THE FUNDAMENTAL PRINCIPLES OF CHEMISTRY THE FUNDAMENTAL PRINCIPLES OF CHEMISTRY' AN INTRODUCTION TO ALL TEXT-BOOKS OF CHEMISTRY BY WILHELM OSTWALD u AUTHORIZED TRANSLATION BY HARRY W. MORSE LONGMANS, GREEN, AND CO. 91 AND 93 FIFTH AVENUE, NEW YORK LONDON, BOMBAY, AND CALCUTTA 1909 COPYRIGHT, 1909, BY LONGMANS, GREEN, & Co. All rights reserved THE UNIVERSITY PRESS, CAMBRIDGE, U.S.A. PREFACE Two tasks are set for the workers in any science. One of these is to enrich the chosen field by the discovery of new facts and the statement of new experiences. The other task is no less important, but its value is perhaps not so evident at first glance. It is to ar- range the facts already known in the best order and to bring out the relations between them as clearly as possible. Whenever progress in the first of these tasks has been rapid the second be- comes the more necessary, for it offers the only possible way of attaining mastery over the manifold separate experiences and of bringing the science as a whole into a convenient and serviceable form. The extraordinary development of the experimental side of the science of Chemistry has in some measure thrust into the back- ground the work which has been done on the methodical side. This work has not been wholly lost, but an examination of the various theories which have been advanced in the past few dec- ades, especially in the field of organic chemistry, indicates that most of them were born of the necessity of a day and that they were ephemeral in their influence. A desire for generalization is an important and justified one, and the only reason for the un- satisfactory outcome of all these theories is to be sought, in my opinion, in a fundamental error. Hypothetical assumptions were used in their development. Hypotheses were set up in each case with special reference to the phenomenon to be explained, and I believe that the right way has been obscured in many instances. Indication of the right way is given by the experience of other sciences which are older and simpler than Chemistry and which have therefore already attained the necessary ripeness. Mathe- 1 Q J.9.9.9 vi PREFACE matics, Geometry, and Mechanics began an examination of their fundamental principles years ago, and a firm foundation has now been set up for each of these sciences. The present time is de- cidedly philosophical in its trend, and in the past few years this task has been taken up with renewed vigour. The results of this labour form a valuable and fruitful portion of modern scientific knowledge. The end sought is the discovery of final truths and the relations between them, and these, when found, give safe foun- dation for further investigation. This does not mean the setting up of analogies and hypotheses, but the careful analysis of concepts and indication of the general facts of experience from which they are derived. In Chemistry research of this kind has been undertaken only casually and over small portions of the field. Franz Wald is one of the independents who has been working along this line for many years. General appreciation of the fundamental character of such investigation extends very slowly indeed. Three years ago, on the occasion of the Faraday lecture, I made an attempt to arouse the interest of chemists in these matters, but the result was not very encouraging. But few expressions of opinion were offered on this occasion, and these were largely contradictory in nature. It was quite evident that the question at issue was not clearly understood, and the entire matter was strange, even to chemists of note. But I know from personal experience that patient and continued labour can accomplish wonders even when the case seems hopeless. One must wait for the right time, and I am convinced that the time for this matter has arrived. The present book has for its object the presentation of the actual' fundamental principles of the science of Chemistry, their meaning and connection, as free as possible from irrelevant addi- tions. It represents in a sense the carrying out of a thought ex- pressed in the preface to my " Grundlinien der Anorganischen Chemie." It was there suggested that it was possible to work out a chemistry in the form of a rational scientific system, with- PREFACE vii out bringing in the properties of individual substances. In order to accomplish this, many exceedingly elementary things must be restated with special reference to the connection between them^ and it was also necessary to bring out many new connections in regions hitherto untouched. The difficulties which arise during such a first attempt became very clear to me as the work progressed, and I recognise them fully. They may serve as my excuse for the many irregularities in presentation which will be found in the book. There was no doubt in my mind that the work must be done sooner or later, and this is my justification for undertaking it and carrying it out to the best of my ability. The pedagogic importance of the matter is of the same order as its scientific importance. Questions concerning fundamental principles meet the teacher at every step, and the mental char- acter of the developing chemist is frequently determined by the way in which they are answered. This will explain my choice of a sub-title. I do not mean that the beginner should absorb the entire contents of this book before he learns about oxygen and chlorine as chemical individuals. I am quite of the opinion that a close personal acquaintance with a considerable number of important and characteristic substances is and always must be the fundament of all instruction in Chem- istry. But when this acquaintanceship has once been obtained it can be nothing but an advantage to the student to point out to him the great connections by which these separate facts are bound together into a unit; they may then be shown free from all that is individual and accidental, united into a great, simple whole. The book should be a guide to the teacher. It may serve to show him how such generalizations are to be handled and how they can be woven into his daily instruction in elementary chem- istry. Generalizations are the fundamental base of the chemical symphony; and the various separate parts may be varied accord- ing to need or desire. To make use of another simile, Generali- zations are the bony skeleton of the chemical body, and the teacher viii PREFACE must always let the bones appear through the individual chemical facts if he wishes to make of his teaching a true work of art. In two other books (" Grundlinien der Anorganischen Chemie" and " Schule der Chemie ") I have endeavoured to show practical solutions of this problem. I have often said that there may be any number of equally good solutions for it, and I hope that the present volume may serve as proof of this. May these " Funda- mental Principles " be of aid to each teacher in finding his own personal solution. W. OSTWALD. GROSS-BOTHEN, September, 1907. CONTENTS PAGES PREFACE . v-viii CHAPTER I BODIES, SUBSTANCES, AND PROPERTIES 1. Bodies. 2. Laws of nature. 3. Arbitrary properties and specific properties. 4. Substances and mixtures. 5. Chemical processes. 6. Energy. 7. Mechanical properties. Volume. 8. Volume. 9. Weight. 10. The conservation of weight. 11. Mass. 12. Density and specific volume. 13. Volume energy and pressure. 14. Quantities and intensi- ties. 15. Heat and temperature. 16. Compressibility. 17. Expansi- bility 1-25 CHAPTER II THE THREE STATES 18. The three states. 19. Solid bodies. Crystals. 20. Elasticity and energy of shape. 21. Surface energy. 22. Change of volume in solids. 23. Expansion of crystals. 24. Liquids. 25. Surface energy. 26. Vis- cosity. 27. Volume. 28. Water an exception. 29. Measurement of density. 30. Liquid crystals. 31. Gases. 32. Boyle's Law. 33. The Law of Gay-Lussac. 34. Absolute temperature and the absolute zero. 35. The gas law 26-46 CHAPTER III MIXTURES, SOLUTIONS, AND PURE SUBSTANCES 36. States. 37. Mixtures. 38. Methods of Separation. 39. Properties of mixtures. 40. Liquid solutions. 41. Solutions other than liquid ones. 42. Mixtures of liquids with solids. 43. Liquid mixtures. 44. Mixtures of gases. 45. Foams 47-59 ix x CONTENTS CHAPTER IV CHANGE OF STATE AND EQUILIBRIUM (a) The Equilibrium Liquid-Gas PAOEa 46. Equations of condition. 47. The liquefaction of gases. 48. Pure substances and solutions. 49. Reversibility. 50. Equilibrium. 51. Sat- uration. 52. The influence of pressure. 53. The vapour pressure of water. 54. Diagram. 55. Change of volume during evaporation. 56. Heat of vaporization. 57. The measurement of quantity of heat. 58. Entropy. 59. The critical point. 60. Phases. 61. Degrees of freedom. 62. Sublimation. 63. Suspended transformation . . . 60-80 (b) The Equilibrium Solid-LiquM 64. Melting and solidification. 65. The effect of pressure. 66. Supercool- ing. 67. The law of the displacement of equilibrium ~ 80-84 (c) Equilibrium between the three States 68. The triple point. 69. The equilibrium law. 70. The vapour pressure curve at the triple point 85-89 (d) The Equilibrium Solid-Solid 71. Allotropism. 72. The influence of pressure. 73. The phenomena of suspended transformation. 74. The step by step law. 75. The vapour pressure of allotropic forms 89-95 CHAPTER V SOLUTIONS 76. General considerations. 77. Kinds of solutions. 78. Solutions of gases. 79. Diffusion. 80. The applicability of the gas laws. 81. Partial pressure. 82. The gas constant as applied to solutions. 83. Other properties of gas solutions. 84. Separation of a gas solution into its constituents. 85. Semi-permeable diaphragms. 86. Separation step by step. 87. Analogy with change of state. 88. Pure substances. 89. Solutions of liquids in gases. 90. Saturation. 91. The influence of pressure. 92. The effect of temperature. 93. The phase rule. 94. Components. 95. Composition. 96. Liquid solutions. 97. Solutions of gases in liquids. 98. The law of absorption. 99. Solutions of liquids in liquids. 100. Unlimited solubility. 101. Maxima and minima. 102. Limited solubility. 103. The effect of temperature and pressure. CONTENTS xi PAGES 104. The critical point for solutions. 105. The separation of liquid solutions into their components. 106. The vapour of solutions. 107. Distillation. 108. Fractional distillation. 109. Singular points. 110. Singular solutions. 111. Gaseous solutions produced from liquid substances. 112. The vapour of partially miscible liquids. 113. Pos- sible cases. 114. The double line. 115. Equilibrium with solid sub- stances. 116. The effect of pressure and temperature. 117. Liquid solutions of solid substances. 118. The eutectic point. 119. Connec- tion with the ordinary solubility curve. 120. Solubility at the melting point. 121. The solubility of allotropic forms. 122. Solutions of higher order. 123. The general properties of singular points 96-165 CHAPTER VI ELEMENTS AND COMPOUNDS 124. Hylotropy. 125. Chemical processes in the narrower sense. 126. Ele- ments. 127. The reversibility of chemical processes. 128. The con- servation of the elements. 129. Synthetic processes. 130. The law of continuity. 131. Graphic representation. 132. Solutions made up of phases in the same state. 133. Two solids. 134. Solutions of dis- similar states. 135. One gas and one liquid. 136. The temperature axis. 137. Boiling point curves. 138. Two liquid phases. 139. One gas phase and two liquid phases. 140. The melting point curve. 141. The sublimation curve. 142. More complicated cases. 143. The appearance of chemical compounds. 144. Summary. 145. The effect of temperature. 146. More general conditions. 147. Two gases. 148. Energy content. 149. The law of constant proportions. 150. Two liquids. 151. Two solids. 152. Analytical methods. 153. Gases. 154. Liquids. 155. Triple systems. 156. Individual cases. 157. The evolution of a gas. 158. Liquid separation. 159. Solid separation. 160. The solution remains homogeneous 166-246 CHAPTER VII THE LAW OF COMBINING WEIGHTS M 161. The law of constant proportions. 162. Combining weights. 163. Ter- nary compounds and those of higher order. 164. The combining weights of compound substances. 165. The law of rational multi- ples. 166. Chemical formulae. 167. Chemical equations. 168. Methods of determining combining weights. 169. The indefiniteness of the combining weights. 170. The general relations of the combining weights 247-264 xii CONTENTS CHAPTER VIII COLLIGATIVE PROPERTIES PAGES 171. The law of gas volumes. 172. The relation to the combining weights. 173. Combining weight and molar weight. 174. Numerical values. 175. The properties of dilute solutions. 176. Molar lowering of the vapour pressure. 177. Osmotic pressure. 178. Numerical relations. 179. Interpretation. 180. The effect on freezing point. 181. The importance of the .solution laws. 182. Colligative properties . 265-289 CHAPTER IX REACTION VELOCITY AND EQUILIBRIUM 183. Reaction velocity. 184. Variable velocity. 185. The law of re- action velocity. 186. Catalysers. 187. Ideal catalysers. 188. Chemi- cal equilibria. 189. More than one phase. 190. The law of mass action. 191. Explanation of anomalous cases. 192. The quantitative investi- gation of equilibria. 193. Is equilibrium affected by a catalyser? 194. Induction and deduction 290-314 CHAPTER X ISOMERISM 195. The relation between composition and properties. 196. Poly- morphism. 197. The determination of the stability of polymorphic forms. 198. Isomerism. 199. Metamerism and polymerism. 200. Con- stitution. 201. Valence 315-330 CHAPTER XI THE IONS 202. Salt solutions and ions. 203. Faraday's law. 204. The concept of ions considered chemically. 205. Univalent and polyvalent ions. 206. The molar weight of salts. 207. The application of the phase law. 208. Electrolytic dissociation 331-341 INDEX . 343-349 THE OF CHEMISTRY CHAPTER I BODIES, SUBSTANCES, AND PROPERTIES 1. BODIES. Chemistry is a part of inorganic natural science. It has to do with those objects in the universe which are without life, with non-living bodies. Those parts or divisions of space which are evidently different from their surroundings are called bodies. They exhibit these differences to us primarily through the impressions which our organs of sense receive from them. Beside this immediate im- pression through our senses we make use also of indirect expe- rience by observing the mutual action of various bodies on each other, but all our impressions depend finally on direct sense im- pressions received from the bodies involved. The concept of a body has arisen because certain properties are found to be common to the same portion of space, and because these properties persist in spite of spatial changes in the system. I recognise the body which I call a flask, primarily by the way in which light reaches my eyes from a certain spot. I can then satisfy myself that my sense of touch receives a definite impres- sion at the same spot, and that the impression so received is in accord with the visual one. I find further that I must do a certain amount of work in order to bring about a change in the position of this portion of space (characterized by these -proper ties) with respect to its surroundings. The flask is said to be heavy. If I perform this necessary amount of work, all the properties men- 1 2 FUNDAMENTAL PRINCIPLES OF CHEMISTRY tioned, and many others beside, move together into a new position and may be four\d there unchanged in their relations to one an- other. Daily experience lias taught me that certain properties are connected and appear together, and the sum of all such experience is contained in the concept body. Experiences of this kind, which are frequently and regularly repeated, are called laws of nature. It is a law of nature that certain properties are so connected that they cannot be transported independently from one place to an- other. They always move together. Another expression for such repeated experiences is concept. A concept is a law of nature expressed in an abbreviated form. It is usually expressed in a word or a name, but in science there are many other ways of in- dicating concepts. Chemical formulae are not words, but we shall use them later as a means of representing very definite concepts. The word " body " is used to designate the following concept : Certain definite properties (especially colour, lustre, shape, and weight) are connected as a matter of experience. 2. LAWS OF NATURE. The name natural law is not a very fortunate one, for it suggests an analogy with human laws which may lead to wholly false impressions. By a law of nature we mean that as a matter of experience there is a relation between certain phenomena, such that they occur either together or in regular sequence in time. That law of nature which says that bodies exist expresses the experience that we always find the prop- erty of weight at the same place in space where we find lustre, hardness, a definite shape, etc., and that all of these properties can only be moved from place to place together. It is of course quite impossible for us to examine all the cases where such a relation exists, and we can therefore never state with absolute certainty that such a connection has always existed in the past and always will persist in the future. But we have found such a condition in all the cases which we have had time to ex- amine, and we therefore assume that we shall find it true in the future. The conclusion about bodies and their properties has BODIES, SUBSTANCES, AND PROPERTIES 3 been under examination for a long time by a very great number of observers, and it has always been confirmed. There is there- fore a very high degree of probability that it will always be con- firmed in the future. A law of nature is therefore to be considered as the expectation of a connection between possible experiences. This expectation is founded on the fact that in every case which has been observed up to the present time the same connection has appeared. And the oftener the expectation is tested with confirmatory result the greater is the probability of its future fulfilment. It is evident that the concept of a natural law contains nothing of unconditionality nor of necessity. Observation of various ex- periences, related in time and space, is the foundation of such a law, and the prediction of similar future relations, founded on such observations, gives the law its chief importance. Natural laws are therefore much like guide-posts, which tell us what to expect as a result of certain experiences, or what conditions must be ful- filled in order that certain things may happen. The last relation explains the extraordinary importance of these natural laws; for, with a knowledge of these laws as a basis, we can not only predict future events to a certain extent, we can also cause them arbitrarily to occur. For example, if the room is cold, we put coal into the furnace. This does not of itself make the room any warmer, but if we kindle the coal and let it burn, the room becomes more comfortable. On the basis of our knowledge of the natural law that coal can be kindled and gives out heat when it burns, we know in advance that we can warm the room by putting coal into the furnace and setting it afire. Every time we apply this law, and in so doing test its truth, we find it confirmed, and we are so convinced of its reliability that we have no hesitation in spending the money neces- sary to provide a supply of coal for winter. 3. ARBITRARY PROPERTIES AND SPECIFIC PROPERTIES. - Not all the properties which we find in a given body have this 4 FUNDAMENTAL PRINCIPLES OF CHEMISTRY peculiarity of remaining together. There is no way by which we can change the weight of a body, unless we take away a part of it or add a piece to it, but we can change its temperature, its electrical condition, its motion, etc. We can therefore distinguish between two classes of properties: those which persist with the body and whose sum makes up the concept of the body, and those which can be arbitrarily attached to or taken away from it. The first are called specific properties, the others accidental or arbitrary prop- erties. The distinction is so important that it is the basis for the separation of two of the sciences : Chemistry has to do with specific properties, while the arbitrary properties are the province of Physics. We can, for example, make any body hot or cold, we can elec- trify it, we can illuminate it with red or blue light, we can magne- tize it, etc. In all of these cases we are dealing with arbitrary properties, and their study belongs to Physics, and not directly to Chemistry. But the metallic nature of silver, its good conductivity for heat and electricity, its stability in air and at high tempera- tures, its solubility in nitric acid, these we cannot take away singly or change one at a time. The study of such properties be- longs to Chemistry. The amount of a body and its external shape are arbitrary properties, for they can be changed at will. In Chemistry we therefore study bodies without paying any attention to amount and shape. Bodies which are considered only in connection with their specific .properties are called substances, and they form the materials for the study of Chemistry. Substances are said to be alike chemically when they have similar specific properties. 4. SUBSTANCES AND MIXTURES. If our description of the specific properties of a body is to be definite, it is evident that these properties must be the same in all parts of the body under consideration ; otherwise there would be no way of deciding which of the properties, appertaining to different parts of the body, should be chosen as defining the body. BODIES, SUBSTANCES, AND PROPERTIES 5 By no means all of the bodies which exist or which we make have properties which are the same in all of their parts. If we ex- amine the various pebbles which form the bed of a brook we shall find among them some which are the same in every part, so that any piece chipped off has the same colour, hardness, density, etc., as the whole pebble or any other piece of it. But we shall also find other pebbles which show immediately by their variegated colours that they consist of several materials, and a closer investigation will show that, in general, the parts which differ in colour differ also in their other properties. Bodies of the first sort are called homogeneous bodies ; those belonging to the second class are called mixtures. In what follows we shall confine ourselves expressly to the homo- geneous bodies, since they are the only ones with definite specific properties. Substances are always homogeneous bodies. We say, for instance, that knife-blades, files, hatchets, scissors, and similar instruments all consist of the same substance, steel ; because the specific properties of all these bodies, such as hardness, lustre, density, rusting in moist air, etc., are the same. To the chemist a broken knife is no different from a perfect one, and a dull one is just like a sharp one, for they are all steel; but to a mechanic there is an important difference. The same object is often of interest to several sciences, but each one has a separate set of interests in the body and examines a different set of rela- tions. When a knife is magnetic it interests a physicist; as a his- torical object it may appeal to an archaeologist or an antiquarian; as an implement it would be an object of study for an ethnologist, etc. Each of these scientists will examine the same object from a different point of view. 5. CHEMICAL PROCESSES. It is quite possible to change the specific properties of a substance, but all its properties change at the same time. We say in this case that one substance disappears, and that another, having new properties, appears. If we pour nitric acid over silver, brown fumes of unpleasant odour are formed 6 FUNDAMENTAL PRINCIPLES OF CHEMISTRY which were not present before, while the silver disappears after a short time, leaving a colourless liquid behind. This liquid is different from the nitric acid which was used, for nitric acid re- mains clear when a solution of common salt is added to it, while the same salt solution produces a precipitate in the liquid which contains the silver. This precipitate is white at first, arid changes to gray in the light. Processes like this are known in great number. The combus- tion of coal, the rusting of iron, changes in animal and vegetable substances exposed to the air, these are examples of such changes. All of these phenomena have in common the fact that certain sub- stances disappear and others with other properties are formed, and changes of this sort are called chemical reactions. In order to de- cide whether a chemical process has taken place or not, we must know the properties of the substances with which we started, and compare them with the properties of the substances which appear later. If they are different, a chemical reaction has taken place. The change in properties is not always so striking as in the cases cited. It is often necessary to measure the properties of the sub- stances involved before and after the experiment in order to discover differences and render judgment on them. 6. ENERGY. The properties of various bodies were charac- terized as the relation which these bodies bear, directly or in- directly, to our organs of sense. Now our sense organs are affected by only a single general condition, which is that a transfer of energy takes place between them and the outside world. All the properties of bodies are therefore definable in terms of energy. We mean by energy everything which can be produced from work or which can be transformed into work. We have had for a long time a law of conservation for mechanical work, which states that it is impossible to increase the amount of work in a closed system by any sort of mechanical contrivance. And when we learned to transform work into heat, electricity, light, etc., we found that the same law is applicable to all of these. From a given BODIES, SUBSTANCES, AND PROPERTIES 7 amount of mechanical work it is possible to obtain only certain definite amounts of electrical work, light, etc., and when these are changed back into mechanical work, exactly equivalent amounts of the latter are obtained. Energy may therefore be considered as a substance, in the sense that it is under all circumstances con- served and persistent. This substance can be transformed into the most varied forms, but its amount is neither increased nor diminished by any number of transformations. Certain forms of energy are permanently bound to bodies and condition their weight, mass, and volume. These things are not energy themselves, but they are properties or factors of correspond- ing forms of energy, which are called gravitational energy, energy of motion, and volume energy. Other forms of energy can be added to a given body and taken away from it again, and electrical energy, light, and heat are of this kind. It will be seen from this that the difference in the processes which have been classified as physical and chemical depends primarily on the nature of the energy-forms which take part in the process. We shall find later, from a study of chemical phenomena, that there is a special chemical energy, which is connected with the mass, weight, and volume of bodies. It is, in fact, because of the inseparable union of the elements which make up the concept body that chemical phenomena appear only in bodies, that is, in systems possessed of weight, mass, and volume. The inorganic natural sciences can be most completely and easily classified by reference to the various forms of energy. First of all, there are just as many special branches of science as there are forms of energy. We distinguish mechanics, heat, electricity, magnetism, optics (which seems of late to be developing into a branch of electricity), and chemistry. There are, furthermore, other sciences which depend on the mutual relation between several forms of energy. Fifteen pairs can be made from the six branches named, and five of them include chemistry. We there- fore have mechano-chemistry, thermo-chemistry, electro-chemistry, 8 FUNDAMENTAL PRINCIPLES OF CHEMISTRY magneto-chemistry, and photo-chemistry, beside pure chemistry. We shall study especially mechanical energy and heat, and their influence on chemical reactions through pressure and tempera- ture. Only mechano-chemistry and thermo-chemistry are of especial importance in this relation, but we shall have occasion to take into account the most important phenomena of electro- and photo-chemistry also. It can hardly be said that there is a magneto-chemical branch of science, and magnetic energy has in general only slight relation to any form of energy except electrical energy. If we were constructing a system, we should next consider those sciences in which three or more different forms of energy are of importance, the forms being connected by a mutual series of trans- formations. So far no one has developed such a system, and it has been found sufficient to classify cases belonging here under one of the pair-groups mentioned above. We shall find ourselves con- tinually dealing with simultaneous effects of chemical, mechanical, and thermal energy. 7. MECHANICAL PROPERTIES. VOLUME. In accordance with the above classification we have first of all to take up the mechanical properties of substances. Some of these properties are common to all substances, others appear only in individual cases. The general properties are volume, weight, and mass. These properties are in one sense arbitrary, inasmuch as all bodies are divisible at will. But when a body is divided, the value of each of these three properties is divided in the same proportion. For when we divide a body in such a way that the new piece has half the volume of the original one, we find that its weight and its mass have also half of their original values. The absolute values of volume, weight, and mass are therefore arbitrary, but when one of the three is varied the others vary in the same proportion. Any relation between these three values is therefore not an arbitrary one but a constant for any particular substance, and this relation is a specific property. BODIES, SUBSTANCES, AND PROPERTIES 9 The result thus stated is an expression of another very im- portant law of nature, that is to say, it is an oft-repeated and invariably confirmed experience. It has been expressed in the concept matter, and weight, mass, and volume have accordingly been called the fundamental properties of matter. Such a mode of designation has no disadvantages as long as the experiential origin of the concept is kept clearly in mind. But the idea that there is something more in the concept of matter than the expres- sion of a set of experiences and their reduction to a law of nature has persisted from earlier times. Matter is looked upon as some- thing originally existing, which is at the bottom of all phenomena and in a sense independent of them all. The concept of matter can be shown, however, to be made up of the simpler concepts weight, mass, and volume, and it is certainly less fundamental than these. The law of the invariable connection of these properties has already been expressed in the concepts body and substance, so there is no necessity for the formation of a new concept to express the same thing. The word " matter " is so closely connected with the ideas mentioned above that it is not advisable to retain it ; we shall therefore not make any use of it whatever. A practical knowledge of our law must next be obtained by find- ing how weight, mass, and volume are determined and measured. 8. VOLUME. In general we measure a quantity by comparing it with a definite unchangeable quantity of the same kind, thus finding the relation of the quantity to be measured to the constant " unit." We must therefore first of all set up the units of volume, weight, and mass. The cubic centimetre (ccm. or cm. 3 ) is the unit of volume for all scientific purposes. It was originally defined by reference to the length of a bar such that 10,000,000 of these lengths would reach from one of the poles of the earth to the equator. This length is called a metre (m.). The hundredth part of the metre is called a centimetre (cm.), and a cube measuring one centimetre on each edge is the unit of volume given above. 10 FUNDAMENTAL PRINCIPLES OF CHEMISTRY In order to insure the greatest possible constancy to the unit bar, it is made of platinum-iridium, the most stable metal known, and it is preserved at Paris with especial care. Similar metre rods are preserved in the capitals of most of the countries of the world, and the length of each of these copies has been very carefully com- pared with that of the original metre at Paris. If the Paris standard rod should be destroyed in any way, the unit metre would not be lost, since the length of many other rods is accurately known i.i terms of the original standard. Each body has a definite volume, measured and expressed i:i cubic centimetres, and represented by a number. If the body has a definite geometric form, its volume can be found by measuring, for example, its edges in centimetres and calculating its volume from these measurements with the aid of a geometric formula. In the majority of cases bodies have irregular shapes; we shall see later how their volumes can be determined under these conditions. The volume of a body is often defined as the space which it occupies. 9. WEIGHT. By the weight of a body we understand pri- marily the force with which it tends to fall. This force differs slightly at different points on the earth, becoming smaller as the equator is approached and with elevation above the earth's sur- face. But observation has given us the general natural law that such differences affect all bodies in the same proportion. So when two bodies have the same weight at any point on the earth they are also alike in this property at any other point. It is necessary to distinguish between absolute weight and relative weight. The former is measured by the force exerted by a body on its support, or by the force with which it tends to fall, and this is variable from place to place. The relative weight expresses how many times the absolute weight of the body is larger or smaller than the absolute weight of a body chosen arbitrarily once for all, the unit of weight. Such a unit of weight changes in absolute value from place to place, but changes, according to the above law, in the same pro- BODIES, SUBSTANCES, AND PROPERTIES 11 portion as every other body. The relative weight is therefore in- dependent of position, and is a definite number for any given body. The standard for the determination of relative weights is a piece of platinum-iridium, preserved, like the standard metre, near Paris, and protected from destruction by many copies, which have been scattered over the world after careful comparison with the original. It is called the kilogramme (kgm.). The thousandth part of this weight is used as the scientific standard, and it is called a gramme (gm.). The original intention was to make the kilogramme such that a cube of water at its maximum density (+ 4 C.) with an edge of one metre should weigh exactly a thousand kilogrammes. A cube of water a centimetre on the edge would then weigh a gramme. Although the determination of this relation between units was certainly not made as exactly at the time of its meas- urement as it can be at the present time, the desired relation turns out to have been accidentally very nearly fulfilled. We shall therefore take the relative weight of a cubic centimetre of water at + 4 C. as being one gramme. In what follows we shall have to deal almost exclusively with relative weights; we shall therefore for brevity make use of the word " weight " in the sense of relative weight, and in the few cases where absolute weight is involved we shall designate the latter by its full name. The weight of any body is determined with the aid of the equal- arm balance, by placing the body to be weighed in one pan and adding known weights to the other until equilibrium is reached. The sum of the known weights is then equal to the weight of the body. For water the unit volume and the unit weight are the same, that is, both units refer to the same body of water. The num- ber which indicates the weight in grammes of any amount of water indicates at the same time its volume in cubic centi- metres. This statement is exactly true only at a temperature 12 FUNDAMENTAL PRINCIPLES OF CHEMISTRY of + 4 C. ; later we shall take up variations corresponding to other temperatures. 10. THE CONSERVATION OF WEIGHT. We have a remarkable and very general natural law about weight : no matter what processes are carried out on a given body, its weight is never changed. A body retains its weight whether it is warm or cold, positively or nega- tively electrified, etc. ; and even chemical reactions have no effect on weight, provided no substances having weight are added or taken away. If all chance of loss or gain by this means is ex- cluded by shutting up the substances in question in proper vessels, a careful determination of the weight shows that no change takes place even with deep-seated changes in the chemical nature of the inclosed substances. This is called the law of the conservation of weight. This law is sometimes called the law of the conservation of matter, but this is an unscientific expression, since the concept of matter is not defined with sufficient exactness to warrant its use (see Sec. 7). The law of the conservation of weight has lately been subjected to a thorough investigation. Various substances which could react chemically with one another were sealed up in glass vessels, and the total weight of the apparatus was determined before and after chemical reaction between the substances. A general con- firmation of the law was the result, in the sense that the probable changes were smaller than the hundred thousandth part of the total weight involved. Very small changes were, however, noticed which seem larger than the probable error of observation. These changes were all in the direction of a decrease in weight, so that the total weight was smaller after the reaction than before. In case this result is confirmed, it must be concluded that the law of the conservation of weight is not absolutely exact, and deviations from it in the sense of a decrease in weight as a consequence of chemical action must be admitted. Although this question has only lately been scientifically ex- BODIES, SUBSTANCES, AND PROPERTIES 13 amined, and while it is by no means decided, these experiments have been mentioned because they show that the law of the con- servation of weight has nothing " fundamental " or necessary about it. Such a necessity has often been asserted on false theo- retical grounds, but as a matter of fact this law has the same char- acter as all other natural laws. It is only a summary of certain experiences, and its accuracy is therefore limited by the range and accuracy of these experiences. Constant improvement in the methods of observation which are used in scientific work is con- tinually widening the range of experience and its exactness as well, and it happens very often that laws which seemed perfectly exact at an earlier time, when methods of measurement were less perfect than they now are, show exceptions on more careful observation. A new problem then arises: the deviations and exceptions must be measured and compared, and the new relations thus found must be expressed in a new law, if possible. 11. MASS. The mass of a body is determined by its behaviour with respect to causes of motion. Two masses are said to be equal when each is given the same velocity by the expenditure of the same amount of work, and the masses of two bodies which are not equal are measured by the amounts of work which are necessary to give them the same velocity. Mass and work are proportional in this sense, and so a body which requires ten times as much work to give it the same velocity as that of another body has ten times its mass. As a matter of experience we always find the same re- lation between two masses, no matter what velocity they have. It is therefore a natural law that mass is independent of the velocity.* The unit of mass is primarily the mass of a gramme of platinum- iridium. Experience has shown a natural law to hold here: the mass of any body always has a constant relation to its weight, wholly * Only lately the law that mass is independent of velocity has become doubtful for velocities nearly equal to the velocity of light. Bodies in the ordinary sense of the word do not have velocities of this order of magnitude, and we can therefore apply this law in the study of chemistry without danger of any measurable error. 14 FUNDAMENTAL PRINCIPLES OF CHEMISTRY independent of all the other properties of the body. It is con- sequently unnecessary to state the material from w^iich the unit of mass is made, and the unit of mass is therefore the mass of a gramme. The fact just mentioned, that mass and weight always have the same relation in any body, permits us to deduce the law of the con- servation of mass from that of the conservation of weight. For if weight is unchanged, for example, by chemical reaction, then mass is also unchanged, since it can be calculated from weight by multiplication by a constant factor, which does not change under any known conditions. As a matter of fact the law of the conserva- tion of mass can also be proven directly, and it has been found of the same order of accuracy as the law of the conservation of weight. These two quantities, mass and weight, are, however, the only properties of a body which are strictly conservative. All other properties can be varied within broad or narrow limits. And this is just as true of the specific properties as it is of the arbitrary ones. In the case of the latter the variation can usually be carried so far that the value of the property reaches zero (that is, the body no longer exhibits the property at all), while specific properties can be varied only within definite and usually rather narrow limits. 12. DENSITY AND SPECIFIC VOLUME. If we designate vol- ume by V, weight by W, and mass by M , we can have the six V V W M W M relations , , , , , and between these three quantities. W M M V V W All these relations represent specific properties of a substance. For, inasmuch as the three properties, volume, weight, and mass of any substance, can only be changed so that they remain pro- portional to each other, the relations between them are always independent of the arbitrary amount and shape of the body ex- amined. They are therefore specific properties in the sense of the definition given. (Sec. 3.) BODIES, SUBSTANCES, AND PROPERTIES 15 We have iust seen that and are, of these relations, the ones W M which are the same for all bodies, no matter what their other prop- erties may be. The unit of weight and the unit of mass have been so chosen that they can be expressed by the same number, and the relation (and as well) is therefore always unity.* Because of this independence of all the other differences between bodies this relation is of no use in the characterization of different bodies, and we shall therefore not have occasion to refer to it again. Further, - = and = , because we have chosen our W M V V units so that W = M. Relative weight (W) is very much easier to determine than V W mass (M), and we therefore in practice measure and , even V M when or is needed for any special reason. We need there- V W fore to consider only the relations and Jr . W The relation 77, that is, the weight divided by the volume or the weight of unit volume, is called the density or the specific gravity. The relation , the volume divided by the weight or the volume occupied by unit weight, is called specific volume. This and the previous relation are reciprocal, which means that one of them is obtained by dividing unity by the other. They therefore ex- press the same property, merely being different in form. The * It must be remembered that this equality holds only when W is used to indicate the relative weight. Absolute weight varies from place to place, while mass is invariable. There can therefore be no possibility of a general equivalence of these two quantities. 16 FUNDAMENTAL PRINCIPLES OF CHEMISTRY density is the more commonly used as the expression of this prop- erty, but the specific volume is the better from a theoretical point of view. For while weight is an invariable property of each body, volume changes with pressure and temperature. It is better to express the relation in such a way that the invariable quantity is taken as basis. is for this reason better than . In the case of water at 4 C. volume and weight are expressed by the same number; their ratio is therefore unity. The den- sity of water at 4 is 1.00, and its specific volume has the same value. The various substances which occur in nature, or can be made artificially, show great variations in density. Some of them have values as high as 22.5, equivalent to a specific volume of 0.0444. In the direction of small density there is no limit known, for any given volume can be filled with a gas as dilute as we choose. It seems probable from general considerations that there is a limit of some kind in this direction, even though we have no means of sufficient delicacy to prove it. 13. VOLUME ENERGY AND PRESSURE. The mass of a body and its weight can be changed only by adding to it or taking away from it amounts of other bodies. With the volume it is different, for it can be changed in many ways by uniting certain forms of energy with the body. We shall have occasion to examine only mechanical and thermal influences in this connection. Mechanical energy can appear in several different forms, and we have here to deal with the one called volume energy. It takes part in the changes which occur in the volume of a body when pressure is applied to or removed from the body, and it is measured by the product of pressure and change of volume. For instance, work must be expended to pump up a bicycle tire, and, furthermore, it requires more and more work to send a pump- ful of air into the tire as the pressure rises. It also requires more work to pump up a large tire than a small one, because the former BODIES, SUBSTANCES, AND PROPERTIES 17 has the larger volume. In order to calculate the work, the unit of pressure must be established. The unit of volume we have already. It is customary to use the Atmosphere as the unit of pressure. This name comes from the use in previous times of the average pressure exerted by the air at the surface of the earth. This pres- sure is measured with a barometer by balancing it against a column of mercury of variable height. A barometer reading of 76 cm. represents the normal value, and one atmosphere is defined as the pressure exerted by a column of mercury 76 cm. high. 14. QUANTITIES AND INTENSITIES. Volume and pressure show certain characteristic differences in the way in which they enter calculations. Volumes can be added indefinitely by simple physical addition, and they can be separated just as easily. They are therefore quantities in the narrower sense, if the possibility of direct addition and subtraction is accepted as characteristic of real quantities. On the other hand, pressures cannot be added by physical addition, nor can they be separated in the same way. If a mass of air, for example, under a certain pressure is divided into two or more parts without change in its total volume, the pressure in each part is the same as that in the original mass of gas. By bringing together several bodies under the same pressure we do not multiply the pressures, but leave the original one un- changed. And when two different pressures are combined, the result is not the sum but a mean between the two, which is, beside dependent on other conditions. We have therefore to distinguish between quantities which can be added, and values of another sort, which are called intensities. Two equal quantities give the double quantity when they are brought together; two equal intensities result in an unchanged intensity. It is, for example, quite impossible by any spatial ar- rangement to give to the air which surrounds us, at a pressure of one atmosphere, a larger or a smaller pressure. Its pressure can only be changed by the use of outside energy, as heat, or some form of mechanical energy. 2 18 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Important differences in the measurement of these .two values are to be expected. A scale for the true quantities is easily pro- duced by first making a number of equal quantities or units, and then by merely bringing together two, three, or more units finding the second, third, etc., value of the quantity. A series of intensi- ties can evidently not be made in this way, for a total intensity is not changed by bringing together several intensities of the same value. A different process must therefore be used. Observation has shown that intensities are different when they act differently. The pressure in two vessels is said to be the same if they have no effect on each other when they are connected. Neighbouring regions of the atmosphere have, in general, the same pressure, and the air therefore remains at rest as long as this rela- tion remains unchanged. In other cases such regions do influence each other, and then we say that the pressures were different. When there are different pressures at various points in the earth's atmosphere, the air is set in motion as a result of the difference. The pressure is said to be higher at the place where air is moving away, and lower at points toward which the air is moving. If a number of different pressures are in question, each of them may be compared with all the others in the way just shown. The result of such a comparison can be expressed in a natural law which states that all pressures can be arranged in a series such that it begins with the lowest pressure and ends with the highest. Each pressure between these falls into its proper place. The special peculiarity of pressure which appears in this (and the same peculiarity is found in all other intensities) can be expressed in the following law: When one pressure is higher (or lower) than another, and this other is higher (or lower) than a third, then the first pressure is higher (or lower) than the third. And in the same way we can say: If one pressure is equal to another, and this other is equal to a third, then the first pressure is equal to the third. BODIES, SUBSTANCES, AND PROPERTIES 19 These statements appear self-evident. As a matter of fact we are so accustomed to use them that it is difficult to believe that any other relation could be possible. Such important and far-reaching conclusions, which are not at all self-evident, can, however, be drawn from these laws, that it is necessary and useful to state them carefully. The numbers form a similar one-sided series, and pressures can therefore be related to them, using certain assumptions, and ex- pressed and measured in terms of them. The most general arrangement of pressures can be made with the help of energy relations, and we will therefore look at this way. First of all it must be remembered that energy is a quantity in the narrower sense, for any given amount of mechanical work or heat can be divided, and several portions of the same kind of energy can be combined into a single sum. The electrical energy which the subscriber draws from the wires is measured by suitable instruments and added up, and every month the company's agent comes around to read the meter, and collects rates proportional to the energy used. Experience has shown that each form of energy can always be separated into two factors, one of which has the properties of a quantity, and the other those of an intensity. The first is called the capacity factor or the quantity factor of energy, and the other is called the intensity factor. In order to set up a scale for an in- tensity factor, what we do is to bring into any system measured amounts of energy, taking care that the capacity factor remains the same. The intensities resulting from this method of procedure are then proportional to the corresponding amounts of energy, and so a scale of intensities is produced. In order to preserve such a scale, and make it available for future reference, a special measuring device is necessary. It is customary to use the ending " meter " to indicate devices for measuring intensities. A thermometer is an instrument for measuring the intensity of 20 FUNDAMENTAL PRINCIPLES OF CHEMISTRY heat, the temperature. An electrometer is one for measuring the intensity of electrical energy, the voltage. A manometer is one which measures the intensity of volume energy, the pressure. All manometers depend upon the fact that a certain amount of work is performed by the pressure. This amount depends upon the construction of the instrument, and the motion so produced is made easily visible by some special arrangement. The manom- eter of a steam engine indicates the steam pressure in the boiler, and it contains a metal spring which is bent by the pressure. The spring is connected to a pointer by which the amount of the motion can be read. The mercury manometer depends upon the fact that a column of mercury is supported by the pressure, the column changing its height until it is in equilibrium with the pressure exerted on it. In order to make a scale of intensities, a pressure scale, for example, according to the general scheme indicated above, a manometer might be connected to a vessel filled with air. The pressure inside and outside the vessel is first of all to be equalized by opening the vessel ; the corresponding reading on the manom- eter gives us a starting point; then a known amount of air is forced into the vessel. The manometer rises and its position is noted. The same amount of air is now added for the second time, and the new reading of the manometer indicates a change of pres- sure twice as great as the former one. The next addition of air gives the third point on the scale, and so on. In the same way we might produce a pressure scale in equal steps by filling the vessel with water and providing it with a vertical cylindrical tube into which equal amounts of water are poured one after the other, giving a graded series of heights in the tube. In all cases of this kind equal amounts of work expended in the apparatus are to be calculated from the value of the intensity which is present in the apparatus at the time. For example, the work required to lift the successive amounts of water in the appara- tus just described will not be equal but will increase as the height BODIES, SUBSTANCES, AND PROPERTIES 21 of the column of water increases, if we carry each amount of water from the lowest level to the top of the column. The definition holds, however, if we consider each addition of water to be car- ried only from the level attained by the last previous operation. This peculiarity of intensities is a very important property, which must always be kept carefully in mind. 15. HEAT AND TEMPERATURE. Beside the mechanical prop- erties of bodies, their thermal or heat properties are of special im- portance in chemistry. The kind of energy which is called heat is found in all bodies, together with volume, weight, and mass. We must therefore know something about this form of energy in order to accurately describe the properties of bodies. Varying amounts of volume energy can be added to a given body according to the pressure exerted on it, and in the same way varying amounts of heat can be added to a body according to the temperature which is given to it. Temperature is that property of heat which indi- cates how different heats behave towards one another. If a body loses heat by contact with another, we say that it had the higher temperature and that the other had the lower temperature, and in the same way two bodies have the same temperature when neither takes away nor adds heat to the other. It will be seen that these are similar to the relations found for pressure. We recognise by means of the thermometer whether or not a transfer of heat takes place. A thermometer is a small vessel filled with mercury and connected with a, very narrow tube in which the mercury rises to a definite point, which depends upon expan- sion of the mercury under the influence of a change of tempera- ture. If the thermometer is brought in contact with a body, heat transfer takes place in general, and the mercury rises or sinks as heat passes from the body to the thermometer or from the ther- mometer to the body. When the mercury ceases to move, this indicates that both have the same temperature. Each tempera- ture corresponds to a definite position of the mercury. The tem- perature of various bodies may therefore be compared by means 22 FUNDAMENTAL PRINCIPLES OF CHEMISTRY of a thermometer. In order to obtain a common basis for the ex- pression of temperature the following procedure has been generally adopted among scientists. It has been shown by experiment that the temperature of melting ice is always the same, for if various thermometers are placed in melting ice and the mercury heights noted, it is found on repeated experiment that the mercury in each thermometer always comes back to exactly the same point. It has been shown in the same way that the temperature of boil- ing water is constant.* The points at which the mercury stands in melting ice and in boiling water are determined for a given thermometer, and the space between these points is divided into 100 equal parts. The ice point is called 0, the boiling point 100, inter- mediate temperatures are correspondingly numbered. The de- grees are further divided into tenths, hundredths, thousandths, and so on. Laws similar to those which were developed in Sec. 14 for pressure will be found applicable for temperatures also. If two bodies show the same temperature when tested with a thermometer, no transfer of heat will take place between them when they are brought into direct contact. It follows from this that two temperatures, each equal to a third, are also equal to each other. This principle is purely one of experience, and cannot be derived from the general law that two quantities, each equal to a third, are also equal to each other. Temperatures are not quan- tities, they are intensities, and if two bodies which have the same temperature are brought together the result is not double the temperature, but the same. It must, therefore, be independently shown that this general principle which is applicable to 'quanti- * The boiling point changes with pressure but always has the same value at the same barometer height. Knowing the effect of a change in barometric conditions, we can take it into account and base our boiling point on an ar- bitrarily fixed barometric height. BODIES, SUBSTANCES, AND PROPERTIES 23 ties can be applied to temperatures and to intensities in general. Experience has shown the correctness of such an application for all known intensities. 16. COMPRESSIBILITY. The space occupied by a body changes with pressure and temperature. It decreases with increasing pres- sure, and the proportional amount of this change is called the com- pressibility of the body. It is evident that the decreasing volume brought about by any given increase of pressure must be propor- tional to the volume occupied by the body, for if the change of volume is determined for the unit of volume, it must be n times as great for n times unit volume, since volumes can be added directly. For small changes of pressure the decrease in volume is propor- tional to the change of pressure ; but if a great change in volume is produced by pressure this proportionality can no longer be as- sumed to be true, for a body whose volume has been made smaller is no longer the same as the original body which occupied a larger space, and we cannot assume that its properties have remained unchanged. Within the region where the change of volume is proportional to the change of pressure the following expression for the com- pressibility holds, p being the change of pressure, v the change of volume, and V the original volume: the coefficient of com- AJ pressibility z is given by z = , that is, the compressibility is found by dividing the observed change of volume by the total volume and the change of pressure. If V = 1 and p = 1 then z = v ; that is, the compressibility is equal to the change in volume ex- perienced by the unit of volume under unit pressure. The nu- merical value of this property usually varies greatly with the nature of the body in question, and we shall later consider more carefully the principal cases. 17. EXPANSIBILITY. Volume varies with temperature as well as pressure, and here we can use an expression similar to the one which holds for compressibility. The coefficient of expansion is 24 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the expansion of the unit of volume under the influence of a change of temperature of 1 degree. If V is the volume and v the change of volume corresponding to a temperature change t, the expansibility i) a is expressed by the formula a = . Here again the expansion v is proportional to the total volume V, other conditions remaining the same. The same relation, however, cannot be premised for the effect of temperature, for by varia- tion in the temperature a body acquires different properties, and in the majority of cases the coefficient of expansion a has different values for the same body at different temperatures. These values approach one another more nearly the nearer the temperatures under consideration. They are said to be continuous functions of the temperature, but this holds only when the body does not change suddenly or discontinuously into another body under the influence of temperature, as is the case with ice, which changes into water on heating. There are a few bodies which decrease their volume instead of expanding when they are heated. This is, however, a rare case, and the general rule is an increase of volume with increasing temperature. If a body is inclosed in a stiff shell, so that it cannot expand when heated, the pressure will change, and as a rule it increases, since most bodies increase their volume on heating. The same condition can evidently be realized by first heating the body at the original pressure and then decreasing its volume by an increase of pressure until the original value of the volume is reached. Under these circumstances the compressibility is a determining factor, and therefore only two of the three quantities, compressibility, expansibility, and change of pressure on heating are independent ; the third is determined by the two others. Change of pressure with temperature has so far been given no generally accepted name. Let us call it the " temperature pres- sure," and we will set up a numerical expression for its value. It BODIES, SUBSTANCES, AND PROPERTIES 25 is evidently independent of the volume, for the latter is by definition to remain unchanged, and can therefore have no influence on the numerical value of the property. We will find expression for this in our formula. If a body has volume F, its change of volume v with change of temperature t is given by the equation given above as v = aVt. The change of volume with change of pressure p is given by v = zVp, and by our definition these two are to be equal, so aVt = zVp, or ~ = . ~ is our temperature pressure; t z t it is the change of pressure at constant volume for unit change of temperature, and its value is the relation of compressibility to expansibility. It is evident then that any one of these three quan- tities can be calculated when the two others are known. All three are dependent on temperature and pressure, as has been shown. They are, beside, specific properties of substances, that is, they are equal for the same substances. It would be better to say that those substances are said to be the same in which these properties have equal values. CHAPTER II THE THREE STATES 18. THE THREE STATES. Beside the properties which be- long equally to all bodies, there are others which are evident in very different degrees in different bodies, and which therefore serve to subdivide bodies into groups or classes, according as one or more of these properties is present or not. The totality of this degree of difference is expressed in the three states in which bodies occur. There are solid bodies, liquid bodies, and gaseous bodies. We are justified in using the name " states " to indicate these three things, because external peculiarities are of determining im- portance in their differentiation. Solid bodies have a definite shape of their own, and persist in it, while liquids take on a shape which is determined by external causes. Liquids continue, however, un- changed in volume in spite of all changes of shape. Gases have neither a definite shape nor a definite volume, and the value of these two properties is in every case determined by the vessel which contains them. Other important properties are always connected with these, and we will consider them somewhat minutely. 