2 oo 
 
 Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo 
 
 Richard's Compressed Air i2mo, i 50 
 
 Robinson's Principles of Mechanism 8vo, 3 oo 
 
 Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo 
 
 Smith's (O.) Press-working of Metals 8vo, 3 oo 
 
 Smith (A. W.) and Marx's Machine Design 8vo, 3 oo 
 
 Sorel's Carbureting and Combustion in Alcohol Engines. (Woodward and 
 
 Preston.) Large i2mo, 3 oo 
 
 Thurston's Animal as a Machine and Prime Motor, and the Laws of Energetics. 
 
 I2mo 5 i oo 
 
 Treatise on Friction and Lost Work in Machinery and Mill Work... 8vo 9 3 oo 
 
 Tillson's Complete Automobile Instructor i6mo, i 50 
 
 mor., 2 oo 
 
 * Titsworth's Elements of Mechanical Drawing Oblong 8vo, i 25 
 
 Warren's Elements of Machine Construction and Drawing 8vo, 7 50 
 
 * Waterbury's Vest Pocket Hand Book of Mathematics for Engineers. 
 
 afXsf inches, mor., i Oo 
 Weisbach's Kinematics and the Power of Transmission. (Herrmann 
 
 Klein.) 8vo, 5 oo 
 
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 THE UNIVERSITY OF CALIFORNIA LIBRARY 
 
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 INTERNATIONAL ATOMIC WEIGHTS. 
 
 TABLI-; FOR 1908. 
 
 Ag 
 
 107.93 
 
 Silver. 
 
 N 
 
 14.01 
 
 Nitrogen. 
 
 Al 
 
 27.1 
 
 Aluminium. 
 
 Na 
 
 23.05 
 
 Sodium. 
 
 Ar 
 
 39.9 
 
 Argon. 
 
 Nb 
 
 94 
 
 Niobium. 
 
 As 
 
 75.0 
 
 Arsenic. 
 
 Nd 
 
 143.6 
 
 Neodymium. 
 
 Au 
 
 197.2 
 
 Gold. 
 
 Ne 
 
 20 
 
 Neon. 
 
 B 
 
 11.0 
 
 Boron. 
 
 Ni 
 
 58.7 
 
 Nickel. 
 
 Ba 
 
 137.4 
 
 Barium. 
 
 O 
 
 16.00 
 
 Oxygen. 
 
 Be 
 
 9.1 
 
 Beryllium. 
 
 Os 
 
 191 
 
 Osmium. 
 
 Bi 
 
 208.0 
 
 Bismuth. 
 
 P 
 
 31.0 
 
 Phosphorus. 
 
 Br 
 
 79.96 
 
 Bromine. 
 
 Pb 
 
 206.9 
 
 Lead. 
 
 C 
 
 12.00 
 
 Carbon. 
 
 Pd 
 
 106.5 
 
 Palladium. 
 
 Ca 
 
 40.1 
 
 Calcium. 
 
 Pr 
 
 140.5 
 
 Praseodymium. 
 
 Cd 
 
 112.4 
 
 Cadmium. 
 
 Pt 
 
 194.8 
 
 Platinum. 
 
 Ce 
 
 140.25 
 
 Cerium. . --^ 
 
 , Ra- 
 
 225 
 
 Radium. 
 
 Cl 
 
 35.45 
 
 Chlorine. 
 
 R1^ 
 
 85.5 
 
 Rubidium. 
 
 Co 
 
 59.0 
 
 Cobalt. 
 
 Rh 
 
 103.0 
 
 Rhodium. 
 
 Cr 
 
 52.1 
 
 Chromium. 
 
 Ru 
 
 101.7 
 
 Ruthenium 
 
 Cs 
 
 132.9 
 
 Caesium. 
 
 S 
 
 32.06 
 
 Sulphur. 
 
 Cu 
 
 63.6 
 
 Copper. 
 
 SB 
 
 120.2 
 
 Antimony. 
 
 Dy 
 
 162.5 
 
 Dysprosium. 
 
 Sc 
 
 44.1 
 
 Scandium. 
 
 Er 
 
 166 
 
 Erbium. 
 
 Se 
 
 79.2 
 
 Selenium. 
 
 Eu 
 
 152 
 
 Europium. 
 
 Si 
 
 28.4 
 
 Silicon. 
 
 F 
 
 19.0 
 
 Fluorine. 
 
 Sm 
 
 150.3 
 
 Samarium. 
 
 Fe 
 
 55.9 
 
 Iron. 
 
 Sn 
 
 119.0 
 
 Tin. 
 
 Ga 
 
 70 
 
 Gallium. 
 
 Sr 
 
 87.6 
 
 Strontium. 
 
 (id 
 
 156 
 
 Gadolinium 
 
 Ta 
 
 181 
 
 Tantalum. 
 
 Ge 
 
 72.5 
 
 Germanium. 
 
 Tb 
 
 159 
 
 Terbium. 
 
 H 
 
 1.008 
 
 Hydrogen. 
 
 Te 
 
 127.6 
 
 Tellurium. 
 
 He 
 
 4.0 
 
 Helium. 
 
 Th 
 
 232.5 
 
 Thorium. 
 
 Hg 
 
 200.0 
 
 Mercury. 
 
 Ti 
 
 48.1 
 
 Titanium. 
 
 I 
 
 126.97 
 
 Iodine/ 
 
 Tl 
 
 204.1 
 
 Thallium. 
 
 In 
 
 115 
 
 Indium. 
 
 Tu 
 
 171 
 
 Thulium. 
 
 Ir 
 
 193.0 
 
 Iridium. 
 
 U 
 
 238.5 
 
 L^ranium. 
 
 K 
 
 39.15 
 
 Potassium. 
 
 V 
 
 51.2 
 
 Vanadium. 
 
 Kr 
 
 81.8 
 
 Krypton. 
 
 w 
 
 184 
 
 Tungsten. 
 
 La 
 
 138.9 
 
 Lanthanum. 
 
 X 
 
 128 
 
 Xenon. 
 
 Li 
 
 7.03 
 
 Lithium. 
 
 Yt 
 
 89.0 
 
 Yttrium. 
 
 Mg 
 
 24.36 
 
 Magnesium. 
 
 Yb 
 
 173.0 
 
 Ytterbium. 
 
 Mn 
 
 55.0 
 
 Manganese. 
 
 Zn 
 
 65.4 
 
 Zinc. 
 
 Mo 
 
 96.0 
 
 Molybdenum. 
 
 Zr 
 
 90.6 
 
 Zirconium.