19. SOLID BODIES. CRYSTALS. Solid bodies are charac- terized by the fact that they have a definite shape, and that this persists until it is changed by work of some kind. This shape can in some cases be arbitrary (or accidental), as, for example, in the case of a glass flask or a piece of glass which is obtained by break- ing a vessel. In other cases regular forms occur, as, for example, the cube and similar forms, as in the case of common salt. These peculiar forms are called crystals. The majority of solid bodies have 26 THE THREE STATES 27 crystal form, but often obscured and made difficult to recognise by accidental causes. The crystals of a substance may be either large or small according to circumstances, and may look otherwise very different from each other ; but it has been found that, in spite of all differences in size and shape, the crystals of a substance always show regularity. They consist of planes which cut each other at the same angle. For example, all crystals of common salt are bounded by planes perpendicular to each other; they therefore form cubes and rectangular parallelopipedons. If we imagine the surfaces which bound the various crystals of the same substance to be displaced parallel to themselves (this will cause no change in the angle at which they cut each other), it is always possible to produce one definite form. In the case of common salt this will be a cube, and in all cases where the same form can be thus pro- duced the crystals are said to have the same crystal form. The crystal form is just as much a specific property of bodies as their density and colour, for the smallest visible piece shows the same crystal form as a larger piece of any size, provided the shape has not been arbitrarily changed. It has been stated (Sec. 3) that the arbitrary shape of a substance is not to be taken as a characteristic. Here, however, it is stated that the crystal form is a specific property of solid substances. The contradiction is only an apparent one, for crystal forms are not arbitrary, but natural. They result without human aid when- ever and wherever such substances are produced. Attention has been called to the fact that the shape of a body is by no means completely determined by its crystalline properties. These de- termine only the fact that it is bounded by surfaces which are in- clined to one another at certain angles; the mutual position of these surfaces and the resulting size and shape of th*e crystals can of course vary in the most manifold way. The actual shape of a body is therefore not determined by its crystalline properties, and these only determine certain definite relations between the surfaces of the infinitely varied forms in which a substance can appear. 28 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Groups of crystals of the same substance are often found in nature. If the individual crystals which make up such a cluster are compared, each will be found different from every other one ; but in spite of this the agreement in the angle at which surfaces meet shows a certain similarity in the individual crystals, which is so evident that a crystallographer can, at the first glance, recog- nise the same crystal form in all these individual crystals. All solid bodies do not have crystal form. Some, like glass, rosin, melted sugar, and so forth, have none, and these are called amorphous (shapeless) bodies. They may be recognised by the fact that plane surfaces, cutting each other at a definite constant angle, never naturally form on them. Their bounding surfaces are usually curved, and if they are broken they show a curved fracture. Crystals, on the other hand, usually show plane sur- faces where they are broken, and these surfaces are parallel to some of their natural plane bounding surfaces. There is another important difference between crystals and amorphous bodies. In all crystals properties which are connected show direction with different values in the same body when they are measured in different directions. Elasticity, hardness, refrac- tion, often even colour, may vary in different directions in a crystal. This is not true of amorphous solid bodies, for their properties show the same values in all directions. 20. ELASTICITY AND ENERGY OF SHAPE. It has been said that solid bodies retain their shape, and if we inquire into this more closely we find that work or mechanical energy must be used to make them change their shape. As long as work is not expended on them their shape remains unchanged. We are dealing then with a special kind of mechanical energy, which is called elasticity or energy of shape. The work which is expended in changing the shape of a solid body may be used up in two different ways. After the body has been acted upon, for example, after it has been bent, it may take on its original form again. Under these circumstances it gives THE THREE STATES 29 back the work expended on it, just as a clock spring once wound up drives the mechanism of the clock while it is unwinding. Such a body is said to be elastic. It can take in energy of shape and give it out again and the quantity of energy taken in is, in general, proportional to the change of form. On the other hand, the body may continue in its new shape after work has been expended on it. This work has apparently disappeared, for the body does not give it up again by changing back to its original form, and it will in fact be necessary to expend more work to get it back again. If the law of the conservation of energy is true, we must inquire what has become of the expended work, and the answer is that it has been transformed into heat. This can be shown, for example, by bending a stick of tin repeatedly back and forth at the same place. It soon becomes noticeably warm. Such bodies are said to be inelastic, and the property which results in changing work into heat within them is called their viscosity. We shall find this same property again in liquids, but it is very much greater in solid bodies. Both these properties are always present in every solid body, but in very different proportions. Some metals, like steel, can absorb large amounts of energy of shape. They can be greatly deformed, and still give up the work used in deforming them at the same time that they assume their original form. Other bodies can change their shape only very slightly, and if one of these is de- formed too far, energy of shape is transformed into heat. The limit which separates these two regions is called the elastic limit. Even the most perfect elastic bodies have an elastic limit, and change their shape when it is exceeded. In the same way ap- parently inelastic bodies, like lead, possess elasticity within very narrow limits. 21. SURFACE ENERGY. If a change in shape is carried still further, a new phenomenon appears. The body in question breaks or tears. This happens in any given case the more easily as the change of shape is made more rapidly. The most impor- tant point here is that new surfaces are formed. These are the 30 FUNDAMENTAL PRINCIPLES OF CHEMISTRY centre of another kind of energy called surface energy. A break or tear can be expressed as the mechanical expenditure of work which leads to the production of surface energy. A larger or smaller portion of the expended energy is usually transformed into heat, and an efficient machine for pulverizing bodies means one in which the fraction of expended energy which is trans- formed into heat is small. We shall consider surface energy more minutely when we come to liquids. It is better to consider it at that point, because the production of new surfaces in solid bodies is always connected with a change in several forms of energy, and it is difficult to separate and determine the part which belongs to surface energy. 22. CHANGE OF VOLUME IN SOLIDS. The influence of pressure and temperature on the volume of solid bodies is very slight. The compressibility of solids is so small that it escaped measurement for a long time, and it can only be measured with difficulty at the present time. The expansion of solids under the influence of a change in temperature is somewhat greater, and many of the phenomena of daily life depend upon the fact that such bodies have a larger volume at high temperatures than at low ones. A glass stopper which is stuck in a bottle can be loosened by heating the neck of the bottle. This expands before the stopper itself becomes warm, and the latter can then be removed. The numerical value of the coefficient of expansion depends very largely on the nature of the substance itself, but does not change very much with- temperature. The following table gives the co- efficients of expansion of some substances at ordinary temperature ; that is, at 18. They indicate, according to our definition, the fraction of the volume which the volume changes for a change in temperature of one degree. THE THREE STATES 31 COEFFICIENTS OF EXPANSION AT 18 DEGREES Lead 0.000083 Aluminium ,. . . . 0.000065 Silver 0.000055 Copper . 0.000048 Gold 0.000041 Steel 0.000030 Platinum-Iridium . .~ 0.000026 Glass 0.00002-0.00003 Quartz, melted 0.0000012 The coefficient of linear expansion of a body is different from that for cubic expansion. It is the increase of length brought about in the unit of length for a rise in temperature of one degree. It may be calculated with sufficient accuracy by dividing the co- efficient of cubic expansion by three. There are a few solid bodies which behave in quite a different way, decreasing their volume with a rise of temperature, but none of the more common substances show this property. 23. EXPANSION OF CRYSTALS. In the general increase of volume which takes place during expansion every dimension of a body of any shape whatever is changed. If the substance is amorphous all these expansions are proportional to the dimen- sions, so that the geometric shape remains the same at various temperatures. In the case of crystals this is no longer generally true. They expand differently in different directions, and there are in fact crystals which expand in certain directions on being heated and contract in other directions. But these changes always take place in such a way that straight lines in the crystals remain straight and planes remain planes. If spheres are cut out of various crystals and subjected to change of temperature, only those from certain crystals remain spheres, and these, of course, show a change in radius. Others lose this spherical shape and change into uniaxial or triaxial ellipsoids. 32 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Uniaxial ellipsoids are egg-shaped or flattened bodies which are formed by the rotation of an ellipse about one of its axes. Triaxial ellipsoids are produced when the ellipse changes during the rota- tion about one of its axes, becoming narrowed or flattened in such a way that its points no longer describe circles but similar ellipses. A section of a uniaxial ellipsoid, cut perpendicular to the axis of rotation, is a circle. A similar section of a triaxial ellipsoid is an ellipse. These facts determine the division of all crystals into three principal groups : regular, uniaxial, and triaxial. A crystal behaves in a precisely similar way when its volume is changed by a change of pressure instead of by heating or cooling it. In this case also spheres either remain spheres or else change into uniaxial or triaxial ellipsoids. Expansion under the influence of heat and compressibility may therefore, either of them, be used as indication of the classes to which various crystals belong. But not very much is known about the compressibility of crystals be- cause of its exceedingly small numerical value. Other properties, the velocity of light and heat conductivity, for example, show similar differences in different crystals. Here experience has shown the general law that a crystal may be classi- fied with perfect definiteness by the investigation of any one of these properties. 24. LIQUIDS. Liquid bodies differ from solids in having no shape of their own. They take on any shape which may be im- pressed upon them by external causes. When a liquid is poured into a vessel its shape is determined by the bottom of the vessel below, and at its surface by the force of gravity, under the in- fluence of which it sinks as deeply as possible. The result is that a liquid fills the lower part of a vessel completely, while it is bounded above by a plane perpendicular to the direction of gravity. 25. SURFACE ENERGY. A kind of energy is active at the sur- face of every liquid, tending to make this surface as small as pos- sible. It is called surface energy, and its intensity factor is surface THE THREE STATES 33 tension. Under its influence falling drops of rain take on the shape of spheres, because the sphere has, among all geometrical forms, the smallest surface and the greatest volume. Small drops of mercury also take on a spherical shape, the effect of surface tension outweighing that of gravity. The larger the drops the more evident the effect of gravity, and larger drops are always flatter in shape than small ones. When a liquid is bounded by a gas its surface tension is always evident in the sense just mentioned. If a liquid is bounded by a solid two cases are possible, a surface tension in the same sense as in the case of the gaseous bounding medium may appear, or we may have a surface tension of opposite character. In this case the surface does not tend to become as small as possible, but as large as possible, and we say that the solid body is wet by the liquid. Mercury on glass is an example of the first case; oil on glass, of the second. For this reason a drop of mercury on a glass surface assumes a shape approximately spherical, while a drop of oil on glass spreads out and appears to form a contact surface as large as possible. The majority of liquids and solids corre- spond to the second case, that is to say, most liquids wet most solid bodies. When the surface of a solid is wet by a liquid, it acts like a surface of liquid, and therefore apparently seeks to be- come as small as possible. The rise of liquids in tubes is an ex- ample, and for the same reason the edge where a liquid comes in contact with the wall of a containing vessel always curves upwards. The surface of a liquid which wets the containing vessel is there- fore really only plane at the centre. Near the edge the surface takes on a dished appearance, and when the vessel is only a centi- metre wide or less the whole surface of a liquid is curved. 26. VISCOSITY. The tendency of liquids to assume any shape which is impressed upon them by external forces indicates that it does not require the expenditure of work to change the shape of a liquid (it being understood that no work is expended in other ways, as, for example, against gravity). This is the definition of 3 34 FUNDAMENTAL PRINCIPLES OF CHEMISTRY an ideal liquid, and all real ones deviate more or less from it. As a matter of fact the expenditure of work is always necessary to move the parts of a liquid about each other, and this work is different in amount in different liquids. In ether and warm water it is comparatively small; in molasses it is large. This property, which is a measure of the work done during the mutual motion of the parts of a liquid, is called the viscosity of the liquid, and it is small in ether and warm water, and large in molasses. As the viscosity of a body becomes greater and greater, it changes from a liquid to a solid. This is evident in wax, for example, which acts like a viscous liquid when it is warm, and like a glassy, brittle solid when it is cold. Glass is a viscous liquid at high temperatures, and when it is cooled it passes continuously from this condition into that of a solid. The solid bodies which are pro- duced from liquids in this way are always amorphous (Sec. 19), and amorphous solids soften on heating and change continuously into liquids, which are at first very viscous indeed, but which lose their viscosity gradually on a further increase in temperature. 27. VOLUME. Although liquids have no shape of their own, they do have a definite volume. This does not mean that they cannot change in volume, but only that the volume has a definite value under definite conditions of pressure and temperature, and that it changes by only a comparatively small amount w T ith a change in these two conditions. If we could double the pressure which is exerted on all bodies on the surface of the earth by the column of air above them, the volume occupied by water would only be decreased one forty-three millionth part of the total volume. An increase of pressure of one atmosphere would therefore decrease the volume of a litre of water by only 43 cubic millimetres. The change in volume is so small that accurate apparatus is necessary to demonstrate and measure it. Liquids in general act very much like water in this respect, but most of them can be more easily compressed. The various THE THREE STATES 35 liquids are all different, however, and each of them has its own compressibility. Compressibility is measured (Sec. 16) in terms of the fraction of the total volume by which the volume of the liquid is changed as the consequence of unit change of pressure. If we use in this calculation unit volume, the result is the numerical value of the compressibility, and it is called the coefficient of compressibility. The atmosphere is the ordinary unit of pressure, and in terms of this unit the compressibility of water, as above stated, is 0.000043. This value varies with temperature and also with pressure. The space occupied by a liquid changes with temperature, and, as a rule, the volume of a liquid increases with increasing tempera- ture. Equal volumes of various liquids expand by very different amounts under the influence of the same increase in temperature. The expansibility of a liquid is therefore a specific property of a liquid, just as its compressibility is. It is expressed by the frac- tion of the volume at which the liquid expands for a rise of temperature of one degree. This fraction changes, in general, with the temperature, the expansibility becoming greater and greater as the temperature rises. Mercury is somewhat of an ex- ception, for between and 100 it expands nearly proportional to the gases, and since the expansibility of a gas is the basis of temperature measurements, the expansibility of mercury can also be used for this purpose. The mercury thermometer is an instru- ment based on this property. It consists of a vessel filled with mercury connected with a fine capillary tube. When the mercury changes its volume with change of temperature, the column in the tube changes its length, and its position can be read on a scale placed close to the mercury column. The volume of mercury increases by 0.0181 for a change of temperature from to 100. Its coefficient of expansion is therefore 0.000181. As a matter of fact what one observes in a thermometer is not alone the expansion of mercury, but the difference between the expansion of the mercury and that of the glass vessel in which it is 36 FUNDAMENTAL PRINCIPLES OF CHEMISTRY inclosed. The expansibility of glass is very much smaller than that of mercury and so the latter rises in the tube when the tem- perature Arises. If, however, the expansibility of glass were greater than that of mercury, the mercury would fall in a thermometer as the temperature increased, and if the two expansibilities were equal, there would be no change in the reading of the thermometer when the temperature changed. 28. WATER AN EXCEPTION. There is an important excep- tion to the rule that the volume of a liquid increases with increase of temperature. In place of expanding between and 4, water contracts. It has its least volume at 4, and when the temperature rises above this point, it acts like the other liquids, its volume in- creasing with rising temperature. In winter, when the tempera- ture is below zero, ponds and lakes cool down only as far as 4. The water at the surface, which is cooled by contact with cold air, or by radiation, sinks to the bottom, since it is heavier than the warmer water. When a temperature of 4 is reached through the whole body, the water at the surface cools still further; but it is now lighter than the water in the main body of the pond, and re- mains on the top until it finally begins to freeze. The ice which forms is also lighter than liquid water, and therefore remains floating on the surface. This is the reason why still bodies of water do not freeze solid in winter. If a glass vessel like a thermometer is filled with water and sub- jected to changes of temperature, it will be found that the column of water in the tube does not show a minimum height at 4, but at about 8. What we observe in such an apparatus is the difference between the expansibility of the liquid and that of the vessel. If the temperature is raised from 4 to 5, the water expands a little, but the expansion of the glass vessel outweighs this expansion and the column of water in the tube sinks. It is only at about 8 that the expansion of the water outweighs that of glass, and from this point on the column of water rises with a rising temperature. The density and the specific volume of water are necessary in THE THREE STATES 37 many measurements and calculations. A table of their values is therefore appended. Temper- ature. Specific Volume. Density. Tempera- ture. Specific Volume. Density. 1.000132 0.999868 15 1.000874 0.999126 1 1.000073 0.999927 16 1.001031 0.998970 2 1.000032 0.999968 17 1.001200 0.998801 3 1.000008 0.999992 18 1.001380 0.998622 4 1.000000 1.000000 19 1.001571 0.998432 5 1.000008 0.999992 20 1.001773 0.998230 6 1.000032 0.999968 30 1.00435 0.99567 7 1.000071 0.999929 40 1.00782 0.99224 8 1.000124 0.999876 50 1.01207 0.98807 9 1.000192 0.999808 60 1.01705 0.98324 10 1.000273 0.999727 70 1.02270 0.97781 11 1.000368 0.999632 80 1.02899 0.97183 12 1.000476 0.999525 90 1.03590 0.95838 13 1.000596 0.999404 100 1.04343 0.95838 14 1.000729 0.999271 29. MEASUREMENT OF DENSITY. It is very much easier to measure the density and the specific volume of liquids than it is to measure them in solids, and it is usual to base the determina- tion of these properties in solids on a previous determination of their value in a liquid. Liquids fill easily and completely any space which is offered to them. Their volume can therefore be very conveniently determined, while the determination of the volume of solids, especially those with irregular shapes, is much more diffi- cult to carry out. The simplest method consists in filling a vessel of known volume with a liquid and determining its weight. This W V gives us both V and W, and we can calculate d = and v = . The vessel used for this purpose may be either a flask with a long neck, provided with a mark half way up the neck, or a flask whose volume is fixed by a ground stopper. The weight of the empty flask, its " tare," as it is called, and its volume are determined once for all, and it is then only necessary to determine the weight 38 FUNDAMENTAL PRINCIPLES OF CHEMISTRY of the flask filled with a liquid, in order to obtain the numerical value for its density and specific volume. The volume of the flask is determined by weighing it after it has been filled with a liquid of known density. This weight divided by the density gives the volume. Water is the liquid usually chosen for this purpose, for its weight, when taken at 4, gives the numerical value of its volume. Labour is saved by making the volume of the vessel a round number of cubic centimetres, 1 or 10 or 100, for example. In the first case the weight of the liquid gives the density directly. In the other case one needs only to point off the right number of decimal places to obtain the density. In every determination of weight it must be remembered that the air introduces an additional factor because of its buoyant effect, and this must always be taken into account. Another very common method of determining the density of liquids consists in floating a vessel with a long cylindrical neck in the liquid, and observing the point to which it sinks. Accord- ing to Archimedes' principle such a float sinks until the displaced liquid weighs as much as the float itself. The first method enables us to compare the weight of equal volumes, the second method, the volume of equal weights ; for the reading on the neck of the float, or hydrometer, as it is called, gives the volume occupied by an amount of liquid of the same weight as the hydrometer. If the divisions on the neck are made in terms of the total volume of the hydrometer, the specific volume of the liquid may be read off directly, just as densities were directly obtained in the first case. It is possible to obtain densities directly by an application of Archimedes' principle. For this purpose a body is so arranged that it sinks in the liquid and thus always displaces equal volumes. The buoyant force on this sinker is then determined, that is, how much less it weighs in the liquid than in air. This buoyant force is equal to the weight of liquid displaced, and the volume of liquid displaced is equal to the volume of the sinker. If the sinker has THE THREE STATES 39 a volume expressed by a round number of cubic centimetres, its loss in weight gives the density of the liquid. The measurement is carried out by hanging the sinker on a balance by a fine thread and weighing it first in air and then in the liquid. In order to determine its volume, it is weighed in water at 4. Here its loss of weight is equal to its volume if the weight is calculated in grammes and the volume in cubic centimetres. The methods just described can also be applied to the determina- tion of the density and specific volume of solid bodies. Using the first method, the flask would first be weighed empty. Any amount of the solid body is then placed in it, and the whole is weighed again. This gives W ', the weight of the solid body. The flask is now filled to the mark with water and weighed again. The in- crease in weight is the weight of the amount of water which fills that part of the volume of the flask which is not occupied by the solid body. If this weight is now subtracted from the weight of water which fills the entire flask, the difference is the weight of water displaced by the solid body, and this is equal to its volume V. When Archimedes' principle is to be applied in the determina- tion of the density of solids, this may best be done by hanging the body on the balance by means of a hair or very fine wire, and determining its weight in air and then its weight when submerged in water. The first determination gives W directly; the second gives W minus the buoyant effect, that is, minus the weight of water displaced. The second value is subtracted from the first, and the result is the weight of water displaced, which is equal to the volume of the solid. 30. LIQUID CRYSTALS. In Sec. 26 we spoke of a transition between liquids and solids which was indicated by the fact that the viscosity became very great, while at the same time a measure- able elasticity appeared. The body recovered from slight deforma- tion when the deforming force was removed. Beside this there is another kind of transition exhibiting characteristics which are, in some degree, contradictory to those previously discussed. Solids 40 FUNDAMENTAL PRINCIPLES OF CHEMISTRY which are produced from liquids continuously are amorphous and isotropic, but the bodies which we are considering here, although crystalline, have a comparatively very small viscosity, and an elasticity which is so small as to be almost unmeasurable. They are therefore called liquid crystals and crystalline liquids. Their crystalline properties are especially evidenced by their optical peculiarities; light has different velocities in different directions in them, and this results in peculiar refraction effects which are especially evident in polarized light. In other respects they be- have like liquids, forming drops as a result of their surface tension. Liquid crystals show all degrees of viscosity, and those which are nearest like solids take on shapes somewhat like crystals. Their points and edges are, however, always rounded by the action of surface tension and because of the soft nature of the substance. In others crystal forms only appear under especially favourable circumstances, and those which are nearest like liquids no longer show any semblance of crystal form, appearing merely as round drops. Liquid crystals are rather rare, and among the many thousand different substances which are known there are only a few dozen which form them. 31. GASES. Gases differ from liquids in that they have neither shape nor volume of their own. They fill any space which is offered to them completely, and not only partially, like liquids. A gas fills any space which is offered to it because of what is called its pressure. This pressure is the intensity factor of volume energy (Sec. 14). No such property is present in solid and liquid bodies. They have a definite volume, and fill a space offered to them only as far as this volume reaches. 32. BOYLE'S LAW. As the volume occupied by a given amount of gas becomes greater, its pressure, which is the measure of its tendency to fill a greater space, becomes less and less. The relation between volume and pressure is of the simplest form. These two factors are in inverse proportion to one another, and THE THREE STATES 41 therefore when the volume is increased to n times its original value, the pressure decreases to - of this value. This is called IV Boyle's Law, from its first discoverer. If the pressure measured in terms of a definite unit is designated by P, Boyle's Law is ex- pressed by the formula where K has a constant value which depends upon the amount of gas involved, and is proportional to this amount. A definite value can be used to describe solids and liquids either in terms of weight or of volume, since these two things are proportional in the case of solids and liquids. The volumes of various gases are, how- ever, only proportional to the amounts of gases involved when they are under the same pressure. Under different pressures the weight of a given volume of gas is proportional to the pressure. This expresses the fact that more and more of a gas can be brought into the same volume as the pressure is increased. This is ex- pressed by the equation PV = K, and K can therefore be used as a measure for the amount of gas, i. e. for its weight. K takes on a definite meaning when P is made equal to 1, for then V = K, i. e. the constant K is the volume of the gas when unit pressure is acting upon it. And of course if F = l, K repre- sents the pressure of a gas which occupies unit volume. Physicists have agreed to adopt as the unit of pressure the hydrostatic pressure of a mercury column 76 cm. high, and this unit is called an atmosphere, because it corresponds approximately to the average pressure of the atmosphere on the earth's surface. Gases which are in equilibrium with the surrounding air exist under this pressure. Gases which are shut off from the atmos- phere by water or mercury exist under a pressure which may be greater or less than one atmosphere, depending on whether the column of liquid adds its pressure to that of the atmosphere or not. In order to express the true pressure under which the gas exists the pressure of the liquid must be taken into account. 42 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Since the density of mercury is 13.6, a water column 13.6 cm. high is equivalent to a mercury column 1 cm. high in making correc- tions of this kind. The pressure of the atmosphere as measured by the barometer is not constant; it shows variations in both directions about its average value, and must therefore be determined separately every time we wish to measure the pressure of a gas which is not com- pletely isolated by solid walls from the external air. Atmospheric pressure is measured by means of the barometer, which gives the value for this pressure directly in terms of centimetres of mercury. In the consideration of Boyle's Law it has been assumed that the temperature remained constant, and nothing has been said about the value of this factor. This tacit assumption is an ex- pression of the natural law that Boyle's Law holds for any tem- perature whatever. The pressure or the volume of a gas changes when its temperature is changed, but for each temperature Boyle's Law holds good. 33. THE LAW OF GAY-LUSSAC. The fact that gases change their volume with change of temperature has just been mentioned. All gases show an increase of volume (or an increase in pressure if the volume is kept constant) when the temperature is raised, and all gases change their volume in the same way under the in- fluence of a rise in temperature. It will be remembered that every solid and liquid substance has its own special coefficient of ex- pansion. Among the gases this property is independent of the nature of the substance. The same is true of the compressibility, for Boyle's Law applies to all gases quite independent of any differences in their nature. If the volume of any gas under a definite pressure is measured at (the temperature corresponding to a mixture of ice and water), and the gas is then heated at the same pressure to 100 (the temperature of boiling water), the same increase in volume is observed no matter what the nature of the gas under investiga- THE THREE STATES 43 tion may be. The increase is found to be |$f of the volume at 0, or, expressed as a decimal, 0.367 of this volume. If this tempera- ture difference is divided into 100 parts so that each part corre- sponds to the same increase in volume, the parts are then called degrees, and the increase of volume for each degree is 2Tff> or 0.00367 of the volume at the freezing point. 34. ABSOLUTE TEMPERATURE AND THE ABSOLUTE ZERO. The freezing point is, of course, an arbitrarily chosen point, and temperature can be measured far below it. If degrees of tempera- ture are so chosen below the freezing point that the change of volume for 1 change of temperature is ^^ of the volume at the freezing point, it is evident that 273 such degrees can be laid off below this point. At 273 C. the volume of the gas would be zero, and if the temperature could be decreased below this point, the volume would become negative, a state of things which has no meaning whatever. It is interesting to see how the experiments which have been made in low temperatures bear on this assumption. As a matter of fact investigators have succeeded in reaching a point about 10 above the temperature at which the volume of the gas would become zero, i. e. 263 below the freezing point. All attempts to go further in this direction have met with the greatest difficulties. It is very probable that we will not be able to reach a much lower temperature, and we may therefore take this point, 273 below the freezing point, as the foundation of our temperature scale, without any fear that negative temperatures will have to be taken into account in the future. If this tempera- ture of 273 C. below the freezing point is called zero, the scale is termed an absolute one, and if the same degrees are used as in the ordinary thermometric scale, the freezing point of water lies at 273 and the boiling point of water at 373. In other words, degrees in the absolute scale are found by adding 273 to the cor- responding reading in the Centigrade scale, or to express this in a formula, T = t + 273 where T indicates absolute degrees and t indicates degrees on the Centigrade scale. Absolute tern- 44 FUNDAMENTAL PRINCIPLES OF CHEMISTRY peratures are sometimes designated by A., just as Centigrade tem- peratures are followed by C. This method of expressing temperature is often of great scientific advantage, but we will be able to consider at this point only one of the advantages resulting from its use. This is the great sim- plicity which is given to the expression for the behaviour of gases as affected by changes in temperature. If VQ represents the volume of a gas at the freezing point of water and V t its volume at the temperature t C., the latter volume is greater than the volume at C. by ^ of the latter volume. r Expressed in a formula, + 273J- If, however, we calculate temperature from the point where the volume of the gas would be zero, its volume is simply proportional to the numerical value of the absolute temperature. Expressed in a formula, VT = rT where V T is the volume at the absolute temperature T, and r is the volume at the absolute temperature 1. It has already been stated that the absolute zero, which is 273 lower than the freezing point of water, has never been attained. The question therefore arises how we have determined r. The answer to this question is evident if the equation V T = rT is trans- formed into r = -~. The volume is simply observed at any tem- perature T and divided by the value of this temperature in terms of the absolute scale. If, for example, the volume is observed at the ice point, it is to be divided by the absolute temperature of the ice point, which is 273. The expression for the influence of temperature on the volume of a gas now takes on a form which is analogous to the expression for the pressure. We have obtained for each temperature the THE THREE STATES 45 y expression = r where r is constant. And just as in Sec. 32 the constant corresponds to the volume under unit pressure, here the constant indicates the volume at temperature 1. If we consider a given amount of gas at the absolute temperatures 7\ and T 2 , we V V V V have r = ^ and r = . It follows directly that -=~ = =* or v T *i l * *i ** ~ = -=*. The volumes occupied by a definite quantity of gas at Kj J- 2 different temperatures (the pressure remaining the same) are in the same proportion as the temperatures on the absolute scale. In all of this we have assumed that the pressure may have any value whatever, provided it remains unchanged. This involves the supposition that the same change of volume results from a given change of temperature whatever the pressure may be under which the experiment is made. This assumption is justified, as experiment has shown and as the following consideration also proves. Suppose we have determined the expansion under the pressure 1. If we now double the pressure at both temperatures, the volume will be by Boyle's Law one half of the previous volume in each case. The relation between the volumes remains the same, for when both members of a proportion are multiplied by the same factor the proportion remains unchanged. The law of ex- pansion for gases expresses a proportion between the volumes at various temperatures, and says nothing about the absolute values of the volumes. 35. THE GAS LAW. One more question remains to be an- swered. How does the volume of a gas change with a change in both temperature and pressure? In the formula for constant temperature (Sec. 32), PV = K, K indicates the volume under a pressure of one atmosphere. This formula holds for all temperatures, for Boyle's Law is independent of temperature. Suppose the temperature is T, then K is the volume under unit pressure and at temperature T. This volume, 46 FUNDAMENTAL PRINCIPLES OF CHEMISTRY however, varies according to the formula K = rT (Sec. 34), and if this value for K is substituted in the previous equation the re- sult is PV = rT. P, V, and T here represent any values whatever of pressure, volume, and temperature, while r corresponds to the volume at temperature 1 and pressure 1. The values for pres- sure, volume, and temperature are therefore variable while r is constant for a given quantity of gas. r is therefore a measure of a quantity of a gas at any temperature and any pressure, and its PV numerical value is r = -=-. This equation PV = rT is called the gas equation. It is of the utmost importance in physics as well as in*ehemistry. CHAPTER III MIXTURES, SOLUTIONS, AND PURE SUBSTANCES 36. STATES. If we arrange the solid bodies which we find in nature or prepare artificially, with respect to their specific properties, the following facts will be evident. There will be a large number of different bodies possessing the same specific properties. Many of these can therefore be arranged in classes in such a way that each class contains all the bodies of the same spe- cific properties. These bodies are said to consist of the same substance. There are, therefore, a great many more different bodies than there are different substances. The possibility of making such an arrangement depends, as we have already seen, upon differences in specific properties. We will therefore ex- amine these properties more closely, and in doing this the follow- ing question immediately arises : Suppose we assume that we have gathered together various bodies, each of which possesses one specific property which it exhibits in the same way, will the other properties then be different and will different classifications re- sult, depending upon the property which is chosen for the classi- fication ? The answer to this question can be readily given. We are, in general, able to give a clear description of the different substances of which various bodies consist. It must therefore be possible to classify bodies definitely according to their specific properties, and we will consider how this is to be done. Certain properties show only gross differences when examined directly. There are, for example, a very large number of different bodies which are white, but which have other properties differing greatly from body to body. Here one specific property, white colour, is 47 48 FUNDAMENTAL PRINCIPLES OF CHEMISTRY common to all these bodies, while all the other properties may be different. This white colour is, however, definitely connected with certain optical properties and especially with index of re- fraction. If the refraction of these different white bodies is meas- ured, it will be found that it is in general different in different bodies, and if the bodies are now classified with respect to their refractive index it will be found that those bodies which have the same index of refraction will also show correspondence in all their other properties. A still safer method is to examine several properties, and the general principle holds true that if several specific properties are the same in two bodies, all other specific properties will also be the same. The same classification will therefore result whichever one of these properties is chosen as the basis. That this special peculiarity is true of the bodies which occur in nature, or can be prepared artificially, is shown by much of our everyday experience. It is a natural law that bodies can be classified in such a way that all the specific properties of a class are the same, no matter where the bodies classified may have originated. In other classes other values of the specific properties will be found. In this respect bodies are like plants and animals, for they can also be arranged in classes in such a way that all the individuals belonging to a class show similar properties different from those of other classes. The different classes of plants and animals may be distinguished by investigating and determining their properties, and the various classes of bodies can be characterized by their properties in the same way. In order to solve this problem completely all the prop- erties of all bodies must be determined. This is evidently an im- possible task, but it is also an unnecessary one. If several poplars, for example, or several crows are carefully examined, and their properties noted, it is safe to conclude that the same properties which have been observed in them will be repeated in all other MIXTURES,. SOLUTIONS, AND PURE SUBSTANCES 49 poplars and crows. The justice of such a conclusion can be tested at any time and to any extent by examining other members of the class to see whether or not the properties are repeated. In the world of chemistry and physics the same method can be followed, and results have shown that the natural law given above holds true in every case. It is therefore unnecessary to investigate all the properties of all bodies; it is sufficient to determine the properties of one body from each class, and even this problem is a never-ending one, for new properties are continually being recognised and new bodies being discovered as the result of investigations in natural science. Chemistry has for its problem to give as complete a description as possible of the properties of all substances, and here, as in all other natural sciences, the completion of the task is an ideal which can be always approached but never attained. Natural laws are of great assistance in this, and their value is evident in the case just cited, for owing to our possession of knowl- edge of a few properties we were able to recognise the class in which a body belongs, i. e. we can predict all the other properties of this body. We do not need to investigate all bodies, and our labour is confined to the study of one body from each class. Other natural laws will enable us to make further predictions and thus to spare an enormous amount of labour. In spite of all these aids the sphere of chemistry as well as that of any other science will always be one of unlimited extent. 37. MIXTURES. Not every solid body which we find in nature or prepare artificially agrees with the description given above con- cerning the constancy of its properties. There are very many cases where examination with the eye alone shows different prop- erties at different points on the same body. Most of the natural rocks, for example, which make up the crust of the earth, consist of fragments differing in colour and appearance. Grayish grains, reddish prisms, and shining plates may all be seen in the same bit of granite. 50 FUNDAMENTAL PRINCIPLES OF CHEMISTRY : It is, however, possible to imagine a piece of granite to be broke up into such fine bits that it is no longer possible to see parts diffe ing in properties in the same fragment. Each fragment consists of only one substance. It would then be possible to pick out all the like fragments and pile them into a heap. The result would be three portions, one consisting of grayish hard grains, this is quartz; another of reddish prisms of feldspar; and the third of little glistening pieces of mica. The properties in each portion are now the same, and each portion is therefore called a substance. It has been proven by means of this mechanical separation that granite is a mixture of three different solids, and we must there- fore take into consideration mixtures as well as substances. In cases where the constituents show evident differences in appear- ance, and where the fragments are not smaller than the tenth of a millimetre, visual examination is often sufficient to enable us to recognise a mixture. If the fragments are smaller, and the same assumption of differences in appearance holds true, the microscope enables us to distinguish parts which are not smaller than the half of a light wave, i. e. about -^-$--3 of a millimetre. It is difficult to distinguish smaller particles, but by the application of strong illumination from the side the microscope enables us to recognise particles about 100 times smaller than this, i. e. particles with a diameter of 3-6 millionths of a millimetre, provided they are surrounded by a transparent medium. Mixtures can also be recognised by the fact that they diffuse light, and therefore appear cloudy. Pure substances, on the other hand, are optically homogeneous, and light is transmitted regu- larly through homogeneous masses. If a homogeneous substance is reduced to powder, the resulting product is a mixture of the substance with air, and this mixture appears opaque. If a solid body or a liquid is cloudy, it may be concluded with certainty that it is a mixture. Cloudy mixtures of gases have only a tem- porary existence, for gases form homogeneous solutions in all proportions. MIXTURES, SOLUTIONS, AND PURE SUBSTANCES 51 This means of recognising mixtures is no longer a valuable one when the particles become small in comparison with the wave length of light. At this point new and remarkable phenom- ena appear, in which the surface tension, corresponding to the very great surface of separation, begins to play an important part. We will therefore for the present omit them in this elementary consideration. 38. METHODS OF SEPARATION. We have already made use of the difference in appearance of the parts of a mixture (colour, lustre, etc.) to assist in a mechanical separation performed by hand. This means that we made use of the properties which are evident to the eye, the optical properties. If these are not suffi- ciently characteristic, other properties may be used in the same way, provided it is possible with their aid to gather the different fragments at different points and so mechanically to separate them. A difference in density can be made use of in this way. According to Archimedes' principle, a body floats on the surface of a liquid denser than itself, and sinks to the bottom in one which is not so dense. If we drop a mixture of two different solids whose density is sufficiently different into a liquid whose density lies between the two, the denser solid will drop to the bottom and the lighter one will rise. In a short time the two substances will have been separated, and they may be collected and investigated each for itself. In carrying out this process it is not necessary to know the densities of the two substances beforehand. If the mixture is thrown into a liquid which is denser than either of the two sub- stances composing it, both will float. If a second lighter liquid which can mix with the first in all proportions is carefully added, the liquid will decrease in density, and presently a point will be reached where its density is less than that of one of the sub- stances but greater than that of the other. One of the substances will then sink to the bottom, the other will float on the surface, and the separation is complete. 52 FUNDAMENTAL PRINCIPLES OF CHEMISTRY The mixture can always be produced again from its compo- nents. To be sure a piece of granite is not produced when the grains of quartz, feldspar, and mica resulting from our separation are mixed together. As far as our chemical considerations go, it makes no difference what size or shape the bodies have which we are investigating, and to a chemist the mixture of the three components in the form of grains is in no way different from the mineral in which these grains were closely bound together. In this sense any mixture whatever can always be produced from its components, just as we can always separate it into its components by some means or other. 39. PROPERTIES OF MIXTURES. Nothing is changed in the specific properties of a set of substances when we bring them to- gether in a mixture. The properties of a mixture can therefore be calculated from the properties of its constituents by the Rule of Mixtures, as it is called. If, for example, one part of the mixture is composed of x parts of the homogeneous body A and 1 x parts of the body B, and if a is the value for a specific property of the body A and b is the value for the corresponding property of the body B, the value of the property in the mixture of A and B will be ax + (1 x)b. If the mixture consists of three compo- nents, a similar formula, xa + yb + (1 x y)c will be appli- cable. The word " parts" must be taken to mean parts by weight when the specific property is based on the unit of weight, and parts by volume when it is based on the unit of volume. The formula for mixtures of two components can be used in two ways. Where the properties of the constituents are known and the fraction x, in which one constituent is present, is given (and from this the fraction 1 -# of the other constituent), then the value of the property in the mixture can be calculated. Or x can be calculated when the value of the property in the mixture has been determined, by experiment, for instance. If the value of the property in the mixture is called m, we have ra= xa + (lx)b, MIXTURES, SOLUTIONS, AND PURE SUBSTANCES 53 or from this x = ( - r J. This last formula is often used in cal- culating the constitution of a mixture of two bodies from a meas- urement of one property. It can also be used in difficult cases to determine whether we have to do with a mixture or not. In these cases it is necessary -to determine the proportions in which the two constituents appear, and the value of one of the specific properties of each constituent. From this data the value of this same property in the suspected mixture is then to be cal- culated. If the calculated value does not agree with the measured value within the limit of error of the measurements, we are cer- tainly not dealing with a mixture. If it does agree, it is very prob- able that we are dealing with a mixture; but there are some cases where homogeneous substances exhibit properties which agree with those calculated from the Rule of Mixtures as above described. 40. LIQUID SOLUTIONS. Liquids differ from solid bodies in their chemical properties as well as in their mechanical ones. The Law explained in Sec. 36 applies to solid bodies with a few excep- tions which will be taken up later, but the relations in the case of liquids are much more complex. Nearly all solid bodies can be arranged in classes in such a way that their properties differ by distinct steps from class to class, remaining constant within the individual class. There are many liquids which can be arranged in classes in the same way and which therefore follow the same law, but there are many more liquids whose properties can have any values whatever between certain limits. These intermediate forms are produced by mixing two different liquids in various pro- portions. In some cases this does not result in the formation of a new homogeneous liquid, but in many cases it does. The liquids which do so mix are said to dissolve each other, and the resulting product is called a solution. These solutions are just as homogeneous as the substances from which they are prepared, and the most careful optical examination shows no trace of individual constituents. They can therefore not 54 FUNDAMENTAL PRINCIPLES OF CHEMISTRY be placed in the same class with the mixtures which we learned about in the case of solid bodies. They have no very evident properties which distinguish them from the other liquids which obey the Substance Law of Sec. 36. It is only when they are transformed in some way (made to change their state, for instance) that fundamental differences between them and the other class of liquids become evident. For the present we will content ourselves with calling attention to the existence of solutions as distinguished from substances in the narrower sense of the word. The discus- sion of the differences between them will be left until later. 41. SOLUTIONS OTHER THAN LIQUID ONES. Solid bodies can also form solutions, that is, they can form solids with properties varying continuously between certain definite limits. But such solutions occur much less frequently than in the case of liquids. They occur most frequently among amorphous substances (Sec. 19) (which can be regarded as liquids with very great viscosity) and only very infrequently among crystalline substances. ^Tien they do occur among crystalline substances, it is usually among those which are " isomorphous." With gases the case is entirely different. All gases form solu- tions with each other in all proportions, and it is not always easy to decide whether a given gas is a solution or a pure substance. The fundamental method of deciding this point will be discussed in the next chapter. 42. MIXTURES OF LIQUIDS WITH SOLIDS. Relations very similar to those given in the case of several solid bodies appear when solids are mixed with liquids. The mixture may show properties which approach those of one or other of its constit- uents, depending on which of them is present in greater amount. The cloudy liquids, which contain only a small amount of a solid substance in a large amount of a liquid, are to be considered here. The semi-liquid and clay-like masses, which consist of about equal parts of solid and liquid (here the relative amount of the two con- stituents may vary within very wide limits), also belong here. MIXTURES, SOLUTIONS, AND PURE SUBSTANCES 55 Finally, we must include in this class apparently solid masses with only a very small amount of a liquid mingled with them. To the eye all of these are characterized by their muddiness or opacity. Only in those cases where the two constituents have the same index of refraction does this cloudiness disappear. And even then it disappears only when the mixture is illuminated by light of one particular wave-length, and it appears again when light of another wave-length is used. This fact explains the re- markable colour-phenomena which are observed in all of these mixtures. While these colour-phenomena are very interesting, they cannot be discussed further in this book. There are several ways of separating such a mixture, the most usual of which is filtration, and this is carried out by allowing the mixture to pass through a sieve. This sieve can have coarse meshes when the solid body is present in large pieces, but its meshes must be made finer and finer as the size of the particles to be separated decreases. The sieve most commonly used in chemical work is filter paper, and this consists of a thin mass of hair-like bits, through whose interstices the liquid can easily pass while the solid particles are held back. Paper with various sizes of pores must be used for various sizes of solid particles to be retained, and when the pores are very fine the liquid passes through the paper slowly. In general it is desirable to finish a filtration as rapidly as possible, and choice must therefore be made in each case of a paper with pores corresponding to the size of the solid grains to be retained. Gravity is usually depended on to carry the liquid through the paper, but the separation can be made more rapid by causing a difference of pressure on the two sides of the paper, either by in- creasing the pressure above the liquid in the filter or by decreas- ing it below. In technical work the first method is the more usual one, but in the laboratory the second is generally applied. A second method of separation is based on the direct action of gravity on such a mixture. The solid substance usually has the greater density, and when such a mixture is allowed to stand 56 FUNDAMENTAL PRINCIPLES OF CHEMISTRY quietly a separation results, the solid collecting at the bottom of the containing vessel while the liquid remains above in a pure state. This method of automatically clearing a muddy liquid is applied in a very great number of cases, and it appears everywhere in natural processes. If the mixture is subjected to the action of a centrifugal force, the solid particles, which have the greater rela- tive* mass (greater density), are thrown outward, and separation results. The effect increases as the square of the velocity, and can therefore be greatly increased by increasing the velocity. This is why a separation can be made much more quickly and com- pletely by means of a centrifuge than by merely allowing the mixture to stand and settle. Separations of this sort are always incomplete, provided the solid is one which is wet by the liquid, and this is almost invariably the case. The liquid comes out clear, to be sure, but is not com- pletely separated, and the solid is completely removed, but not in a pure state, since it is not quite free from the liquid. The amount of impurity which is present in the solid after separation in this way can be reduced as far as desired by pressure or the centrifuge, but it can never be made actually zero. When the solid is present in larger proportion, masses more or less like dough or clay are formed, which act like liquids with great viscosity, but which are different from these in some ways. The possibility of forming such plastic masses into any shape by mechanical action conditions their use in practical things, as in mortar and clay. Finally, when the liquid is present in very small amount it collects on the surface of the solid and is held there by surface tension. All solid bodies which have been lying in the air are covered with such a layer of water, which does not act like a liquid and cannot be wiped off. It can be driven off by heating the body strongly, but even then it does not evaporate as easily as ordinary water. Recognition of this fact is of importance if the weight of a solid is to |^e determined. Massive bodies with a small MIXTURES, SOLUTIONS, AND PURE SUBSTANCES '57 surface carry with them only a very small amount of water in this way, but the amount increases as the surface of the body increases, and becomes considerable when we have to deal with a fine powder or with thin sheets. The presence of this thin layer may be made apparent by the following experiment : Draw out a tube or a glass rod by heating it in the glass-blower's lamp. Break off the fine thread so pro- duced and draw one piece of it over the other. The freshly formed surfaces will cling to each other in a very evident way. But after the pieces have been lying in the air for a time the surfaces will glide over each other without any sign of clinging. Clean surfaces of any solid will cling to each other in this way, because solids as well as liquids seek to take on as small a surface as possible, as a result of surface energy. The thin layer of water which forms in the air prevents the surfaces from coming into contact and removes the possibility of this action. 43. LIQUID MIXTURES. When two different liquids are brought together they either form a homogeneous solution or else remain separate (Sec. 40). The result depends very often on the relative amounts of liquid which are brought together, for many liquids form solutions when a small amount of one is mixed with a large amount of the other, but do not do so beyond a certain definite point. If the relative amount of the first liquid is increased a true mixture of the two is formed. Two cases are here possible. First, the two liquids may remain almost entirely separate. The less dense of the two will then float above the denser and a horizontal surface of separation will be visible between them. Second, the two may be so shaken to- gether that one becomes more or less finely divided throughout the other. The one will then take on the form of spherical drops which float about in the other. In this case the conditions men- tioned in Sec. 37 will be found, and any difference in the indices of refraction of the two liquids will cause the mixture to appear more or less opaque. Both of these cases may be seen if first water 58 FUNDAMENTAL PRINCIPLES OF CHEMISTRY and then oil be poured into a flask, and the whole afterward shaken. Such a mixture of two liquids in which spherical drops are formed is called an emulsion. Considerations similar to those developed for solid-liquid mix- tures in the previous section apply to the separation of the con- stituents of liquid mixtures. Filtration is only applicable when the liquid which is to be held back can be prevented from wetting the material of the filter, for otherwise it will run through and spoil the separation. But even very fine emulsions of compo- nents only slightly differing in density can be separated by the centrifuge. Milk is a good example, and it is an emulsion of butter-fat in an aqueous solution of milk-sugar and casein. Where the emulsified liquid is very finely divided indeed, the separation becomes much more difficult on account of the effect of surface energy, which then becomes active and prevents separa- tion in a way which we cannot discuss further. 44. MIXTURES OF GASES. Gases dissolve each other in all proportions, and it is therefore impossible to make a mixture of two or more gases. Gases can, however, form mixtures with either liquids or solids. Two cases are always to be considered. In general, and because of surface tension, such a mixture will consist of more or less spherical drops of one of the bodies, sus- pended throughout a nearly continuous mass of the other. De- pending on whether the mass or the suspended portion is gaseous, the resulting phenomena are very different. If the gas is the major mass in which fine particles of a solid are floating, we have a dusty gas. If the floating particles are liquid, we have to do with a fog. The density of the floating par- ticles, whether solid or liquid, is always very much greater than that of the gas about them, and the particles must therefore be very small indeed if the mixture is to have any duration as such. For any given amount of the floating body the resistance to fall increases in proportion to the total cross section of the body, and this means that as the particles are made smaller the resistance to MIXTURES, SOLUTIONS, AND PURE SUBSTANCES 59 fall increases as the inverse square of the linear dimensions of the particles. In cases of very fine division the resistance is so great that such a mixture can remain hours or even days without any apparent separation due to gravity. In general it is easier to pro- duce a very fine state of division among liquids than among solids. 45. FOAMS. In the other case, where the gas forms the iso- lated particles, the resulting mixture is called a Foam (Schaum). This name is applied primarily to a mixture in which a liquid forms the main body of the mass; but if this hardens, a solid gaseous mixture of precisely similar structure results, and the same name has also been given to this. Ordinary pumice stone is just such a solid foam, which has been formed by the solidifica- tion of an originally liquid mass of rock. Surface energy plays an important part here, and this some- times results in great stability of the resulting foam. The stability seems in general to be greater when the liquid portion is of a rather complex nature, and especially when it contains some substances with great and some with small surface tension. The foams re- sulting from pure liquids are usually very unstable. CHAPTER IV CHANGE OF STATE AND EQUILIBRIUM (a) The Equilibrium Liquid Gas 46. EQUATIONS OF CONDITION. Substances retain their properties unchanged only when the conditions under which they exist remain unchanged. These conditions may be of the most manifold kind, for all the arbitrary properties previously mentioned correspond to differences in them. Of all the possible ones two are of especial importance to us. These are temperature and pressure, the intensity factors of heat and volume energy respectively. In our discussion of the various states in which bodies may exist the influence of these two conditions was repeatedly mentioned, and we found that the very first specific property we discussed, density or specific volume, was influenced in a quite characteristic way by both temperature and pressure. If a greater range of temperatures and pressures is included, it is found that their influence may be still more im- portant, and that it may even determine the passage of a substance from one state to another. If the behaviour of a substance is investigated at various pres- sures and temperatures, it is found that the substance can be made to pass through a complete series of conditions by varying the values of these two factors. A general view of all these changes is best obtained by considering first the changes in condition cor- responding to change in temperature, the pressure remaining constant (isobaric changes), and then those corresponding to a change in pressure, the temperature remaining constant (isother- mal changes). 60 CHANGE OF STATE AND EQUILIBRIUM Gl 47. THE LIQUEFACTION OF GASES. Let us begin with a gas. If we raise its temperature at constant pressure it does not change its state : it remains a gas, merely changing its volume in accordance with the Law of Gay-Lussac. If, however, we lower its temperature, we find a point where the gas changes to a liquid. This point may vary, according to the nature of the substance, between the widest limits of our known temperature scale. Some gases have been liquefied only with the greatest difficulty, because of the very low temperatures necessary for their liquefaction. These difficulties have been overcome one by one, and now there is no gas known which has not been actually liquefied. The change of a gas into a liquid takes place suddenly, or, better, discontinuously ; for just above a certain definite temperature the substance under examination has all the properties of a gas, and just below the same temperature it has those of a liquid. Its density usually increases greatly, and all its other properties show a sudden and usually considerable change. Certain new proper- ties, surface tension among them, appear. In agreement with our general definition such a transformation is to be considered as a chemical change, for one substance a gas disappears and another a liquid having a new set of prop- erties appears. It has been customary to call this change of state a physical change, because it can be so easily reversed. But there are also many chemical processes which can be just as easily reversed ; and beside this, the general laws, in accordance with which these changes take place, are precisely the same laws as those which describe undoubted chemical change. It is there- fore better to consider a change of state as a chemical change of the simplest sort. 48. PURE SUBSTANCES AND SOLUTIONS. In changes of this type two separate cases are to be distinguished, and their char- acterization is of great importance. Either the whole of the gas changes into a liquid as liquefaction goes on, without the tempera- ture being changed (the pressure remaining constant), or the tern- 62 FUNDAMENTAL PRINCIPLES OF CHEMISTRY perature must be carried lower and lower as liquefaction proceeds, in order to cause the remaining portions of the gas to liquefy. Gases of the first class have a constant temperature of lique- faction, and they are pure substances, or substances in the narrower sense of the word. Gases of the second class are called solutions. It has been usual to call gases of this latter kind gaseous mixtures, retaining the name " solution " for a certain class of liquids only. A general consideration of the facts shows that it is better to extend the idea solution to all three states, and to consider gaseous and solid solutions together with the liquid ones. Experience has shown that a solution can always be made up from pure substances, and further, that it can always be broken up into the same pure substances again. Study of the pure sub- stances should therefore precede the investigation of solutions. An unlimited number of solutions can always be made up from the same two pure substances, by giving the relative amount of the constituents any desired value. Infinitely more solutions than pure substances are therefore possible. From both points of view a knowledge of the pure substances is of far greater im- portance than a knowledge of solutions, and we will devote our- selves exclusively to them for the present. 49. REVERSIBILITY. The phenomena just described are re- versible. If the liquid which has been obtained by liquefaction of the gas is warmed a little, it will change back into a gas at the same temperature as the one at which it liquefied. Gases obtained in this way from liquids are often called vapours. As long as it was believed that gases existed which could not be liquefied, this term had a definite meaning. At the present time the difference no longer has such a meaning, and the word " gas " is used for sub- stances in this state, leaving the word " vapour " to indicate their relation to the same substance in the liquid and solid state. The change of a liquid into a gas (or vapour) is called vaporiza- tion or boiling. The two mean the same in reality, but it is usual to use the term " boiling" only when the vaporization takes place CHANGE OF STATE AND EQUILIBRIUM 63 in such a way that bubbles rise through the liquid, while vaporiza- tion is used to indicate the formation of vapour at the surface of the liquid. Pure substances and solutions show the same differences in vaporization that they show in liquefaction. Pure substances go through the whole process at constant temperature, while solu- tions show a changing temperature during the process. But the direction of the change is opposite to that which takes place during liquefaction. After vaporization has begun at a definite tempera- ture, the temperature must be raised higher and higher in order to make the evaporation complete. This is, of course, because here we are starting with the liquid solution and passing to the gaseous one, while in the other case we began with the gaseous and passed to the liquid solution. This mutual relation is expressed by saying: a pure substance remains pure independent of its state, and a liquid solution changes into a gaseous solution, and vice versa. This is an important conclusion. 50. EQUILIBRIUM. A further conclusion may be drawn for pure substances. Such a substance can be transformed at a given pressure from one state to another at constant temperature. At this temperature, therefore, and this pressure any given amount of liquid and any given amount of vapour can exist together with- out exerting any influence on each other. Such a condition is called an equilibrium, and it has something in common with a mechanical equilibrium in that it no longer changes with time, provided the conditions (in this case pressure and temperature) do not change. This may be expressed by saying that under these conditions the relative and absolute amounts of vapour and liquid have no influence on the equilibrium. The case of solutions is different, for among them every equilibrium between liquid and vapour corresponds to a different temperature. A pure substance remains pure whether it 'is in the state of liquid or in the state of vapour;- it is therefore customary to use the 64 FUNDAMENTAL PRINCIPLES OF CHEMISTRY same name in both cases, and to add the state when this is neces- sary. The name " water " (in the chemical sense) is used to desig- nate not only the familiar liquid, but also its vapour, and we distinguish, when necessary, between liquid water and water vapour. Ice is, of course, water in the solid form. The transformation of a pure substance from one state to an- other takes place under a given pressure at constant temperature. The most easily observed case of this transformation is that from liquid to gas at the boiling point. If water is heated in a vessel under ordinary atmospheric pressure vapour forms more and more rapidly until 100 C. is reached, and this temperature con- tinues unchanged, without regard to the amount of water left in the vessel or the amount which has boiled away, until all the water is gone. This gives a means of producing a definite temperature, and use is made of this fact in the determination of the funda- mental points of our thermometric scale. Water has been chosen for this purpose rather than any other substance, because water is the easiest to obtain in the pure state. Pure substances have a constant boiling point, while the boiling point of a solution changes, increasing as evaporation proceeds. This latter fact is, of course, a characteristic means of recognising solutions. 51. SATURATION. If we examine the condition of a gas with respect to the possibility of changing it into a liquid, by cooling it or increasing the pressure upon it, we find several cases. There is first of all a region of low pressure and high temperature where it cannot be transformed into a liquid. This is called the unsatu^ rated condition, referring to saturation, which we are about to dis- cuss, and a vapour in this region is called an unsaturated vapour. If the pressure is increased or the temperature decreased until liquid can exist together with the vapour, the condition is one of saturation, and we have* to do with the saturated vapour. By saturation we are therefore to understand, in general, the condi- tion of a phase which is in equilibrium with another. We might, of course, speak of a liquid as saturated with respect to the vapour ; CHANGE OF STATE AND EQUILIBRIUM 65 but this is not customary, because the density of a liquid usually varies only very slightly under changes of pressure and tempera- ture, while the change in the density of a gas under the same variation of conditions is very great. The word "saturation" is therefore used for those phases in which these changes (and in- cluded with them changes in concentration) are easily observed. If we go further with the lowering of the temperature, the in- crease of pressure, or the increase of concentration, until the saturation point is passed, we reach the region of supersaturation. 52. THE INFLUENCE OF PRESSURE. If the transformations just described are investigated at another pressure the following result will be found in general. Substances which have been found to be pure under one pressure behave, in general, in the same way under other pressures. But the temperature at which the transformation takes place is a different one under a different pressure. The higher pressure always corresponds to a higher temperature. On the other hand, substances which behave like solutions under one pressure will act in the same way under other pressures. Among solutions also the temperature at which transformation into another state begins is higher for a higher pressure, as is also the temperature at which the transformation is complete. For pure substances there is, therefore, a perfectly definite re- lation between the pressure and the temperature at which liquid and vapour can exist in equilibrium, and the two increase and de- crease together. This pressure is called the vapour pressure of the substance at the corresponding temperature, and the temperature is called the boiling point of the substance at the corresponding pressure. When we speak of the boiling point simply we always mean the boiling point corresponding to a pressure of one atmos- phere, the temperature at which boiling would begin in an open vessel. 53. THE VAPOUR PRESSURE OF WATER. The relation between temperature and vapour pressure for water is shown in the accom- 5 66 FUNDAMENTAL PRINCIPLES OF CHEMISTRY panying table. Temperatures are given in Centigrade degrees and pressures in centimetres of mercury. Two sets of values are given below 0. The first of these corresponds to solid water (ice) ; the second, to super-cooled liquid water. VAPOR PRESSURE OF WATER. Tempera- ture. Pressure. Tempera- ture. Pressure. Ice. Liquid Water. Liquid Water. - 15 0.126 cm. 0.145 cm. + 18 1.538 cm. - 14 0.138 cm. 0.157 cm. + 19 1.637 cm. - 13 0.151 cm. 0.171 cm. + 20 1.741 cm. - 12 0.165 cm. 0.185 cm. + 21 1.850 cm. - 11 0.181 cm. 0.200 cm. + 22 1.966 cm. - 10 0.197 cm. 0.216 cm. + 23 2.088 cm. - 9 0.215 cm. 0.234 cm. + 24 2.218 cm. - 8 0.235 cm. 0.252 cm. + 25 2.355 cm. - 7 0.256 cm. 0.272 cm. + 30 3.156 cm. - 6 0.279 cm. 0.294 cm. + 35 4.185 cm.. - 5 0.303 cm. 0.317 cm. + 40 5.497 cm. - 4 0.330 cm. 0.341 cm. + 45 7.150 cm. - 3 0.359 cm. 0.368 cm. + 50 9.217 cm. - 2 0.389 cm. 0.396 cm. + 55 11.78 cm. - 1 0.422 cm. 0.426 cm. + 60 14.92 cm. - 0.458 cm. 0.458 cm. + 65 18.75 cm. + 1 0.492 cm. + 70 23.38 cm. + 2 0.529 cm. + 75 28.93 cm. + 3 0.568 cm. + 80 35.55 cm. + 4 0.609 cm. + 85 43.38 cm. + 5 0.653 cm. + 90 52.60 cm. + 6 0.700 cm. + 95 63.40 cm. + 7 0.749 cm. + 100 76.00 cm. + 8 0.802 cm. + 110 107.5 cm. + 9 0.858 cm. + 120 149.1 cm. + 10 0.917 cm. + 130 203.0 cm. + 11 0.981 cm. + 140 272 cm. + 12 1.048 cm. + 150 358 cm. + 13 1.119 cm. + 160 465 cm. -f 14 1.194 cm. + 170 596 cm. + 15 1.273 cm. + 180 755 cm. + 16 1.357 cm. + 190 944 cm. + 17 1.445 cm. + 200 1169 cm. CHANGE OF STATE AND EQUILIBRIUM 67 54. DIAGRAM. This relation can also be made clear by laying off temperatures along a horizontal straight line in a plane, and then laying off the pressure (in centimetres of mercury, for ex- ample), corresponding to each temperature, along a vertical line. Arbitrary units of lengths are to be chosen for each quantity with regard to the scale in which the drawing is to be carried out. The upper ends of the pressure values will then all lie on a continuous curved line which is called the vapour pressure curve, or the curve 80 -^70 5O TEMPERA TURE FIG. 1. of saturated vapour. The vapour pressure curves of all substances are similar in shape, and they are like the vapour pressure curve of water shown in Fig. 1. They all turn their concave side up- ward and become steeper with increasing temperature. The course and position of the curve is, however, very different for different substances, and there are no two substances which are different in other things but which have the same vapour pressure 68 FUNDAMENTAL PRINCIPLES OF CHEMISTRY curves. These curves are just as much specific properties of sub- stances as are their densities or specific volumes. It happens, however, that two different substances do have the same vapour pressure at the same temperature. Their vapour pressures will, however, be different at all other temperatures, and the two vapour pressure lines have crossed each other at the temperature in question. But this is a rare case. In general it is not necessary to determine the whole course of the vapour pressure curves of substances in order to determine whether or not they are different. It is usually sufficient to deter- mine one single point. This point is usually the boiling point at atmospheric pressure, because this is the easiest point to deter- mine, and the boiling points of various substances are frequently used as an indication of difference or similarity. 55. CHANGE OF VOLUME DURING EVAPORATION. When temperature and pressure are so regulated that liquid and vapour can exist together, the following changes take place in the volume occupied by the two phases. The liquid expands as the temperature rises. Of course the increase of volume is less when the pressure is increased at the same time than it would be if the pressure were kept constant, but the influence of pressure is so small that the resultant appears as an increase of volume. This increase is a very small one, be- cause of the slight coefficient of expansion of liquids. With the vapour it is entirely different. As described by Boyle's Law, the volume is inversely proportional to the pressure. At the low vapour pressures which correspond to low temperatures it is very great, but it becomes very rapidly smaller as the tempera- ture rises, corresponding to a rapid increase in the vapour pres- sure. In this case also an opposing effect is present, for, as the result of an increase in temperature, the specific volume would in- crease, according to the Law of Gay-Lussac, provided the pressure remains the same. But the influence of change of pressure is so great that the vapour which is in equilibrium with the liquid CHANGE OF STATE AND EQUILIBRIUM 69 behaves in the opposite way from the liquid itself. Its specific volume decreases with rising temperature, and decreases very rapidly. When the specific volume of the vapour in question has once been measured, the constant r in the gas equation =- =r can be determined for this vapour by inserting the observed values for volume, temperature, and pressure in the formula. If r is known this process can be reversed and the volume calculated for each value of pressure and temperature according to the formula rT v= . It is easy to calculate the specific volume of a saturated P vapour in this way if the vapour pressure curve is known, for this curve represents corresponding values of pressure and tempera- ture for equilibrium between the vapour and liquid. The gas equation only gives correct results when the specific volume is large. As it becomes small, because of the rapidly in- creasing pressure corresponding to increasing temperature, calcu- lations made by means of the simple gas formula become less and less accurate. The deviations are of such a nature that the real volume always comes out smaller than the calculated one, and this deviation becomes greater as the pressure is increased. Additions have been made to the gas equation to express these deviations, but we cannot take them up here. The following table gives the same relations for liquid water and water vapour again, the results having been obtained directly from experimental measurements. The first column contains the temperature in Centigrade degrees; the second, the vapour pressures of water at these temperatures, expressed in centimetres of mercury; the third and fourth give the values for the specific volume of the saturated vapour and that of liquid water, expressed in cubic centimetres. It is evident that the specific volume of the vapour decreases very rapidly with rising temperature, while that of liquid water increases slowly, as indicated above. 70 FUNDAMENTAL PRINCIPLES OF CHEMISTRY ' Tempera- Vapor Specific Volume. ture. Pressure. Vapor. Liquid. 0.46 203500 1.00 20 1.74 57800 1.002 50 9.20 ' 12030 1.012 100 76.0 1681 1.043 120 149.1 945 1.060 160 465 317 1.101 180 765 203 1.127 200 1169 140 1.158 It will be seen from these values that a great increase in volume results from the change from liquid water into water vapour. At C. the volume increase is about 200,000 times. At 200 the increase is only about 120 times. 56. HEAT OF VAPORIZATION. When a liquid changes into a gas the change is accompanied by a change of volume. At the same time a very considerable amount of heat must be absorbed if the temperature is to remain constant, or, as we say, if the process is to take place isothermally. This heat has been called latent heat, because it is added to the system without producing a rise of temperature. This expression is, however, only a makeshift, which was applied because the phenomenon was not understood, that is, its connection with other facts was not known. The more general explanation is, that every chemical process in which a given body is transformed into another having other properties is accompanied by a change in the energy of that body. This energy may appear in many different ways. A change of volume under a certain pressure represents an amount of work which is measured by the product of pressure and volume. Energy, in general, means either work or anything which can be obtained from work or transformed into work. Since work can always be transformed into a proportional amount of heat, the latter is also CHANGE OF STATE AND EQUILIBRIUM 71 a form of energy, and confirmation of this is found in the fact that heat can be transformed into mechanical work by means of steam or gas engines. The above principles can therefore be expressed by saying that one body can never be transformed into another without the co-operation of work. This work can be either posi- tive or negative, that is to say, energy can either be taken in or given out during the process. During the evaporation of a liquid heat is taken in; during the liquefaction of a vapour an equal amount of heat is given out. If we investigate evaporation at various temperatures and pressures it is found that at high values of these factors the heat of vaporization becomes smaller and smaller as the values of temperature and pressure increase. 57. THE MEASUREMENT OF QUANTITY OF HEAT. Since heat is a form of energy it is a quantity in the narrower sense of the word, which can be added, and which is therefore capable of direct measurement when once the unit has been determined. It would be better to use the same unit for all the forms of energy, for then amounts of energy which are produced from each other, or which could be transformed into each other, would be char- acterized by the same number. There is such a system of units, and it is called the absolute system, but it has not yet been gen- erally introduced. Especially in the case of heat another unit is in general use, which was determined upon at a time when we knew nothing about the mutual transformation of the various forms of energy. This unit is based upon the properties of the most familiar of all pure substances, water, as weight and density are also based on water. The unit chosen for quantity of heat was the amount which would raise the temperature of a gramme of water 1 C. This unit is slightly variable with temperature, and an agreement was made to base this definition on 18, which was taken as being ordinary room temperature. This unit is called a calorie, which is abbreviated to cal. If a gramme of water vapour at atmospheric pressure is passed into a weighed amount of water, the water becomes warmer, and 72 FUNDAMENTAL PRINCIPLES OF CHEMISTRY its rise of temperature is very much greater than would result from adding one gramme of liquid water at the same temperature as the steam, that is, at 100 C. The difference, which corresponds to the heat of liquefaction of one gramme of water vapour under the given conditions, is 536 cal. This number is found by mul- tiplying the weight in grammes of the water used by the rise of temperature in degrees Centigrade. The quantity of heat is pro- portional to the quantity of water heated, and also to the rise of temperature; it is therefore proportional to the product of these two quantities. That division of chemistry which has to do with changes of heat accompanying transformations between substances is called thermo-chemistry. Just as we can determine the heat value cor- responding to the transformation of water vapour into liquid water, and vice versa, so we can find the corresponding heat value for any other chemical process by carrying out the necessary measurements. 58. ENTROPY. Two forms of energy, volume energy and heat, are involved in the phenomena of evaporation, and they exhibit a great similarity. Volume energy can be considered as the product of two factors, the pressure and the increase of volume ; and in the same way a change in heat energy can be considered as the product of two factors, of which one is the temperature. This corresponds to the pressure, for both values are intensities and not quantities. That this is true of temperature is evident from the fact that two bodies which have the same temperature do not show twice the temperature when they are brought together. The temperature remains unchanged. The other factor, which is a quantity in the narrower sense, and which is therefore additive, is not as well known as volume, which is the corresponding factor of volume energy. This comes from the fact that we have become accustomed in working with heat to use the energy itself, that is, the amount of heat, and with this, one of its factors, temperature. The other CHANGE OF STATE AND EQUILIBRIUM 73 factor has so far been used only in mathematical physics, although it offers no greater difficulties to the understanding than a quan- tity of electricity or a momentum. In the case of volume energy the matter is reversed. Here the two factors, pressure and volume, are in common use, while volume energy itself is by no means so generally used. The capacity factor of heat energy is called entropy; the product of entropy and temperature gives heat energy. We must there- fore be able to find entropy by dividing energy by temperature; 536 heat units are absorbed by a gramme of water changing to vapour under atmospheric pressure. The corresponding increase of entropy is to be found by dividing this number by the tempera- ture 100 C. or 373 A., and the result is |f| = 1.44 entropy units. 59. THE CRITICAL POINT. The facts we have just been con- sidering give rise to several general questions. First, vapour pressure increases with rising temperature. Can this go on with- out limit? Second, the specific volumes of liquid and vapour approach each other with rising temperature, and the change of volume during vaporization becomes smaller and smaller. Will it finally become zero? Third, the heat of vaporization (or the change of entropy) becomes smaller and smaller with rising tem- perature. Will it also finally become zero ? Fourth, when both these things become zero, in case this happens, will they arrive at zero simultaneously or at different points? These questions have been answered as follows by experiments. As the temperature is increased, the vapour pressure, that is, the pressure of the vapour which is in equilibrium with the liquid, does not increase continuously. The vapour pressure line has a definite end at a highest temperature and a highest pressure, and these two highest values correspond to the point where the specific volume of the vapour is the same as that of the liquid. At the same point the heat of vaporization and the change of 'entropy both be- come zero, and there remains no difference whatever between the liquid and its vapour. This means, of course, that liquid and 74 FUNDAMENTAL PRINCIPLES OF CHEMISTRY vapour cease to exist in contact with each other, and this means the end of the vapour pressure line. Above this point there is no longer a transformation of liquid into vapour, and any values whatever may be given to pressure and temperature. All this is expressed in the diagram of Fig. 2. Here densities (not spe- cific volumes) of vapour and liquid have been plotted horizon- tally, and temperature vertically. The density of the vapour in- creases with rising temperature while that of the liquid decreases. The two approach one another and finally coincide at a definite point. This point is called the critical point, and it corresponds to a definite temperature and a defi- nite pressure which are called DENSITY the critical temperature and the F IG> 2. critical pressure. The common specific volume at this point is called the critical volume. It is evident that the critical point cor- responds to a point where liquid and vapour become identical. The critical data vary with the nature of the substance, and we find critical temperatures lying at every part of our temperature scale. Critical pressures lie closer together and have values be- tween 25 and 100 atmospheres, depending on the nature of the substance. Critical volumes vary from 1.5 to 5, and therefore show no very great difference. The critical volume is, in general, greater if the critical temperature is high. It is easy to observe the most important phenomenon corre- sponding to the critical point, that is, the identity of liquid and vapour, by sealing up a rather volatile liquid in an exhausted glass CHANGE OF STATE AND EQUILIBRIUM 75 tube so that it fills about one half the volume of the tube. If the temperature is now increased, the difference between the liquid and the vapour above it becomes smaller and smaller, and at the critical temperature the surface between them disappears and the tube is filled with a homogeneous substance. If the tube is then slowly cooled a peculiar brownish fog appears suddenly at the critical temperature. The denser liquid appears immediately in the lower part of the tube, the lighter vapour collects above it in the upper part. 60. PHASES. The changes of state just described, which are produced in a substance by changes in temperature and pressure, may be considered processes in which mixtures result from homo- geneous substances. A mixture of gas and liquid is produced from a homogeneous gas by compression and cooling. If a homo- geneous liquid is cooled, there results a mixture of it and a solid substance. If the temperature is still further lowered, the mixture changes into a homogeneous substance again,* the constituent corresponding to the first state disappearing and leaving its suc- cessor, which corresponds to another state. The components of mixtures produced by a transformation of this sort are called phases. Phases, therefore, are homogeneous substances which appear in mixtures. They may be either pure substances or solutions. In our general definition of a substance we took no account of shape or quantity. Our definition of a phase is the same in this respect, and all the parts of a mixture which have corresponding specific properties are included in one phase. Two or more phases are in equilibrium when they can exist to- gether without any effect on each other's properties. The first condition to be realized here is that they must all be under the same pressure and at the same temperature, otherwise it is impossible that they should exist together without any change * Mixtures may result from solutions under these circumstances. A salt solution, for example, may form a mixture of solid water and solid salt. The facts as given in the text hold for pure substances and the case of solutions will be taken up later in a special chapter. 76 FUNDAMENTAL PRINCIPLES OF CHEMISTRY taking place. Beside this, other conditions must be fulfilled, and we will consider these a little later. If two or more homogeneous substances are brought together they do not, in general, form phases which are in equilibrium. They usually affect each other mutually even when pressure and temperature are the same. The processes which take place under these circumstances make up the greater part of what is called chemistry. 61. DEGREES OF FREEDOM. If pressure and temperature are considered as variable we can affect the condition of substances in two ways, and it is only when definite values have been given to these two factors that the condition of a substance is determined. We are free to do as we choose with temperature and pressure (to a certain extent at least, which is bounded by the appearance of new states), and it is therefore said that each substance possesses two degrees of freedom. It makes no difference whether the sub- stance in question is a pure substance or a solution, whether it is solid, liquid, or gaseous, although the effect of pressure and tem- perature on a solid is very small and on a gas is very great. Conditions are changed, as we have seen, when a second phase appears. If we have made the condition that liquid and vapour shall exist together, we have used up one of our " freedoms," and only one is left. This corresponds to the fact that to each tempera- ture there corresponds a perfectly definite vapour pressure which is only dependent upon the nature of the liquid. If we have decided upon the temperature in this case we are no longer free in the choice of a pressure. And in the same way we no longer have any choice of a temperature when we have prescribed a certain pres- sure. Temperature can then have only one value, and that is the boiling point of the liquid at the pressure chosen. If we change the temperature or the pressure under these conditions, one of the phases will disappear. We may conclude from this that the condition that a second phase shall exist in contact with a given phase is the same thing as disposing of one degree of freedom, and that therefore the sum CHANGE OP STATE AND EQUILIBRIUM 77 of phases and degrees of freedom is a definite number. How large this number is depends upon whether we are dealing with a pure substance or a solution. The simpler considerations apply to the pure substances, and we will therefore take up their behaviour first. If a new phase is produced from a pure substance by a proper variation of pressure and temperature, the properties of both phases are determined, for although we can change the relative proportions in which the two phases exist by changing the volume or the entropy, we cannot produce any change whatever in the properties of either phase. This is, of course, the definition of a pure substance. It exhibits no change of properties when it is partially transformed into a new phase. We have, therefore, no further freedom to produce change. The number of degrees of freedom belonging to a single phase is two, for we can give it any temperature and any pressure within the limits between which the substance remains in the same state. If we now fix the condition that a second phase is to exist in equi- librium with the first, we have disposed of one degree of freedom, and only one remains. This is another expression for the fact already described, that when two phases of a pure substance are in equilibrium only one definite temperature corresponding to each pressure (and one pressure corresponding to each temperature) can be found at which the two phases will continue to exist together. If a third phase be added, the last degree of freedom has been dis- posed of, and we will see that in a pure substance three phases can only exist together at one definite pressure and at one definite temperature. If we sum up phases and degrees of freedom in each case the result is always three. One phase has two degrees of freedom; two phases, one ; three phases, none. For pure substances we may state the law : The sum of phases and degrees of freedom is three. This is called the phase rule. This rule does not apply to solutions. In the case of a solution 78 FUNDAMENTAL PRINCIPLES OF CHEMISTRY two phases can exist in equilibrium at a given pressure, not only at one temperature, but at any number of different temperatures. One of the characteristics of a solution is the fact that its boiling point does not remain constant at constant pressure, while more and more of the second phase is being produced, but rises continu- ally as the transformation proceeds. The same statement applies to the pressure when the temperature is kept constant. The num- ber of degrees of freedom is therefore greater in a solution than in a pure substance. How large the number is depends upon the na- ture of the solution, and this we shall consider later. Be it said, however, that solutions are classified by the number of degrees of freedom which they possess when another phase is present. As long as no second phase is in contact with a solution it acts just like a pure substance and possesses only two degrees of freedom in temperature and pressure. 62. SUBLIMATION. In a few cases the substance produced from a gas by lowering the temperature is not a liquid but a solid, and in this case the solid changes on being heated into a gas or vapour. Laws which describe these transformations have exactly the same form as those corresponding to the transformation of gas into liquid, and vice versa. For pure substances each new temperature corresponds to a definite pressure at which vapor and solid can exist together. The word " sublimation " is commonly applied to the transformation of a vapour into a solid body. If the vapour pressure curve of a solid body is followed upward into higher and higher pressures and temperatures, the critical point is not reached directly. In all the cases which have so far been investigated a transformation of the solid body into a liquid takes place before the critical point is reached. The solid melts. The liquid thus produced then has its own vapour pressure line, which ends at the critical point. Special relations appear in the case of solutions, for while all gases are soluble in one another without limit, a mutual solubility is a comparatively rare phenomenon among solids. When, there- CHANGE OF STATE AND EQUILIBRIUM 79 fore, various solid bodies separate from a gaseous solution as a result of decrease of temperature or increase of pressure, these do not, as a rule, form solutions, but mixtures of several solids. 63. SUSPENDED TRANSFORMATION. It has been tacitly assumed in the foregoing that when the conditions of temperature and pres- sure are fulfilled under which a new phase can exist, this new phase will appear. This assumption is not quite correct, for there are many cases where the new phase does not immediately appear. It is, however, true that when under such circumstances a little of the new phase is present, its formation continues just as would be expected from existing conditions. It is evident from this that the absence of a trace of a new phase is necessary if its formation is not to take place under conditions which lead us to expect it. If special precautions are taken it is quite possible to heat water to a temperature above 100 C. without its beginning to boil, and without any rapid change into vapour. If water drops are formed in hot fat or oil the temperature can be raised many degrees above 100 C. without the appearance of the gaseous phase. If the temperature is further increased vaporization usually begins sud- denly, and because the temperature is high a very large amount of vapour is suddenly produced with a resulting explosion. In the same way water vapour can exist at pressures which are greater than the vapour pressure at which it is in equilibrium with liquid water. It is not easy to arrange a laboratory experiment to show this, but the process is a common one in nature, and appears when masses of air containing water vapour are cooled because of a meteorological change. When water vapour in this condition comes in contact with liquid water in the form of rain or fog a sudden change takes place which results in cloud-bursts and rain-storms. These facts are all in agreement with the phase rule and present examples of its application. As long as liquid water only is present without vapour we have to do with only one phase,, and pressure and temperature are free. A trace of the other phase requires a 80 FUNDAMENTAL PRINCIPLES OF CHEMISTRY new set of conditions. The two phases are then existent simultane- ously and one degree of freedom disappears. A condition of the kind just described, in which a new phase could exist but as a matter of fact does not appear, can be brought about by overstepping the conditions of saturation or equilibrium. Such a condition is said to be one of supersaturation. The condi- tion can persist, but a sudden transformation takes place as soon as a little of the possible new phase is added. It is therefore not stable in the strict sense, and it is called the metastable condition. If the supersaturation is carried further, almost any circumstance may cause the appearance of the new phase, and there is a limit at which the new phase appears of its own accord, that is to say, without the addition of a small amount of it. Beyond this point lies what is called the labile condition. Throughout all these vari- ous conditions the vapour retains its specific properties, changing continuously with temperature and pressure. All these conditions are only characterized by the appearance or non-appearance of a new phase, and they are therefore not conditions of the vapour as such, but only conditions belonging to the vapour in connection with the new phase. The saturation point of a vapour is therefore in no way indicated by any characteristic change in its specific properties. This should be kept clearly in mind in the general consideration of the facts, as many errors have been caused by lack of care in its discussion. (6) The Equilibrium Solid-Liquid 64. MELTING AND SOLIDIFICATION. It is evident from the foregoing how liquids will behave when the temperature is raised or the pressure is lowered. They change into gases. We must now investigate what happens to liquids when the temperature is lowered and the pressure raised. Let us examine the first case. When a liquid is cooled to a sufficiently low temperature it changes into a solid; it solidifies. With the aid of the very low UNIVERSITY CHANGE OF STATE AND EQUILIBRIUM 81 temperatures which have been attained in the last few years this statement has been proven to be a very general one. This transformation from one state to another is completely an- alogous to the change from a gas into a liquid. Here again two cases are to be distinguished: either the entire transformation takes place completely at one definite temperature, the freezing point, or the temperature sinks lower and lower during the trans- formation, so that solidification takes place within a temperature region of finite, but often very great, extent. In the first case we have to do with a pure substance; in the second, with a solution. The question immediately arises whether a substance which has been shown to be a solution by the vaporization test (by its vari- able boiling point) will also act like a solution during solidifica- tion, exhibiting here a variable freezing point. The answer is in the affirmative. A substance which is characterized as a solution in the one case will also act like a solution in the other case. The character of a pure substance or a solution can therefore be deter- mined by either method. The inverse of the process of solidification is melting, which is the change from the solid into the liquid condition. Exactly similar laws are observable here. Either the whole process of melting takes place at a constant temperature, that of the melting point, indicating that we are dealing with a pure substance, or it takes place at a rising temperature, variable within a finite range. In the latter case we have to do with a solution. The fact that pure substances (pure water, for example) melt and freeze at a constant temperature was observed a long time ago. This fact determines the use of the melting point of water as the lower fundamental point in the making of thermometers and in the definition of temperature. Conversely, the melting point can be used as well as the boiling point to characterize a pure substance, or to prove whether a substance under investigation is a pure substance or a solution. Melting point and freezing 6 82 FUNDAMENTAL PRINCIPLES OF CHEMISTRY point are the same for pure substances. It is simply the tempera- ture at which the liquid and solid phases are in equilibrium. 65. THE EFFECT OF PRESSURE. In all matters pertaining to melting and solidification, we are dealing with a system of two phases. According to the phase rule we must therefore expect one degree of freedom, for then the sum of phases and degrees of freedom will be three, as demanded by the rule; in other words, we must expect that the melting point will vary with a change in pressure. For a long time observations did not appear to support this expectation. It had long been recognised that variations in baro- metric pressure had an effect on the boiling point of water which was very easily observed, but no effect of barometric pressure on the melting point of water had been found. Finally, when very much higher pressures were applied, a shift in the melting point was observed. It is only in the minuteness of the effect that the phenomena differ from those of vaporization. An increase of pressure results sometimes in a rise, sometimes in a decrease, of the melting point, while the boiling point is always raised by an increase of pressure. These two facts, the very slight influence of pressure and the possible difference in direction of the change, are explained as follows: During vaporization the volume increases, and usually by a very large amount. In the case of water at its boiling point under atmospheric pressure the vapour occupies about 1200 times the volume of the liquid. During melting, however, the change of volume is always very small. The volume usually increases dur- ing melting, but in some cases, water especially, the volume de- creases, for ice has a lower density than water and floats upon it. The influence of pressure on the equilibrium is dependent on the direction and amount of this volume change, and it is very great during vaporization and always positive, pressure and tempera- ture rising simultaneously. In the case of melting, the influence of pressure is small. It is positive for most substances, because CHANGE OF STATE AND EQUILIBRIUM 83 they increase their volume somewhat during melting, but it is negative for water, which decreases its volume when it changes from a solid to a liquid. A pressure increase of one atmosphere lowers the melting point of water .0073 C. It is now very easy to understand why the effect of a change in barometric pressure on the melting point of water was not noticed earlier, since changes in barometric pressure are seldom greater than ^ of an atmosphere. We have already used a vapour pressure line to express the re- lation between vapour pressure and temperature for a pure sub- stance. There is a corresponding melting point line. Even when very great changes of pressure are considered this line will include only a very small region of temperature in the neighbourhood of the ordinary melting point, for it is not possible to produce and measure pressures greater than a few thousand atmospheres. It is therefore difficult to say anything very definite about the critical phenomena which correspond to the transformation of a solid into a liquid, and vice versa. 66. SUPERCOOLING. In the transition from liquid to solid phenomena similar to those of supersaturation often appear, and to this case the name supercooling is applied. Liquids can be cooled below their point of solidification without becoming solid, provided every trace of the solid phase is carefully excluded. It is not possible to carry supercooling very far. Presently the metastable condition gives place to the labile, and solidification takes place. The reverse phenomenon, the heating of a substance above its melting point without its changing into a liquid, has never been observed with certainty. There is no general reason why it should not be possible, but it is easy to see that there would be great difficulty in fulfilling the condition that every trace of the liquid phase should be excluded. 67. THE LAW OF THE DISPLACEMENT OF EQUILIBRIUM. The relations just discussed" between the change of volume accompany- ing a change of state and the effect of pressure on equilibrium 84 FUNDAMENTAL PRINCIPLES OF CHEMISTRY are individual cases of a general law which is applicable to all equilibria of this type, and which is the most general expression of equilibrium. In order that a system shall retain its condition unchanged, there must be present in it a cause which brings the system back into its original condition whenever it is disturbed. If, for example, a heavy mass is suspended by a thread it takes up a position of equilbrium, such that work must be performed in order to remove it from this position. If then it is moved in any way, an effect results which brings the mass back again into its position of equilibrium. The equilibria which we are considering are of this same kind. If we produce a change in our conditions, processes are induced which oppose the force applied. If the volume of a mixture of water and ice is forcibly reduced changes will be induced which will make the pressure applied as ineffective as possible, and in this case a process accompanied by a decrease of volume will take place. A part of the ice will melt because its volume is greater than that of the water which can be produced from it. By the melting of ice heat will be absorbed and the temperature will drop until a new condition of equilibrium has been attained. The higher pressure therefore corresponds to a lower temperature. If the experiment is carried out with another substance which expands on melting (paraffin, for example), a decrease in volume can only be brought about by the solidification of a part of the substance. Heat is set free during this solidification and the temperature rises. The new equilibrium at higher pressure lies therefore at higher temperature. In the transformation of liquid into vapour the relations are simpler, because the transformation is always accompanied by an increase of volume, and never the reverse. This corresponds to the second of the two cases. Vapour disappears during the de- crease of volume, heat is set free, and the new equilibrium at higher pressure lies at higher temperature. CHANGE OF STATE AND EQUILIBRIUM 85 (c) Equilibrium between the three States 68. THE TRIPLE POINT. In systems consisting of two phases of a pure substance there still remains one degree of freedom. We can therefore make use of this by causing a third phase to appear. All the degrees of freedom have then been disposed of, and we must therefore conclude that such a condition can only hold for a pure substance at one single temperature and one single pressure, since there is no longer any freedom for change. Let us state a case of this sort for water. If we have liquid water and water vapour, these can exist together at a whole series of very different temperatures. If ice is to be present at the same time the temperature must be very nearly 0, for, as we have seen, very great changes in pressure affect the melting point only very slightly. The condition that vapour shall also be present means that the pressure must be very small, for water vapour can only exist in the presence of liquid water at at a pressure of 0.458 cm. of mercury (see Sec. 53). At this pressure the melting point of ice is +0.0074. The temperature has been defined as the melting point under atmospheric pressure, and since a decrease in pressure corresponds to a rise in the .melting point of ice of 0.0074 for each atmosphere, the melting point at pressure zero must be +0.0074. At a pressure of 0.458 cm. it would lie 76 degrees lower than this point. This difference is so small, how- ever, that the number 0.0074 is practically not changed by it. Ice, water, and water vapour can therefore exist together at a pressure of 0.458 cm. and a temperature +0.0074. Such a point at which three phases of a pure substance can exist together is called a triple point. Every pure substance has, generally speaking, such a point, but in many cases our experimental means are insufficient to enable us to reach it. 69. THE EQUILIBRIUM LAW. One objection can be raised to the preceding considerations, and it leads to an important gen- 86 FUNDAMENTAL PRINCIPLES OF CHEMISTRY eralization. It has been said that the vapour pressure of water at the triple point is 0.458 cm. But ice has also a perfectly definite vapour pressure, and the question arises, how great is the vapour pressure of ice at the temperature in question ? It might evidently be either the same as that of water or different from it. Let us assume that the vapour pressure of ice is different from that of water at the triple point. We must then conclude that equilibrium at the triple point is impossible and that the con- dition represented by this point is not unchangeable with time; for if the vapour pressure of water were greater than that of ice, water must evaporate and precipitate as ice. If the vapour space were, at the beginning of the experiment, filled with water vapour at the pressure corresponding to that of the water, this vapour will be supersaturated with respect to ice; that is, the vapour pressure will be greater than that corresponding to equilibrium with ice, and vapour must then change into ice until the corre- sponding pressure has been attained. But when this condition has been reached the vapour space is filled with vapour which is unsaturated with respect to liquid water and more water will evaporate. If the temperature is kept constant all the water must therefore evaporate and change into ice, and this means that water cannot exist together with water vapour and ice. If the opposite assumption is made, that the vapour pressure of ice is greater than that of water at the same temperature, similar reasoning leads to the conclusion that ice cannot exist in the presence of water and water vapour. Experience has shown that it is possible to produce a triple point which is independent of time, and therefore corresponds to a true equilibrium condition. The conclusion from this fact of experience is that at the triple point the vapour pressure of the solid and the liquid phase must be the same. This result can be given more general expression. If the ex- istence of a condition of equilibrium has been proven, it is always safe to conclude that for every imaginable change in this condition CHANGE OF STATE AND EQUILIBRIUM 87 forces will be produced which preclude the possibility of such a, change. If forces of this sort did not obtain for every possible way in which the change might take place, we would only need to so arrange the system that the change could take place. The system will usually be found to be in the condition required, and we can then conclude from the fact that the change does not take place that forces were present which prevented the change. In the case just described the necessary condition is the equality of the vapour pressures of the two coexistent phases. This entire chain of reasoning may be summarized as follows : A system which is in equilibrium in one sense is in equilibrium in every sense. This principle has been most fruitful as an aid to the discovery of numerical relations. If it has once been proven for any system whatever that it is in a condition of equilibrium, we can state the direction in which the equilibrium will change for any given change of the system, and we can then be sure that the determining factors will so equalize one another that the process will not take place. Each way therefore leads to an equation between these determin- ing factors, and through this to a numerical relation between the corresponding properties. We shall later have occasion to illus- trate this rather abstract reasoning by further examples of its application. In the application of this fundamental principle it must be re- membered that relations are not to be derived in a logical or mathematical way without recourse to experience. The experience which must always be obtained is the proof that a real equilibrium exists. This means that we must make observations on the system and show that it does not change its condition under constant temperature and pressure. The individual principles derived by means of this fundamental law are therefore just so many expres- sions of the experimental facts about the equilibrium. The fact of the existence of equilibrium is the general statement which in- cludes in itself all of these separate principles. 88 FUNDAMENTAL PRINCIPLES OF CHEMISTRY 70. THE VAPOUR PRESSURE CURVES AT THE TRIPLE POINT. - This reasoning can be reversed and leads to the conclusion that outside the triple point the vapour pressure of ice and water must be different, for outside of this point ice and water are not in equilibrium in the presence of water vapour. At a lower tempera- ture water freezes and changes into ice, and at a higher tempera- ture ice melts and changes into water. From the fact that water is unstable and cannot exist in the presence of ice at a lower tem- perature, but changes into ice, we must conclude that the vapour pressure of water is the greater. When water and ice are placed together in a space containing water vapour, but not in actual contact, and at a temperature below + 0.0074, the water will distil over to the ice because of its higher vapour pressure, and this will continue until all the water has evaporated and changed into ice. Experiment has confirmed this conclusion. TEMPERA TURE FIG. 3. On the other hand, ice above +0.0074 has a higher vapour pres- sure than water, and under the same conditions, where actual contact is excluded, ice will evaporate and precipitate as water until all the ice has disappeared. These considerations can all be indicated by plotting the vapour pressure lines of ice and water as they change with temperature, and Fig. 3 is a diagram CHANGE OF STATE AND EQUILIBRIUM 89 of this sort. The lines for water and ice are plotted in the same units and they cut one another at +0.00074, the point where the two vapour pressures are the same. What has been explained for water in its various states holds for all other pure substances, as far as their triple points have been attained and measured. (rf) The Equilibrium Solid-Solid 71. ALLOTROPISM. A given substance can have only one form as a gas or as a liquid, but the number of solid forms in which it can exist is not limited. Whenever a substance has several solid states these have the same relation to each other as the states in general. There is a definite temperature at which a solid substance melts, and there is also a definite temperature at which one solid form of a substance changes into another solid form. This can be seen very clearly in the case of mercuric iodide. At ordinary temperatures this is a scarlet substance which retains its colour without much change as the temperature is raised until 126 is reached. If it is heated above this point its red colour disappears, and a sulphur-yellow colour takes its place. At the same point all of its other properties change; its crystalline form, its density, its hardness, etc., take on new values. If the temperature is lowered the transformation takes place in the opposite sense. The red sub- stance is produced from the yellow, and all the original properties appear again unchanged. This transformation is one which corresponds to an ordinary change of state, and more exact investigation has shown that this change is in no way different from the one previously described. Transformations of this sort, which are called allotropic changes, can therefore be included among general changes of state. It has already been stated that changes of this sort do not appear in liquids and gases, and it can be said, in general, that any sub- stance may have one gaseous, one liquid, and several solid forms. 72. THE INFLUENCE OF PRESSURE. At the temperature at which the allotropic transformation of one solid form into another 90 FUNDAMENTAL PRINCIPLES OF CHEMISTRY takes place the two forms can exist together. Above or below this temperature, which is called the transition temperature, only one or the other of the two forms is stable. As in the case of the boiling and the melting points we must expect that the allotropic transi- tion point will be variable with pressure. Transformations of this sort are in general accompanied by only a very small change of volume. We may, therefore, expect that the effect of pressure on the transition temperature will be only a slight one. As in the case of boiling and melting, heat is always absorbed when the substance changes from the condition which is stable at the lower temper- ature into that which is stable at the higher temperature. Pres- sure has therefore exactly the same influence on the transition point as on the melting point. An increase of pressure changes the transition point in such a way that the form possessing the smaller volume is most stable at higher temperatures. If then the form which belongs in the upper region of temperature has the smaller volume, the transition temperature will be lowered by an increase of pressure. If this form has the greater volume, an increase of pressure results in a rise of transition temperature. The effect of pressure is very small in either case, but it has been measured, and the results have been in agreement with the predictions of the theory. 73. THE PHENOMENA OF SUSPENDED TRANSFORMATION. - The phenomena of allotropism are in some respects different from those of boiling and melting. Phenomena similar to those of super- saturation are very common among the allotropic forms, and those which are unstable under existing conditions can, nevertheless, ex- ist for a very long time, even in contact with the more stable form, transformation taking place very slowly indeed. It is for this rea- son that such unstable forms can very often be observed and in- vestigated without any sign of their instability becoming evident. The phase rule says, to be sure, that in general, and under given conditions of pressure and temperature, only one single form can exist. The existence of two forms is connected with a series of simultaneous values of pressure and temperature, while three can CHANGE OF STATE AND EQUILIBRIUM 91 only exist at one single temperature. As far as this is concerned, we should only find two allotropic forms of a substance existing near a transition temperature, and only one single solid form should be stable at that point. This is far from being the case. We recognize, for example, three solid forms of carbon, diamond, graphite, and coal; and there is no apparent tendency of two of these forms to disappear with formation of the third. We know phosphorus in two forms, one red and one yellow, and both of these can be kept for a very long time at ordinary temperatures without either of them changing into the other. In this case, however, we do find that yellow phosphorus tends to change into the red form, which is the more stable of the two, but the transformation takes place very slowly indeed. The important fact is that transformations of this sort never take place instantaneously, but always need a certain time for their completion. In those changes of state which we have previously described this time is short, and melting, for example, takes place with a velocity only dependent on the rate at which the necessary heat is supplied. The time of transformation among allotropic substances is, in -general, much greater, and in some cases so great that a measurable transformation has never been observed: Cases of this sort can be arranged in a continuous series with those where transformation takes place at a measurable rate, and often a mere increase of temperature (which usually means a very greatly increased velocity of transition) results in the production of a measurable transition velocity. W T e are therefore justified in as- suming that in these cases also the transformation actually takes place, though too slowly to come within range of our observation. Such an assumption oversteps the bounds of experience, however, and we only use it because we know no reason why such cases should be in any way different from the ordinary ones. 74. THE STEP BY STEP LAW. Those forms of a substance which are unstable in contact with another form of the same sub- stance can be brought within the range of observation in two ways. 92 FUNDAMENTAL PRINCIPLES OF CHEMISTRY One of these is to produce the substance in a form which is stable, and then to so vary temperature or pressure, or both, that the limit of stability is overstepped. If the new phase which would be stable in this new region is kept out, the less stable form persists for a shorter or longer time according to conditions, and some- times even for an unlimited time. We have already termed such a condition metastable. There are, however, forms which have no region of stability within the limits of pressure and temperature which we can attain. Yellow phosphorus is a form of this kind. As far as we can find out red phosphorus is far more stable than yellow phosphorus under all conditions. In spite of this fact yellow phosphorus is not only better known than red, but it was also discovered at a much earlier date. And in the chemical manufacture of phosphorus it is always the yellow that appears first and never the red. In this case it is impossible that this form has remained present in spite of varia- tion in the conditions of stability. There must be a reason why such unstable forms appear in spite of the fact that more stable forms are possible under the same conditions. We have here in fact a general law of nature. W T hen one form of a substance is transformed into another, the first form to appear is not the one which would be the most stable under the new conditions. Those forms appear first which are more stable than the form just left, but which are the least stable among all the possible stable forms. If the various forms of a substance which can exist under given conditions are labelled 1, 2, 3, 4, in the order of stability, 1 being the least stable form, then when the substance voluntarily leaves the state 1 the most stable form 4 is not the one which will appear. The form 2 will appear first, and, depending on whether this is metastable or labile, it will either remain unchanged or pass over into 3. If there is a form 4, which is more stable than 3 under the same conditions, form 3 will form first from 2 and then afterwards change into 4. A very great number of facts are known which confirm this law. If, for example, water is placed in a small glass CHANGE OF STATE AND EQUILIBRIUM 93 retort, the air driven out by boiling, and the tube then sealed, liquid water can be obtained as a distillate when the neck of the re- tort is cooled, even when a freezing mixture at a temperature of 5 to 10 is used in the condensation. Ice is, of course, the more stable form at this temperature, but ice does not appear first. Liquid water is the first form to appear, and it is more stable than water vapour under the conditions existing, but less stable than ice. In just the same way, when mercuric iodide is sublimed in a vacuum at a temperature below 126, the yellow form appears first, although the red form is more stable. And this is the reason why phosphorus condenses from the form of vapour first of all in the unstable yellow form which is then transformed under proper con- ditions into the more stable red form. By proper conditions we mean, in this case, a high enough temperature to give a measurable value to the velocity of transition. In this way we very often obtain a knowledge of forms which have no region of stability whatever. If these forms are metastable they can be kept for any length of time without changing into the more stable forms, if they are protected from contact with the latter. If they are labile forms they can only be kept for a certain time, but this time may take on the appearance of eternity because of a very low transition velocity, and this case is not at all an un- . common one. 75. THE VAPOUR PRESSURE OF ALLOTROPIC FORMS. The matter of stability is one of great importance in the study of allo- tropic forms. It is very often difficult to decide questions of sta- bility by direct observation, and it is a question of great importance whether there is not another independent means of determining stability. This question can be answered in the affirmative. There are several means, and the simplest is found in the measurement of vapour pressure. Let us consider two different forms of a substance brought into an empty space in contact with its vapour. Two cases are possible. The vapour pressures of the two forms may be the same, and then 94 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the two forms will be in equilibrium, and neither will increase in amount at the expense of the other. In accordance with the prin- ciple already given, that any system which is in equilibrium in one way must be in equilibrium in all ways, two forms which are in equilibrium with respect to their vapour will also remain without influence on each other when they are brought into direct contact. The other case is that in which the two vapour pressures are dif- ferent. Then the two forms cannot be in equilibrium, and the one with the lower vapour pressure must be the more stable. Under the conditions given both forms will send out vapour. As soon as the vapour pressure corresponding to the more stable form is reached, this form will no longer evaporate, but the other form will continue to change into vapour. The vapour will therefore be- come supersaturated with respect to the first form and precipita- tion will occur upon this. The vapour cannot then be saturated with respect to the second form and the latter must continue to evaporate. It is evident that the only way in which a stationary condition can be attained is that the form with the greater vapour pressure shall completely evaporate, leaving only the form with the lower vapor pressure in contact with its vapour. Similar reasoning can evidently be applied to any process which leads to the production of a third phase common to the two forms. In case equilibrium does not exist the transformation through the. common third phase must evidently take place in a definite di- rection. The case just discussed is, however, the simplest one; and in general the others require the presence of a second sub- stance. From this reasoning we must conclude that at the transi- tion point where two allotropic forms are in equilibrium with each other, the vapour pressure of each must be the same, and this agrees perfectly with the conclusions reached by a consideration of the vapour pressures of a substance in the solid and the liquid states. The same conclusion is applicable to the melting point, which is analogous to the transition point, and at any point out- side the melting point the less stable form has the higher vapour CHANGE OF STATE AND EQUILIBRIUM 95 pressure. The reasoning used in connection with Fig. 3 can be applied directly to allotropic forms. Some allotropic forms have no transition points which we have been able to find. In this case one of the forms is unstable as com- pared with the other over the entire region known to us (this region is bounded in the direction of higher temperatures by the melting point). The unstable form in this case always has a higher vapour pressure than the stable form, and no point is known where the two vapour pressures are the same. CHAPTER V SOLUTIONS 76. GENERAL CONSIDERATIONS. Solid bodies which we find in nature, or prepare artificially, obey, in general, the substance law expressed in Sec. 7. They have perfectly definite forms, sharply distinguished, and unconnected in any way. Liquids and gases, however, often show deviations from this law. Among them we find substances possessing all possible values for their properties between certain limits, and in place of sharply differ- entiated individual forms we find an unlimited number of inter- mediate ones. Such intermediate forms are called solutions. They are very frequent in nature, and they are easy to make by bringing together or mixing various gases or liquids. Under these circumstances solids form inhomogeneous mixtures in which the components can be distinguished either directly or by microscopic examina- tion, and out of which the constituents can be separated by me- chanical means. When gases are brought together they always form homogeneous substances, and liquids very often act in the same way. In this case it is impossible to distinguish any con- stituents of the mixture, and it is impossible to separate them by mechanical means into the substances from which they were made. The properties of these solutions are different from those of the constituents from which they were produced, and their formation therefore comes under the head of a chemical process. There has been a long discussion over the question whether solution is a physical or a chemical process. Differences of opinion on this point must remain unsettled as long as no definite agree- 96 SOLUTIONS 97 ment about the use of the word has been reached. We have already decided that chemical processes are those in which, from given substances, others with other properties result, and in ac- cordance with this definition the process of solution must be char- acterized as a chemical one. This, of course, does not mean that we have predetermined anything about the relation between a solution and its constituents, nor does it mean that we have said anything about the question whether or not the constituents are to be considered as existing in the solution. The process of solution is to be distinguished from a change in state especially by the fact that at least two different substances are always necessary to form a solution. By a change in state, or still more generally by the formation of a new phase, solutions can always be separated into substances which obey the general law of substances. Those which obey this law we have called pure substances, and these are the ones whose transformation into other states can be carried out at constant temperature and con- stant pressure. Any solution is therefore completely characterized by stating the nature and proportion of the pure substances of which it is composed, or into which it can be separated. The formation and the splitting up of a solution are reversible. If, for example, a solution has been made up of one third of a substance A and two thirds of a substance B, this same solution can always be broken up so that one third A and two thirds B result, assum- ing, of course, that it is possible to make a complete separation. There are therefore solutions containing 2, 3, or more constit- uents, and these are called binary, ternary, etc., solutions. We shall have to do almost entirely with binary solutions, for among them the simplest relations obtain. 77. KINDS OF SOLUTIONS. A solution may be gaseous, liquid, or solid. It has been said that solid substances generally obey the law of substances, and this means that they do not, in general, form solutions. An exception must be made to this statement, for solid solutions do occur, but comparatively very rarely, and 7 98 FUNDAMENTAL PRINCIPLES OF CHEMISTRY they are usual only between solid substances which are similar to each other. When we are dealing with gaseous and liquid sub- stances we must always bear in mind that they may be solutions, but when we are dealing with solids it is very much more probable that they are pure substances. A chemist who wishes to produce pure substances always tries to get them into the solid state if possible. This is usually brought about by lowering the tempera- ture, but in the course of our discussion on the properties of solu- tions we shall learn about other means of attaining the same end. Gaseous solutions are produced when two gases are brought together. They can also result when a gas comes in contact with a liquid or a solid, provided the latter substance vaporizes. Cases where a gaseous solution is formed by the interaction of liquid or solid bodies are not absolutely excluded, but such a special set of conditions are necessary that we shall not consider this case for the present. Whenever cases of this sort appear possible in the course of our later discussion special attention will be called to them. 78. SOLUTIONS OF GASES. Gases have the property of form- ing solutions in all proportions and on every occasion. Whenever any two or more gases are brought together in any proportions whatever, the immediate consequence is always the formation of a homogeneous gaseous substance from all of these constituents. Cases are not at all rare in which liquid or solid bodies are pro- duced by the interaction of gases. A chemical reaction in the narrower sense of the word takes place which leads to the forma- tion of a new pure substance. This process can be considered as taking place after the mutual solution of the gases involved, and such a process is characterized by the appearance of heat, light, or some other form of energy. The process of solution takes place among gases without any change of energy, and therefore without any change in temperature and without the emission of light. For the present we shall confine ourselves to these cases in which subsequent chemical phenomena do not appear. SOLUTIONS 99 79. DIFFUSION. When two different gases are placed in the same vessel they arrange themselves first of all in the order of their density, the heavier gas passing to the lower part of the vessel and the lighter gas occupying the upper part. This state of things does not continue, and after a longer or shorter time, varying with the nature of the gas, the temperature, and the shape of the vessel, the two gases will be found equally distributed through the entire vessel. We have already learned that any single gas fills com- pletely any vessel in which it is placed. It is evident from what we have just said that a gas exhibits the same property even though the vessel is already filled with another gas. In the case of an empty vessel there is, however, this difference: A gas when placed in the vessel fills it very rapidly, almost instantaneously, while the equalization takes place very slowly when another gas is already present in the vessel. The equalization can be accel- erated by mixing the two gases mechanically, as, for example, by moving a solid body back and forth in the vessel; but mutual penetration results even though mechanical mixing is entirely avoided. In this case it may take days or weeks for vessels of some size to become uniformly filled, while the same result could be obtained in a few seconds by mechanical agitation. By mechanical aid the distance which the gases have to travel to produce a homo- geneous mixture is very much shortened. The actual solution, how- ever, results from the mutual penetration of the two gases, which is called diffusion. If solution has once been completed between two or more gases, these gases never voluntarily separate again. The denser constituent of a gas solution does not gather at the bottom of the vessel, leaving the lighter constituent in the upper part. The condition of solution is therefore one which is volun- tarily assumed by several gases when they are brought together in the same space, and it is a state which they do not voluntarily leave. It is therefore a condition of comparative stability. 80. THE APPLICABILITY OF THE GAS LAWS. Solutions of gases behave exactly like pure gases toward changes in pressure 100 FUNDAMENTAL PRINCIPLES OF CHEMISTRY and temperature. The properties described in Sections 32-35 therefore afford no means of discriminating between pure gases and solutions of gases. But gas solutions do not behave like pure gases when they are transformed into liquids or solids by lowering the temperature or raising the pressure. The transformation in the case of pure gases can be carried out completely at constant values of temperature and pressure. In the case of gas solutions a range of temperatures and pressures more or less considerable in extent must be passed over between the point where the new phase begins to separate and the point where the transformation is ended. This general fact has already been used in Sec. 48 in our preliminary characterization of solutions. 81. PARTIAL PRESSURE. When two gases at the same pres- sure are placed in a vessel which they completely fill, they first take up positions above each other in the order of their density, and mixture and solution take place afterward. Suppose that the common pressure is p and the volumes v 1 and v 2 . If the two gases are now brought into solution, either by mixing them mechan- ically or by waiting for their complete diffusion, it will be found that the pressure p does not change. Each of the two gases has changed its volume, for each now fills the whole volume of the vessel, that is, v l +v 2 . The pressure must have experienced a corresponding change, for, as observation shows, the two gases together now exercise the same pressure as was previously exer- cised by each separately. This shows the applicability of Boyle's Law for the case of gaseous solutions. For the first gas the original volume was v lf the final volume was v l + v 2 , and the formula would be pv^ = p 1 (v 1 + v 2 ), p t indicating the unknown pressure exercised by the gas over the whole volume. From this we obtain p< = In a precisely similar way we obtain for the final pressure of the two gases p 2 = SOLUTIONS 101 Addition of the two equations gives Pi + P 2 = p> an d this means that in any solution of two gases we can ascribe, its owir, pressure to each gas which is present, and that this, pressure ,will be the same as that which the gas would exerf if' it : -wfi^e pF'e# and since ~ = r, we L have r v + r 2 + r 3 =r. This means that the gas constant r for a gas solution can be regarded as the sum of the gas con- stants of the constituents, when these are calculated in terms of the partial pressures. The law of partial pressures was discovered by John Dalton, and he expressed it by saying that gases exert no pressure on each other. He was led to this by the facts of diffusion, for this showed that a gas is not hindered in its expansion into a given space by the fact that this space is already occupied by another gas. The fact that gases which have not been mechanically agitated can exist one over the other for a time shows that they do exert a pres- sure on one another. It is therefore better to avoid this some- what misleading expression for the behaviour of gas solutions, and to use the law of partial pressures as the more correct expres- sion of their behaviour. The experiment described in Sec. 81, which showed that when two or more gases pass from the state of a mixture into that of a solution no energy is given out, is the most direct expression for the behaviour of gases during solution, and the equation r=r 1 +r 2 -f is the most general expres- sion for the thermal and mechanical relation between a gas solution and its constituents. SOLUTIONS 103 83. OTHER PROPERTIES OF GAS SOLUTIONS. As far as other properties are concerned, gas solutions and their constituents are connected by a relation very similar to the one just described. Every property of a gas solution can, in general, be represented as the sum of the properties of its constituents, if these constituents are considered as occupying the total volume of the solution, and as being homogeneously distributed. This is true of colour, index of refraction, electrical properties, etc. The properties of gas solutions are therefore simply the sum of the properties of the constituents. This is the only kind of solu- tion where a calculation of this sort is possible. Liquid solutions (and solid solutions as far as we know anything about them) do not follow this rule, and the properties of these solutions are dif- ferent from those calculated from the properties of the constituents by the rule of mixtures. In this respect gas solutions behave like mechanical mixtures. This suggests immediately that the only change produced when two gases are dissolved in each other is one of volume. No error results when the properties of a gas solution are calculated from those of its constituents, and the assumption that pure gases exist " as such " in a gas solution has a perfectly clear meaning when taken in this connection. The properties of a gas solution vary continuously with its com- position. It is therefore said that these properties are continuous functions of the composition of the solutions. If an indefinitely small amount of one pure gas is added to a large amount of another, the properties of the second gas are changed by an infinitesimal amount. Since there is no difficulty in bringing together gases in any desired proportion, the properties of a solution may be given any desired value between those of its constituents. Between two solutions of different composition it is always possible to prepare any desired number of other solutions whose composition lies be- tween these limits, and corresponding intermediate values of the properties of the solutions can be produced in this way. All of these facts are contained in the statement just made, that the 104 FUNDAMENTAL PRINCIPLES OF CHEMISTRY properties of solutions are continuous functions of their composi- tion, and this is a general property of solutions even in those cases where the properties of the solution can no longer be calculated from those of its constituents as they can in the case of gases. 84. SEPARATION OF A GAS SOLUTION INTO ITS CONSTITUENTS. The formation of a gas solution from various gases and the homogeneous distribution of the constituents in any given space is a process which takes place of its own accord. We must there- fore conclude that a voluntary separation of such a solution into the gases which make it up (into its constituents) does not take place. As a matter of fact we know of no process which takes place of its own accord, that is, without the expenditure of external work, which also takes place of its own accord in the opposite direction. In order to produce the constituents from the solution work is, in general, necessary, and it is also necessary to find a way in which such separation can be carried out. The condition to be fulfilled is evidently the following : we must apply to the solution some cause of motion which will give to the various constituents of the gas different kinds of motion, different velocities, for example. By making use of differences of this sort it is possible to cause the various constituents to collect in different vessels. There are not very many processes which are applicable in this way. The most evident effects are produced when gases pass through porous solid partitions. When various gases under the same conditions of temperature and pressure are forced through a partition of baked clay, they pass through at different rates. If we have to deal with two gases, one of which transfuses rapidly and the other slowly, then the gas which passes most rapidly will leave the solution first, and the one which transfuses more slowly will remain behind. Various diaphragms act differently in this respect, but the order in which gases transfuse is usually the same. An ideal limiting case could be obtained if we had a diaphragm which permitted SOLUTIONS 105 only one gas to pass and held back the other completely. As a matter of fact there is no diaphragm which acts in this way, but an approximation to this condition can be obtained. We will first of all investigate the ideal limiting case, and then determine what deviations are produced by the imperfection of the experimental method. 85. SEMI-PERMEABLE DIAPHRAGMS. Suppose that we have prepared a solution of gases A and B, and that this solution is placed in a vessel, one wall of which permits only A to pass and not B. Such a wall is said to be semi-permeable. A will leave the solution and pass through this wall, and if we arrange to remove A from the other side of the wall as fast as it passes through, the process will only end when B remains alone in the vessel and A has all passed out. It should be kept in mind that this result can only be obtained when A is taken away from the other side of the diaphragm. If this condition is not fulfilled A will only pass through the wall until the partial pressure of A, without and within, has become the same. At that point the cause which forced A through the wall is no longer present. It is in taking away A from the outside of the wall that the work must be expended which was spoken of above. 86. SEPARATION STEP BY STEP. If an actual diaphragm is used in place of this ideal one, it will exhibit differences in porosity ; but these differences will not be absolute, and a process similar to the one just described will not lead to a complete separation of A and B. More A than B will pass through the wall, and the solu- tion will thus be separated into two parts, of which one contains more of A and the other more of B. If each of these parts is now treated separately in the same way, the first quarter will be still richer in A and the last quarter still richer in 5. The two inter- mediate portions will be about alike, and they will be almost like the original solution. These two intermediate portions are then to be combined and separated again by transfusion into two parts, each of which can be broken up into a fraction rich in A, another rich in 106 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Bj and two intermediate portions. The end fractions, resulting from the most complete separation of the two gases, can then be further treated, and the process continued until the separation has become practically complete. The following diagram, which shows the practical results of such a separation, illustrates the facts just described more completely FIG. 4. and more systematically than any description. The separation is begun by collecting T V of the total amount of the solution after it has passed through the diaphragm. The velocity corresponding to the passage of each tenth is plotted vertically on a horizontal line divided into 10 parts, and the result of the first separation will give a nearly continuous line, somewhat like 1 in Fig. 4. Each tenth SOLUTIONS 107 is now treated separately and divided into two parts, each of which is separately collected. The first half of the first tenth will pass through at nearly the highest velocity and the second half will pass through more slowly. The second tenth is separated in the same way into two halves, the first of which will be very nearly like the second half of the first tenth, while the second half will pass through more slowly. The second half of the first tenth is combined with the first half of the second tenth. The third tenth is then separated into two halves and the neighbouring halves combined in the same way. By carrying this process through to the last tenth fractions will be obtained which can be represented by Fig. 5 b, where a FIG. 5. represents the first separation. The double line indicates the frac- tions separated, the single line the halves which are afterwards mixed together. The next thing is to separate the tenths into halves again and combine the neighbouring halves as before. This gives the distribution illustrated by c. Now the extreme twentieths of b and c, which are most nearly alike, are combined as indicated by the parenthesis signs. This gives 10 parts again, and with these the entire operation of separation is to be repeated. The result of such a series of separations is shown by the lines 2, 3, 4, and 5 of Fig. 4, and the process is continued until in place of the line running almost continuously between the two end values, represented by 1 of Fig. 4, a line like 6 of Fig. 4 is produced, con- sisting almost entirely of two horizontal parts. Theoretically an infinite number of operations would be neces- 108 FUNDAMENTAL PRINCIPLES OF CHEMISTRY sary to produce a complete separation, but all of our methods of measurement of properties are finite in their accuracy, and a prac- tically complete separation results from a finite number of opera- tions. The result in this case will be two different gases each of which passes through the diaphragm with a definite constant velocity, so that during the entire process the properties, both of the fraction which passes through and the fraction which remains behind, are unchanged. It is in this that these pure gases differ from the original solution, and from the entire set of solutions pro- duced during the separation. The solution changed during its passage through the diaphragm ; the fraction which diffused most rapidly went through first and was collected outside; the fraction which diffused most slowly accumulated in the residue. 87. ANALOGY WITH CHANGE OF STATE. This case is evidently analogous to the one described in Sec. 48, where we discussed the difference between a pure substance and a solution. In that case, however, the change was into another state, and a mechanical sep- aration was therefore possible, while in the case of a gas solution separation has been achieved by difference in permeability of the diaphragm for the gases. The similarity is most evident in the case of the ideal diaphragm which permits separation to be car- ried out in a single operation, just as when a change of state has been produced. In both of these cases a pure substance is char- acterized by the fact that the residue does not change its properties by a partial transformation into another region, and that it passes into this other region under constant conditions. A solution changes its properties continuously, and therefore passes into the other region under continuously changing conditions. Experience has shown that when such a separation has been carried out by means of any particular diaphragm, the pure substances produced in this way will behave like pure substances with respect to any other diaphragm, that is, they will pass through under constant conditions. The definition of a pure substance is therefore a gen- eral one and quite independent of the special diaphragm used. SOLUTIONS 109 And in the same way substances which have been produced and defined as pure substances by their behaviour toward permeable diaphragms also act like pure substances when they are tested by being subjected to a change of state. The definition is therefore a perfectly general one. 88. PURE SUBSTANCES. Looked at in this way, pure sub- stances may be considered as limiting cases of solutions. When all solutions are arranged in continuous series according to their properties, so that every solution differs from its neighbours by only an indefinitely small amount, the pure substances form the end members of such series. Solutions always show themselves to be more or less variable during a transformation into another state and during their passage through a separating diaphragm. When these variations become smaller and smaller until they finally disappear, then a pure substance has taken the place of a solution. It is because they have their place at the ends of such continuous series that pure or constant substances are especially adapted to serve as the starting point for the description of the properties or the composition of solutions. An unlimited number of solutions can be made up from two pure substances, and the properties of these solutions can vary in an unlimited number of steps between the values for the properties of the pure substances. The properties of the solutions can all be expressed by the prop- erties of the pure substances. Everything which needs to be said about a gas solution has been expressed when the properties of the pure substances and the relation in which they are present in the solution are known. This explains the scientific importance of a knowledge of the properties of pure substances, and this knowl- edge was recognized as the main object of chemistry at the very beginning of this book. So far we have assumed, for the sake of simplicity, that the solution contains only two pure substances and that it can be separated into only two. The discussion becomes more com- plicated, but is in no way fundamentally changed, when three 110 FUNDAMENTAL PRINCIPLES OF CHEMISTRY or more pure substances or constituents are considered in place of two. 89. SOLUTIONS OF LIQUIDS IN GASES. Gas solutions can also be formed when a gas and a liquid are brought together, provided the liquid can evaporate, that is, provided it can pass over into the state of a gas. The law which describes this case is just as simple as the general law of gas solutions. It was shown in Sec. 49 that when a liquid is brought into a vessel of volume greater than the volume of the liquid, it changes partially or wholly into vapour. If the space above the liquid con- tains another substance in the form of a gas, our law says that the liquid will behave exactly as though the gas were not present. It will change into vapour partially or wholly according to circum- stances, and the pressure of this vapour will appear as a partial pressure added to the pressure exerted by the gas already present. Just as in the case of gases (Sec. 79), this law describes only an end condition, and, as in that case also, this final condition re- quires a longer time for its establishment when a gas is present in the space above the liquid than when this space is empty. Let us first examine the case where the volume is so great that the liquid changes wholly into vapour at the existing temperature. If the space is empty, the vapour so produced will exert a definite pressure which is given by the equation ^ = r. If a gas is al- ready present in the space at a pressure P, after vaporization is complete, the total pressure of the gas solution will be P+p. If the volume is so small that only a part of the liquid can evapo- rate, so much of it will pass into the vacant space that a definite density and a definite pressure, corresponding to the vapour pres- sure p of the liquid at the existing temperature, result. If a gas at pressure P is present in the same space, exactly the same amount of the liquid will evaporate, and the total pressure of the gas solu- tion so produced will be P+p. SOLUTIONS HI If we are dealing with a volatile solid body instead of a volatile liquid the conditions are exactly the same. These laws were also discovered by Dalton, and he derived them as consequences of his fundamental principle that various gases in the same vessel exert no pressure on one another. What Dalton really meant is best expressed by saying that when several gases exist in the same vessel each of them has the same effect on the properties of the resulting solution as though it alone were present. 90. SATURATION. In analogy with other cases which will be considered later we will call the condition in which liquid and gas solution exist together one of saturation of the gas with liquid. This use of the term is not a customary one, but it is perfectly cor- rect, and it is usual to say that the gas is saturated with the vapour of the liquid. The condition of saturation is characterized by the fact that the composition of the solution becomes independent of the proportions of the substances which form it. If more liquid is added it remains liquid in contact with the gas solution, and the composition of the latter is not changed by any such addition of liquid, provided temperature and pressure are kept constant. The only thing which has been changed in this case is the relative amounts of the two phases which are present. In our discussion of the equilibrium between the various states of a substance we learned the principle that the absolute and relative amounts of the phases which are present have no influence whatever on the equilibrium. We have now a further example of this principle, which is, in fact, a very general one. It is not difficult to show the necessity of this principle. A mutual influence of the two phases can appear only at their surface of con- tact. Suppose that equilibrium already exists at this surface be- tween the neighbouring portions of the two phases. Equilibrium already exists between these parts of each phase and those parts of the same phase which are further removed from the boundary surface, for all properties are the same in every part of the phase. The region occupied by any phase can therefore be increased at 112 FUNDAMENTAL PRINCIPLES OF CHEMISTRY will without any change in the condition of equilibrium, and therefore the amount of any phase has no effect on the existence of equilibrium. In the case in question the addition of liquid only means that the amount of the liquid phase is increased ; the com- position of the gas solution remains quite unchanged by any such addition. 91. THE INFLUENCE OF PRESSURE. It is not difficult to see what influence pressure has on this equilibrium. If the pressure is increased, the density of the gas will increase proportionately. If an amount of the volatile liquid which is insufficient to cause saturation is allowed to enter the space occupied by the denser gas, then the conditions are the same as before. The liquid evapo- rates and adds its partial pressure to that of the gas. When this partial pressure has reached the vapour pressure of the liquid no more of the latter will evaporate, and we will again have a saturated gas solution. This will have a different composition from the former one, for while the partial pressure of the vapour has remained the same,* that of the gas was greater from the beginning. In the resulting saturated solution there is therefore a larger proportion of the gas, corresponding to the higher pressure. It may be said that in general the composition of the saturated gas solution will vary in such a way that the ratio of gas to vapour varies proportionately with the partial pressure of the gas. It is- evident from this that saturation does not depend only on the nature of the substances which take part, although this has been assumed very often as a deduction from the well-known case of a solution of solids in liquids. Saturation is a case of equili- brium, varying with the nature of the phases which take part, and in which the same substances may appear in very different rela- tions under different conditions. * This statement is not entirely correct, for the vapour pressure of a volatile liquid is not entirely independent of the pressure under which the liquid exists. The effect of pressure is, however, small, and can be neglected here for the sake of simplicity. SOLUTIONS 113 02. THE EFFECT OF TEMPERATURE. The saturation equili- brium in question is dependent upon temperature as Well as upon pressure. At constant volume it is evident that the proportion of vapour in the gas solution must increase as the vapour pressure of the liquid increases. As the temperature rises, more and more of the volatile liquid will dissolve in the gas, and at the critical point solution in all proportions will be the result. The nature of the gas has no particular influence, and the effect of temperature is therefore the same whatever gas is used. The effect of tempera- ture is also independent of pressure, which means, as we have shown, that it is independent of the density of the gas. The varia- tion of solubility with the temperature is therefore a function only of the properties of the liquid which is dissolving in the gas. This is one conclusion from the principle that a gas in any given space behaves in exactly the same way whether the space is filled with other gases or not. 93. THE PHASE RULE. If we endeavour to bring this case under the phase rule of Sec. 61 it will be found necessary to ex- tend this rule somewhat. We have here two phases, a liquid one and a gaseous one, and nevertheless we have two degrees of free- dom, for we can vary the temperature without fixing the pressure. Pressure is therefore free, and the sum of phases and degrees of freedom is four in place of three as in former cases. Another difference goes hand in hand with this one. In the earlier cases of transformation from state to state each phase could be trlans- formed completely into each other phase (liquid water into water vapour or ice, etc.). This is no longer the case here. The gas phase consists of a solution of gas and vapour in proportions changing as temperature and pressure are changed. The liquid phase is the liquid which has dissolved a small and variable amount of the gas. And so while in the earlier case the condition and the properties of a phase were completely determined by two varia- bles, pressure and temperature, in the case under consideration this no longer holds true. The composition of a phase can be a 8 114 FUNDAMENTAL PRINCIPLES OF CHEMISTRY variable one. If two constituents are involved a single statement determines the composition of the phase, and that is the propor- tion by weight in which the two constituents are present. If three constituents are involved two such statements are necessary. If, for example, A, B, and C are the three constituents, the composi- A ."A-, tion is given when two proportions ~ and -~, for example, are Jo D known. The third proportion can be obtained from these by C division. If then B constituents are involved, B l statements are necessary to fix the composition of a phase. Beside the freedoms corresponding to pressure and tempera- ture, we have therefore to consider others which depend upon the composition of a variable phase. Solutions are phases of variable composition. Depending on whether the composition can be expressed -by 1, 2, B l arbitrary variables, we speak of 2, 3 B constituents. Beside the two freedoms corresponding to pressure and temperature, we therefore have for B constituents B 1 further degrees of freedom. These degrees of freedom can either be controlled directly, or by setting the condition that several phases shall exist together in equilibrium. If we are controlling them directly, we are dealing with a single phase, and we have therefore 2+5 1=5 + 1 de- grees of freedom where B is the number of constituents. If two phases are to exist together, only B degrees of freedom will be left, and if P phases are to exist together, this means an addition of P 2 phases, and the number of degrees of freedom is dimin- ished by P-2. This gives B- (P-2)=5-P + 2 degrees of freedom. If F is the number of degrees of freedom the general law says F=5-P + 2orF+P=5+2. In this latter form the phase rule is perhaps easiest to remember. The sum of degrees of freedom and phases is equal to the number of components plus 2. It is easy to see that the phase rule can be applied to the simpler SOLUTIONS 115 cases which we have already studied, in which only one compo- nent was present. The sum of phases and degrees of freedom must in this case be 3, and we found this to be the case in Sec. 61. The rule is also applicable to the case which led to the present discussion. We had two components and two phases; the sum is 4, and two degrees of freedom remain. And in fact in a system consisting of liquid and gas both temperature and pressure can be changed freely and independently, as we have already seen. 94. COMPONENTS. The idea of a component was necessary in the expression of the phase rule, and it is therefore advisable to find out exactly what is understood by this term. Where we assumed only one component, the case was characterized by the fact that every phase which could be produced from another phase by a change of pressure and temperature could be produced from this other phase alone. No other phase was necessary for its production, and no other phase remained behind after the transformation; each phase could be transformed completely into each other phase. When this condition is fulfilled, and only then, we speak of one component. We can express this by saying that we are dealing with one component, when one single phase is sufficient for the production of any phase. It is evidently not necessary that these phases should be in equilibrium. If we wish to make ice we can use water vapour at any pressure whatever, provided the temperature is lowered to a corresponding point. The phase from which the other phase is produced can therefore be chosen anywhere in the whole region of pressures and temperatures within which the system is to be investigated, provided, of course, that this phase can exist under the conditions chosen. If one phase is not sufficient to produce any other phase in the system in question we speak of several components. In every such case we are dealing with a solution, and solutions may there- fore be defined as homogeneous substances produced by com- bining several components in arbitrary proportions. We shall 116 FUNDAMENTAL PRINCIPLES OF CHEMISTRY consider pure substances as components in this sense, that is, as substances from which solutions can be made, for it is a general fact of experience that any solution can be prepared from pure substances. It is, however, not necessary that this should be the case. Solutions might be used in the preparation of new solutions, but this process is more limited in its application. If we have, for example, two solutions containing the same components but in different proportions, it is possible to prepare by proper mixing all these solutions whose composition with respect to one com- ponent lies between the composition of the two solutions, but not those containing a larger proportion of one or other of the com- ponents. It is in every way most useful to consider the pure sub- stances into which the individual phases can be analyzed as the components of the system. This is not, however, strictly necessary, for if we chose those among the possible phases of a system which lie at the extreme limits, as far as composition is concerned, it is evident that even though they are not pure substances it will be possible to make up all the other phases from them. The whole possible set of systems have been subdivided into those in which two phases are sufficient for the formation of all the other phases, and others in which three, four, five, etc., phases are necessary. Based on this, we speak of two, three, or more components of a system, for since the relative amounts of these which are necessary to produce all the other phases can be ar- bitrarily varied within certain limits, they provide us with a cor- responding number of degrees of freedom as far as composition is concerned. The number of degrees of freedom so produced is always one less than the number of phases required. Considered from this point of view, the pure substances are limiting cases of solutions, and they are especially characterized by the fact that all possible solutions can be prepared from them, while this is not the case with solutions of fixed and finite com- position. It would be possible, if we could have negative amounts of a substance, to represent all possible cases as resultant from SOLUTIONS 117 two (or three or more) solutions. This supposition does not, however, correspond to any known physical possibility, and there- fore pure substances are of importance in defining and expressing the properties of solutions. 95. COMPOSITION. The fact that in a system containing only one component any phase can be formed from any other without residue is often expressed by saying that each phase has the same composition as every other phase. This expression has evidently been borrowed from the more complicated cases, for certainly in this case no phase is " composed " of any other substances, and all are equally simple. Such a system is said to be of the first order. Second order systems are those where two phases are neces- sary for the formation of a third, and the nomenclature is similar for systems of higher order. It is evident that our whole discussion is without meaning unless more than one phase is present. As long as only one is present, it is without meaning to ask the question whether it can be produced from other phases not present and unknown. It is only when a second phase has appeared as a result of a change in pressure or temperature that the question whether or not the second phase has the same composition as the first can be asked and answered. The question is identical with asking whether the change from one to the other goes on under constant conditions or not. If it does, the properties of the residuum of either phase must always be the same, whatever the amount of this phase transformed or re- maining. Since the properties of solutions vary continuously with their composition, a phase which changes its properties continu- ously during transformation into another phase must also be a solution, for its composition must have changed if its properties did. A decision in the reverse direction is not so simple a matter. It is quite imaginable that a solution passing from one phase to another changes into a solution of the same composition, and then the transformation will of course take place under constant conditions of temperature and pressure. But under other con- 118 FUNDAMENTAL PRINCIPLES OF CHEMISTRY ditions, at other temperatures and pressures, or in the formation of a phase in some other state, such a solution will, in general, change into a solution having another composition, and then the trans- formation will no longer take place under constant conditions. For when the new phase has a different composition from the old one, there must be a change in the composition of the residue dur- ing the transformation, and this would bring with it a change in the conditions of transformation in the boiling or freezing point, for example. It may be concluded that our former definition of a solution, as a homogeneous substance which freezes and boils under continu- ously varying conditions, agrees well with the other definition that solutions are homogeneous phases which can be formed from com- ponents in any arbitrary proportions whatever. 96. LIQUID SOLUTIONS. Gaseous solutions exhibit the same general properties as pure gases, and liquid solutions are so similar to pure liquids that it is usually quite impossible to tell whether or not a liquid is a solution by any indirect process of investigation. It is only by exposing it to an action which causes it to go over in part into another condition (by freezing or boiling, for example) that the characteristics of a solution appear. Freezing or boiling does not take place at constant temperature and pressure, and a condition of equilibrium dependent on the proportion of the two phases is set up. It makes no difference whatever how a solution is produced from its constituents as far as its properties are concerned, and this statement applies equally to all kinds of solutions. If a solution consists of the two substances A and B, it is the same whether the substance A is added in the liquid, solid, or gaseous state, provided, of course, the proportions by weight are the same and tem- perature and pressure agree in each case. The states correspond- ing to the various substances involved are only important when the solution is to be investigated in equilibrium with other phases, that is, when the substances involved are actually present in their SOLUTIONS 119 original states in contact with the solution. Two wholly different groups of properties are therefore to be distinguished in the study of solutions: those which appertain to the solution alone, and those which express equilibrium between the solution and other phases. In the first case only one single phase, the solution itself, is present or needs consideration. In the other case at least two phases are to be considered. This same difference was found between systems of pure substances involving one and more than one phase. In the first case we are dealing with specific properties, and in any other case we are dealing with an equilibrium. We have already considered the general properties of liquids, and a similar set of properties belong to liquid solutions. The coefficients of compressibility and of expansion are small and vary from case to case. Each solution as well as each pure substance has its own special values for these and all other properties. The difference is found in the fact that while among pure substances properties differ by jumps, among solutions it is usually possible to produce one which differs in properties from another by as little as we choose. The properties of liquid solutions are continu- ous functions of their composition, calculated in terms of the pure substances of which they are composed. They are not like gas solutions, however. Their properties can not be calculated by the simple rule of mixtures from those of their constituents. It is usually true that the real value of any property is found on care- ful measurement to differ measurably from the value calculated by this rule. The deviation may be either positive or negative, that is, the real value can be either smaller or larger than the cal- culated one. The form in which the property is expressed often determines the direction of the variation. The volume occupied by a solution is, in general, different from the volume occupied by the constituents before they were mixed. If it is smaller, the devi- ation would be called a negative one. But this means, of course, that the density of the solution is greater than that calculated by 120 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the rule of mixtures, and if this is taken as the form in which the property is expressed, the deviation will be a positive one. Such deviations are, in general, smaller as the solution is more dilute; that is, as one or other of the constituents is present in great excess. No deviation is, of course, possible in the pure substance, which is at the limit of the series of solutions. The amount of the deviation must therefore be small in dilute solutions, approaching zero with dilution. The conclusion is based on the general law that all the properties of solutions are continuous functions of their com- position. If then the composition is varied by an infinitesimal amount, properties must vary by an equally small amount. Solvent and Solute are often distinguished in speaking of solu- tions. These are arbitrary terms, and we understand by solvent that constituent which makes up the larger portion of the solu- tion. If we consider a solution made of equal parts of its con- stituents this could not be applied, and if the composition were changed so that it passed through this point (50 per cent of each constituent), then the two constituents would have to change names suddenly. The solvent would become the solute, and vice versa. The properties would, of course, vary only slightly and continuously. We shall be careful to apply the term " solvent " only where we wish to indicate that one constituent is in excess under the particular circumstances in question. 97. SOLUTIONS OF GASES IN LIQUIDS. Liquid solutions may be formed when either gases, liquids, or solids are dissolved in a liquid. They are occasionally formed between solids or gases, but these cases are rarer and will be considered separately. The first case to be considered here is a solution of a gas and a liquid. A general law is applicable in this case, for all gases can form liquid solutions with all liquids. In this respect these liquid solu- tions are like gaseous ones, but they do not agree with the latter because the proportions of gas and liquid are not unlimited. Only a limited amount of a gas will dissolve. If a very small amount of a gas is brought in contact with a given SOLUTIONS 121 amount of a liquid under given and constant conditions of tem- perature and pressure, the gas disappears as a phase and a homo- geneous liquid results. The properties of this liquid differ less and less from those of the pure liquid used as the proportion of gas to liquid is made smaller and smaller. The properties of the solu- tions formed from the two constituents vary continuously with the properties of the pure liquid as one limit. In this respect liquid solutions are like gaseous ones, but their properties cannot be cal- culated beforehand from those of the constituents. If now we increase the proportion of gas little by little, these added amounts will at first disappear and the properties of the so- lution so formed will differ more and more from those of the pure liquid. Between any two different solutions formed of different proportions of liquid and gas any number of other solutions can be added, made up of proportions lying between those of the two end solutions. In other words, these solutions make up a continu- ous series with respect to composition as well as properties, or we can say, the properties of solutions are continuous functions of their composition. When the relative amount of the gas has reached a definite value no more gas will be dissolved by the liquid, and the excess of gas forms a separate phase in contact with the solution. No matter how much gas is now added, no change is produced in the properties of the solution, and the gas added simply collects in the gas phase. Such a solution in equilibrium with another phase is said to be saturated (Sec. 51). 98. THE LAW OF ABSORPTION. A very different system is pro- duced when the volume of the system of gas and liquid is kept con- stant instead of the pressure. Imagine a liquid brought into a vessel which is not wholly filled by it, and a small amount of a gas added. A solution of gas in liquid will be produced,* but the gas * Generally a part of the liquid will also evaporate and the gas phase will become a solution. To avoid making our discussion too complex at first we will assume that the liquid has so small a vapour pressure that it may be neglected. 122 FUNDAMENTAL PRINCIPLES OF CHEMISTRY phase cannot wholly disappear because the liquid does not fill the whole volume of the vessel. Only a part of the gas will go into solution, and the remainder will fill the free space under reduced pressure. If now we add more gas, a new distribution between gas and solution will result. Each addition of gas will deter- mine an equilibrium between the two phases, and we are to see whether it is possible to express the conditions of equilibrium in a definite way. First of all we must remember that an equilibrium of this kind is not affected by the absolute or relative amounts of the two phases. It is only to be expressed in terms which are independent of these values. The concentration expresses what we need, and this is the relation between amount of substance and space which it occupies. In the gas phase it is equal to the density. For the solution we could develop the idea of a partial density, analogous to that of partial pressure (Sec. 81), and then the concentration will be equal to the partial density, that is, to the amount of the dissolved gas divided by the volume of the solution containing it. The term " concentration " is more usual, and we shall therefore use it as well as the partial density. For a solution of a gas and a liquid the following law holds : At equilibrium the partial densities of the gas in the two phases are in a constant ratio which is independent of the pressure. If the pressure in the gas phase (and the density, which is proportional to the pressure) is trebled, the partial pressure of the gas in the liquid phase will also be trebled, and this means that saturation will occur when three times the original amount of gas has been dis- solved. The ratio of the density in the gas phase to the partial density in the liquid one is called the relative solubility of the gas. Our law can be also expressed as follows : The relative solubility of a gas is independent of pressure. But the absolute solubility, the weight of gas taken up by unit volume of the liquid, is propor- tional to the pressure and therefore to the density of the gas. This important law was discovered by Henry and later tested SOLUTIONS 123 and confirmed by Bunsen. It does not hold for all gas solutions, but only for those which contain a comparatively small amount of gas. 99. SOLUTIONS OF LIQUIDS IN LIQUIDS. If small amounts of one liquid are added to another liquid, a liquid solution generally results with properties nearly similar to those of the liquid present in excess. We must assume that every liquid dissolves every other one, though often only in extremely minute amount. Since every liquid dissolves every gas, and since every liquid possesses a cer- tain (often very small) vapour pressure, we must conclude that every liquid will dissolve the vapour of every other liquid^ As far as the properties of the resulting solution are concerned, it makes no difference how it is prepared, and if a solution can be made from a liquid and a vapour, it can also be made from the liquid and the liquid obtained by liquefying the same vapour. Experience has confirmed this general conclusion in those cases where we possess delicate methods of analysis for the dissolved liquid. Every increase in our knowledge of methods extends the number of solvents for the substance in question, [and the conclu- sion is justified that with fine enough methods we could prove the solubility of all liquids in one anothejrj Such an assumption corre- sponds most nearly to all of our experience so far. A conclusion of this kind, by which a limited set of experiences is expanded to include a wider range of similar but unexplored cases, is called an inductive conclusion, and in the case described it would be called an incomplete induction. A conclusion of this sort brings with it no certainty, but only a probability, and the de- gree of its probability depends on the degree of similarity in the two cases compared. Such conclusions play a very important part in the natural sciences and aid greatly in our advancement in knowledge. But until an actual experimental proof has been secured it must be remembered v that an error is always possible. 100. UNLIMITED SOLUBILITY. --If the amount of the second % liquid which is added to the first is increased indefinitely two cases 124 FUNDAMENTAL PRINCIPLES OF CHEMISTRY are possible. All these additions may be dissolved, and new homo- geneous solutions with continuously varying properties may be formed. Or, after a certain relative amount has been added, a further amount of the second liquid does not go into solution, but remains as a second liquid phase in contact with the first. The first case is that of unlimited solubility. As more and more of the second liquid is added, its proportional amount increases, and the solution becomes more anjl more like the second liquid. All possible solutions therefore form a continuous series, passing from the first liquid to the second, and bounded by these two liquids. If these are pure substances, their solutions form a continuous set with properties varying between the prop- erties of these pure substances. So far the liquid solutions agree in their behaviour with the gaseous ones; but in these latter un- limited solubility is the rule, while in the liquids it is a special case, and not the most usual one at that. Another important difference is, that although the properties of liquid solutions form a continuous series from those of one "con- stituent to those of the other, they cannot be calculated by simple addition. The properties of liquid solutions usually exhibit more or less pronounced deviation from those calculated from the rule of mixtures, and these deviations have so far not been found to exhibit any general regularities. If the composition of all possible solutions of two components is plotted along a horizontal line, and perpendiculars are erected at each point expressing the value of any property of the various solutions, the ends of all these perpendiculars will form a contin- uous line, and the two ends of this line will express the value of the property in question for the pure components. For gases this line will be straight, for in this case the properties of the compo- nents are not affected by the process of solution, and they therefore vary in the proportion of the fractions of the components in the solution, all of which is expressed by the straight line. In liquid solutions this line is, as a rule, not straight, although there are SOLUTIONS 125 some cases in which the deviations from the straight line lie within the experimental errors. Such a line is always continuous, that is, it has nowhere any sharp corners or breaks. This fact was to be anticipated as the result of the continuity in proportional relation in which the com- ponents can be dissolved. This principle has often been doubted, and it has been proven by careful experimental investigation that, as a matter of fact, continuity is present in all those cases which have been carefully examined. The inductive conclusion that continuity is a general phenomenon is therefore a very probable one. 101. MAXIMA AND MINIMA. A deviation from a straight line can take place in such a way that the curved line lies either above or below a straight one drawn between the two c end points. These cases are shown in the curves a and 6 of Fig. 6, and both these cases have been ob- served. More complicated lines are also possible. With greater and greater curvature lines like c and d can appear. In this case the properties of certain solutions no longer lie be- tween the properties of the pure substances of which they are formed, but extend beyond them. These curves have a maximum or a minimum, and in such cases there always exists a solution possessing the same value of the property as belongs to one of the pure components. The com- position of this solution is found by drawing a horizontal line from the point corresponding to the component and finding the place where it cuts the curve. If the curve shows a minimum, FIG. 6. 126 FUNDAMENTAL PRINCIPLES OF CHEMISTRY this solution is similar to the component possessing the lower value of the property. If it exhibits a maximum, the solution is like the other component. All this is evident at a glance from Fig. 6. ' It is also evident that a maximum or a minimum will occur more easily, that is, as a result of a smaller deviation of the curve from a straight line, when the values of the property are nearest alike in the two components. If these values are the same, the two end points of the curve lie at the same height above the base line, and any deviation from a straight line necessarily leads to a maximum or a minimum. In this limiting case all the values of the properties of the solution lie outside those of the components. The presence of a maximum or a minimum (a singular value in general) often indicates special peculiarities of the corresponding solution. We shall have occasion to examine cases of this sort later. 102. LIMITED SOLUBILITY. Let us now examine the case where two liquids dissolve each other only within certain limits. Starting with the component A, the first additions of B will be dis- solved, but solution will no longer take place beyond a certain value. Since all solutions are soluble in one another the same reasoning holds for the constituent B as more and more of A is FIG. 7. added to it. As soon as one of the two components is present in excess it is no longer present as a pure substance, since it con- tains some of the other substance in solution. The two liquids which exist together under these circumstances without further solution are therefore solutions, one of which contains principally A and the other principally B, and both are saturated solutions. Laying off the composition of the solutions along a horizontal line, as in Fig. 7, we will find a point a near A which expresses SOLUTIONS 127 the largest proportion of B which can be dissolved in A. A similar point b will be found near B, and this expresses the largest pro- portion of A which can be dissolved in B. All those compositions which lie between these points have no existence as solutions. If the two components are brought together in proportions lying between A and a, a homogeneous solution will be formed containing principally A and therefore similar to the pure sub- stance A. And in the same way a homogeneous solution will be formed between B and b having properties which are similar to those of the pure substance B. What will happen then if the two components are brought to- gether in a relation like that of c ? One single solution cannot be the result, and as a matter of fact two will form, the solution a and the solution b, and depending on whether the relation of the two components lies nearer to a or b, more of the corresponding saturated solution will be formed. The relation ca : cb exhibits directly the relation between the amounts of these two solutions that will be formed. Both solutions will be saturated, and this means that they have constant composition as long as pressure and temperature remain unchanged. This agrees with the phase rule, for we have dis- posed of two degrees of freedom in pressure and temperature, and of two others by assuming the existence of two liquid phases. The number of degrees of freedom in the case of two components is four. We have therefore disposed of all of them, and the com- position of each phase must have a fixed value. 103. THE EFFECT OF TEMPERATURE AND PRESSURE. The limiting points a and b are dependent on pressure and tempera- ture, and it is easy to derive the following conclusion with the aid of the discussion in Sec. 67. When liquids dissolve one another there is only a small change of volume, and therefore a change of pressure will exert only a slight influence on the equilibrium between the solutions. The points a and b will therefore shift but little with a change of pres- 128 FUNDAMENTAL PRINCIPLES OF CHEMISTRY sure. The shift corresponding to an increase of pressure will take place in such a way that the pressure will decrease, and this means that a process which results in a decrease of volume will be set up. In 'the majority of cases a decrease of volume accompanies the process of solution, and when the total volume is decreased because one solution dissolves more of a component of which it previously contained a smaller amount, this process will be assisted by pressure. If the process of solution in either direction is ac- companied by an increase of volume, increased pressure will de- crease the solubility in that direction. The effect of temperature can be examined in the same way. An increase in temperature will set up a process which results in the absorption of heat. If a mutual increase in concentration cor- responds to this condition, such an increase will result from an increase of temperature, and vice versa. Both of these cases have been experimentally observed, but the first case appears to be the more usual one. The mutual solubility of two liquids which are only partially soluble in one another generally increases with in- creasing temperature. It must be kept in mind that each of the two points a and b can shift independently of the other, for the change of volume, or the heat transfer, is not, in general, the same for a definite change of concentration at a or at 6. A corresponding effect must there- fore be especially determined for each of these points, and it is quite possible that under a given change of pressure one of these points will be shifted toward the centre of the line and the other toward the end. 104. THE CRITICAL POINT FOR SOLUTIONS. If we are deal- ing with a pair of liquids of partial mutual solubility, and vary the temperature in such a way that the points a and b approach one another closer and closer, they will finally coincide. The region in which two saturated solutions could exist becomes under these conditions narrower and narrower, and finally disappears. If the change of temperature is now carried further in the same SOLUTIONS 129 direction it will be found that one is dealing with liquids soluble in each other in all proportions. We can pass from the one case to the other continuously. Before this point is reached the following changes will have taken place in the properties of the two solutions. The points a and b have approached one another, and this means that the com- position of the two solutions has become more and more nearly the same. When the two points coincide this means that the two compositions have become the same. We have assumed that pressure and temperature were the same in the two solutions; they therefore exhibit no difference whatever and have become alike. The surface of separation between them, which existed because the two liquids did not mix, must disappear, and both solutions will now form a homogeneous liq- uid. Fig. 8 is an expansion of Fig. 7, produced by plot- ting the coexisting points a and b higher and higher as the temperature is in- creased, and this figure in- dicates the relations just described. We already know of a case where two phases become alike as a result of continuous changes in their properties. This was the case of liquid and vapour under constantly increased temperature. The temperature-pressure point at which this takes place we call the critical point. Now we can also speak of a critical point for solutions, and we under- stand by a critical point one at which two phases become alike. This latter case is somewhat more complicated because we are now dealing with a system of two components. In the previous case there was only one single critical point for 9 a FIG. 8. 130 FUNDAMENTAL PRINCIPLES OF CHEMISTRY each substance. In a system of one component the sum of the phases plus the degrees of freedom is three. If vapour and liquid exist together one degree of freedom is left, and if we add the con- dition that both are to be alike we have exhausted our last degree of freedom, and there is only one temperature and one pressure which can satisfy the conditions. These are the critical tempera- ture and the critical pressure. Beside these we will also have determined a critical density or critical specific volume, and with this all the characteristics of this point are exhausted. In the case of a critical point for a solution we have two phases and the condition that they are to be alike. Three of our four degrees of freedom are fixed. Pressure is still left free, and the critical temperature of solution is affected by a change of pres- sure. Or we can choose the critical temperature of solution, provided the pressure is fixed accordingly. A large change of pressure has only a small effect on the solubility of liquids and therefore the change in the critical temperature will be small. Experimentally it will only be possible to reach the critical temper- atures of solutions which correspond to pressures in the neighbour- hood of one atmosphere. Instead of a critical point in the narrow sense, we are really dealing with a critical line which actually extends over a very small range of temperatures when the pressure is varied through a great range. Changes of this sort are of about as much practical importance as the change in the melting point with pressure. 105. THE SEPARATION OF LIQUID SOLUTIONS INTO THEIR COMPONENTS. The general reversibility of the process of solu- tion brings with it the fact that liquid solutions can be split up into their components as well as built up out of pure substances. This is the fact, and the process is very much like the separation of a gaseous solution into its parts through the agency of a porous partition (Sec. 84), though the means used appear to be totally different in this case. SOLUTIONS 131 The separation of the components of a solution can be accom- plished by lowering the temperature until a solid phase separates. We already know that solid phases consist of pure substances in the great majority of cases, and this gives us an immediate method of separation. It is much like the application of an ideal semi- permeable diaphragm which permits of the passage of only one component, and therefore yields pure components as a result of the separation. We have not yet taken up the consideration of equilibrium between liquid and solid phases, and we will there- fore leave this case for later consideration. The other possible method of breaking up a solution into its components depends upon the production of a gaseous phase, either by an increase of temperature or a decrease of pressure. It is experimentally very much easier to work at high tempera- tures than it is to work under reduced pressures. The first method has therefore far more general application, and the second method is only used in cases where an increase of temperature i-s to be avoided for any reason. A knowledge of the laws which describe the corresponding equilibrium affords an immediate insight into the whole matter. 106. THE VAPOUR OF SOLUTIONS. Let us consider the case in which a liquid solution is in equilibrium with its vapour. This represents a combination of two cases which we considered sepa- rately for the sake of simplicity in an earlier chapter, Sections 89 and 97. In the first case we assumed that the gas phase could form a solution but the liquid phase could not, and in the other case we made use of the reverse assumption. It was stated that these assumptions represent limiting cases, and that in the general case both phases would form solutions. It is usual to consider first of all an isobaric relation, and this means that wed^rn^j^^jjjfj^ tions show__the same pressure. Jf this pressure is one atmosphere the temperatures represent the ordinary boiling points of the solutions. 132 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Each of these boiling points can be regarded as the property of a solution, and we can then apply the reasoning used in Sec. 100 in dealing with them. Each ^serjesjjf solutions containing the two components A and B will possess a continuous series of boiling, points lying between those of the pure constituents, provided the liquids dissolve one another in all proportions, and this we will continue to assume for the present. This boiling point curve may have any of the forms shown in Fig. 6, and all of these have been experimentally observed. I If any solution is heated to the boiling point its vapour will, Vn general, have a different composition from the liquid. The difference is always of such a nature that the evaporation results _in a higher boiling point for the residue. This is often expressed fc>y saying tnat the more volatile portion is the first to change into vapour, for if the boiling point was lowered by evaporation the vapour pressure at the existing temperature would soon become greater than one atmosphere and further evaporation would proceed in an explosive manner. This contradicts our assump- tion that we are dealing with an equilibrium, and it is a fact that all experiments have shown a rise in the boiling point during evaporation. |Of course the boiling point can only change when the compo- sition of the solution changes/^ If the boiling point curves of neigh- bouring solutions are examined one can predict the direction in which the composition of a liquid solution will change when it is boiled. It will always change toward that composition which corresponds to a higher boiling point. If, for example, we draw in Fig. 6 a perpendicular to the base line at the point e, which represents the composition of a solution, this perpendicular will cut the. boiling point curves. Boiling this solution will result in a shifting of its composition toward the right, when the boiling point curve has one of the forms a, b, or c, and its composition will be shifted toward the left when the curve has the form d. SOLUTIONS 133 The composition of the vapour varies in the opposite direction, for if more of the substance A is to remain in the residue, more of B must have passed into the vapour. If such a solution is boiled it will therefore not evaporate at constant temperature but at one which increases constantly until the last portion has been volatilized. Instead of a definite boiling point, such as we find in pure substances, we have here a boiling region corresponding perfectly to the definition of a solution which we made at the very beginning of our discussion (Sec. 48). Similar relations are found when the experiment is reversed, beginning with a temperature so high that the entire solution is present in the form of vapour. If it is now cooled down step by step the first drop of liquid will appear at a definite temperature. This will not be the temperature at which a liquid of the same composition begins to boil, but it will be the temperature at which the last portion of such a liquid evaporated. We are assuming in both cases that vapour and liquid are continually in equilibrium. Just as we had a region of boiling, we now have a region of liquefaction, and these two regions are superimposed just as the boiling point of a pure substance coincides with its condensa- tion point. In order then to describe the entire phenomenon we must determine two temperatures for each composition : a lowest tem- perature where the first vapour can exist together with the liquid, and a highest one where the first drops of liquid can exist in the presence of the vapour. Between these two points lies the region of evaporation and condensation. Every composition of a solution corresponds to two such points each of which lies on a continuous curve. The entire condition of things is represented by Fig. 9. The two curves must coincide at both ends, for the two ends correspond to pure substances, and at these points the entire process of evaporation or condensa- tion takes place at a single constant temperature. In the rest of their course the two lines are separated, and the one correspond- 134 FUNDAMENTAL PRINCIPLES OF CHEMISTRY ing to the vapour lies above the one which corresponds to the liquid. The course of this double line can be determined in two ways after the boiling points have been found as a function of their composition. One way is to transform a solution of known composition en- tirely into vapour, meas- uring the temperature at which the first drop of liquid appears when the vapour is cooled. This gives a point on the va- pour line lying directly above a corresponding point on the liquid line (in Fig. 9 the point d above FlQ - 9- the point /). Another way is to determine the com- position of the first distillate, that is, of the vapour which is in equilibrium with the liquid. This composition corresponds to the lowest boiling temperature of the solution, and if the point r represents this composition, the intersection of a perpendicular erected at r, and a horizontal line through the liquid point / will lie at the point d, which is the corresponding vapour point. It follows from this construction that when the two lines are known, the composition of all liquid and gaseous phases which can exist in equilibrium can be determined by drawing horizontals through the double line. Points cut by such a horizontal line represent the two compositions which are in equilibrium. This reasoning can be applied to both cases, a and b, of Fig. 6, whether the boiling point curve is concave upward or downward. If the boiling point line exhibits a maximum or a minimum, new SOLUTIONS 135 relations appear which we shall examine immediately. First of all let us apply these general considerations to the separation of a liquid solution into its components. 107. DISTILLATION. The vapour above a liquid solution has, in general, a different composition from the liquid itself. By liquefaction the vapour of any solution can be separated into two fractions of different composition, and such a separation is com- plete when one of the components possesses no measurable vapour pressure, since in this case the vapour will consist of only one of the components. In this case it is only necessary to remove the vapour continually as fast as it is produced by heating in order to have one component in the residue, and the other in the fraction which has passed through the vapour form. Use is made of this when pure water is to be produced from ordinary river or spring water. Ordinary water contains various substances which have been dissolved out of the earth while the water was in contact with them. These substances have no measurable vapour pres- sure at the boiling point of water, and when the vapour which has been produced from "impure" water is liquefied, "pure water" is produced which is free from these dissolved substances. The process by which a liquid is changed into vapour, and the vapour so formed is condensed to a liquid again, is called distilla- tion. In order to carry out such a process a vessel is necessary in which the liquid can be boiled and changed into vapour. Such a vessel is usually called a retort. Beside this an arrangement for condensing the vapour is necessary, and this is called a condenser. In the laboratory these vessels are usually made of glass, but in technical work metal apparatus is employed because large glass vessels are too easily broken. The fact that it is possible to produce pure substances by dis- tillation is of great importance to the chemist, and the discovery of distillation, which was first practised in the early middle ages, was a very great advance which assisted greatly in the study of pure substances. 136 FUNDAMENTAL PRINCIPLES OF CHEMISTRY 108. FRACTIONAL DISTILLATION. If both constituent^ are volatile, the separation resulting from a single distillation is a very incomplete one, for the two fractions which are obtained by the process^^eacti conTam both components, present in propor- tions differing from those of the original substance. Separation can be made practically complete by proper repetition of the process of distillation. The conditions here are very similar to those which have been described in Sec. 84 for the 4 separation of a gaseous solution by a porous diaphragm. When the diaphragm permits only one com- ponent to pass and retains the other completely, this corresponds to the case where only one component changes into vapour. The analogy extends also to various degrees of permeability and vola- tility. Two substances which are under all circumstances alike in their diffusion through diaphragms, or in their volatility, could not be separated at all, but two such substances could not be dis- tinguished from one another at all, and they would therefore be the same substance. The same directions as were given in Sec. 86 for the separation by means of a porous diaphragm can be applied to separation by distillation. The solution is first of all to be separated by distillation into 10 (or any other number) parts. Each part is then to be distilled again, and the two halves kept separate, similar fractions being combined and subjected to re- peated distillation until the whole solution has been separated into its components. In this case also an infinite number of dis- tillations would theoretically be necessary to produce an absolute separation, but long before this point is reached our means of de- tecting the last remnant of the foreign component in the nearly pure liquid would fail, and this means that the separation is prac- tically complete. The process of separation by distillation can be greatly sim- plified by conducting it in such a way that the processes just described are carried on simultaneously. This can be done by partially condensing the vapour as it rises from the solution. The SOLUTIONS 137 solution so produced runs back into the retort and comes in con- tact with more vapour. In this way it is partially vaporized again, and the rising vapour contains more of the more volatile component. The less volatile component is at the same time con- densed and separated from the vapour, leaving a more volatile fraction in the form of vapour. The result is that in a single dis- tillation a number of successive distillations are carried on in such a way that finally only the fraction with the highest vapour pres- sure remains in the vapour, while that with the lowest vapour pressure is condensed and flows back into the liquid. This process is carried out by causing the vapours to pass through a " distillation tube/' in which such a regular partial condensation is produced. The technical arrangement of this apparatus varies with the size of the apparatus in question. In large plants it usually consists of chambers, one above the other, in each of which the temperature is regulated by cooling devices. In the laboratory a wide glass tube filled with glass beads is placed above the distilling vessel, and the heat of this vessel is so regulated that the tube is cooled sufficiently by the air about it to produce the desired result. It is evident from the description of the process that distillation must take place more slowly in such an apparatus than it does when the vapor itself is condensed, since part of the vapor is sent back into the retort. A practical separation is, however, attained in a much shorter time with such an apparatus, for a single distillation, accompanied by partial con- densation, is equivalent to a large number of simple distillations. 109. SINGULAR POINTS. We have still to discuss the question how solutions behave whose boiling point passes through a maxi- mum or a minimum as their composition changes. Let us examine that portion of the lines c and d which lies to the left of the turning point of the curves. It agrees with one of the two lines a or b, neither of which has any such turning point. The same is true of the other portion of these lines, and so in this HMMHWMST W ^BV region the composition of the vapour and the residual liquid will 138 FUNDAMENTAL PRINCIPLES OF CHEMISTRY so change during distillation that the residue will change in com- position toward a rising boiling point, while the distillate will change inthe opposite direction. But at the singular point this _ - - ie "^ J l - - - / ^x* x "^--V_ - v^. - 5?^ ^J. v ____ ^- will not hold, for there the boiling points rise or falTon both sides. . r<\* y^^ ->_ ^Vn'^W' '*"*'- -^- - -= _ - ^_^~~^ J ^ ^. - ^ -*y -f~ -^^"^^o** The conclusionto^be^dr^wiij^ ofliquid and vapour must be the same at a singular jpcjmTliaST^^ andsonochange in comosition caii result inthe formation of asoTutiohaving a higKer(or a lower) boilin|^)pjntjlia^^ lt6?~SiNGULAR SOLUTIONS. This leads us to the important conclusion that a solution whose boiling point has the highest (or lowest) possible value cannot be separated into its constitu- ents by distillation, because its vapour has the same composition as the liquid. Such solutions behave in this respect like pure substances. In one respect they are, however, very different from pure sub- stances. If the boiling point curve for various compositions of the solution is plotted at other pressures, it will be found that, in general, the singular point corresponds to another composition. Boiling point curves at various pressures are shown in Fig. 10, and it is evident that the maximum is displaced to the right at higher pressures. Although a given solution may behave like a pure sub- stance when distilled at at- . 10. mospheric pressure, it will behave like an ordinary solution at a pressure of two atmospheres, since the vapour will be different from the liquid residue. Such substances behave like pure substances only at one definite pres- SOLUTIONS 139 sure and at the corresponding temperature. They change their state without separating into two different portions, but we will nevertheless classify them with the solutions. They differ from ordinary solutions only in the peculiarities mentioned, and we shall therefore call them singular solutions. Such solutions were formerly classed with the pure substances, but since we have learned that they behave like ordinary solutions at other pressures we now call them solutions. The behaviour of solutions of substances whose boiling point curve shows a singular point can now be accurately predicted. If thj3cojnj)0j5it^ dilation will result in a separationjnto^ne_mire constituent and P3eperSsmithe composTtio^oithe solu- tion which constituejrLwjll/be sejmialej always be the one which is n jjjje^^rjmje^jg^e. It will of the composition of the si The separation of such a singular solution into its components can be effected by a distillation at another pressure. The solu- tion can in this way be separated into a certain amount of one pure constituent and another singular solution corresponding to the new pressure. This latter portion may then be distilled at the original pressure, and it will now behave like an ordinary solution. A new separation results, some of the other pure constituent being formed, and the other fraction will be the original singular solu- tion (but now in less amount). By repeating the distillation alter- nately at the different pressures the separation may be carried as far as desired. To effect separation as rapidly as possible the pressures must be as different as possible, for, in general, the differences in these singular solutions are greater as the pressures are chosen further apart. This will be evident from Fig. 10. These relations become more evident if both lines, the one representing the composition of the liquids, the other the com- position of the vapour, are drawn in the way already shown in 140 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Sec. 106. Both phases have the same composition at a singular point. The two lines must therefore have a point in common there. These lines are, however, continuous, and the boiling point line of the vapour must always lie above that of the liquid. This common point can therefore not be a point where the curves cut each other, but merely a point where they are tangent to one another. Double lines will re- sult like those shown in Fig. 11. As far as this method of repre- sentation is concerned singular solutions are like pure sub- stances. The double lines on either side of the singular point are in all respects similar to those of pure substances. It may be asked why phenomena of this same type were not men- p IG n tioned in discussing the sep- aration of gases by means of porous diaphragms, provided such singular solutions ever occurred in the case of gases. The answer is that such solutions do not occur among gases. We concluded from the considerations in Sec. 101 that if singular values were to appear in the proper- ties of a solution, these properties must deviate from those which could be calculated from the simple rule of mixtures. In the case of gases the rule of mixtures holds for all properties and no devia- tion exists. The possibility that a curve expressing the properties of a gaseous mixture should exhibit a maximum or a minimum a singular point of any kind is therefore excluded. 111. GASEOUS SOLUTIONS PRODUCED FROM LIQUID SUB- STANCES. We can now answer the question of Sec. 77 whether a gaseous solution made up of liquids can exist. Such a case is possible when the boiling point line possesses a minimum. In SOLUTIONS 141 FIG. 12. this case solutions will exist with boiling points lower than those of the two constituents. If the constituents are mixed together at a temperature which lies below their boiling points, but above this minimum, the solution will change into vapour, and the change will be complete if the tem- perature is kept constant. All the solutions which lie be- tween a and b of Fig. 12 are gaseous at the temperature indicated by the line it, while the constituents are liquid at the same temperature. By varying this temperature the range of existence of such solutions can be increased or decreased. This range is bounded on one hand by the boiling point of the lower boiling con- stituent, on the other hand by the boiling point of the singular solution. 112. THE VAPOUR OF PARTIALLY MISCIBLE LIQUIDS. For the discussion of equilibrium in the case of two liquids which are not soluble in each other in all proportions, but which form two liquid phases, or two mutually saturated solutions, let us first con- sider the limiting case in which the two pure liquids are insoluble in each other. Strictly speaking such a case does not exist, but certain actual cases approach this so nearly as to almost realize it. If two liquids do not dissolve in one another at all they do not influence each other, and their vapour pressure suffers no change. If therefore two such solutions are brought into an empty space, each of them will be in equilibrium with its vapour as though the other liquid were not present. In other words, the vapour pres- sure of each liquid will remain unchanged, and the common vapour pressure of the mixture will be equal to the sum of the individual pressures. 142 FUNDAMENTAL PRINCIPLES OF CHEMISTRY As a matter of fact all liquids must be considered as soluble in each other, and the real question to be answered is : what devia- tion from the ideal case is brought about by the solution of each in the other? The^answer is. that the vapour pressure is always smaller than the sum of the vapour pressures of the two indi- vidual liquids. The partial pressure of each of the liquids form- ing a solution is always decreased by the formation of a solution, and this law holds without exception. If one of the constituents of the solution is very slightly volatile, so that its vapour pressure is practically unmeasurable, the decrease in the vapour pressure of the other liquid is all that is observed, and the vapour pressure of the solution is smaller than that of the pure volatile constituent. If the second constituent has a measurable vapour pressure of its own, the total pressure of the solution may be either smaller or larger than that of the more volatile constituent. Whether one or other of these cases is realized depends upon the effect of the less volatile of the constituents on the vapour pressure of the more volatile one, and also upon the difference in the vapour pressure of the two constituents. If this difference is large the first case may appear. The lowering of vapour pressure due to solution may be greater in amount than the vapour pressure of the dis- solved substance, and in this case the total pressure of the solu- tion will be less than the vapour pressure of the more volatile constituent. The converse naturally holds for the boiling point. If the two liquids do not dissolve one another at all, the boiling point of the mixture will be lower than that of the lowest boiling constituent, for boiling will begin when the sum of the two partial pressures equals the pressure of the atmosphere. If solution takes place, the boiling point of the lower boiling constituent may be either lowered or raised by the addition of the other substance. The first case will be realized by the addition of a liquid having a boil- ing point nearly like that of the other liquid. The boiling point will be raised by the addition of liquids with a high boiling point. SOLUTIONS 143 These considerations can be directly applied to the case of two liquids which are only partially soluble in one another. Nothing further need be said concerning conditions in the com- mon phase. The variable composition of an unsaturated solution corresponds to a variable boiling point, and the corresponding double lines may run either up or down. Where solution is incomplete two mutually saturated liquid phases will be formed, each possessing composition which does not depend upon the proportions in which the two constituents were mixed. We must therefore conclude that the boiling points of such mixtures of two pairs of liquids will be constant. For whatever the proportions in which the constituents are present, we always have two liquid phases of the same composition, varying only in the amount in which each is present. Since the amount can have no effect on the vapour pressure or the boiling point, it is always the same phases which are boiling, that is to say, boiling point and vapour pressure in the region of saturated solutions will be independent of the proportions in which the constituents were originally mixed. The same result is reached by applying the phase rule. In the region in question there are present two liquids and a vapour, three phases in all. The sum of phases and degrees of freedom is in this case four, and there therefore remains one degree of freedom. If the temperature is fixed the entire condition of the system is determined and nothing is changed by a change in pro- portions, that is to say, the pressure is independent of the propor- tions in which the two components are present. If the pressure is fixed the temperature will be also independent of the proportions. If we now draw the boiling point line representing all possible re- lations of the constituents, this describes the intermediate region in which two liquid phases can exist together, and it will be a hori- zontal straight line, for such a line means that a mixture containing every possible proportion of the two constituents will have the same boiling point. 144 FUNDAMENTAL PRINCIPLES OF CHEMISTRY The two saturated liquid solutions which can exist together as two phases in all proportions we will call limiting solutions. It should be noticed that the boiling point and the vapour pressure of each' limiting solution by itself must be the same even though the other phase is not present. These points we have found to be the same when one of the liquid phases was present with any amount of the other, however small. It is therefore possible to approach the condition in which only one of the liquids is present as closely as we desire without causing any change in the vapour pressure. The law of continuity demands that at the moment when one or the other of the liquids disappears the vapour pressure must still remain the same. The same conclusion may be reached in a different way by the use of the general principle : A system which is in equilibrium in one sense is in equilibrium in every sense. We have already made use of this principle to show that the vapour pressure of ice must be the same as that of water when these two substances are in equilibrium; since otherwise one of the phases must increase at the expense of the other, which contra- dicts the assumption of equilibrium. In this case also we must conclude that when the two liquids do not affect one another while they are in direct contact, they cannot do so in any indirect way. Suppose our two limiting solutions to exist side by side in two vessels covered with a bell-jar filled with their vapour. .If the vapor pressure of one of these limiting solutions is greater than that of the other, a distillation from one to the other will take place ; that is to say, the system is not in equilibrium. In the same way it can be shown that not only the total vapour pressure above each solution must be the same, but also that the partial pressure of the two constituents must be the same ; for if they were not the same a distillation would result, and in this case it would be a distillation from both directions. In one of the liquids the vapour pressure of A would be greater and in the other B, since the sum of the two has already been shown to be the same. A would there- a SOLUTIONS 145 fore distil from one vessel to the other, and B would distil in the opposite direction. Both liquids would under these circumstances change in composition, which is again a contradiction of our as- sumption of equilibrium. 113. POSSIBLE CASES. The vapour pressure and boiling point lines, which describe the regions between the limiting solution and the pure constituents, will have a regular course from the ends of the hori- zontal straight line, repre- senting the limiting solution, to the values for the pure constituents. Three cases are possible, and they are repre- sented by the lines a, 6, and c of Fig. 13. It can be shown that only a and b can occur, while c includes a contra- FIG. 13. diction. Let us consider first of all a in Fig. 13, which represents boiling point lines. From earlier considerations we know that the vapour has a composition which is different from that of the liquid, as shown by the drop at the beginning of the boiling point line. The composition of the vapour from the left-hand limiting solution will lie to the right of this point and that of the vapour from the right- hand limiting solution will lie to the left of its composition. Both vapours have the same composition, as has just been proven, and so the composition of the vapour must be represented by some point between the two limiting solutions. If one of the limiting solutions is distilled, the distillate will consist of two fractions, each of them a limiting solution, and of course the same will hold true if any given mixture of the two limiting solutions is distilled, for the vapour in this case will be exactly the same as before. If we apply the same reasoning to the case b we find that the 10 146 FUNDAMENTAL PRINCIPLES OF CHEMISTRY vapour of the right-hand limiting solution must have a composi- tion represented by a point which lies to the left of the limiting solution point. In the case of the left-hand limiting solution we find however a different result from that of the former case. The composition of the vapour must lie to the left of the limiting solu- tion, for there the boiling points drop to the left, and the composi- tion of the vapour must always differ from that of the liquid in the direction of decreasing vapour pressure. We must therefore conclude that in this case the vapour will have a very one-sided composition, for the proportions of the two constituents in it are represented by a point which lies far to the left. This composition lies outside the two limiting solutions in a region where the two liquids give a homogeneous solution, and to the side belonging to the more volatile liquid. If either of the limiting solutions be dis- tilled the distillate will not in this case separate into two layers, but will be homogeneous, and will contain a large proportion of the volatile constituent. In the case c the same considerations lead us to the result that the left-hand limiting solution would yield a distillate of composi- tion lying to the left of that of the limiting solution, while the right yields a distillate whose composition lies to the right. These two conditions are impossible of fulfilment, and such a system is there- fore an impossible one. As a matter of fact only the two cases a and b have ever been observed. 114. THE DOUBLE LINE. These considerations are extended and confirmed when the double line, which includes the composi- tion of the vapour phase, is used in place of the single line in repre- senting the boiling points based upon the composition of the liquid phase alone. It has been shown that, in general, the line cor- responding to the vapour must lie above that of the liquid, and in Fig. 14 there is represented the case a with the addition of the vapour line, which lies, as it should, above the liquid line. First it should be noticed that this line must be everywhere a curved one. Since vapours are soluble in one another in all proportions, SOLUTIONS 147 FIG. 14. no horizontal parts can ever appear like those which correspond to the appearance of two liquid pairs when liquids are mixed. Beside this the vapour line must touch the horizontal part of the liquid line between the two limiting solutions, for the two limiting solutions send out vapour of the same composition, which can be condensed to a definite mixture of the two liquid phases. This mixture when boiled must therefore send out a vapour having the same composition, and it can therefore be transformed into vapour completely without any change in the boiling point. This particular mix- ture behaves in this respect like a pure substance, for it has a definite boiling point and not a boiling region like the solutions. At this point there- fore the vapour line must have a point in common with the horizontal liquid line, that is, it must be tangent to it. In earlier cases, Sec. 110, we found that singular solutions could exist. In this case we find a singular mixture of two liquid phases which behaves like a pure substance during vaporization. It is immediately evident that this distillate is a mixture, and there is no difficulty whatever in distinguishing such a singular mixture from a pure substance in spite of its constant boiling point. We will find later, when we come to the consideration of solid bodies, that there may be analogous cases where it is by no means so easy to decide this point, and we shall find that the con- siderations just discussed will be of help to us in this later case. The composition of such a singular mixture is, in general, variable with the temperature, and this affords a further means of distinguishing such a mixture from a pure substance. 148 FUNDAMENTAL PRINCIPLES OF CHEMISTRY In the case 6, Fig. 13, no singular mixture appears, for the com- position of the vapour lies outside the region included between the two limiting solutions, so that the distillate is not a mixture but an unsatu rated solution. This solution has, however, a con- stant composition as long as both liquid phases are present. The composition of this distillate lies so far to one side that no mixture can exist which can be distilled entirely without a change in the boiling point. If such a mixture could exist it would be a singular mixture. In this case the larger proportion of the vapour will be made up of the lower boiling constituent, and after distillation has proceeded for a time there will remain only the limiting solution which is richer in the higher boiling constituent, and its composi- tion will vary by further distillation and with a corresponding rise in the boiling point toward a greater and greater content of the less volatile constituent. In Fig. 15 the vapour pres- sure line is added above the liquid line corresponding to b of Fig. 13. The composition of the distillate is found by continuing the horizontal part of the liquid line until it cuts the vapour line at the point d. It is evident from the con- ditions shown by the diagram that this composition must always lie far to one side, that is, it represents a high percentage of one or other of the constituents. 115. EQUILIBRIUM WITH SOLID SUBSTANCES. The state in which the constituents of a solution exist before solution can of course have nothing to do with the properties of the solution itself. No special relations are to be expected in solutions themselves, but special relations do exist in mixtures where a solid phase is present. The following general considerations should be kept FIG. 15. SOLUTIONS 149 in mind. Equilibrium between solid phases is usually simpler than between liquids, because solid substances do not, as a rule, form solid solutions. They are generally pure substances, and they usually remain so even when other solids are present. The result is that in such systems only one of the phases exhibits the variable character of a solution, while the other phase has a con- stant composition and therefore constant properties. This holds primarily for a liquid phase, but in the case of gases also simplify- ing conditions prevail because the majority of solid substances do not possess a measurable vapour pressure. The vapour pres- sure of such solutions consists therefore almost entirely of a single constituent, and the laws which describe the conditions in such a system are simpler than they would be if the vapour also had to be considered as a solution. In other words, we should have to deal with specially simple phenomena of saturation. In general, when a solid substance is placed in a liquid it is dissolved, that is to say, a liquid solution is formed. When the amount of the solid added is small, the properties of the solution are very similar to those of the liquid substance or solvent. As is in general the case for solutions, they may exhibit all possible values of their properties, varying with the composition and bounded by certain definite limits. In this respect these solutions are in no way different from others. If the amount of the solid substance is increased beyond a cer- tain limit, it will no longer be dissolved but will remain as a solid in contact with the solution. It is customary to call such a solu- tion which exists in contact with another phase a saturated one, and it is said to be saturated with respect to the solid substance. The solution has taken on a definite composition and definite prop- erties, and a further increase in the amount of the solid phase has no effect on these. This corresponds to the general case of equilib- rium between several phases, for such an equilibrium is independ- ent of the relative and absolute amounts of the phases concerned. The proportions of liquid and solid corresponding to saturation 150 FUNDAMENTAL PRINCIPLES OF CHEMISTRY are dependent in the first place upon the nature of the two sub- stances. There are many cases where the solubility is so small (that is, .where the amount of the solid which corresponds to equi- librium in the solution is so small) that there can be doubt whether there has been solution at all. Of late years, however, improved means for recognising small amounts of dissolved substances (by measurement of electrical conductivity, for example) have shown that many substances previously considered to be insoluble really possess a definite, though of course very slight, solubility. We have therefore reason to assume that a small but finite solubility exists in all cases, even though it has not been experimentally proven. In the condition of saturation the liquid solution exhibits a definite relation between the original liquid (which can in this case be designated as solvent, although both components take part in the formation of a solution) and the dissolved solid sub- stance. This relation is usually expressed in per cent, indicating the number of parts by weight of the solid substance which are contained in 100 parts by weight of the solution. Saturation is sometimes expressed in parts by weight of solid to 100 parts of solvent, but since the first method of expression is the best, we shall always make use of it to the exclusion of the other. 116. THE EFFECT OF PRESSURE AND TEMPERATURE. The condition of saturation leaves two degrees of freedom. The sum of the phases and degrees of freedom is four for two constituents, and when only two phases are present two degrees of freedom re- main. A change in the proportions of saturation with temperature and pressure must therefore be expected. As far as the effect of pressure is concerned, it must be kept in mind that the change in volume accompanying the formation of a solution from a liquid and a solid substance is usually very small. A decrease in volume is the usual case, but occasionally we find an increase. In the first case an increase of pressure at constant temperature will cause an increase in the solubility. In the second case it will cause a decrease, but the effect is so small that it is difficult to measure, SOLUTIONS 151 and practical interest in the effect is satisfied with the proof that the change takes place in the direction indicated by the theory. Similar considerations hold for the effect of temperature at con- stant pressure. The solution of solid bodies in liquids may take place either with absorption of heat or with the opposite result, according to the nature of the substances, that is, either with an increase or a decrease in the entropy of the system, and a corresponding effect of temperature on the equilibrium must be expected. Those sub- stances which absorb heat during solution (this is indicated by a de- crease of temperature during solution) increase their solubility with increasing temperature, and vice versa. This principle has been confirmed by experiment in a very great number of individual cases. Attention must here be called to special conditions which make this matter somewhat more complicated than appear in the state- ment just given. The amount of heat which accompanies solu- tion is not independent of the concentration itself. If, for example, equal amounts of saltpetre are added, one after the other, to a given amount of water, the solution of the first portion of the salt in pure water will be accompanied by the absorption of a larger amount of heat than is absorbed by the addition of the second amount of the salt, and the third portion corresponds to still less heat absorbed. But the principle upon which the above rule is based holds only for equilibrium and for a change in equilibrium. The direction of the change in equilibrium, due to a change in temperature, is to be found by answering the question : what amount of heat is taken in or given out by the system during a change in equilibrium f We must choose that particular value for the heat of solution which corresponds to saturation. In other words, we must determine what heat change takes place when the saturated solution takes up or loses a given amount of the salt. This problem appears at first glance to be insoluble ; but there are several ways of reaching an approximate solution, and it is only when these relations have been taken into account that complete agreement between theory and observation has been found. 152 FUNDAMENTAL PRINCIPLES OF CHEMISTRY A general idea of the effect of temperature on solubility can best be obtained by a diagrammatic representation such as the one used in Sec. 104 to represent conditions in solutions of liquids. The diagram is simpler in this case since only one concentration corresponds to each temperature, while in the former case we had two. The solid phase does not dissolve a measurable amount of the liquid, and we need only to represent the concentration of the liquid solution. In the majority of cases such solubility diagrams are very nearly J2GP J00 $60 20 \A IO 2O 3O 4O 5O 6O TO 80 90 1OO CONCENTRA TION FIG. 16. straight lines. Fig. 16 shows the solubility line of saltpetre in water. Furthermore such a line is always a continuous one as long as the properties of the solid phase suffer no change. 117. LIQUID SOLUTIONS OF SOLID SUBSTANCES. A solution of salt in water freezes at a lower temperature than pure water. If therefore ice at is mixed with salt these two solid substances turn into liquid and the result is a liquid solution, a solution of salt and water. This behaviour is a general one. With a very few exceptions SOLUTIONS 153 (which have their cause in the formation of solid solutions) the melting point of a solid substance is lowered when it is not in con- tact with its own pure liquid, but is placed in contact with any liquid solution of which it either forms or can form a constituent. The melting point in this case does not correspond to equilibrium between a solid and a pure liquid, but to equilibrium between a solid and a solution. The lowering of the melting point is greater the greater the content of this solution in dissolved substance, and the lowering could go on indefinitely if it were not limited by cor- a FIG. 17. responding conditions determining the behaviour of the other solid substance and its solution. In Fig. 17, a represents the melting point of the pure substance A, temperature being as usual plotted upward and composition hori- zontally. Solutions of A and B, represented according to their composition as lying between A and B, will have melting points which lie lower as the composition of the solution is further from the point A. Experience has shown that this lowering of the melt- 154 FUNDAMENTAL PRINCIPLES OF CHEMISTRY ing point is nearly proportional to the amount of B which is present in the solution, and this means that the line ok is nearly straight. Precisely similar considerations are to be applied for the second substance B whose melting point lies at 6, at a distance above B, which may be, according to circumstances, greater or less than a above A. For the melting point of B in contact with solutions which contain the substance A dissolved in B we will find a line running downward like bk. If both these lines are followed fur- ther and further they will finally cut one another at a point k. Let us discuss the meaning of the point k. The line ak represents equilibrium conditions between solid A and liquid solutions of A and B. The line bk represents equilib- rium between solid B with liquid solutions of A and B. These solutions are the same as those in the previous case, the only difference being that now B is present in greater percentage, while in the first case A made up the greater part. The point k belongs to both lines, it is therefore characteristic of a temperature and a composition such that both solid A and solid B are in equilibrium with a solution of definite composition. At this point three phases, two solid and one liquid, are coexistent. One degree of freedom remains, and either the pressure or the temperature can be arbi- trarily chosen. In general the formation of a liquid solution from solid A and solid B is accompanied by a very slight change of volume. The change in this equilibrium point with pressure will therefore be very slight, and it is in fact so slight that it is difficult to show experimentally. We may therefore leave this variable out of consideration for the present, and we must conclude that there is a definite temperature and a definite composition depend- ent only on the nature of the two solid substances A and B, at which a solution of these two substances can exist in equilibrium with both solids. It will also be noticed that this temperature is the lowest at which one of the two substances can be in stable equilibrium with the solution containing both. Equilibria at tem- peratures lower than this are not necessarily excluded, and if the SOLUTIONS 155 presence of solid B is avoided, the line ak can be observed for some distance beyond k, as indicated by the dotted prolongation in the figure, while similar reasoning holds for the prolongation of bk. Such states are unstable ; they are first of all metastable, and become labile if the line is carried further. If we confine ourselves to states of complete stability, k is definitely the lowest point of equilibrium between the solid and liquid forms of A and B. 118. THE EUTECTIC POINT. If, therefore, a solution of com- position K is made to freeze by the introduction of a trace of both solids A and B, the temperature cannot sink lower than k, no matter how much of the solution freezes; and this is true because k is the lowest temperature at which the two substances in the solid state can exist in the presence of their solution. Nor can the temperature rise, for by the separation of a solid constituent from a solution the temperature can only sink. If the temperature could rise under these circumstances equilibrium would be im- possible. The only thing that can happen is that the temperature must remain constant. This brings with it the condition that in spite of the separation of a solid from the solution the composition of the solution must remain constant. If this condition is to be fulfilled, the two solid substances must freeze out of the solution as a mixture having the same composition as the solution with which it is in equilibrium. As far as this one property is con- cerned this solid mixture behaves like a pure substance, for it is formed from its solution at constant temperature, and remains at exactly the same constant temperature k all the time it is melting. A solution of composition K which freezes in such a way that a constant solid mixture of A and B separates is called a eutectic solution, and the solid mixture is called a eutectic mixture. The temperature k is called the eutectic temperature, and the point k which characterizes composition and temperature is called the eutectic point. The eutectic solution behaves towards its eutectic mixture like a pure substance, since it no longer exhibits the changing freezing point which is characteristic for solutions. 156 FUNDAMENTAL PRINCIPLES OF CHEMISTRY If any solution which has not the same composition as the eu- tectic, but which contains, for example, a larger amount of the substance A, is made to freeze, the substance A separates in the solid form. The liquid solution becomes therefore richer in B, and its freezing point is lowered. This process goes on as more heat is taken away; the freezing point becomes lower and lower, and if subcooling is avoided it sinks until the eutectic point is reached. From this time on it remains constant. A does not sepa- rate alone from the solution, and the solid which separates is now the eutectic mixture of A and B. The same holds for solutions with an excess of B, but in this case pure B separates first and the eutectic mixture follows. This behaviour brings to mind the singular solutions with a maximum or minimum of the boiling point (Sec. 109). There also we had a definite solution and a vapour of the same composi- tion as a liquid, behaving so far like a pure substance. There is, however, a difference to be noticed, for in the previous case we were considering equilibrium between two solutions, one liquid and one gaseous, both having the same composition. Here we are dealing with a liquid solution on the one hand and with a solid mixture on the other. It is easier therefore to determine the difference between a eutectic mixture and a pure substance than it was in the first case, where we had to do with a liquid and a gaseous solution. For if the solid phase is a mixture, the laws which hold true for mixtures, and especially those which describe the relation be- tween the properties of the constituents and those of the mixture, must be in evidence. Experiments made on this point have proven that eutectic mixtures are true mixtures with respect to all their properties, that is, it is possible to calculate their properties from those of their constituents by means of the law of mixtures. 1 19. CONNECTION WITH THE ORDINARY SOLUBILITY CURVE. - Let us inquire into the connection between the relationship just explained and the curve of Sec. 117, which represents the variation SOLUTIONS 157 in the solubility of a solid substance with the temperature. It will be found that we are dealing with a piece of one of the two lines leading from the melting points to the eutectic point. In the majority of solutions of various salts in water one of the melting points (that of the salt) usually lies so high that the vapour pres- sure of the solution, made up of a large percentage of liquid salt and a small percentage of water, is very high indeed. Solutions of this sort are very difficult to make and to observe, and we know but very little about them. 350 30(f 25O 200 15O /OO 50 ff m u jo 30 4O 3O FIG. 18. 7O 8O 9O IOO On the other hand, the solubility of a salt at temperatures below zero is often small, and it is only infrequently that any practical interest exists in the equilibrium between such a solution and ice. It is for this reason that the region in which solid water (ice) is in equilibrium with the liquid solution has also remained unknown in the majority of cases. Let us, for example, extend Fig. 16 so that all the equilibria between saltpetre and water appear in it. In Fig. 18 this has 158 FUNDAMENTAL PRINCIPLES OF CHEMISTRY been done, and we have from a to k the composition of such salt- petre solutions as are in equilibrium with ice at the corresponding temperatures. These are, in other words, the freezing points of these solutions of saltpetre. The eutectic point corresponds to a content of 10.9 parts of salt in 100 parts of solution, and lies at 2.9. From that point on we have equilibria between liquid solution and solid salt to the melting point of the salt, which lies at 331, and these points lie between k and 6. This branch of the curve corresponds to the solubility curve ku of Fig. 16, and in order to make it more evident it is drawn as a heavy line. The region between u and b we know nothing about, for reasons already mentioned.* 120. SOLUBILITY AT THE MELTING POINT. When a solid substance in equilibrium with its saturated solution is melted by raising the temperature sufficiently high, its solubility at this tem- perature is the same for the solid and for the liquid state. This is again a necessary consequence of the principle that when a system is in equilibrium in one sense it must be in equilibrium in every sense. If the solid form can exist in contact with the liquid form (and this is the definition of the melting point), both must exist in contact with the saturated solution. This is, however, only possible when the solubility of the two forms is the same at this temperature, for if the solubilities were different, similar con- siderations to those given in Sec. 69 for vapour pressure can be applied, and with their help we could prove the impossibility of the coexistence of the two forms. Heat is always absorbed during melting, and therefore the heat of solution of the liquid form must differ from that of the solid form by an amount equal to the heat of melting.. According to the law of the conservation of energy two conditions must exhibit * The point b does not lie on the direct prolongation of the known portion of the solubility curve. One reason for this is that saltpetre undergoes an allotropic transition at 129.5 and the appearance of the new form therefore corresponds to a new solubility curve as indicated in the figure. SOLUTIONS 159 the same difference of energy whatever the way by which the system is changed from the first condition to the second. Imagine the solid body first to be dissolved as such at the melting point, and let its heat of solution be s. Suppose that in the second case we melt the body first, allowing it to absorb the heat of melting^ /, and then dissolve it. It will take up the heat of solution /. In accordance with the principle just mentioned we will have s = l+f, and in this formula the heat absorbed by the system is to be called positive. The change of solubility with the temperature is directly con- nected with the heat of solution, and both are either positive or negative. When heat is absorbed during the process of solution the solubility increases with rising temperature. If, therefore, the heat of solution exhibits a sudden decrease, as it does at the melting point, where it becomes smaller by the amount of the heat of melting, the increase of solubility with the tem- perature must also exhibit a sudden decrease. This means that the solubility curve of the liquid will exhibit a less increase (or a greater decrease) for a given change of tempera- ture than that corresponding to the solid body. We have already found, however, .that the two solubilities must be the same at the melting point. This means that the solubility curve of the liquid must connect with that of the solid body at the melting point at an angle, as is shown in Fig. 19. On the other hand, we may suppose the liquid to be subcooled, arid the question as to its solubility in this condition is then to be CONCENTRA TION FIG. 19. 160 FUNDAMENTAL PRINCIPLES OF CHEMISTRY considered. This condition corresponds to a regular continuance of the liquid state beyond the melting point, for the melting point is not a singular point for the liquid, but is characteristic of equilibrium between the liquid and the solid phase, and is there- fore equally dependent upon both phases. The solubility curve of the subcooled liquid must therefore bear such relation to that of the solid body that it indicates a greater solubility of the solid body in the subcooled liquid, and in the same way if it were possible to superheat the solid body without melting it, its solubility above the melting point must be greater than that of the liquid. Both these facts are immediately evident from Fig. 19, where the regions of suspended transformation are indicated by dotted lines. The general conclusion is that the solubility of the less stable form is always greater than that of the more stable form, and this same conclusion might have been reached directly by reasoning similar to that of Sec. 69, merely replacing vapour pressure by solubility in the discussion. The fact that it is possible to arrive at the same conclusion in various ways is a confirmation of the correct nature of the reasoning involved. Fig. 19 is fundamentally in agreement with Fig. 3 of Sec. 70, which represents the relation between vapour pressures of stable and unstable forms. In this discussion we have made one assumption for the sake of sim- plicity, and this assumption must be kept clearly in mind, because it is not always a permissible one. It was that the liquid form of the dissolved substance should be present in contact with the solution without dissolving any of the other substance, which we have termed the solvent. This is almost always true of solids, as we have already frequently stated, but in the case of liquids it is not generally true. We must therefore inquire what changes are introduced into our conclusion when this circumstance is taken into account. If the liquid form is changed by dissolving some of the other substance it is no longer in equilibrium with the solid. We know SOLUTIONS 161 from Sec. 117 what the nature of the change in equilibrium must be. By solution of a second substance in the liquid phase the equilibrium temperature is always lowered, and the lowering is proportional to the amount of dissolved substance. Equilibrium between the saturated solution, the solid, and the molten phase will therefore not exist exactly at the melting point of the solid form, but will lie at a lower temperature, arid the lowering of the equilibrium point will be proportional to the solubility of the solvent in the molten phase. We have in fact another case where two liquids, the solution and the molten phase, can only exist in equilibrium when each of them has become a saturated solution with respect to the other. We have two constituents and three phases, two liquid phases and the solid, and we have therefore one degree of freedom. The temperature corresponding to equilibrium is therefore variable with pressure. But since none of 'the three phases is gaseous, pressure can have but slight influence on the equilibrium. The remaining degree of freedom can be fixed by assuming a definite pressure, that of one atmosphere, for example. It can also be fixed by the formation of a fourth phase, a vapour phase, for example. There is then no degree of freedom, and this means that the vapour phase can only exist in the presence of the three other phases under definite conditions of temperature and pressure. 121. THE SOLUBILITY OF ALLOTROPIC FORMS. Similar rea- soning may be used in the discussion of the relation existing at saturation between allotropic forms of the same substance. This can be immediately predicted, for the change from one allotropic form to another is fundamentally in no way different from the change from one state to another, and it is especially similar to the changes occurring during melting and solidification. At the transition temperature of two allotropic forms which are in equi- librium their solubility must be the same, and the solubility curves of the two forms will cut one another at that point at an angle. On either side of this point that form which is unstable in the 11 162 FUNDAMENTAL PRINCIPLES OF CHEMISTRY temperature region in question will have the greater solubility.* In general we can say that the less stable form will have the greater solubility, and vice versa. But this statement holds only for solu- tions of two constituents, and when more are present the relations are much more complex. This leads to the question how forms behave which are unstable in the entire observable range of conditions, and the answer is that in the whole region they will be more soluble than the stable form. This affords a further means of recognising mutual rela- tions of stability between allotropic forms, even when the proof of actual transformation is impossible because of very small re- action velocities. A necessary assumption in all this is that the solutions of the various forms must have exactly similar properties when their concentrations are the same. If the solutions are in any way different, the proof just given for the transition of one form into the other, as shown by the dissolved portion, cannot be applied. The substances in question behave as any two different substances would which have no definite relation to each other. The reason- ing which leads to these conclusions is applicable for all solvents, and it therefore follows that the general relations are independent of the nature of the solvent just as they are independent of the nature of the dissolved substance. If we are dealing with allo- tropic forms giving identical solutions the above considerations hold under all circumstances. 122. SOLUTIONS OF HIGHER ORDER. These general princi- ples have been applied to solutions of the second order, that is, to such as can be separated into or prepared from two pure sub- stances. There are, beside, solutions of higher order which can be separated into three, four, or more constituents, and which therefore require the same number of pure substances for their * Figure 18 is in agreement with this. The solubility curve of the new form will have a steeper slope than the ordinary solubility curve, since the appearance of the new form is accompanied by an increase of entropy. SOLUTIONS 163 preparation. The special laws which describe such solutions become more and more complex in the higher orders, but the general relations remain the same. It is always possible to sepa- rate each of these solutions into its constituents, for the concept of solution depends upon the differences which exhibit them- selves when an originally homogeneous substance is subjected to operations which result in the formation and separation of new phases. 123. THE GENERAL PROPERTIES OF SINGULAR POINTS. Among solutions of higher order there will be found singular solutions which permit of a change of phase without any change in the properties or the composition of the residue. As far as such a transformation is concerned they behave like pure substances. In agreement with singular binary solutions they possess this property only at a definite temperature and a corresponding pressure, and they lose it when these are varied. Two cases are to be distinguished among singular binary solu- tions. The solution may either change into another solution, or into a mixture having the same composition as the original solu- tion. The first case corresponds to solutions with a constant boil- ing point; the second, to eutectic solutions. The transformation of two mutually saturated liquid solutions, described in Sec. 114, belongs to the second case. These solutions boil at a constant temperature and form a vapour of constant composition. But complete transformation of such a mixture into vapour under constant conditions can only take place when the total composi- tion of the mixture is the same as that of the constant vapour. Of course the liquid mixture can be primarily made up of any amount whatever of the two solutions, and it will then boil at the definite temperature. This will, however, only continue while both liquid phases are present. If one of the phases boils away before the other under continued distillation, boiling can no longer take place at constant temperature, and the remaining solution will continue to boil with a rising temperature. The transfer- 164 FUNDAMENTAL PRINCIPLES OF CHEMISTRY mation has not taken place under constant conditions. It is therefore necessary that both solutions should be present in such proportions that their total composition is the same as that of the vapour, and only under these conditions will both solutions disappear at the same time. The ternary and higher solutions behave in a similar manner. There are cases where a solution evaporates to form a liquid of the same composition. The temperature and the pressure are necessarily constant during this transformation, for the new phase has the same composition as the old one. The composi- tion of the residue remains unchanged, and it therefore has a con- stant boiling point. This boiling point is always a maximum or a minimum, so that solutions which are formed from the singular one by a slight change in composition in either direction, all have a lower or a higher boiling point. If this were not the case the solu- tion would send out vapour of such composition that the residue would have a higher boiling point than the distillate, and if solu- tions with higher and lower boiling points chosen from the imme- diate neighbourhood of the singular solution are examined, they will be found to change in composition during distillation. The three singularities, constant boiling point, constant com- position of residue and distillate, and maximum or minimum boiling point, are therefore necessarily connected, and each of them conditions the others. They are -called singular values of the properties of these systems, and we may draw the general con- clusion that these singular properties always appear simultaneously for definite values of the variable conditions. This is primarily true of solutions, but it can also be extended to include all systems which vary continuously. So far we have been considering cases where one phase changes into one other phase. Precisely similar reasoning can be applied where one phase changes into several other phases. The case of the eutectic solution, Sec. 118, is an example of this. Here the total composition of the two phases must be the same as the com- SOLUTIONS 165 position of the single phase from which they are formed. There are, then, beside singular solutions, singular mixtures which change under constant conditions completely into a new phase. For such singular mixtures the proportion of the two phases at equi- librium can no longer be arbitrarily chosen, as is the case for mixtures in general. The proportion at equilibrium must have a definite value w r hich is determined by the composition of the new phase into which they are changed. If any other relation of the components of the mixture is chosen, one of them will be exhausted before the other during transformation, and it would then be impossible for the whole process to take place under constant conditions. Among solutions of the third or higher order a new possibility must be added to those already mentioned. A singular mixture may change into another mixture which is also a singular one. In other words, it is possible for m phases to change into n other phases in such a way that the temperature and pressure remain constant during the whole transformation, (m and n are whole numbers.) Such a constant transformation is only possible when the total composition of the new phases exhibits the same propor- tional content of the constituents as the original mixture. In other words, the total composition of the residue must not vary at any time during the process, and if this is to hold the new phases must form with relations of composition and amount such that the constituents are in the same proportions as in the original mixture. Then the temperature or the pressure corresponding to trans- formation will be a maximum or a minimum. CHAPTER VI ELEMENTS AND COMPOUNDS 124. HYLOTROPY. The mode of phase change in which the newly formed phases have at every moment the same properties arid the same total composition as the original system is called a hylotropic transition, and the general relations corresponding to it are termed hylotropy. The assumption of reversibility in the changes of state so far discussed means only that the total com- position of the original system was like the resulting one after the transformation had taken place. A hylotropic transformation demands that the relation of constituents in the old system shall be the same as in the new system at every moment during the whole process. This special assumption brings with it the condition that the system shall have singular properties, and therefore that a hylotropic transformation can only take place at a maximum or minimum value of pressure and temperature. The simplest case of hylotropic transformation is found in the change of state of a pure substance. Whenever a substance changes its state, that is, forms a new phase, at constant values of pressure and temperature, it is defined as a pure substance. Solutions are characterized by the fact that they form new phases only under variable conditions. It is possible to transform a solution into vapour at constant temperature, but in order to carry out this process the pressure must be continually decreased during vaporiza- tion. It is also possible to carry out the transformation at constant pressure, but then the temperature must be continuously raised during the process. We have just been discussing singular solutions and singular 166 ELEMENTS AND COMPOUNDS 167 mixtures, and have found transformation under constant condi- tions to be the rule among them. They are therefore hylo tropic just as pure substances are, and we must therefore keep clearly in mind how they differ from pure substances. Singular or hylotropic solutions and mixtures have this property only at one single defi- nite value of temperature and pressure. If transformation takes place at any other pressure and the corresponding temperature, such a solution or mixture no longer exhibits hylotropy. The new phase has a different composition from the residue, exactly as would be the case with any other solution or mixture. The difference between singular solutions and mixtures on the one hand and pure substances on the other is therefore that the former are hylotropic only at one single point among all their possible conditions of existence, while the latter are hylotropic within the limits of a finite region. This region may be large or small; in certain cases it is so large that it includes the range of all attainable conditions. Important properties and differences among pure substances are dependent on this fact. What is meant by the statement that a pure substance is only hylotropic between the limits of a definite range of temperature and pressure ? It means that the substance changes its proper- ties and composition during a phase change, provided this change takes place outside the limits of this region. But this latter set of properties belongs to solutions and mixtures. If the region within which hylotropy appears is called the region of stability of the pure substance in question, we can then say that at the limits of the region of stability pure substances change into solu- tions or mixtures. Whether a solution or a mixture is formed from the pure substance at the limits of this region depends upon circumstances. Gases always form solutions, and solutions will therefore be usually formed at high temperatures. On the other hand, when the limit of stability lies at ordinary or low tempera- tures, mixtures can appear. For reasons explained in Sec. 67 pressure can have but small effect when solids or liquids are in 168 FUNDAMENTAL PRINCIPLES OF CHEMISTRY question. It may, however, have a very large effect among gases. The actual proof of the limits of stability may be carried out, as already explained, when we consider the differences between mix- tures, solutions, and pure substances. At high temperatures and low pressures, and where we must decide whether a gas is a pure substance or a solution, separation through a porous partition will be the usual means. It should, however, be remembered that a system which can be proven to be a mixture or a solution by any means whatever is characterized as such. All possible proof can therefore be made use of. 125. CHEMICAL PROCESSES IN THE NARROWER SENSE. It is always possible to separate a solution into at least two pure sub- stances, and every mixture also consists of at least two. The number of pure substances present in a system, or which can possibly be produced from it, is therefore increased whenever the limit of stability is passed. A single pure substance changes at this point into at least two other pure substances. This is a process which differs in important details from those which we have so far investigated. During a change of state a pure substance changes into another pure substance, and during the formation and separation of solutions the number of pure substances remains unchanged. We are now dealing with new processes in which the number of pure substances changes. Pro- cesses of this sort, where several other pure substances are pro- duced from a given set of pure substances, are called chemical processes in the narrower sense. The following cases are possible : the number of pure substances may increase, decrease, or remain the same during the process. Processes of the first sort are usually called analytical processes or separations. Those of the second sort are called synthetic processes or combinations. The third sort are called " double decompositions" or metastases when at least two pure substances take part. Cases where only one pure sub- stance takes part, changing into another, we have already taken up. These are changes of state in the broader sense of the term, ELEMENTS AND COMPOUNDS 169 and they include what has been called polymvrphy. If we apply the law of the conservation of weight to these cases the following rules may be deduced. If a substance breaks up into two or more, the weight of each of the new substances must be less than that of the original substance, because the sum of the weights of the new substances must be equal to the original weight. In general, the old substance can be prepared from the new ones. The latter are therefore called its constituents. The weight of each con- stituent must then be smaller than that of the substance of which it is a constituent. Whenever a chemical process has taken place, and we find that a newly formed substance weighs less than the original substance, we may be sure that a decomposition has taken place, even though we have not seen or weighed the other substance which must have been produced. 126. ELEMENTS. Of course the constituents which have been produced in this way are subject to further examination. It is possible that they may change into mixtures or solutions when temperature and pressure are changed, or they may not show any such effect. In the first case the mixture or the solution can be separated into pure substances, and one tries to transform these again into mixtures or solutions. This can be carried on until we have substances which cannot be transformed under any con- ditions into mixtures or solutions. Such substances cannot be decomposed or analyzed: they are called elements, or simple substances. Perhaps a better term than the latter would be undecomposed substances. If we remember that the number of substances has been con- stantly increasing during this series of transformations, at least two being produced from one at every step, the supposition is very evident that the number of elements ought to be very much greater than the number of compounds. Experience has, however, taught us that the opposite is true. We know of more than 50,000 differ- ent compounds, but we know less than 80 elements. This apparent contradiction disappears when we find that 170 FUNDAMENTAL PRINCIPLES OF CHEMISTRY various compounds do not lead to wholly different elements when they are decomposed, but that one and the same element can be prepared from very many compounds. By far the greater number of all known compounds contain one and the same element, carbon. The paths which lead from compounds to elements run together to a comparatively small number of points, while, on the other hand, they separate in numberless directions when we start from the elements and pass to the compounds. Elements possess two distinct characteristics. First, in all chemical transformations which are not hylotropic and which start from an element, weight can only increase, for all non- hylotropic transformations are transformations into chemical compounds. Such a change can take place only when other ele- ments combine with the first one to form compound substances. The weight of the new substance produced from the element must therefore necessarily be greater than that of the element itself. It is in fact equal to the sum of the weights of all the ele- ments which enter. The second characteristic is that an element possesses a region of stability which reaches over the entire range of attainable pressures and temperatures. It must be noted that the application of other forms of energy than heat and volume energy very often leads to the formation of new substances. Elec- trical energy is especially active in this way. The concept of the region of stability must therefore be expanded to include all the forms of energy. It must be kept in mind that when an element suffers a hylo- tropic transformation the two forms may form a mixture or a solu- tion. A pure substance will then lose its second characteristic and change into a solution without the occurrence of a chemical process in the narrower sense. The concept of the region of sta- bility must therefore be based on chemical processes in the nar- rower sense and on non-hylotropic transformations. An element is a substance which cannot be transformed into another non-hylotropic substance within the entire range of attainable energy influences. ELEMENTS AND COMPOUNDS '171 By energy influences we must understand any process which is carried out without the actual addition of other substances. The two definitions are knit together by the law of the conserva- tion of weight, for if a substance can change into another non- hylotropic substance, this is only possible if it forms a mixture or a solution of at least binary composition. Such a system can always be separated into its constituents by some means or other. If therefore a new hylo tropic substance is produced, at least one other substance of the same kind must be produced at the same time. Since the total weight of the two substances must be equal to the weight of the original substance, according to the law of the conservation of weight, each of the new substances must have a less weight than the original substance. If this is excluded by definition the substance can only suffer hylotropic transformations of such a nature that the weight does not change, or chemical transformations with the addition of other substances, and in this case the weight can only increase. 127. THE REVERSIBILITY OF CHEMICAL PROCESSES. So far we have regarded the chemical state of any given system as a de- termined function of existing conditions, especially pressure and temperature. By changes in these conditions changes in the system are brought about. This assumption contains another, which is that every process is reversible, that is, that any trans- formation caused in this way can be reversed with the production of the original system. According to the assumption already made, it is only necessary to arrange for the original conditions, and especially for the original values of pressure and temperature; for if the condition of the system is only dependent on those varia- bles this must result in a return to the original condition. This assumption holds for the simple cases which we have so far considered. A pure substance can, in general, be transformed forward and backward into any of its various states. The ease with which this takes place may be, however, very different in different cases, and the mutual transformation of solid allotropic 172 FUNDAMENTAL PRINCIPLES OF CHEMISTRY forms often takes place so very slowly as to almost, and sometimes quite, pass the limits of experimental investigation. Even in these cases, however, it is usually possible to solve the problem by roundabout methods, so that the law of reversibility appears to be generally true for these simple processes. The same holds true for the formation and decomposition of solutions. There is in general not the slightest difficulty in producing solutions of any given constituents, provided the substances are capable of form- ing such solutions at all. The separation of solutions into their constituents is a much more difficult and painstaking task, since many methods of separation require an unlimited number of operations. Even here, however, we can feel sure of the general possibility of separating all solutions into their constituents. It may be mentioned that the task becomes more difficult as the order of the solution increases. This means, of course, that there are more constituents to separate. The principle of the reversibility of chemical transformations is by no means capable of such general application to chemical reactions in the narrower sense of the word. The transformation of compound pure substances into simpler ones, and finally into elements, is theoretically always possible, but sometimes practical only by roundabout methods. But the preparation of substances from simpler ones, or from the elements, is in many cases im- possible at the present time. In other words, the analysis of a substance, and especially the elementary analysis by which its ele- ments are determined, is always possible. Synthesis, on the other hand, is not always possible, and there are a large number of sub- stances which exhibit transformations in one sense only and which cannot be produced from their elements. Experience has, however, taught us something about synthesis. In the earlier stages of the development of chemistry but very few syntheses were known, and chemistry was the art of decom- posing substances. The old name " Scheidekunst" characterizes this point. The progress of science brought with it the discovery ELEMENTS AND COMPOUNDS 173 of more and more syntheses, and at the present time the majority of pure substances are not found as such in nature, nor are they produced from natural products by partial decomposition. Most of them are prepared in synthetical ways. Certain substances which are formed in living plants and animals have so far resisted our attempts to prepare them synthetically, but many other sub- stances which are produced in the same way have already been prepared, and there is no real difference of a fundamental kind between the substances which are now prepared synthetically and those whose synthesis has not yet been accomplished. An inductive conclusion therefore seems scientifically justified: the boundary between substances which can be synthesized and those which cannot yet be prepared artificially is only set up by the conditions of our knowledge and skill. Cases in which a syn- thesis, which cannot be carried out at the present time, will be- come possible as the result of scientific investigation are probably so numerous that it seems only a question of time and labour. Sooner or later we shall probably find a method for the synthetic preparation of any substance whatever. 128. THE CONSERVATION OF THE ELEMENTS. The relation between a compound and the elements which can be prepared from it, " its" elements, more briefly but less correctly, is a fixed and definite one; that is, given a certain substance, the elements which can be prepared from it are determined. The method which must be used for its decomposition may be one of many, but this fact has not the slightest effect on the final result of the decomposition ; that is, on its elementary analysis. On the other hand, the relation between the elements and their compounds is not a fixed and determined one. There may be several pure substances and solutions whose elementary analysis shows the same elements, even though these substances may possess different properties. In the various states (including allotropic solid forms) we have already seen several examples of this. Those substances which can be transformed into one another, hylotropic 174 FUNDAMENTAL PRINCIPLES OF CHEMISTRY substances so called, will always give the same results on ele- mentary analysis. The method can have no influence on the re- sult, and we could therefore analyze the substance in one case directly and in another case after we have transformed it into its hylotropic form. In both cases we must obtain the same result. Another expression for the same fact may be used, it is not possible to transform one element into another. This fact is called the law of the conservation of the elements. If this law did not hold, elementary analysis might give different results for the same substance, one analysis being carried out in such a way as to lead directly into one set of elements, while on another occasion these might be transformed into another set. From the law of the con- servation of the elements it is also possible to show that the results of elementary analyses are always definite. A difference in the results obtained from the same substance by elementary analysis in different ways would be equivalent to a transformation of the elements produced in one way into those produced in another. In so far as the chemical processes in question are reversible, the law just given holds for the synthesis of chemical compounds. When it is possible to prepare a compound substance from its elements, the same elements are necessary as were found by the elementary analysis of the compound. The necessity of this principle is contained also in the law of the conservation of the elements, for if it were possible in a reversible case to prepare the compound from elements other than those obtained by its de- composition, it would only be necessary to prepare the compound from its corresponding elements and then to decompose it into other elements. The result would be that the first elements were transformed into others. 129. SYNTHETIC PROCESSES. In order to reach a general idea of those phenomena which are to be classified as belonging to solutions and those which belong to chemical reactions in the narrower sense, it will be found necessary to classify carefully the various possibilities. This is most easily done if we first fix ELEMENTS AND COMPOUNDS 175 the case for solutions and then make the assumption that when the two pure substances A and B are brought together, forming the new substance AB, this new substance can form solutions with both A and B. In other words, every type of chemical combina- tion can be made by combining the possible cases of solutions, pair by pair, until all are exhausted. One limitation must be borne in mind. The two types of solution must have one constituent in common at the point where they are brought together, and this is to be the newly formed substance AB. We can limit the problem still further by assuming that the phenomena of combination of A and B are observed at constant temperature and pressure. Out of all the changes observable under these conditions, such as change of colour, of entropy, or the heat condition, in general of volume or of state, only the latter are to be considered. The question is, then, what changes of state can take place when we bring together the two substances A and B in varying proportions ? Beginning with the pure substance^!, we will make mixtures of 0.9 parts of A and 0.1 part of B, 0.8 of A to 0.2 of B, etc., to pure B, observing any change of state which may take place in any of these mixtures. In certain cases it will be desirable to choose the steps closer together to determine especially those proportions where a new state appears or an old one vanishes. Theoretically every possible proportion must be examined ; this is practically impos- sible, and it is also unnecessary, because of the law of continuity. 130. THE LAW OF CONTINUITY. In previous considerations we have frequently made use of this law without specifically stating or naming it. It is to such a high degree a matter of daily expe- rience that we usually assume its truth without question. But for its correct application it is necessary to examine more closely into its meaning and range. By continuous things we understand such as exhibit no differ- ences in immediately adjacent parts. This does not mean that parts which are far apart either in space or in time may not be 176 FUNDAMENTAL PRINCIPLES OF CHEMISTRY different. For example, the colour of the cloudless sky is not the same at the horizon and at the zenith. But immediately adjacent parts of the sky do not differ from each other, arid we are therefore accustomed to say that the blue-gray colour of the horizon passes over continuously into the deep blue of the zenith. A thing is dis- continuous when immediately adjacent parts are evidently different. The law of continuity expresses the fact that those properties of an object or a process which are mutually dependent are simul- taneously continuous or discontinuous. Discontinuity is not ex- cluded, but the law does say that when any one property becomes discontinuous at a certain point, all the other properties which are definitely connected with the first one become discontinuous at the same point. When water freezes, for instance, it is not only the mechanical properties which show a sudden change when the liquid changes to a solid; the volume, the index of refraction, the heat capacity, and all the other specific properties also change suddenly. And, on the other hand, no property of water shows a discontinuous change when the water is heated, compressed, or otherwise subjected to a continuous change of condition without any change in state. Proper application of this law demands that certain difficulties connected with the definition of the concepts involved should be carefully explained. The proof of continuity or discontinuity is dependent on experimental aid. A green pigment, produced by mixing blue and yellow, would be continuously green as judged by the eye alone. Under the microscope the yellow and blue grains can be seen side by side. A coat of this pigment looks smooth to the unaided eye, but the microscope would show it to be most uneven and full of grains. In the same way other proper- ties would appear continuous, as measured in terms of a unit of a few tenths of a millimetre, while they become discontinuous when a smaller unit is applied. The application of the law demands corresponding caution whenever it is to be used at a boundary of this kind between continuity and discontinuity. ELEMENTS AND COMPOUNDS 177 A still further difficulty is to be found in the concept of " defi- nitely connected" properties. For example, the vapour pressure of water at is the same as that of ice at the same temperature, in spite of the fact that the two states are discontinuously different. For our own special purpose we shall apply the law of continuity in the following way : When we change the proportions of A and B step by step, and no new phase appears as we go from one step to the next, we will assume that, within the limits of this step, no discontinuous change has taken place in any of the variable prop- erties. It is, of course, still possible that within the limits of this step a new phase has appeared, disappearing again a little later, so that its appearance would be overlooked unless the intermediate region were examined. This possibility diminishes as the steps are chosen closer together, and can be practically excluded. The most important practical application of the law of con- tinuity is in interpolation. If a number of values of one property and the corresponding values of another continuously variable property have been determined, it can be assumed that the values lying between these deter- mined points will follow each other continuously. But this does not yet de- termine these intermediate points definitely. Suppose the two properties laid off on horizontal and vertical axes, and that 1, 1'; 2, 2'; 3, 3', etc., are the points deter- mined. An unlimited num- ber of continuous lines can be drawn through these points, and some of them are indicated in Fig. 20. But among all these curves one is the most continuous, and it has less twists than any of the others. It will be easily recognised from the 12 23 FIG. 20. 178 FUNDAMENTAL PRINCIPLES OF CHEMISTRY figure, and this is, in general, the curve which actually repre- sents the relation in question. This can always be shown by measurement of intermediate points. Interpolation within the entire range of measurements can be carried out with an accuracy which can be made as great as de- sired by the determination of intermediate points. This accuracy becomes less and less as the law of continuity is applied to extra- polation beyond the limits of the measurements. Points lying near the last measured one can be fixed with considerable certainty. In Fig. 21 the assumption that X/ is the real point corresponding xt X? x; x; FIG. 21. to 'X lt and that X" and X"' are not, is perfectly justified, pro- vided the heavy line represents a set of measurements. But at X 2 ', X 2 ", and X 2 '" t corresponding to X 2 , points equally far apart with XS, X^', and AT/", no conclusion as to which is the correct point is possible, because they all lie too far from the last measured point. Extrapolation is generally to be avoided, and in those cases when it is used it must be specially justified. The absolute temperature (Sec. 34) is determined by extrapolation, and in this case its use is certainly of value. ELEMENTS AND COMPOUNDS 179 131. GRAPHIC REPRESENTATION. In order to give clear and evident expression to the following relations we will make use of diagrammatic representation. The composition of systems made up of the two pure sub- stances A and B will be laid off along a horizontal line, the content of A decreasing and that of B increasing as we pass from left to right. The left end of the line corresponds to pure A, the right to pure B, and the middle point represents a system made up of equal parts of A and B. By " parts" we may mean parts by weight, but the diagram remains the same for any other method of determining quantity. We could replace it just as well by volumes or " combining weights." The diagrams are to show what phases can exist when pure A and pure B are brought together in various proportions, and to make this clear we shall use heavy lines for solid, light lines for liquid, and dotted lines for gaseous phases. Pressure and temperature are assumed to remain constant, and we have therefore disposed of two degrees of freedom. The phase rule tells us that the sum of phases and degrees of freedom for two components (which is the number we are to begin with) is always four. Our system can therefore contain either one phase or two. Three or four phases are only possible when definite fixed values for pressure and temperature are chosen, such that the substances in question can exist in three or four phases in equilibrium. For our purpose these cases may be omitted for the present, since we are not dealing with any particular substance. We shall find them again later when we come to the investigation of the effect of changes of pressure and temperature on such systems. If only one phase is present, one degree of freedom still remains ; so wherever a single line appears in a diagram, this means a phase of variable composition varying between the limits of this region of a single phase. The line ab of Fig. 22 shows such a case, and this line describes a liquid varying in composition between 0.6 of A with 0.4 of B, to 0.3 of A with 0.7 of B. 180 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Wherever two lines are shown two phases are indicated, and there remains no degree of freedom. Each of the two phases has therefore a constant composition. Such pairs of lines cover a finite region only, and the difference in total composition, indi- a b L l^_^__t it | | I I I t A as & FIG. 22. cated by the extent of the lines, corresponds to a change in the amount of each phase which is present. The ends of such double lines correspond to the composition of one of these constant phases. The double line ab of Fig. 23 indicates that within this region a liquid phase is in equilibrium with a gaseous one. At the left, where A is present in excess, we find a gaseous phase of variable composition. At a a liquid phase appears, at first in very small amount, and the composition of the gaseous phase at a is fixed by the position of this point. The appearance of the second phase determines the fact that from this point on the first phase shall have a constant composition. From a to b the gaseous phase has a FIG. 23. therefore the composition a. At b the gaseous phase disappears. The composition of the liquid phase is therefore determined by this point. This composition is the same throughout the entire liquid line, and even the liquid which forms at a in the presence of the gas has the same composition. The lines are not superimposed in these diagrams, but are placed side by side for greater clearness. No difference is indi- cated by the position of a line above or below another; either case means the same thing as far as we are concerned. ELEMENTS AND COMPOUNDS 181 132. SOLUTIONS MADE UP OF PHASES IN THE SAME STATE. - Let us express the facts we have already learned about simple solutions (Sections 76-122) in this new way by means of a dia- gram, and first of all let us consider solutions made up of two components in the same state. For the sake of abbreviation we shall in future designate gaseous phases by g, liquid ones by /, and solid ones by s. In Fig. 24, I, II y and III represent the case of two gases. They may form solutions in all proportions, and in this case the dia- gram is merely a continuous dotted line (/). Or the temperature jr a FIG. 24. may lie above the boiling point of one of the components but below the boiling point of a series of solutions. In this case (//) the addition of B to A will result first of all in a gaseous solution which will vary in composition up to a certain point. At this point a liquid phase, having a boiling point which is the tempera- ture of the experiment, will appear. The composition of the gas phase is shown by the point a and that of the liquid phase by b. Between a and b the liquid phase has increased at the expense of the gaseous one, and at b the gas has entirely disappeared. Be- tween b and c we find a liquid phase only, and this of variable composition, but one which has a boiling point always higher than the temperature of the experiment. At c the boiling point of another liquid solution is reached, and c indicates the composi- tion of this solution, while d shows the composition of its vapour. This liquid phase disappears again at d, and from here to the end 182 FUNDAMENTAL PRINCIPLES OF CHEMISTRY of the line (pure B) we find again gaseous solutions of varying composition. The third case is still more complicated. It occurs whenever the liquid region in the middle of the diagram is not continuous, and when separation of the solution into two liquid phases takes place. The conditions under which such a case can occur are not often met with, but for the sake of completeness we must examine it with the others. This exhausts the cases which can occur if we assume that no point of inflection appears in the boiling point curves of the binary solutions. Whether such a case can actually be excluded or not we cannot here determine, and it can only be said that such a thing has never been observed. Succeeding diagrams are given with the same assumption, and it remains for future experi- ment to discover what would happen if the incorrectness of the assumption should ever be proven. In the case of two liquids four different phase schemes are pos- sible, and these are shown in Fig. 25. The two liquids may be Hdc m - FIG. 25. soluble in each other in all proportions, and the corresponding diagram will then contain a single line (/, Fig. 25) like the one ELEMENTS AND COMPOUNDS 183 for gases. Or the liquids may possess only partial mutual solu- bility, and in this case the two ends of the diagram will be single lines representing the series of possible solutions of variable com- position. Saturation will then occur in both sides of the diagram, and between the two points indicating this fact we must draw a double line to indicate that two liquid phases, each of constant composition but in varying proportions, can exist together in equilibrium. This is all shown in II, Fig. 25. We have still to consider the limiting case in which the two solutions are not measurably soluble in each other. For this case the double line reaches from side to side of the diagram as in Ila, Fig. 25. This case is actually not different from the general case of II. In the third case a gaseous solution appears between the two liquid ones (///, Fig. 25). Such a condition of things is only to be expected when the two liquids are near their boiling points, and when some of the possible solutions have boiling points which lie above the temperature of the experiment. At a definite point of composition vapour will then begin to form, and its escape leaves a residue which is less volatile, so that it ceases to boil. We have then a region of two phases, vapour and liquid, and both have constant composition. Finally a point is reached where the total composition is the same as that of the vapour, and at this point the liquid phase disappears. The vapour phase can now change in composition until a liquid phase separates again, and the phenomena just described will then appear in reverse order. The fourth case IV will be seen to be a combination of cases // and ///, and therefore needs no further explanation. 133. Two SOLIDS. Two solids give not less than ten different phase combinations. As long as no phase belonging to another state appears, only one case is possible (7, Fig. 26), provided we assume as usual that solid solutions are to be left out of considera- tion. This diagram shows the two solid phases existing together through the whole range without any mutual effect. But when liquid and vapour, or both, occur between the two ends of the dia- 184 FUNDAMENTAL PRINCIPLES OF CHEMISTRY gram, a corresponding complexity appears. Let us first assume that both solids vaporize without previously melting. Let us assume that the temperature is lower than the boiling point of either substance (as we have already assumed in saying that they are solids), and that the sum of their two vapour pressures at the m VI FIG. 26. temperature of the experiment is greater than the constant pres- sure at which the experiment is made. Then the addition of B to A will soon cause the appearance of a vapour phase containing all the B so added and as much of A as corresponds to its vapour pressure. We have then solid A and a gaseous solution of A and B. ELEMENTS AND COMPOUNDS 185 The addition of more B results in an increase in the amount of the vapour phase although the total composition remains un- changed. This can only be true when A evaporates in amount proportional to the added B, and it can be carried on until all of A has evaporated. From this point on the composition of the gas solution changes until B is present in excess, and appears as a solid phase with the vapour. The vapour has from this point a constant composition, but decreases in proportion to B, until finally, at the end of the diagram, only pure B is present. II ex- hibits these phenomena in their entirety. A precisely similar diagram corresponds to the appearance of a liquid phase in place of the gaseous one. The condition for this is that the temperature shall lie below the melting points of the constituents, but above the eutectic point. The first addition of B to solid A results in the formation of a saturated liquid solution in the presence of an excess of A, and further additions increase the liquid portion with a corresponding decrease in the solid phase. Solid A finally disappears and the liquid phase begins to change in composition and continues until it is saturated with solid B, when this appears as a solid phase in contact with the solution, which has remained constant. From this point on the liquid phase decreases and the solid phase increases until we arrive at pure solid B. Diagram F, which corresponds to this set of changes, differs from II only in that the dotted gas line is replaced by the continuous liquid line. These two simple forms become more complex when the more complicated gg lines can appear (as in Fig. 24, II and ///) in place of the simple gas line lying between the regions containing two phases. Figure 26, /// and IV, illustrates this, and in place of the simple liquid line of V we may have the more complicated lines // to IV of Fig. 25. These cases are shown in VI to VIII, Fig. 26. It is finally possible that vapor shall be present on one side of the diagram and liquid on the other in contact with the solid phase. This is shown in the cases IX and X. In other words, 186 FUNDAMENTAL PRINCIPLES OF CHEMISTRY diagrams like //, ///, and IV are produced when a short thick line is added at each end to the gg diagrams of Fig. 24 correspond- ing to the assumption that here a solid phase is present with the gas; and in the same way V to VIII are formed by the same process from the // diagrams of Fig. 25. The two last diagrams IX and X are produced from the diagrams of Fig. 27 in the same way. This method of examining the cases insures that we shall not miss any possible combination. 134. SOLUTIONS OF DISSIMILAR STATES. Beside the three cases, gg, II, and ss, in which constituents in the same state form solutions, we have also the three cases gl, gs, and Is, representing solutions made up of constituents differing in state. In the latter case the symmetry which was observed in the former case naturally disappears. 135. ONE GAS AND ONE LIQUID. Starting from the gas side we have first of all gaseous solutions to the point which represents the vapour pressure of the liquid. From this point on liquid satu- rated with gas appears as a second phase, and this increases at the expense of the first phase until finally all the gas disappears. The JL FIG. 27. end of the series is made up of liquid solutions of varying com- position ending in pure E. This simplest case is shown in / of Fig. 27. The second more complicated case starts in exactly the same way, but within the region of liquid two liquid phases appear. In other words, we find a combination of / and //, Fig. 25. When a gas reacts with a solid substance the simplest case is that shown in I of Fig. 28. Here the solid substance vaporizes until its vapour pressure at the temperature of the experiment has been reached. From this point the liquid phase exists in the pres- ELEMENTS AND COMPOUNDS 187 ence of the gaseous phase to the end of the diagram, because solid substances do not form solutions with gases. This simple diagram may be complicated in many ways. A liquid may appear before the gas is saturated (77). This liquid n FIG. 28. may previously form two phases (777), or it may change into a gaseous phase before the solid appears (IV); or a second liquid phase may appear between these two conditions. This exhausts the possibilities. Somewhat similar to these are the conditions which may develop between a liquid and a solid, and Fig. 29 represents the corre- sponding set of phases. Because of the fact that two phases are possible for a liquid, but not for a gas, we have one additional case, so that in toto six different phenomena may take place. A description of these is unnecessary, for no important new relations appear. An inclusive examination of the thirty cases just described will show that characteristic diagrams appear when a solid substance is concerned in the process. Under these conditions the region of two phases runs in every case to the end of the diagram at the side representing the solid substance. In the case ss, where two solids are present, we find double lines at each end. This is the natural 188 FUNDAMENTAL PRINCIPLES OF CHEMISTRY expression for the general assumption that solid substances do not form solutions, for II a of Fig. 25, where a similar assumption has been made, shows a similar double line reaching to the end of the ST. IV- vr- FIG. 29. diagram. It may be mentioned that the complexity is least among gases, and that it increases among liquids, becoming greatest for solids. 136. THE TEMPERATURE Axis. The considerations just given become in many respects more connected and evident if we do not limit ourselves to a single temperature. Both temperature and pressure have been assumed to be constant, and we had there- fore to decide beforehand which of the two possible degrees of freedom we would assume. Pressure has a very marked influence on gases, but a very slight one on liquids and solids, and therefore the freedom of pressure would bring with it for liquids and solids no important change in the relations already given. On the other hand, the effect of temperature is present in a marked degree for all three states, and a much more complete representation is ob- tained when the temperature is varied. Representations of the ELEMENTS AND COMPOUNDS 189 total effect resulting from change of both pressure and tempera- ture, together with the change in composition, would require three variables. This means a diagram in three dimensions which is difficult of representation, although it is actually the most complete. We will therefore continue to represent composition along a hori- zontal line whose length is unity, and we will measure temperature in a direction perpendicular to this line. Each point in any of our previous diagrams is then transformed into a line and each line into a surface. As temperature is changed, any given point cor- responding to the appearance of a new phase does not remain in its original position along the axis of compositions, and the lines will therefore, in general, possess curvature. They will be con- tinuous when they represent continuous changes of the system, and discontinuous when they represent discontinuous changes. The surfaces which are bounded by lines of this sort are of two kinds, corresponding to two kinds of lines, single and double ones. Surfaces corresponding to one phase will be developed by the single lines, and surfaces corresponding to two phases by the double lines. Just as double lines are produced when neighbouring phases extend past one another, so these surfaces of two phases are seen to be produced by the superposition of two neighbouring surfaces each corresponding to a single phase. Horizontal lines drawn through such a diagram give phase dia- grams similar to those already explained, corresponding to a defi- nite temperature and to whatever pressure is assumed for the whole diagram. Vertical lines express a series of conditions belonging to a system of constant composition and constant pressure but varying temperature. They correspond therefore to our ordinary laboratory experiments in open vessels placed over a flame, since in this case the temperature changes while pressure and composition remain the same. At high temperatures all substances change into the gaseous state and at low temperatures into the solid. Our diagrams will therefore have the gaseous state, in general, in the upper part and 100 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the solid state in the lower part, with liquid conditions lying be- tween. Each line which separates the condition of a gas from that of a liquid is a boiling point curve, for it represents the tem- perature at which the corresponding systems boil. Each line which separates a solid region from a liquid one is a melting point curve, for it represents the temperature at which the liquid and solid phases can exist together. Finally, those comparatively rare lines which separate gaseous from solid substances, and which therefore represent the transition of a solid into a gaseous state, and vice versa, we will call sublimation curves, since sublimation has been defined as the vaporization of a solid without the appearance of a liquid phase. The melting point is only slightly affected by pressure, the boiling point and sublimation point are affected very strongly. It is therefore, in general, possible to make the vapori- zation point approach the melting point, and sometimes even to pass it by decreasing the pressure. At low pressures phenomena of sublimation will therefore be more common than at high pres- sures. Even at atmospheric pressure they are comparatively rare. 137. BOILING POINT CURVES. The general course of the boiling point curves for binary solutions has already been shown in Sec. 106. We shall therefore consider the three types with special regard to their possible phase diagrams at constant tem- perature, that is, their isothermal phase diagrams. A boiling point curve without a singular point is like all similar curves. It is a double line, one branch of which corresponds to the composition of the liquid, the other to that of the gas phase, as in Fig. 30. Between these two lines lies a region common to two phases, gas and liquid. The double line therefore divides the whole field into the gas region g above, the liquid region / below, and these two are superimposed between the double line to form the region of two phases gl. In this and in following dia- grams the regions will be indicated by these letters. If we draw horizontal lines at various levels through the diagram, the line marked 1 will be found to lie entirely in the gas region. ELEMENTS AND COMPOUNDS 191 On the other hand, line 2 cuts all three regions and gives us a phase diagram gl I. In the region / we find again the simple liquid diagram // /. In the case of a boiling point curve with a maximum such as Fig. 31, we find the gas line 1 above. Then at 2 we find the liquid between two gaseous regions with regions of two phases between. This is the case gg II. The line at 3 gives us the diagram gl y FIG. 30. and 4 is a simple liquid line. In the case of the boiling point curve with a minimum, as shown in Fig. 32, we find first of all a charac- teristic section 2 corresponding to gl I and another 3 correspond- ing to the diagram // 777. This exhausts all the cases in which gases appear with simple liquid phases. 138. Two LIQUID PHASES. The formation of liquid double phases is brought about by the superposition of two liquid solu- 192 FUNDAMENTAL PRINCIPLES OF CHEMISTRY tions, the one containing more A and the other more B. The region of two phases therefore becomes a nearly vertical band in the middle of the diagram. This band may end in a critical point at higher temperatures and occasionally at lower temperatures. Fig. 33 represents the first case. Above the band we have at 1 a continuous liquid line. At 2 we have the phase diagram // II. As the solubility becomes less because of lower temperature the band FIG. 31. extends itself to the boundaries at the ends, and we have at 3 the double line corresponding to the insoluble pair of liquids // II a. This exhausts the system made up of liquid phases, for if the band is closed below, the same set of phase diagrams is produced, reversed in their order. 139. ONE GAS PHASE AND Two LIQUID PHASES. Phase diagrams containing systems of this kind are produced when the ELEMENTS AND COMPOUNDS 103 FIG. 32. II 13 FIG. 33. 194 FUNDAMENTAL PRINCIPLES OF CHEMISTRY bands of the boiling point curves, or the regions of existence of two liquid phases, appear side by side at the same height, that is, at the same temperature. All the three forms of the boiling point curve are therefore to be combined with such a region of two liquids, and it makes no special difference whether these forms cut one another or not. The boiling point curve can be displaced FIG. 34. to a very large extent by a change in pressure, while the liquid line remains practically unchanged. It is therefore in our power to cause the two regions to superimpose or separate. The con- clusion is evident that those compositions which would give rise to contradictions if they crossed one another in the' diagram can- not be expected to actually occur, and they may therefore be ex- cluded in further considerations as physically impossible. ELEMENTS AND COMPOUNDS 195 First let us consider the combination of a rising boiling point curve with a region of two liquids, as in Fig. 34. Only the charac- teristic section is shown in the diagram, and this is one which is different from any previous diagram. The case gl II will be rec- ognised and all the other sections result in cases already examined ; these, therefore, need not be considered further. When a con- FIG. 35. vex boiling point curve is combined with a region of two liquids, as shown in Fig. 35, no new phase diagram results, and this holds whether the two regions cut one another or not; but the special case shown in Fig. 36 gives a new phase diagram // IV. A further possibility is shown in Fig. 37, and a form similar to this might be imagined. From previous considerations (Sec. 113), concerning 196 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the possible shape of interrupted boiling point curves, it will be seen that such a combination is not to be expected since a corre- sponding penetration is impossible. The case Fig. 38 is a possible one. The characteristic section is the same in both cases, as closer examination will show. 140. THE MELTING POINT CURVE. The general course of a regular melting point curve has already been explained in Sec. 117. It is applicable whenever the two substances are soluble in FIG. 36. all proportions in the liquid state, but not at all soluble in the solid state. The curve is made up of the two nearly straight branches running down toward the middle of the diagram and cutting each other at a lowest point at the eutectic temperature (see Fig. 39). In analogy with the boiling point curve we may expect this to be a double line, and if so, where is the other branch ? So far, all the lines we have drawn have been based on the composition of ELEMENTS AND COMPOUNDS 197 the liquid phase. Now we must also include the solid one. The solid phase at one end of the diagram consists of pure A , and at the other end of pure B. The other branch of the curve is therefore made up of the two vertical lines which bound the diagram. They run from the melting point of the pure substance in each case downward to the eu tec tic temperature. The left-hand verti- cal corresponds to the left portion of the melting point curve, and the right to the right portion. At the eutectic point both solid substances can exist in equilibrium with the molten mixture or the liquid solution. We have before us a diagram similar to the boiling point curve of Fig. 32, with one difference. Here one branch of the double line lies at the very edge of the diagram, and it is made up of two separate pieces. If horizontal (isothermal) lines are drawn through the diagram at various heights we obtain the following cases : at 1 the simple line for a liquid; at 2 the system ls\ at 3 sis; and at the bottom of the diagram, below the eutectic temperature, ss. As is evident, equilibrium with solid phases is indicated by the fact that the regions of two phases extend left and right to the edge of the dia- gram. Among liquids and gases variable solutions (regions of a single phase) generally appear at the edges of the diagram. There is no other type of melting point curve, and so the possible cases of equilibrium between solid and simple liquid phases are FIG. 37. 198 FUNDAMENTAL PRINCIPLES OF CHEMISTRY FIG. 38. FIG. 39. ELEMENTS AND COMPOUNDS 199 exhausted. More complicated cases in which two liquid phases are present will be taken up a little later. 141. THE SUBLIMATION CURVE. Solid substances do not usually form solutions with gases any more than with liquids, and we may therefore expect the sublimination curve for two solid substances to show the same peculiarities as those of the melting point curve. The relations are, in fact, still more simple than in the latter case, for the gas laws are always applicable. For each solid A there will be a temperature at which the vapour pressure will equal the pressure under which the experiment is made. This temperature we may call its boiling point. If some of B is added to A it will vaporize and assume a part of the pres- sure in the gaseous phase. The partial pressure of A will then be decreased and the temperature must be lowered if the total pressure is to remain the experimental pressure. The larger the content of B the lower the partial pressure of A will become, and this will only end when B is completely vaporized. Finally, a tempera- ture will be reached at which the sum of the vapour pressures of the two solids equals the experimental pressure. At this point both solids can exist in the presence of the gaseous solution of their vapours, and this is, moreover, the lowest temperature at which a vapour phase can appear in the system. This temperature is evidently analogous to the eutectic point, and the same reasoning holds when we begin with pure B. The representation of these relations must therefore exhibit a form precisely similar to the melting point curve. In Fig. 17 a and b are the boiling points of the two solids and e is the " eutectic boiling point." As in the previous case, the second branch of the curve is made up of the two vertical boundaries of the diagram. And in the same way we can obtain from Fig. 39 a corresponding set of phase diagrams : 1 is gg 7, 2 is gs, 3 is sgs, and 4 is ss, the gas line replacing the liquid line in each case. Even the peculiarity that the single phase regions extend to the edges of the diagrams at each side is also found here. 200 FUNDAMENTAL PRINCIPLES OF CHEMISTRY 142. MORE COMPLICATED CASES. We have now a general idea of the effect of the appearance of new phases on the systems of liquids and gases already considered. Solid phases always appear at the two ends of the diagram, coming in from outside. It will only be found necessary to run in solid phases at the two boundaries at right and left in the earlier diagrams in order to exhaust all the possibilities. Such diagrams can become very complex indeed when various phases are formed and intermingle at various temperatures, and for our purposes we shall not need to follow them further. For isothermal conditions the intermix- ture of phases can only lead to simplification of the diagrams already discussed, under the assumption that the regions remain separated. If the rules we have used are applied to various phase diagrams, it will be found that the symmetrical ones (those in which the two substances are in the same state) are precisely similar whether the solid appears at the right hand or at the left. If the two sub- stances are in different states, different diagrams result, and the two Is diagrams become four in number when another solid phase appears. If these combinations are examined, it is found that all the diagrams previously considered from another view-point appear again. This formal method of exhausting all possibilities by ar- ranging systems in various ways, examining them from different points of view, and then comparing the independent variables, is of great importance. It is, in fact, the only way to be sure that no possible groups have been overlooked. 143. THE APPEARANCE OF CHEMICAL COMPOUNDS. After these preliminaries we are in a position to consider an important question. When two pure substances are brought together, will a chemical compound be formed beside the possible set of solutions which may be produced from them ? The characteristic of a chem- ical compound will be that when A and B are brought together in all proportions phase diagrams will be produced which are ELEMENTS AND COMPOUNDS 201 different from any of those which describe mere solutions. Such diagrams are of frequent occurrence. They therefore demand a new discussion of the phenomena involved, and the assumption that a new substance AB has resulted from the interaction of the two substances A and B will be found an important aid in the description and representation of these new phenomena. After experimental determination of the facts we might prove from the structure of new diagrams that they lead to the assump- tion of a new substance. We will however assume it proven that such an assumption is practically applicable. We will examine the consequences which can be drawn from this assumption. This is not only the more convenient process of the two, it also corre- sponds more nearly to the historical development of the matter; for long before the development of the phase rule it had been shown by experiments of another sort, especially by the separation of substances in pure form, that new substances do appear under these circumstances. In the course of discussion it will be shown that this process can be carried out and described by means of phase diagrams, if this is done systematically. For the first part of our discussion we shall assume constant pressure and constant temperature for the sake of clearness, but later all such limitations must be set aside. We shall proceed as follows : Let us assume that two substances, A and B, are present in definite conditions of state. There are six possible cases, and these are gg, II, ss, gl, gs, and Is. Any one of these pairs can give rise to a new gaseous, liquid, or solid sub- stance, so that eighteen cases are possible. Each pair of sub- stances in a definite state can also give rise to from two to ten different solutions, and all of these combinations must be com- bined with each other. The number of phase diagrams to be in- vestigated is therefore a large one. There are 366 such diagrams in all. All of these cases will not be considered, for it is easy to draw any one of them after the general principle has been made plain. We shall content ourselves with answering the following 202 FUNDAMENTAL PRINCIPLES OF CHEMISTRY question : Are the phase diagrams which result from the assump- tion of the formation of a new substance AB different from the ordinary solution diagrams, or are they similar to them; and if they are similar, to what extent is this the case ? The answer to this question will enable us to conclude from an examination of a phase diagram whether or not a new substance AB has been formed. This question has already been answered as far as its general outlines are concerned. In many cases similar diagrams result from the formation of a compound and from the formation of a solution. The formation of a new substance is therefore neither proven nor excluded. In other cases new phase diagrams will be found, and when this is the case it may be concluded that a new substance has been formed. There are no phase diagrams which belong only to solutions and which do not belong to compounds. The examination of the phase diagram can therefore never exclude the possibility that a new substance has been formed. The Case ggg. Let us first of all assume that the two original substances A and B are gaseous, and that they can form a com- pound AB which may be either gaseous, liquid, or solid. The three possibilities we shall express by the symbols ggg, gig, and gsg, the newly formed state being placed between those already existent. The corresponding phase diagrams will be obtained by combining the two pairs. The case gsg is made up of two gs phase diagrams, the second drawn in the reverse direction. In the diagrams which we have previously considered the " higher" state has always been placed at the left hand, so that the order has been gls. If the succession of states is reversed, right and left must also be reversed in the phase diagram.. In the case ggg we find a combination of two gg diagrams. According to Fig. 24, which is repeated for the sake of clearness as Fig. 40, three different gg diagrams are possible, and these must all be combined in every possible combination. This results in six cases, I I, I II, I III, II II, II III, and III III. These six ELEMENTS AND COMPOUNDS 203 diagrams are all shown in Fig. 41, and here the vertical stroke in the middle of the diagram shows the proportions of A and B in the new compound AB. This is only mentioned for the sake of a FIG. 40. clearness, for of course we do not know as yet whether the sub- stance AB has been produced or not, and this can only be deter- mined by investigation. Comparison of the diagrams in Fig. 41 with those of Fig. 40 will show that all the cases of Fig. 40 are present in Fig. 41. They EL --- V T -1 ' -i-l .--. VL r . FIG. 41. result from the combination of the simple solution line I of Fig. 40 with 7, II, or 777. It is only the order of the various cases and not the length of a region which expresses anything definite in our 204 FUNDAMENTAL PRINCIPLES OF CHEMISTRY diagrams, and 7, II, and III of Fig. 41 are therefore identical with I, II, and 777 of Fig. 40 or Fig. 24. The diagrams IV, V, and VI of Fig. 41 are new. We may conclude as follows : If new phase diagrams of the form ggg IV, V, and VI are found for two gaseous substances A and B, a new substance AB has been produced. If diagrams similar to ggg I, II, and 777 appear, they may repre- sent either chemical combination or mere solution. The Case gig. If a liquid is formed from two gases the corre- sponding phase diagrams result from an exhaustive combination of the gl diagram with itself, the second diagram being plotted in the reverse direction corresponding to Ig. According to Fig. 27 there are only two gl cases, and these can give three combinations, 1 1, I II, and 77 77. Corresponding diagrams are shown in Fig. H T JJL r 1 FIG. 42. 42. The first two graphs are exactly the same as gg II and 777, so that in these cases no proof is to be had of the formation of a new substance. 777 is, however, new, and the observation of such a case is sufficient ground for the conclusion that a new substance has been formed. The Case gsg. By combination of the five gs diagrams fifteen possible diagrams may result, representing a solid compound pro- duced from two gases. They all differ from previous diagrams in having a region of solid phase in the middle. This can never be the case for a mere solution, for among solutions solid phases can only appear at the two ends of the diagram. Every addition results in lowering the melting point of the pure substance, that is, in the formation of a liquid phase. These diagrams are further ELEMENTS AND COMPOUNDS 205 FIG. 43. 206 FUNDAMENTAL PRINCIPLES OF CHEMISTRY characterized by the fact that at the point indicating the relation in which A and B combine to form AB, a change of phase occurs immediately beside the solid phase AB. All possible orders of change are found, from gas to gas, from gas to liquid, and from liquid to liquid. This change of phase takes place in such a way that the proportional content of the changing phase decreases towards zero as the point representing the composition of the com- pound is approached. At this point only the solid phase is present, and as we pass away from it the new phase appears at first in very small amount. Similar conditions will appear later in all cases where the prod- uct of the combination of A and B is a solid. In these cases we can therefore recognise with certainty the formation of a .compound. Not only that, the possibility of determining the composition by weight of this compound (that is, the ratio of A to B in it) is also given. The Case Igl. Here we have to consider the same diagrams as in the case gig, that is, two gl diagrams. In this case they must however be combined in the reverse sense. The gas side of each must be turned toward the other, and the liquid side toward the ends of the diagrams. I n , , , i - ^_. FIG. 44. Of the three cases shown in Fig. 44 the first two will be found in agreement with ///// and IV. They can therefore not serve to indicate a chemical process. Ill is a new case, and it can there- fore serve as basis for the conclusion that a new substance has been formed. ELEMENTS AND COMPOUNDS 207 The Case III. Ten combinations can be made of four // dia- grams, and they are given in Fig. 45. Five of them 7, II, HI, IV, and VI correspond to four of the // diagrams, and IV and VI are alike. Five others are new, and lead to the conclusion that new compounds are formed. VI. I 1-..-. FIG. 45. It will be noticed that II IV, which is unsymmetrical, and which ends in a liquid phase at each end, can be combined with the other diagrams in two different ways, by taking it either forward or back- ward. If this peculiarity is taken into consideration three more diagrams will result. These diagrams have not been added, for 208 FUNDAMENTAL PRINCIPLES OF CHEMISTRY they would merely add themselves to other diagrams characteristic of the formation of compounds, and would therefore give no reason for question. The Case IsL The six Is cases permit of twenty-one combina- tions among themselves, and this is the number of diagrams neces- sary to represent the cases which may arise when two liquids combine to form a solid. It is unnecessary to discuss all these diagrams, for in each of these cases a solid phase appears in the middle and none at the ends of the diagrams. Such diagrams are excluded for solutions, and any case of this kind leads to the con- clusion that a new substance has been formed. The Case sqs. This case also is made up of combinations of 7 A five gs diagrams with each other, giving fifteen individual cases in all. It differs from the case gsg in an important particular, for here we no longer turn the ends with the solid phases toward each other, but those with gaseous phases. The result is that we find repetition of several diagrams which already appeared for solutions under the case ss. It is therefore necessary to present a com- plete series of diagrams for this case, and these are shown in Fig. 46. If this figure is compared with Fig. 26 it will be found that all those solution diagrams in which gases appear between the solid phases are represented here. These are II, IX, X, III, IV, VII, and VIII, and these correspond to I -VI I of Fig. 26. Diagrams VIII to XV are new, and can be used as an indication of the presence of a new compound. This large number of cases does not correspond to any particular experimental fact of value. The great majority of chemical pro- cesses take place in such way that liquids or solids are formed from gases, or solids are formed from liquids, and reactions in the inverse sense are rare. The formation of a gas from solid ma- terials is the rarest of all. Processes of this sort are most usual at high temperatures. The Case sis. We found six Is diagrams and a complete set ELEMENTS AND COMPOUNDS 210 FUNDAMENTAL PRINCIPLES OF CHEMISTRY of combinations of these results in a total of twenty-one cases. For the case Isl we found it unnecessary to discuss the individual cases, m JV VI VOL IX FIG. 47. and it was merely necessary to say that agreement with the solution diagrams was impossible. In this case, where the solid phases ELEMENTS AND COMPOUNDS 211 appear at the edges of the diagram and not in the middle, agree- ment with some of the solution cases is certain to be found. Even in this case, however, it is not necessary to examine all the cases indicated. We have only to look for agreement with the ss diagrams, and the following reasoning is sufficient. In Fig. 26 the greatest number of two phase regions which can occur in a diagram is five (in IV). Out of all the possible diagrams for sis we therefore need to examine only those in which not more than five double lines indicating two phase regions occur. This limits our investigation to thirteen diagrams, and these are shown in Fig. 47. Only two of these diagrams are new, VII and XI; the others will all be found under ss. It will also be noticed that two dia- grams occur twice in the same form, IV and VIII, and VI and IX. They differ only in the position of the point corresponding to the formation of a new compound. It will be seen from this that dia- grams like these are not of assistance in deciding whether a com- pound has been formed or not. Not only this ; even when the fact of formation of a compound has been found in other ways, such diagrams do not even permit of the determination of the region in which the new substance would appear. In all the earlier cases the diagrams could at least assist in this latter way. The Case sss. A complete set of combinations of the ten ss cases with each other would result in fifty-five diagrams. In every case, however, a solid phase appears in the middle of each diagram, and this means that no solution diagram whatever can be similar to any one of them. Even when no liquid or gaseous phase appears in the diagram, so that through the whole set of proportions of A to B only solid phases are present, the diagram corresponding to the appearance of a solid compound AB is different from the one which represents a mere solid mixture of A and B. Fig. 48 shows the corresponding phase diagrams. II is the case where a solid compound appears ; I represents a mere mixture. The shift in the heavy line in II expresses the fact that at this point one solid phase 212 FUNDAMENTAL PRINCIPLES OF CHEMISTRY disappears and another takes its place. If A and B were mixed together in the proportions represented by this point a single solid phase would result, the compound AB. For any other proportions FIG. 48. mixtures of AB with A or B will occur. All this is evidently wholly different from the case where no compound appears. In this case no finite proportion of the two substances could be found cor- responding to the presence of only one solid phase. The Case ggl. This combination is the first of the second group of phase diagrams in which a new substance is formed from two constituents in different states. In this case therefore it is no longer the individual cases of a single group which are to be combined with each other, but cases from two groups. The number of combinations will therefore no longer be found with the aid of the series 1 +2 + 3 + . . . +n, where n is the number of cases in the group. The number of combinations will be given by the product mn, where m and n are the number of cases in the two groups in question. In the case ggl groups gg and gl take part. The number of cases is therefore 3x2 = 6, and they are shown in Fig. 49. Com- parison with the solution diagrams gl will show that these appear again (7 and 77), but the four other diagrams are new. The Case gll. It is unnecessary to present the ten diagrams corresponding to this case in order to understand clearly the result of these combinations. The addition of the continuous liquid line of Fig. 25 7 to the two gl diagrams leaves the latter unchanged, and these diagrams will be found to describe cases in which com- bination occurs. The eight other cases are all more complicated and afford proof of the appearance of a compound. ELEMENTS AND COMPOUNDS 213 The Case gsl. In every case when a compound is a solid new diagrams appear. This case would include in all 5 X 6 = 30 new diagrams, which it is unnecessary to present. The Case ggs. The addition of the continuous gas line gg I to the five gs diagrams gives five cases which agree formally with m -ra I- -i VZ Tzzza , , i -T > FIG. 49. the solution diagrams gs, and are therefore of no value as criteria. In the same way the addition of gs I to the three gg cases gives diagrams which are all repetitions. Seven of the fifteen diagrams in this case are similar to corresponding solution diagrams. The eight others are new and characteristic of chemical combination. The Case gls. Four of the twelve possible cases are like solu- tion diagrams gs, II to V. The solution diagram gs I is not re- peated in this case, since it contains no liquid phase. The Case gss. The fifteen different possible cases contain no case which is like a solution diagram, and this is because the solid phase occurs in the middle of the diagram. The Case Igs. Four of the ten cases are like solutions Is, and these are all the cases in which a gas phase can appear between 214 FUNDAMENTAL PRINCIPLES OF CHEMISTRY a solid and a liquid in a solution diagram. The six other cases are new and characteristic of chemical combination. The Case Us. Eleven of the twenty-four diagrams which result by combining // with Is correspond to solution dia- grams, and many repetitions are found. The other diagrams are new. The Case Iss. The sixty diagrams of this group are new, as is always the case when the compound is a solid. 144. SUMMARY. A general review of the possible cases of a binary chemical combination shows that all the phase diagrams corresponding to a mere mutual solution of the substances involved can also appear when chemical combination has taken place be- tween the two substances. The only exception to this case will be found in the fact that two solids can form a mixture without ex- erting any influence on each other. The phase diagram of a solution contains no answer to the question whether mere solution or chemi- cal combination has taken place. There are, however, a large number of more complex diagrams which do afford a criterion of the appearance of a chemical compound. The clearest cases of all are those in which solid substances are formed. In this case the phase diagram is always different from a solution diagram, and in this case it is always possible to determine the composition of the new substance in terms of its constituents. It is evident from this that the question whether a new substance has been formed or not can best be answered by investigating the matter under such experimental conditions as will probably yield a solid phase. It is usually best to have recourse to high temperatures to bring about chemical processes, and this is principally because reaction veloci- ties are increased in this way. For the isolation and purification of substances low temperatures will lead much more certainly and rapidly to the desired end. This statement must be made with a reservation that we do not pass out of the region of stability of the new substance when the temperature is lowered. The region of stability of most substances is practically unlimited in the direction ELEMENTS AND COMPOUNDS 215 of lower temperature, so that the reservation just made is really not so important. The certainty to be derived from those cases where solid phases appear depends upon the fact that no solutions are formed among solids. At any rate we have assumed this to be the case. It is, of course, possible that in the other states the solubility may be so small as to be unmeasurable, and in this case a result precisely similar to that found for solids is to be expected. The correspond- ing phase diagrams will be changed, and the regions corresponding to solutions of a single phase, which we have in general assumed to be of finite range, will all disappear. In their place regions of two phases will extend to the point corresponding to the proportions of the compound formed, and at this point a sudden shift will take place, one of the phases disappearing and another taking its place. To make this clear let us take a concrete example, the diagram ggl II on page 213. Here we have assumed that both the gas A and the liquid B have a measurable solubility in the new-formed liquid. If we assume instead that both are practically insoluble in AB, the diagram changes into II of Fig. 50, the two two-phase m FIG. 50. regions approaching each other until they meet at the point cor- responding to the compound. It is evident that in such a case the proportions of combination may be deduced directly from a study of the phases involved. If practical insolubility occurs for one constituent, the corresponding region of two phases moves up to the point representing the proportions of combination. In such a case (Fig. 50 ///) a knowledge of the solubility relations is neces- 216 FUNDAMENTAL PRINCIPLES OF CHEMISTRY sary if any evidence on this point is to be obtained from the phase diagram. Such knowledge of solubility cannot, in general, be assumed, and without it the phase diagram remains just as indeter- minate as in the general case. 145. THE EFFECT OF TEMPERATURE. In Sec. 126 we dis- cussed the effect of temperature on the phase diagrams represent- ing simple solution, and we have now to answer the more general question as to its effect in the more complex case of phase diagrams in which chemical combination takes place. It may be said in general that these diagrams can be considered combinations of the two individual diagrams, as in the case of the isothermals. It would be difficult to exhaust all the possibilities in this way. It is also unnecessary, for the whole interest of the question is confined to the peculiarities of the middle part of the diagram, where the compound appears. In this middle part there will be found a point corresponding to the appearance of the compound as a pure substance. This point will lie where A and B are chosen in such proportions that the compound AB is formed from them without any remainder or excess. On both sides of this point either A or B appears in excess. When a gas or a liquid occupies the centre of the diagram a con- tinuous series of solutions results. When AB is a solid we find a pure solid substance at this point, and on either side of it may be found new phases of any state. From this point of view the three kinds of curves which need to be considered offer no difficulties. Two boiling point curves may meet at the point AB. Two melting point curves or two sublima- tion curves, or finally one melting point and one sublimation curve, may also meet at this point. The last two types cannot meet a boiling point curve, for the solid phase lies at both sides of the point AB, if it touches this point at all. When two boiling point curves meet, diagrams like those in Fig. 51 result. They are characterized by the fact that the liquid at the point AB behaves like a pure substance. This is because two ELEMENTS AND COMPOUNDS 217 limits of the two-phase regions lie at this point, and the vapour has the same composition as the liquid. The two regions and the lines which bound them meet at the point AB at a finite angle. There is always a kink at this point, and the curves can never be contin- uous. If a series of liquids, chosen from this middle region (or in general from any region of one phase which does not lie at the FIG. 51. end of the diagram), are examined by boiling them, it is possible to find out whether a point AB corresponding to a compound exists in this region or not, and, if such a point exists, what its composition is. The proof is of course easiest when the point AB represents at the same time a singular value, as in Fig. 51 // and 777. Even in case / conditions may be such that no doubt will remain as to the presence of an angle between the curves. Under all circumstances the behaviour of these liquids during distillation and the proof of a constant boiling point in the one-sided boiling curves is sufficient evidence of the presence of a compound. Comparison of Fig. 51 with the boiling point curves in Figs. 9 and 11 for simple solutions shows their external similarity. The study of isothermal phase diagrams in such cases is not always sufficient to determine a decision. The cases II and 777 are specially similar, for the liquids corresponding to singular points on the boiling point curves are hylotropic, and can therefore be distilled at constant temperature. The distinction between solu- tion and compound is therefore to be sought in the fact that the boiling point curve for the solution is continuous, while that for the compound has a kink in it. Another difference depends on 218 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the fact that a singular point belonging to a compound is always independent of the temperature, even though this be varied within wide limits by changing the pressure. Singular points of solutions change their position (composition) with a change in temperature, as will be explained more fully later. It will be found when we come to this point that the composition A : B of a compound is not affected by temperature as long as we do not leave the region of stability of the substance in question. In the cases just discussed we found that the isothermal phase diagrams often left us without any answer to the question : is this a solution or is it a compound ? If, however, the investiga- tion is carried through a whole series of temperatures (and of pressures also when this is necessary) a definite answer can always be found. Even this is only generally true when A and B unite completely to form the compound AB. If this condition is not fulfilled, if the combination is not complete and a case of homo- geneous equilibrium between the compound and its constituents results, this test also must fail. In place of the pure substance a solution of A, B, and AB is formed at the point AB. When this is distilled it acts like a solu- tion, and the kink at AB is re- placed by a rounded curve. The matter is simpler when AB is a solid. The melting point curve is then made up by connecting two melting point curves of the typical form shown in Fig. 17. A curve like that of Fig. 52 results, a zigzag, with a highest point corresponding to the melting point of the pure substance, and a lowest singular point corresponding to the eutectic of the neighbouring sub- stances. Attention should be called to the fact that even when several compounds appear between A and B, the only effect is to FIG. 52. ELEMENTS AND COMPOUNDS 219 make the zigzag line more complicated. The number of upper points which appears indicates the number of compounds between A and B. A conclusion previously found for the case of chemical equilibrium may be repeated here, but it can only be applied to the liquid phase (homogeneous equilibrium between solids is excluded by defini- tion). The point is this: the compound AB can exist in solid form, but when it melts we have a solution of A, AB, and B. The result is that in place of the sharp angle of Fig. 52 we find a rounded curve and a rela- tion to the ideal line which is shown in Fig. 53. The sublimation curves can be treated in a precisely similar way, and they will be found to agree in all points with the typical melt- ing point curves. This covers the further case in which a melting point curve ends on one side at AB and a sublimation curve at the other. In any of these cases the isothermal phase diagram must decide the question of the existence and composition of a compound. The temperature diagram can only confirm the matter. Never- theless it will be found that the investigation of temperature curves is one of the most efficient means of deciding such a question. 146. MORE GENERAL CONDITIONS. We shall now lay aside our assumption that phase diagrams are to be used exclusively in deciding whether or not a new compound will appear. And we shall also lay aside the assumption that temperature and pres- sure shall remain unaltered. Our previous discussion has given us one advantage : we have settled all the cases in which the phase diagram alone can lead us to a definite conclusion, and we need therefore only discuss those cases in which the phase diagram of FIG. 53. 220 FUNDAMENTAL PRINCIPLES OF CHEMISTRY a true chemical process is similar to that of a mere solution. We must now find out what other means can be applied to the solu- tion of the same problem, and also how we can decide about tht proportion in which A and B will combine to form the new com- pound substance AB. A similar discussion will be applicable in those cases where the phase diagram indicates the existence of a new compound, but says nothing about its composition. 147. Two GASES. The general and most usual condition in the case of two gases is the formation of a solution, no matter what the proportions of the gases may be. This cannot be distinguished from the case of Sec. 132, the formation of a gaseous compound, if we assume that all the substances which take part are so far removed from their critical point that the appearance of a liquid phase is excluded. We might try to decide whether or not a gaseous compound AB has been produced by lowering the temperature until the region of liquid and solid phases is reached. This would not exclude the possibility that the compound might first be formed at this lower temperature. In other words, the region of stability of the compound may lie below the temperature of our experi- ment. We must see whether it is not possible to decide the ques- tion of the formation of a new substance directly in the gaseous system, without a change of temperature or pressure, by the aid of some other characteristic. As a matter of fact it is possible to decide this question in every case. The question can be decided in the case of gases with the aid of the law of Sec. 83. According to this law all the properties of a gaseous solution can be determined by properly taking the sum of the properties of its constituents. Whenever measurement shows that this law does not hold true, the formation of a new constituent must be concluded. Let us investigate the value of any property first in the pure constituent A, then in solutions made up of 0.9 A and 0.1 B, of 0.8 A and 0.2 5, etc., and finally of pure B. We will now lay off ELEMENTS AND COMPOUNDS 221 the measured values along lines drawn perpendicular to a hori- zontal line divided into ten equal parts. The law of gas solutions may now be expressed by saying that the individual points repre- senting the values of the property in the different solutions all lie on a straight line joining the points representing the value of the property in the free constituents. It must be kept in mind that such specific properties as are based upon the unit of weight must be determined in solutions whose composition is determined by weight, and in case the property is based upon the unit of volume the com- position of the various solutions must be determined by volume. Volume itself affords a simple example when pressure and tem- perature are kept constant. If we investigate the volume of dif- ferent solutions of A and B, made up as described above, the volume of the solutions will be found equal to the sum of the partial volumes a FIG. 54. of the constituents. If a is the volume of A, and if tenths of A are replaced one after the other by an equal volume of B, the total volume remains unchanged in case no new substance appears. All the volume points lie at an equal height, and the result is a diagram like that of Fig. 54. 222 FUNDAMENTAL PRINCIPLES OF CHEMISTRY If a change in the total volume takes place, so that the hori- zontal line is replaced by any other line, a new substance has been produced. The converse of this does not always hold. There are cases where the total volume remains unchanged even though a new substance is formed. In these cases, however, deviations from the solution law for gases appear, and in general we will find change in all the specific properties which are capable of change.* If none of the properties shows any deviation from the simple summation law, no new substance can have been produced. In cases not so simple as the one just discussed we shall have in general the following conditions: a represents the value of the property in pure A, and b the value in pure B. In all solutions of A and B this property will exhibit the values represented by the points on the line ab in Fig. 55. It will of course occur that the property will have zero value in one of the gases, as, for example, when one of the gases is coloured and the other colourless. In this case a or b will lie on the line of abscissas, as represented by the lower line in Fig. 55. The shape which the line ab assumes in case a pure new com- pound is formed may be found from a consideration of the fact that the new gaseous substance will form solutions with the original gases. The gaseous system will then be made up of the new gas with an excess of A or B, and it will therefore have a correspond- ing set of properties. Let us begin with pure A and add to this a small amount of B. This will react with A, changing com- pletely into the new substance, which we will call AB. AB will form a solution with the unchanged part of A, and our familiar laws can all be applied to this system. If more B be added the same process takes place, but the fraction AB becomes larger * We find here an exception from the general law that when a change takes place in a substance all properties show a change in value at the same time* We know already that mass and weight remain unchanged under all circum- stances, even when the most far-reaching chemical changes have taken place. In the special case before us we see that volume also shows this peculiarity. ELEMENTS AND COMPOUNDS 223 compared to A. Continuing in the same way we must finally arrive at a point where all of A has combined with B and where no excess of B is present. The gaseous system then consists of a pure new substance AB. Further additions of B result in solu- tions of AB and B, and the end of the series is pure B. It will be evident that the entire diagram which represents what has taken place is made up of two parts, each of which can be FIG. 55. represented by a straight line like that of Fig. 55. These two straight lines cut each other at a definite angle acb, Fig. 56. If acb were a straight line, this property of the gas AB would indicate a mere solution of the two gases, and this we have excluded in this case. Whether the two straight lines are inclined to each other in this sense or in the opposite, as shown in Fig. 57, depends upon the special values of the property under investigation. Experi- mental investigation usually shows figures like those just described. Occasionally curved lines take the place of the straight ones, giv- ing a diagram like that of Fig. 56, with the sharp corner where 224 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the two lines meet rounded off into a smooth curve. Cases of this sort show a varying behaviour which is of importance when constit- uents are to be separated, and when they appear we must conclude that the combination of A and B to AB is incomplete. Uncom- bined fractions of A and B can exist together with the compound AB, all forming a solution together. We shall not take up the discussion of these more difficult cases at this point. For the 1 1 H-H 1 I FIG. 56. present we will confine ourselves expressly to cases where th combination of A and B in the proper proportions is practically complete. 148. ENERGY CONTENT. Every substance has an energy content, and this is a definite value for every gas. We have no way of determining its total value, for no substance exists which is quite free from energy, but we can measure differences in energy content corresponding to given differences in the condition of a system. It is almost always possible to conduct an experiment in such a way that this energy difference appears as heat, so that measurement of the quantity of heat which enters or leaves the system gives us the desired difference directly. The total energy of a gas solution is the sum of the partial energies of its constit- ELEMENTS AND COMPOUNDS 225 uents. We may conclude from this that a mere change in volume of a gas, without the performance of external work, results in no change in its total energy. This means that when gases which form solutions and not compounds with one another are mixed together, no heat exchange results, provided pressure and tem- perature were the same when the gases were mixed. Conversely, H r FIG. 57. the appearance of a measurable heat exchange when two gases are mixed is a sure sign that a chemical process in the narrower sense has taken place ; that is, a new substance has been formed. The diagrammatic representation of this process is therefore similar to that of the previously described general one. In Fig. 56, a represents the energy of the gas A, and b that of B. Then any solution of A and B will possess an energy content which can be represented by a corresponding point on the straight line ab. If a compound AB is formed we will have two straight lines ac and cb meeting each other at an angle. In the majority of cases this angle lies below the straight line ab in Fig. 56, and this expresses the fact that the majority of reactions between gases result in the 15 226 FUNDAMENTAL PRINCIPLES OF CHEMISTRY giving out of energy. The immediate result of this is an increase in the temperature of the system, and in order to restore the orig- inal temperature a corresponding amount of heat must be with- drawn. If we merely wish to prove the fact of the heat exchange, and not to measure it exactly, it is only necessary to observe the temperature of the gas after mixing A and B. If the temperature is the same as before mixture we have a solution. If it has changed, a compound has been formed. 149. THE LAW OF CONSTANT PROPORTIONS. It is evident from the diagram representing the process by which the compound AB is formed from the substances A and B, that the combination of A and B takes place in a definite proportion by volume, and therefore in a definite proportion by weight. This holds at least for 'this individual experiment. We may conclude that the rela- tion thus indicated by one experiment will hold for all subsequent experiments under the same conditions. Our assumption was that A and B are pure substances, meaning by this that they were substances with perfectly definite specific pfoperties. The same assumption is true of the compound AB. Properties are functions of composition, and therefore constancy in the properties of AB corresponds to constancy in the proportion in which A and B combine to form AB. The question then arises whether this proportion will remain the same at other temperatures and pressures. This question we can answer in the affirmative if we confine ourselves to a certain range of conditions, as will be evident from what follows. A pure substance retains its properties within a finite range of pressures and temperatmes. In other words, there are limits of temperature and pressure within which a pure substance does not assume the properties of a solution. The substance AB will there- fore behave like a pure substance within a definite region. This means that any endeavour to break it up by ordinary methods of phase separation will show it to be hylotropic, and that it will pass as a whole into other states or phases. This is merely another ELEMENTS AND COMPOUNDS 227 way of saying that within this region the substance is formed from A and B in constant proportions, for if the proportion were variable with temperature, so that, for example, at higher temperature less A and more B would combine, we could form AB at this tempera- ture, and then cool it down in its pure condition to the original temperature. If it took on its original composition at the lower temperature, a corresponding amount of uncombined B must separate and we would have a solution. This contradicts the as- sumption that AB is a pure substance, one which retains its character regardless of change in temperature. The conclusion is that AB must have a constant composition at all temperatures and pressures within its region of stability. This law is called the law of constant proportions or the law of constant relations. We have proven it for gases, and we have shown that the concept of a pure substance contains the assump- tion that its composition remains unchanged within its region of stability. The reasoning is the same when pure substances in liquid or solid form are considered instead of gases, and the proof is a general one. In other words, since nothing is said of the state of the substance in our assumptions and conclusions, the proof is independent of state and therefore holds for all the states. The general expression is therefore: whenever a compound pure sub- stance AB is produced from two pure substances A and B, the proportion by weight of A and B which is necessary to form AB is constant within the common range of stability of the three substances. The cases represented in 77 and ///, Fig. 40, remain to be con- sidered. To decide in these cases whether we have to do with a solution or a gaseous compound we need only apply what we have just learned in the middle gaseous region where the compound will appear if one is formed. If this test gives a positive or a negative result, the general question is answered in the same sense. Any similar cases which may appear later can be answered in the same way. It will, in general, be sufficient to investigate the simplest 228 FUNDAMENTAL PRINCIPLES OF CHEMISTRY case, and its application to any special case will be immediately evident. 150. Two LIQUIDS. According to what we have just said, the statement of the simplest case is sufficient for the explanation of doubtful cases where liquids are in question. The simplest case is the one in which only a single liquid phase can exist, what- ever the relation in which A and B are mixed. In other words, whatever compound may be formed is soluble in all proportions in both A and B. The simple laws of gaseous solutions do not hold for liquids, and for this reason the criterion we made use of for gases, deviation from the simple gas law, is no longer of value. This means that the properties of liquid solutions can no longer be expressed in a diagram by straight lines connecting the values of the properties of the constituents. Their place will be taken by more or less curved lines. In one important point we will find agreement with the simpler case. Continuous variation in the proportion of A and B leads to a definite value at which neither A nor B is present in excess, and at this point the whole liquid consists of the pure substance AB. If therefore we investigate a sufficient number of systems lying near together and containing A and B in varying proportions, we will find them, in general, behaving like solutions when they are distilled, frozen, or allowed to crystallize. The system which con- tains the two constituents in the relation of their combining weights will be the only one showing the properties of a pure substance. It will be a matter of chance if we find among the various mixtures one which corresponds to the ratio of the combining weights. But those solutions which have composition most nearly corresponding to this ratio will contain a larger proportion of the pure substance AB than those lying further away, and in this sense the behaviour of the solution approaches that of the pure substance. The tem- perature at which the change into another state takes place remains within narrower and narrower limits as the proportions approach ELEMENTS AND COMPOUNDS 229 that of the pure substance AB. The investigation can therefore be begun on mixtures lying far apart, and narrower limits of com- position are afterwards to be chosen between those mixtures which show the most constant boiling or freezing points, until the pro- portion is found which corresponds to a hylotropic transformation. This general method presupposes that the limit of stability of the substances under investigation is not exceeded in either direc- tion by the temperature differences maintained during distillation or freezing. The question whether or not the decision can be reached under constant conditions is therefore of theoretical im- portance, and the answer to this question is an affirmative one. At the point corresponding to the ratio of the combining weights two wholly different liquids are present in contact with each other. We should therefore not expect the properties of the liquids to show continuous change as we pass through this point. If we plot, as in Fig. 57, the value of any property volume, for example as function of the composition with respect to A and B, the line between A and the pure compound AB will not in this case be straight, nor will the line between AB and B. These two lines will however be continuous over their whole course. They will cut each other at a finite angle, at a point ab, whatever their course may have been on either side of this point. The nature of the substances A and B and the nature of the properties investigated will together determine what this angle is. If in any case the angle is so small that it cannot be recognised with certainty, we may turn to the investigation of some other property with the hope of finding an angle great enough to place the proof of its existence beyond the possible errors of experiment. The problem is therefore, in general, possible of solution. The general form of a diagram which is to indicate the formation of a chemical compound from liquid constituents which form a solution with one another will be like acb of Fig. 56, properties being plotted against composition, as in this diagram. In the present case more or less curved lines take the place of the straight 230 FUNDAMENTAL PRINCIPLES OF CHEMISTRY lines of Fig. 56 between the points representing the properties of the pure substances (the constituents) and the compound. A very large number of curve-forms result, and some of these are FIG. 58. shown in Fig. 58. To the forms shown here we must add also their opposites, those curving upwards instead of downwards. Conditions are most favourable for the investigation when the property of the compound lies beyond any value which it has in the constituents. Under these circumstances we will find a maxi- mum or minimum value for the property in question at a point corresponding to the composition of the compound. This charac- ELEMENTS AND COMPOUNDS 231 teristic is more and more evident the greater the difference between the average value for the constituents and the actual value of the property in the compound. This will be immediately evident from a consideration of Fig. 59. If the difference just mentioned is FIG. 59. slight, the curvature of the lines may be such that a maximum or minimum appears at a point near, but not exactly that correspond- ing to the proportions of the compound, as shown in Fig. 60. FIG. 60. This reasoning is true only under the assumption that the com- pound AB forms completely when its constituents are brought together in the proper proportion. We have already found cases 232 FUNDAMENTAL PRINCIPLES OF CHEMISTRY among gases where curved lines took the place of straight ones and rounded corners replaced sharp angles. It has already been shown that the explanation of these cases lies in the fact that the constitu- ents do not combine completely to form a compound, even when they are present in the proper proportion. A so-called homogene- ous equilibrium exists in these cases between the three substances, constituents A and B and compound AB, which depends upon pressure, temperature, and the proportion in which the constituents are present. The same result can occur between liquid solutions which form a compound. It is precisely in these cases, where the FIG. 61. properties of the compound are not very different from the average value of the properties of the constituents, that such incomplete reactions are most usual. Such cases are doubly indefinite, and the problems involved are in many cases still beyond our present knowledge. It has often been assumed that when the value of the property passes through a maximum or minimum, as a series of solutions in all proportions is examined, the point so indicated determines a chemical compound. It will be evident from Fig. 61 that when the property line is not straight a maximum or minimum ELEMENTS AND COMPOUNDS 233 must appear in every case where the values of the property are the same for A and B, and that such a maximum or minimum becomes more and more possible as the difference in the value of the prop- erty for A and B becomes less. The position of a chemical com- FIG. 62. pound can be determined much more certainly by finding the maximum deviation of the property from the average value of the two constituents, as shown in Fig. 62. Even this method cannot at present be applied with certainty. 151. Two SOLIDS. The question just considered has no appli- cation to solids, for here a phase change takes places generally at the point where the proportion of the constituents corresponds to the value of the constant proportion of a newly formed compound. 152. ANALYTICAL METHODS. The following question will now be considered: How can we determine with certainty the fact that a pure substance has exceeded its region of stability? The consequence of such a change will be the transformation of the substance in question into a solution or a mixture. Among gases we have only the first case to consider, since they do not form mixtures, but among solids the second case is typical. Either case may apply to liquids. The limit of stability can be exceeded by subjecting the substance to changes of pressure and temperature. 234 FUNDAMENTAL PRINCIPLES OF CHEMISTRY In case a mixture is the result of the change, it can be immedi- ately recognised by the characteristics given in Sec. 39. A change in optical properties is easiest to recognise. A substance origi- nally transparent may become milky; changes in colour or other changes in appearance may take place. There are, of course, cases where examination with the eye alone is insufficient; the microscope is often of great assistance, especially when the change involves the appearance and disappearance of solids. Recognition of the change is therefore, in general, possible whenever a mixture results from overstepping the limit of stability. If a solution is produced the following general relations come into consideration. A pure substance does riot change suddenly and completely into a solution; the process is a gradual one, and not like the transformation of one state into another. It is, in gen- eral, impossible to find a definite point separating the region of the pure substance from that of the solution which forms from it. It is usually only possible to determine approximately a point where the p!roof that a chemical process has taken place can be given with certainty. This point depends upon the accuracy of the ana- lytic means, and it might even be stated on general grounds that there is no such thing as' an absolutely pure substance. This contention will have its basis in the fact that there is no point of discontinuity which separates the region of a so-called pure sub- stance from that corresponding to the solution formed from it. Practically, however, the differentiation of a region of stability from one of instability has importance. The region in which experimental proof of a change is impossible is usually evidently different from the region in which analysis can give positive re- sults. In other words, there are very large regions in which the amount of decomposition is exceedingly minutej and the transition to finite values begins at a place where comparatively small changes in temperature and pressure correspond to measurable changes. Such continuity in transformation and the presence of homo- geneous equilibria prevent the application of the criteria of Sections ELEMENTS AND COMPOUNDS 235 145 et seq. Phase diagrams are nearly useless, for we have repeat- edly seen that the finite angles which appear as we go from one part of the diagram to another, and which correspond to the formation of new substances, are all rounded off whenever a homogeneous equilibrium results. The value of such diagrams as characteristics of new substances is therefore more or less eliminated. We must find other characteristics if there are any. The material at hand can be again laid out from the standpoint of states. We must then consider the transformation of pure gases, liquids, and solids into corresponding solutions; the solutions, however, in this case being invariably in the same state as the pure substance. We shall not consider solutions of solids, but only those of gases and liquids. 153. GASES. Whenever a gaseous solution is formed from a pure gas, the experimental recognition of the change can usually be based upon the fact that the simple gas laws no longer hold. Let us assume, for example, that the gas in question is transformed into a gaseous solution by heating it, and that the newly formed gases possess a volume different from that of the original gas. As long as the temperature lies within the region of stability the gas follows Boyle's Law and Gay-Lussac's Law. When the temperature reaches the region of decomposition, the coefficient of expansion of the gas will become greater than %\-$ if the product of decom- position occupies a greater volume than the original gas (and vice versa). In the same case deviations from Boyle's Law will appear, and the gas will show a greater or less compressibility than that indicated by the law. Whether a rise of temperature causes the gas to enter a region of decomposition depends upon whether it takes in or gives out heat or entropy during the decomposition. According to our general definition of equilibrium a system reacts to a forced change in such a way that the result of the force is diminished (see Sec. 67). If a gas can change its equilibrium by a chemical reaction, the addition of heat (a rise of temperature) 236 FUNDAMENTAL PRINCIPLES OF CHEMISTRY will bring about a reaction of such a nature as to diminish the consequences, that is, in this case, to diminish the rise of tempera- ture. If the decomposition is accompanied by an absorption of heat, this absorption will take place. If the reverse is true, and the decomposition is accompanied by the development of heat, the gas will become more stable at higher temperatures. The second case is far the rarer of the two under ordinary conditions, but there is sufficient ground for concluding that cases of this kind become more numerous as temperature is carried higher and higher. Pressure acts in a similar way. If the transformation into a solution is accompanied with an increase of volume, the decomposi- tion under diminishing pressure will go further and further as the volume is made greater. The decrease in pressure is partly com- pensated by the formation of a solution which occupies a compara- tively greater volume. When the volume is forcibly decreased, and the pressure is found to be lower than it would be for a pure substance according to Boyle's Law, this result corresponds to a chemical process opposite in nature to the one just described. Beside this characteristic of the resulting gaseous solution we can also make use of those characteristics described in Sections 84 et seq. Partial solution or partial separation of a part of the gas solution (by diffusion, for example, as in Sec. 84) will result in a residue exhibiting properties different from those of the original gas. In this case, however, we are confronted by a new and important factor which does not prevent the final decision, but which makes quantitative determination impossible. As one of the constituents is removed chemical reaction immediately takes place in the residue. The escaping constituent is, in general, partially replaced, and this is the result of the principle which has just been expressed and applied. Wholly false conclusions as to the amount of the escap- ing substance which was present in the original gas may be drawn if these facts are not kept in mind. Consider the case of a process by which only one of the constituents of the solution is withdrawn. ELEMENTS AND COMPOUNDS 237 According to our general rule, this substance must be continually formed as it is withdrawn. If we then took away all of this sub- stance that was formed we would have separated an amount which was never really present in the original mixture, although it was potentially there. By potentially we mean in this case the entire amount which could be formed from the substances present, provided all hindrance which might prevent the completeness of the reaction in question is removed. This conclusion is an impor- tant one and finds application in many other cases outside of gas reactions. A careful review of the facts in connection with this principle will show that it holds for all homogeneous equilibria in gases and in liquids of all kinds. 154. LIQUIDS. We possess no general quantitative laws for liquids similar to those for gases, and we can therefore place no dependence on any such aids for differentiating between pure substances and solutions in the case of liquids. At the same time the conditions here also exclude the application of the angles at the points of contact of property lines in the phase diagrams, for all these points are rounded off by the existing homogeneous equi- libria. All sharp differences between solution and pure substance are absent as long as we are dealing only with the properties of the liquid phase, and we can therefore never decide by observa- tions of this kind whether and where a pure substance leaves its region of stability. Our process for the partial separation can, however, be applied, and even this assumes the formation of a new phase of some kind. Whether or not a liquid is stable can, in general, be easily decided by distillation. By this process the more volatile portions of the solution will be- the first to escape, and the composition of the vapour will, in general, be different from that of the residue. In the case of a singular solution this does not hold, for here the distillation will be hylotropic. A change of pressure will be of assistance in this case, for with such a change in pressure the solution will lose its singular properties. 238 FUNDAMENTAL PRINCIPLES OF CHEMISTRY A partial freezing out is also insufficient, even though a partial separation may apparently be produced. In this case it is neces- sary to inquire which constituent of the solution is the first to separate. If it is the original substance, this will keep on form- ing from its components in the liquid according to the principles just explained. The whole liquid will therefore appear hylotropic during freezing and the presence of a solution remains undeter- mined. If, on the other hand, one of the constituents separates first, the presence of a solution will be evident. Brief considera- tion of the diagram representing what takes place during freezing shows that in this case the compound is the first to separate. To make this clear let us consider the corresponding diagram, Fig. 63, u FIG. 63. in which the rounding off of the peak in the centre is already shown as a result of the homogeneous equilibrium. The solution has been formed by the decomposition of the compound. Its com- position is therefore that of the compound, and the course of the experiment, which consists in cooling the liquid, will be repre- sented along the perpendicular uu. The melting line must neces- sarily be crossed at the peak. From this it is evidently impossible that one of the constituents should separate as a solid, and under all circumstances the compound will separate in the solid condi- tion. It will be seen that, in general, the determination of one of ELEMENTS AND COMPOUNDS 239 the boundaries of the region of stability for liquids offers difficul- ties and is by no means always possible. Solid substances can only produce mixtures when they exceed their limit of stability, and these mixtures are theoretically always recognisable. 155. TRIPLE SYSTEMS. Up to this point we have only con- sidered systems which could be produced from two pure substances. It will be evident from the great number of possibilities which we have found that a very much larger number of individual cases are to be expected among triple systems. It will be impossible here to develop even a general idea of the possibilities, and we will con- fine our discussion to an especially important group, one which is experimentally most often met with. This group comprises re- actions between dilute solutions having a common solvent. The reason for the special advantage of this group is to be found in the following circumstances: Firstly, dilute solutions occur very frequently in nature. Substances are very seldom formed alone; as soon as several come in contact they form solutions, and when the mutual solubility is limited these solutions will be dilute. Secondly, dissolved substances react with one another much more easily than solids. If chemical processes are to be brought about, it is always best first of all to bring the solids into solution. Suppose we have three substances A, B, and C of such a nature that A and B are soluble in C. Let us consider what happens when a dilute solution of A in C is allowed to react with a dilute solution of B in C. If both A and B are far removed from a con- dition of saturation in C, and when A and B do not combine to form -a new substance, the resulting substance will be a homo- geneous solution. It is of course possible that the solubility of one or the other constituent will be so greatly reduced by combining the two solutions that the corresponding substance will separate as a new phase. This can, however, only take place when one or the other of the two solutions is near saturation, and this we have excluded in our assumption. Such a case is furthermore 240 FUNDAMENTAL PRINCIPLES OF CHEMISTRY so easy to recognise that we can for the future leave it out of consideration. If new phases appear when two dilute solutions are brought together, it is safe to conclude that a new substance has been formed by the interaction of A and B. If new phases do not appear, we must not however conclude that a new substance has not been formed. The new substance may be so soluble in C that no new phase can form. In a case of this kind we must bring to our aid other means for recognising a chemical process. The most general of these is in this case also a change of the total energy of the system, which may be evidenced by the evolution or absorption of heat. Two possibilities may come in question, liquid solutions and gaseous solutions. We shall consider exclusively the first of these, for this is the one of the most practical importance. We have therefore to investigate phase changes in dilute liquid solutions. It should be mentioned at this point that when a substance enters the condition of a dilute liquid solution it follows a set of simple laws, just as it does after it has entered the gaseous state. A little' later we shall see that the similarity goes so far that an equation of condition holds for dissolved substances which corresponds exactly to the gas law. At this point we shall make no application of this relationship. For the present we are interested in a general explanation of the formation of the phases and not in quantita- tive relations within a phase. 156. INDIVIDUAL CASES. Three different cases are possible under our assumptions: either a gas, another liquid, or a solid substance may separate from the liquid phase. All three of these cases are known, and either of them determines the conclusion that under these circumstances a new substance has been formed. This new substance may be a compound of A and B, but it is equally possible that the new substance contains some of the sol- vent C, or that the new substance does not contain the sum of the elements of A and B, but only part of them. In the latter case one or more new substances remain in the solution, these new sub- ELEMENTS AND COMPOUNDS 241 Stances being such as have been formed by the reaction together with the one which separated in the form of a new phase. Reactions in solutions have one thing at least in common with those in gases. The formation of a new substance can always be recognised with certainty when a new phase belonging to another state results from the reaction. The possibility of recognising a new phase which separates in any of the three states gives to solu- tions an advantage over gases in the proof of chemical processes. For in the case of gases a new gaseous substance would not ap- pear as a new phase. For this reason, and also because it is much easier to handle liquids than gases, solutions possess their great practical importance in experimental chemistry. 157. THE EVOLUTION OF A GAS. Let us consider the case in which a reaction between the two solutions of A in C and B in C results in the formation of a gas. It makes no difference as far as the general reasoning is concerned whether this gas has the composition AB or is formed in some other way from the two sub- stances and the solvent, and we shall therefore riot consider this point further. Suppose we add a very small amount of A (we shall use this expression for the sake of brevity in the future dis- cussion in place of saying " solution of A") to a finite amount of B ; no evolution of gas is to be expected. All gases are soluble in all liquids, and the newly formed gas will therefore be soluble in the solution. We have also assumed that the solutions are dilute. The solubility of the new gas will therefore not be very different from its solubility in the pure solvent C. When further addition of A has resulted in the formation of so large an amount of gas that saturation is reached, gas may be evolved on further additions. This does not, however, necessarily take place. Supersaturation will occur, since this takes place easily in solutions of gases in liquids. The condition of supersaturation can be released by any foreign gas, and it is therefore easy to recognise. It is only neces- sary to shake a sample of the mixed solutions with a measured volume of any indifferent gas, atmospheric air, for example, and 16 242 FUNDAMENTAL PRINCIPLES OF CHEMISTRY then to measure the gas volume again. An increase of volume will indicate the presence of a supersaturated solution of gas.* Assuming that no pains have been taken to avoid supersatura- tion, further additions of A will, in general, finally result in reach- ing the labile condition, where the evolution of gas begins of its own accord. As A is further increased, the amount of gas pro- duced will increase until all of B has been used up. From this point on the further evolution of gas ceases. Measurement of the amount of gas produced during the opera- tion of gradually adding A to E enables us to determine the pro- portion in which A and B combine, or it may be the proportion in which they act on one another in some other way. Precisely similar conditions prevail when the process is carried out in the inverse way by gradually permitting an increasing amount of B to act upon A. 158. LIQUID SEPARATION. What we have just said can be repeated almost word for word if we wish to describe what takes place when a liquid which separates as a new phase is formed by the interaction of A and B (and of C also). The limit of satura- tion for the new substance must be reached before this can appear as a separate phase. It is a matter of experience that in the case of solutions of liquids in liquids supersatu ration appears only with difficulty and within very narrow limits, so that the com- plexity introduced by its appearance is absent in this case. On the other hand, there is no general means of releasing supersat- uration similar to the one afforded by the indifferent gas in the previous paragraph. Another thing should be mentioned here, and that is the usually occurring case of local precipitation. As A is added to B it will * It must of course be kept in mind that the liquid will also dissolve the in- different gas according to its solubility, and also that the vapour of the liquid will increase the gas volume in proportion to the vapour pressure of the solution. There is, however, no difficulty in excluding these effects or cal- culating them, and we shall therefore assume that they have been taken into consideration. ELEMENTS AND COMPOUNDS 243 be noticed that at the moment when the two solutions touch, the separation of a new phase is indicated by a milkiness in the liquid. This disappears when the liquid is stirred and the solution becomes clear again. In the neighbourhood of the drop the proportion of A to B is at first much greater than it would be if the two liquids were intimately mixed. The effect which is later to appear every- where is seen first at this place. Later the local proportion will be attained everywhere by the addition of a larger amount of A. When the general proportion is restored by mechanically stirring, the new phase which separates locally is again dissolved and the liquid becomes clear. The combining proportion of A to B can be theoretically de- termined in this case also, for the separation of the new phase ceases when this proportion is reached. It is, however, experi- mentally very much more difficult to determine in this case, for the new liquid usually forms a milky mixture, an emulsion, in which it is difficult to recognise an increased milkiness as more of A is added. It is however possible to separate the phases by letting the liquid stand or by means of a centrifuge, and then to recognise further precipitation of the new phase. The solution of this prob- lem has been indicated, and we need not follow the technical methods any further. 159. SOLID SEPARATION. By far the greatest number of practi- cally important cases depend upon the separation of a new phase in the solid form. In this case it is called a precipitate, for the solid phase almost always has a greater density than the liquid and sinks to the bottom of the vessel. The general phenomena, which occur as one solution is gradually added to the other, are in no way different from those described in the case of gases or liquid phases. In this case also there is a homogeneous region at each end of the series of mixtures which corresponds to the solubility of the new phase in the solvent (as influenced by the dissolved substances). Between these two regions there is a two-phase region in which the precipitate exists in the presence of the solution. 244 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Each constituent acts upon the other to form the precipitate until the point is reached which determines the ratio of the combining weights. When this point has been reached neither A nor B causes a precipitate in the liquid, while in all other proportions in the two-phase region either A or B produces one. Supersatu ration is very frequent among these cases. There are in fact cases where, although a solid phase is possible, it never appears of its own accord whatever the proportion in which the solutions are mixed. It is usually possible to pass the metastable limit by increasing the concentration, and if particles of the solid phase can be obtained, it is possible to prevent supersaturation from the first. In every case, whatever the state of the second phase may be, we have to deal with systems containing three constituents and two phases, and we have therefore three degrees of freedom. Pressure and temperature being determined, one degree of freedom remains. This means that if we fix the concentration of A that of B is no longer free but must possess a definite value, and vice versa. Only one of the two proportions A to C and B to C is free, the third proportion A to B is determined by the two first and is therefore not independent. The above only holds in case the new phase has appeared, and in those regions in which the new phase has not yet been formed one more degree of freedom remains. The solution may have any composition within the corresponding limits. 160. THE SOLUTION REMAINS HOMOGENEOUS. In conclu- sion let us examine the case in which no new phase appears within all the possible proportions in which the two solutions can be mixed. Whether or not a new substance has been produced by the interaction of A and B (with or without the aid of C) may be determined by reasoning similar to that of Sec. 146. In that sec- tion we considered the case where two gases form a homogeneous solution. The energy relations are directly applicable as in Sec. 148. ELEMENTS AND COMPOUNDS 245 When solutions are formed from liquid constituents there is, in general, an energy change, even though we have no other ground for the assumption that a new substance has been formed. The similarity of dilute solutions and gases is marked especially by the fact that these energy changes, which do not correspond to the appearance of a new substance, become less and less as the solu- tions are made more and more dilute. This is in agreement with the behaviour of gases which dissolve one another without change as long as no chemical reaction takes place between them. If a chemical change takes place the energy change, due to the chemical process, appears completely in the heat change produced when dilute solutions are mixed. Any other specific property beside energy change would serve as well, provided it shows a change as compared with the average value of the corresponding mixture or solution. Suppose, for example, that A is coloured, while the newly formed compound is colourless. Then as A is added to B we should see the colour of A disappear until the relation of the combining weights is reached. In general such a property will exhibit changes like those indicated in Fig. 57. Here we find the diagram to consist of two straight lines cutting one another at a point which represents the ratio of the combining weights. It should be mentioned that these simple relations do not hold in some cases. In place of the sharp angle at the meeting of the two lines we may find a rounded corner. In these cases, as with the gases, it is possible to represent the observed facts by assuming a chemical equilibrium which varies with changes in temperature and concentration. The relations just discussed for solutions are of the utmost im- portance. They are of use in the recognition of substances in their solutions, and they therefore form the foundation of analyti- cal chemistry. The use of solutions in place of pure substances is largely dependent upon the fact that the former exhibit simpler and more general relations than the corresponding pure substances, 246 FUNDAMENTAL PRINCIPLES OF CHEMISTRY and this is especially true in a case of the greatest practical im- portance. This is the class of salts, which will be taken up in a later chapter and there defined and characterized as far as their important properties are concerned. In those substances which do not belong to the salt type, and especially among the carbon compounds, solutions are of no advantage, and in these cases sub- stances are used and recognised in their pure condition rather than in solution. CHAPTER VII THE LAW OF COMBINING WEIGHTS 161. THE LAW OF CONSTANT PROPORTIONS. It has been shown in the discussion of the previous chapter that new substances are produced from old ones in two ways. The first of these ways is to bring together several substances, while the second way in- volves the use of only a single substance brought into conditions of such a nature that its region of stability is exceeded. In both of these cases the new pure substances frequently appear in the form of solutions and not in the pure state. The question how constit- uents can be separated in a pure state from their solutions has already been taken up. We may therefore assume in what follows that the new substances which are formed under the existing con- ditions have been brought into the pure state by the proper opera- tions. The law of constant proportions (Sec. 149) deals with the amounts by weight in which new substances are produced from those already present. This means that a definite relation exists between the weights of the original substances and the newly formed products. This relation varies with the nature of the sub- stances involved, but it is independent of pressure, temperature, or any other condition existing during the transformation. The " nature" of the substances involved is characterized by their properties, and substances with the same properties are to be con- sidered as having the same nature. In other words, the relations by weight in which chemical transformations take place belong to the definite and specific properties by which substances are classified as the same or different. Suppose we have two substances, A and B, which can combine 247 248 FUNDAMENTAL PRINCIPLES OF CHEMISTRY into a compound AB, the original substances disappearing and the new substance AB appearing in their place. The law which describes this case states that when these two substances are brought together in a definite proportion a new pure substance is formed which is neither a mixture nor a solution. The same rela- tion is found unchanged whenever a pure substance possessing the properties of the substance AB is transformed or decomposed in any way into the two substances A and B. This second principle can be derived as a consequence of the first with the aid of the law of the conservation of the elements. If AB could be decomposed in such a way as to give the elements A and B in a proportion dif- ferent from the one in which they combined to form AB, we would be able by combining A and B and then decomposing their com- pound to get more A or more B than we had originally. This is contrary to the law of the conservation of the elements. This proof assumes that A and B are elements, but it can also be expanded to include the case where A and B are compounds. If the law did not hold we would be able to obtain an excess of A or B, and by decomposing this into its elements we could obtain an excess of one or the other. It may be said, in general, that every compound shows the same composition, whether it is synthesized from its elements (or from compounds made up of them) or an- alyzed in such a way as to produce them. The elements in a com- pound are present in a definite proportion which appears in both analysis and synthesis. The law of constant proportions holds only for pure substances, it therefore holds for these only within their regions of stability, for outside of these regions the pure substances cannot exist as such. Proof that this proportion is independent of variations of pressure and temperature depends on the assumption that the region of stability is not exceeded. We shall see later that the condition thus assumed is a funda- mental one, and that furthermore the law of constant proportions holds for all pure substances whether they are elements or not. THE LAW OF COMBINING WEIGHTS 249 When any two substances form a new substance by chemical inter- action there is always a relation by weight of these two substances, and in this relation the new compound appears as a pure substance and not as a solution. Compound substances enter into further com- binations as a whole just as elements do. Whether or not a given substance is an element can only be determined by an investiga- tion throughout the whole range of pressures, temperatures, etc. The proof that it does not change into a solution is dependent on the development of the technique of chemistry, and it is therefore evident that there is no absolute difference between simple and compound substances as long as any part of the whole range of temperature and pressure has not been explored in each case. All pure substances agree further in their power to combine to form more complex substances, and this is true whether they have been shown to be compounds or are still classed as elements. The law just explained depends upon an inestimable number of observa- tions, and we shall call it the law of integral reactions . 162. COMBINING WEIGHTS. Let A, B, C, D, etc., be elements which can combine with each other. Suppose also that the relation in which any given element, A, for example, combines with the others has been determined. We have then determined the com- bining proportions of the substances AB, AC, AD, etc. If we take the amount of A which was used for each of these syntheses as our unit, then the amounts of B, C, D, etc., which combine with the unit weight of A, are called the combining weights of these elements with respect to A, and they might be indicated by (B)A, (C)A, (D) A , etc. We might just as well have different combining weights based upon B, i. e. the weights of the other elements which would com- bine with the unit weight of B to form the compounds BA, BC, BD, etc. This would give us a system of combining weights based upon B, and we will designate them with (A)B, (C)s, (D)s, etc. Let us now assert that (B) A x (A)a = 1. Expressed in words the combining weight of an element, determined with respect to a 250 FUNDAMENTAL PRINCIPLES OF CHEMISTRY second element, is the reciprocal of the combining weight of the second, determined with respect to the first. The proof of this depends upon the fact that in both cases we are dealing with the same compound AB and that the relation by weight of A and B, in which they combine to form this substance, or in which they are produced during its decomposition, is definite and determined. If a is the weight of A found in any given experiment, and b is the weight of B, then by definition (A)s = - and (B)A = -. It follows 6 a immediately that (A)sX(B)A=I> This relation is, however, the only one which exists between the two series, for no other compound is common to both. If we have n elements each of them has n 1 combining weights, one for each of the other elements. The number of these combining weights increases without limit when compounds of three and more elements are taken account of. Beside this, compound substances as well as elements have combining weights, for they combine with other substances to form more complex ones, and their be- haviour can be described by the law of integral reactions. This complexity is greatly simplified by a general law which is a conse- quence of the law of the conservation of the elements and the law of integral reactions. 163. TERNARY COMPOUNDS AND THOSE OF HIGHER ORDER. - We may expand the law of constant proportions to include com- pounds of three, four, or any number of elements. Our only as- sumption was that we should deal with pure substances, and not that they should necessarily be elements. If therefore the com- pound AB can combine with the element C to form a compound ABC, a constant relation must exist between the weight of AB and the weight of C, since they combine to form the pure substance ABC. The ternary compound ABC can also be formed by causing the three elements to react with one another simultaneously, determin- ing the proportion in which a pure substance and not a solution is THE LAW OF COMBINING WEIGHTS 251 the result of the action. We can in this way determine the com- bining proportions, and in this case these are for the elements A, B, and C. The composition of ABC is independent of the way in which it is produced. The same proportion must exist whether we form ABC from AB and C, or from A, B, and C. It follows therefore that the amount of AB which must be used with a given amount of C to form the compound ABC is the sum of the amounts of A and B which we must use with the same amount of C. In other words, the combining weight of AB with respect to C is the sum of the combining weights of A and B with respect to C, both being calculated for the same compound ABC. Precisely similar considerations hold for the case in which the compound AC is first prepared and then combined with B to form ABC ; or we could first make BC and allow this to combine with A. The nature of a substance does not depend upon the method of its preparation, and the compounds ABC, ACB, and BCA must be regarded as identical. The weights of A, B, and C which can be made from these compounds, or from which they can be pre- pared, must therefore be in exactly the same proportion in all of them. The following important conclusion may now be drawn for the substance BC : If the combining proportion of B with respect to A and that of C with respect to A be determined, the quantities which combine with the unit weight of A will give us the proportion by weight with which B and C can combine with each other. A in this case has nothing whatever to do with the matter, for B and C are present in the compound ABC in the proportion in which they combine singly with the unit of A, since ABC can be made from AB and 0, and from AC and B. ABC can also be made by combining BC with A, and B and C are therefore present in ABC in the proportion in which they would combine to form BC. This proportion is at the same time the proportion of their combining .weights with respect to A. 252 FUNDAMENTAL PRINCIPLES OF CHEMISTRY The general principle may now be stated : If the combining pro- portions of the elements B, C, D, etc., are determined with respect to an element A, arbitrarily chosen, the values so obtained hold also for the proportions in which the elements B, C, D, etc., will combine with each other. With the aid of this principle it is evident that we can determine the composition of compounds which we have never analyzed quantitatively. If the combining proportions A : B and A : C have been determined, these numbers give us also the combining pro- portions B : (7, although the substance BC has not been analyzed or even prepared. This result raises the question of how it is possible to know anything about a thing which does not exist, and the answer is that in this case we have made application of a natural law. All natural laws possess the property of enabling us to state in advance relations which are still unknown. If a gas is produced by any operation it is safe to state beforehand that if its temperature is raised from to 100 its volume will increase by J^ of its volume at 0, assuming that the pressure is kept constant. It is also cer- tain that if it is kept at constant volume its pressure will increase in the same proportion. All those substances which exhibit the mechanical properties of a gas have so far in our experience always exhibited the thermal properties of a gas, and I am therefore able to conclude with scientific certainty, that is, with very great prob- ability, that a substance about which I know nothing more than the fact that it behaves mechanically like a gas will also behave thermally as such. The natural laws of which we have made use in the foregoing reasoning are the law of the conservation of the elements and the law of the integral reaction of compound substances. This latter law states that these substances can combine with one another without the separation of an excess of any one of their elements. Both of these laws are founded on experience, as all natural laws are, and they are limited and conditioned by experience. For the THE LAW OF COMBINING WEIGHTS 253 present we must consider them as a suitable basis for further con- clusions, for the conclusion we have drawn from them of the exist- ence of combining weights has been strengthened extensively by experience. Any proof of chemical proportions which may be found to be in contradiction with the law of the combining weights would also cast doubt on these more general laws, and we would be obliged to investigate them anew in the light of this new experience. So far experience has been in complete agreement with the law of the combining weights. The combining weight of each sub- stance which has been regarded as an element has been determined with respect to an element arbitrarily chosen, and it has been shown that all the compounds of this element with other elements can be represented by the proportion of the corresponding combining weights. We may say, in short, that substances combine only in the proportion of their combining weights. The latter are specific properties of the elements alone, independent of the special com- pound in which the elements are present. From this point onward we shall indicate by A, B, C, etc., not only the elements considered in a qualitative way, but by each letter we shall mean one combin- ing weight of the element. 164. THE COMBINING WEIGHTS OF COMPOUND SUBSTANCES. - A pure substance enters and leaves a chemical compound as a whole whether it is an element or a compound. It therefore has its own combining weight, and the value of this weight is the next point to discuss. The combining weight of a compound substance is the sum of the combining weights of its constituents. Proof of this statement is contained in the reasoning of Sec. 163. The com- pound ABC can be produced from A, B, and C, or from AB and C. With the aid of the law of the conservation of the elements, and by the method already used, it can be shown that the weight of AB which combines with a given amount of C is the sum of the weights of A and B which combine with the same amount of C. The above conclusion follows directly, for the same reasoning is applicable to compound substances of any nature whatever. 254 FUNDAMENTAL PRINCIPLES OF CHEMISTRY 165. THE LAW OF RATIONAL MULTIPLES. In the preceding discussion we have made the assumption that elements combine in only one proportion. Our conclusion holds therefore only for compounds in which this assumption is valid. There are, how- ever, many cases in which two elements A and B combine in more than one proportion, and we shall next consider the laws according to which these combinations take place. Let us first of all ex- amine the case of a ternary compound, and we shall suppose that it has been produced by the union of a substance AB with an- other substance AC. The resulting substance will not be ABC, for this was obtained by the combination of AB and C. The new substance contains a larger amount of A than the former one. The law of the combining weights is applicable in this case, for the combining weight of AB is the sum of the combining weights of A and B, and similarly in the case of AC. The new compound, which we shall designate with ABAC, because of the way in which we formed it, contains the element A twice and therefore double the combining weight of A. Twice as much A combines with the single combining weight of B or C as was the case in the compound ABC. If we decompose the compound ABAC in such a way that all of C separates from it, a substance ABA remains which contains the double combining weight of A in combination with a single combining weight of B ; and, vice versa, if a substance exists which combines with C to form the new compound ABAC, this substance must contain two combining weights of A to one of B. This method of reasoning can be carried as far as we choose. It is independent of the nature of the elements and compounds involved, and the only assumption required is the validity of the two general laws of the conservation of the elements and the in- tegral reaction of compound substances. The result can be stated in its most general form in the following way: If elements com- bine in several proportions by weight, combination takes place be- tween the corresponding multiples of their combining weights. THE LAW OF COMBINING WEIGHTS 255 Operations of combination and separation, similar to those applied to AB, can also be carried out upon the compound ABC, and in this way we can proceed step by step to compounds con- taining three, four, five, etc., combining weights of A. Any other element can take the place of A, and this justifies the generaliza- tion we have just made. It is also evident from the derivation of this principle that the law holds for binary, ternary, and higher compounds. We can replace the elements A, B, and C by any compounds whatever, provided they fit our assumption that pure substances are to be used, and in this way the proof may be ex- tended to compounds as complex in nature as we wish. . It follows from this that the composition of any pure substance can be expressed by a formula of the form, mA, nB, pC, qD, etc., ra, ??, p, and q being whole numbers. Experience has shown that m, n, etc., are usually small numbers, although values of 100 or more have been observed. The proof of the law becomes more difficult, however, as these numbers become greater, for the differ- ence in the quantitative composition, corresponding to the dif- ference of one unit of the combining weight, becomes smaller and smaller. If, for example, m is 100, a substance of analogous com- position in which m is 101 would show on analysis a difference of only 1 per cent in its content of the element A. 166. CHEMICAL FORMULAE. The law of combining weights states that all substances enter into chemical reaction only in definite proportions by weight, and that these proportions are independent of the nature of the elements which take part in the reaction. It gives us a very simple and evident means of describ- ing the relations between elements and their compounds, and we have already made use of it. For scientific purposes it is neces- sary to represent these definite relations between elements and their compounds by definite symbols. Each compound is desig- nated by a combination of the symbols of the elements from which it can be produced and into which it can be decomposed. If A, B, C, etc., are symbols for the elements, AB is a symbol of 256 FUNDAMENTAL PRINCIPLES OF CHEMISTRY a compound which can be produced from elements A and $, and ABC is the symbol of a compound from which the elements A, B, and C can be obtained. The designation is so far only a qualita- tive one; it states the elements which exhibit the above-mentioned definite synthetic and analytic relation to a given compound. With the aid of the law of the combining weights these symbols can, however, become quantitative. It is only necessary to give to the symbol for an element a further meaning. It must represent one combining weight of the corresponding element. Elements combine only in the proportion of their combining weights, or their multiples, and we have indicated no limitation by thus ex- panding the meaning of the symbol. Substances not included in this class are not compounds but only solutions, and this is there- fore a further means of discriminating between pure substances and solutions. It must also be kept in mind that elements combine not only in the simple proportion of their combining weights, but also in multiples of them. A number is added to the symbol for each element, and this number indicates how many combining weights of the element take part in the formation or decomposition of the compound in question. A formula A m B n C p designates a sub- stance which is made up of m combining weights of A, n combin- ing weights of B, and p combining weights of C. It is evident that this formula also expresses the fact that the combining weights of compound substances are the sum of the combining weights of their constituents. A formula of this kind suggests an idea which needs careful consideration and one which is very often misunderstood. The symbols for the elements make up the symbols of compounds, and this suggests the thought that the elements are actually physi- cally present in their compounds just as their symbols are present in the symbol of the compound. It is however characteristic of a chemical process that substances should disappear, and that others with other properties should take their place. The ele- THE LAW OF COMBINING WEIGHTS 257 ments and their properties disappeared when the compound was formed, and it is therefore impossible that an element should per- sist in its compounds. The idea that the elements have disappeared, but are nevertheless present as such, is an indefinite one, too in- definite for scientific use. The elements can be recovered from their compounds whenever we choose, and this is, as a matter of fact, all that we can say about them. It is somewhat analogous to what happens when an amount of money of various denomina- tions is taken to the bank for safe keeping. The same amount can be obtained from the bank in the same denominations at any time. It by no means follows that the bank has kept the coins paid in during the whole time, but only that the bank has means sufficient to return our deposit. What becomes of the coins in the meantime we do not know, nor is it a matter of importance. A compound can at any time be transformed into its elements again, but we can only conclude from this that the condition for the formation of the elements always exists, and not that the ele- ments persist as individuals in the compound. Certain proper- ties of the elements, their weight, for example, are conserved in the compound, but a given weight cannot be changed by any process whatever, and this fact affords no proof for the persistence of the elements in a compound. The question is not, Are the elements contained '* as such " in the compound ? The answer to this question is decidedly a negative one, for the properties of the elements are not retained in the compound as the properties of the individual gases in a gaseous solution are. A much more important question is the following: Are there other properties of the elements beside weight (and mass) which are retained in compounds? Can any connection be traced between the properties of elements and those of their compounds? The answer is a complicated one, and it forms the content of an extended chapter of scientific chemistry. Here we can only say that no property of the elements, except mass and weight, is conserved unchanged in a compound, but 17 258 FUNDAMENTAL PRINCIPLES OF CHEMISTRY approximate agreement in properties is quite common. The properties of the compound can sometimes be represented as the sum of the properties of their elements. These relations are, how- ever, not exact ones, and the degree of their exactness varies with the nature of the properties in question. Many properties of com- pounds show no apparent relation whatever to those of the elements from which they are made. 167. CHEMICAL EQUATIONS. Chemical formulae serve to de- scribe chemical processes as well as in the representation of the composition of a compound. This application is based on the law of the conservation of the elements, which states that if we start with given substances con- taining certain elements we can only make those substances which contain these same elements. Further, the compounds produced contain the elements only in such proportion that the total amount of each element remains unchanged after the transformation. It is customary to speak of the presence of the elements, because of the fact that the elements in question can always be produced from the compound in their original amounts. Since elements are characterized in this way in the chemical formulae for compounds, the following condition must be ful- filled if any chemical process is to be represented by a formula. The same elements must be present in the same amounts, that is, an equal number of combining weights of each element must be indicated before and after the reaction. It is therefore customary to write chemical reactions in the form of equations, the original substances being placed at the left and the resulting substances at the right, the two sets of sub- stances being connected by the sign = . If an equation is correct the same number of combining weights of each element must be found on the two sides of the equation, otherwise the law of the conservation of the elements would not hold. This is, however, only a necessary and not a sufficient condi- tion for the possibility of a chemical process. There would be no THE LAW OF COMBINING WEIGHTS 259 difficulty in arranging a given finite number of combining weights of various elements in very many different ways, and so setting up between two such groups equations which would be correct as far as the law of conservation is concerned. Such an equa- tion would, however, by no means always express an actual possible process. Many groups of elements are unknown as compound substances, and not every transformation which obeys the law of the conservation of the elements is experimentally possible. Like all other natural laws the law of conservation enables us to draw a line within which all actual reactions take place, though by no means all the cases which lie within this line are practically possi- ble. In fact only a comparatively small number of them may have experimental existence. Which of them have real existence, and how we can discriminate between the actual cases and those which are merely formally possible, can only be determined with the aid of other special laws which cannot be taken up at this point. The chemical reactions which can be represented by such an equation are of two kinds. It very frequently happens that a chemical process takes place only in one direction and not in the opposite direction. If, for example, two mutually soluble liquids are brought into contact they form a solution, but this solution does not separate of its own accord into its constituents. If, how- ever, we have a mixture of ice and water, the amount of water can be increased at the expense of the ice by the addition of heat, and the opposite process can be brought about by taking away heat. Chemical processes in the narrower sense show the same differences. Many of them take place in a definite direction and reasonable changes in the external conditions produce no noticeable effect upon them. There are, however, other processes which can be reversed by changes in the external conditions. The first of these is called a unidirectional or complete reaction, the other involves a chemical equilibrium. It is often desirable in writing a chemical equation to make it clear which of these two processes is described by the equation. 260 FUNDAMENTAL PRINCIPLES OF CHEMISTRY When this is desirable the equality sign is replaced by a symbol which indicates the direction of the process, and this is usually an arrow or a similar symbol. The symbol = is used to de- scribe a unidirectional or complete process, the arrow-points in- dicating the direction in which it takes place. When we wish to describe a chemical equilibrium we make use of the symbol =^, which expresses the possibility of a reaction in either direction. If there is no particular reason for characterizing one or the other of these cases, the ordinary equality sign should be used. 168. METHODS OF DETERMINING COMBINING WEIGHTS. The most direct method of determining the combining weight of an element is to cause it to combine with the standard element, de- termining the combining proportion by analysis or synthesis. For this reason the element which forms the largest number of com- pounds with the other elements should be chosen as standard. In many cases this simple process is not applicable, for the analysis of compounds so produced is sometimes one of special difficulty, and therefore less accurate than the analysis of other compounds of the same element. The following general rule is applicable: If we determine the proportion in which the element to be in- vestigated, X, combines with one combining weight of any other element, B, we have determined the combining weight of X, that is, the amount of X which will combine with one combining weight of the standard element A. This rule follows directly from the general law that the elements combine only in the proportions of their combining weights. The amounts of X and of B which com- bine with the combining weight of the standard element A are in the same proportion as the amounts in which they combine with each other, and this proves the correctness of the method just applied. There are cases in which the process just described cannot be conveniently applied. In place of a compound of X with one other element it is sometimes necessary to choose a compound of X with several other elements. The most general method of THE LAW OF COMBINING WEIGHTS 261 solving the problem consists not in the use of the element X as such, but in using compounds of this element. For example, the problem may be solved by transforming a substance XBC into another substance XDEF. In all of these cases the combining weights of all the elements involved must be known, with the exception of that of X. We obtain in this way an equation representing the chemical trans- formation and containing the weights of all the elements except X. Solution of this equation gives the desired value for X. It must be kept in mind that all of these combining weights which we assume to be known have been determined experimen- tally. Each of them has therefore its probable error, and the value of this error depends upon the nature of the individual element. The result obtained from the numerical equation involving these numbers involves also all of these errors, which increase the prob- able error of the combining weight to be determined. For the sake of exactness it is best to involve as few combining weights as pos- sible, and from this point of view the simplest methods for deter- mining the combining weights are the best. The combining weights are the real units of chemical arithmetic. If the combining weight of B is large, a large amount of B combines with a given amount of A. If C has a small combining weight, a small amount of C combines with the same amount of A. If our calculations are to be accurate, the various combining weights should be known with the same percentage accuracy. On the other hand, we add combining weights when we calculate the combining weight of a compound. The laws of probability show that the absolute probable error and not the relative one should be equal for each element if the accuracy of our result for a compound is to be least affected. Finally, it should be noticed that the accuracy of the combining weights at the present time is dependent in a large degree upon the rarity of occurrence of an element and upon its common applica- tion. The combining weights of the most important elements have 262 FUNDAMENTAL PRINCIPLES OF CHEMISTRY been the subject of much more investigation than those of the rare ones, and they are therefore much more accurate. As science has advanced the accuracy of our knowledge of the combining weights has constantly increased, and their numerical values show a corresponding change. We now have international usage in atomic weights just as we have units of length and weight. The international committee publishes a table every year giving the most probable values for the combining weights, and these are used by all chemists in their calculations. This will make it easy in the future to determine what combining weights are used in any research, even though the author has not mentioned them in his paper. This condition of things dates only from the year 1902, and in all earlier researches great uncertainty in this matter is the rule, unless the combining weights which were used are mentioned by the author. 169. THE INDEFINITENESS OF THE COMBINING WEIGHTS. - The choice of combining weights is an arbitrary one for two reasons, even though no doubt remains concerning the relations by weight which are to be used in calculating chemical results. First, the choice of the standard element is an arbitrary one; and, second, when the same elements form several compounds we must choose arbitrarily which compound we will assume to contain equal com- bining weights of the elements in question. We have already considered one point in connection with the first question. Tables of combining weights based on different standard elements are always proportional, for it is always pos- sible to deduce the same combining proportion for any compound from any table. It is therefore a matter of secondary importance which element is chosen as the standard. At present chemists are united in using oxygen as the standard. This element occurs most profusely on the earth's surface. About one half of all the sub- stances which make up the earth's crust is oxygen. We must look for an answer to the second point in the law of rational multiples, as applied to compounds which contain the THE LAW OF COMBINING WEIGHTS 263 same elements in several proportions. If we have, for example, two compounds of A and B, the second of which contains twice as much B as the first, their formulae may be written either AB and AB 2 , or A 2 B and AB. We assume in the first case that the first of the two compounds contains equal combining weights. In the second case we must assume that two combining weights of B enter the compound. In the other case we assume that the second compound is the normal one with the formula AB, and then the first compound must be assumed to contain two combining weights of A t since it contains the same amount of B combined with twice as much A as in the second compound. In the second case the combining weight of A must be twice as great as in the first case, or the combining weight of B must be half as great. Taken by itself the law of the combining weights affords no means of dis- criminating between these possibilities, nor is the law of rational proportions of any assistance. Both laws hold true whichever assumption is made. The freedom of choice which is left us in this case can be used for the purpose of expressing other relations, and, as a matter of fact, the volume relations of gases afford a means of making a definite choice between the various possibilities. Other facts lead us to a simple and useful set of relations, but the final reasons for the choice of combining weights cannot be taken up here. It need only be said that we have finally arrived at a definite decision which has been accepted by all chemists. 170. THE GENERAL RELATIONS OF THE COMBINING WEIGHTS. Combining weights are of use not only in describing in the broadest way the relations by weight which exist between com- pounds and their elements, but they also have other important functions. Other properties of substances show simple sets of rela- tions when they are calculated on the basis of combining weights, provided these properties can be stated as functions of the amount of substances involved. The most evident way of expressing such properties is to refer them to the unit of weight. This method of reference is in fact a general one in physics, and the definition of 264 FUNDAMENTAL PRINCIPLES OF CHEMISTRY specific volume given in Sec. 12 is one of many examples of its use. As far as chemistry is concerned, it is usually best to refer the volume occupied by a given substance not to the gramme, but to the number of grammes of the substance which is equal to the combin- ing weight. Especially in the case of gases volumes so calculated are either equal or in some rational proportion. Among liquids and solids we have no such simple relation, but in many cases their volumes can be represented as sums made up of the volumes which can be given to the combining weights of the elements. Similar simple relations have also been found for many other prop- erties, and it is now-a-days customary in chemistry to express all the properties which permit such usage in terms of the combining weights. Considered as quantities, the combining weights are the units for the capacity factor of chemical energy. The capacity factor itself is expressed by the number of these units which enter a given system, in other words, the weights of substances taking part must be divided by their combining weights to find the number of these units involved. It is evident that in calculations of this kind the amounts of various substances which combine with each other, or react chemically with each other, will be expressed by equal numbers, or, in case multiple proportions are involved, by numbers which are in simple rational proportions to each other. A system of this kind is in general use in analytical chemistry. Solutions of various substances are prepared which contain a com- bining weight in grammes or a simple fraction of this amount, in a litre of solution. Such solutions react with each other in simple proportions by volume, and when a certain volume of such a solu- tion has been used in a given reaction with another body, measure- ment of the volume is sufficient to enable us to calculate the amount of the corresponding substance in the body under investigation. This method of determining the amount of a substance is called volumetric analysis. <^v**^ *V* OF THE UNIVERSITY CHAPTER VIII COLLIGATIVE PROPERTIES 171. THE LAW OF GAS VOLUMES. In our consideration of the general law of constant combining proportions it was men- tioned that among gases we would find another law of constant volume proportions. All gases change their volume in the same proportion under the influence of changes in pressure and tem- perature, and when two gas volumes have been measured under definite conditions their ratio remains the same whatever changes may be made in their common pressure and temperature. If we examine the numerical values of the volumes in which gases react with one another we find the following experimental law: The volumes are either equal or in simple rational proportion. This law holds not only for the case of two gases which are combining or reacting, but also for all cases where gases appear or disappear. If gaseous substances appear as two or more members of a reaction equation, the gases always exhibit simple proportions by volume, provided they are measured at the same pressure and temperature. The most general method of representing the amount of gas, independent of temperature and pressure, is given by the value of PV r in the gas equation PV=rT, for in this equation we have r = =-. In this form the gas law may be expressed as follows: If two or more gases take part in a chemical reaction their r values are either the same or in a simple rational proportion. 172. THE RELATION TO THE COMBINING WEIGHTS. If the law just expressed is compared with the law of the combining 265 266 FUNDAMENTAL PRINCIPLES OF CHEMISTRY weights a remarkable conclusion may be drawn. It is as follows : Amounts of different gases which correspond to the same r values must be either in the proportion of the combining weights or in the proportion of simple rational multiples of them. This law follows from the two following laws : All gases combine in the proportion of their combining weights. All gases combine in equal volumes or in volumes which are in rational proportion to each other. It follows directly that equal gas volumes are those which are in simple rational proportion, corresponding to weights which are proportional to the combining weights. Furthermore, the weights of equal volumes of gases are numeri- cally the same as the densities of the gases if they are based upon the unit of volume. It follows therefore that: The densities of various gases are in the same proportion as the combining weights of the gases, or simple multiples of them. Because of this direct relation it is possible to deduce the law of the combining weights from that of rational volume proportions. Suppose we have the same volume of any number of gases, a litre, for example (or, in general, amounts of the gases which have the same r), it will then be possible to carry out all the combinations, decompositions, or other chemical processes in which these gases take part in such a way that the total volume of each gas will always take part in the reaction. All chemical processes will take place between whole litres, though it will be necessary of course to use in some cases two, three, or some other number of whole litres in the reaction, but in no case will a fraction of a litre be used or produced. If we call the weight of a litre of each of these gases its combining weight, then it is evident that gases combine with each other only in the proportions of their combining weights, or integral multiples of them. So far we know this only for gases, but a high enough tempera- ture and low enough pressure are theoretically the only conditions which must be fulfilled to transform any substance into a gas. COLLIGATIVE PROPERTIES 267 There is therefore no fundamental reason to place a limit on the application of this law, and it can be extended to include all sub- stances with scientific probability. It is, to be sure, impossible to prove the gas law experimentally for all substances, since in many cases our means are insufficient to change substances into gases and investigate them in this condition. It is, however, possible to investigate the law of the combining weights, which has been derived from this law, for all substances, and it has been shown in the previous chapter that the law of the combining weights describes the facts accurately. The inverse process, i. e. the derivation of the law of gas volumes from the law of the combining weights, cannot be carried out. This means that the former law is the more general one, and that the gas volume law contains in itself, not only the law of the combining weights, but also another law relating to the gaseous state. 173. COMBINING WEIGHT AND MOLAR WEIGHT. The direct relation between combining weight and gas density suggests the idea that we might make use of the freedom left us in the choice of the rational factor of the combining weights (see Sec. 169), and that we might make these two things, combining weight and gas density, proportional, or even equal, by a proper choice of units. This idea was suggested soon after the discovery of the density relations between gases, but it leads to consequences which force us to reject it. It is impossible for us to have combining weight and gas density equal, and at the same time to satisfy the requirement that the combining weight of compounds should be equal to the sum of the combining weights of the elements involved. In order that these two principles should hold at the same time, the volume of the compound in the gaseous state must never be larger than the smallest volume of the gaseous elements which take part. Suppose we have a chemical reaction between gases repre- sented by the equation mA +nB+pC, etc.=rD+sE, etc., m, n, p, etc., and r, s, etc., representing the number of volumes of each 268 FUNDAMENTAL PRINCIPLES OF CHEMISTRY gas, arranged in order of magnitude (m > n > p, etc.), r can never be greater than m, for it must be equal to m or a rational fraction of m. Experiment has, however, shown numerous cases where r is greater than m, and if this is the case unit volume of D contains a fraction of the combining weight of A, and the composition of D cannot be represented in round numbers as the sum of the combin- ing weights of its elements. Experiment shows that it is impossible to choose combining weights in the ratio of the gas densities, and at the same time apply the principle that the combining weights of compounds shall be the sum of the combining weights of their elements. One of these two principles must be given up, and, so far as our discussion has shown, it makes no difference which of the two this is. There are, however, cases where the gas density of an element, i. e. the con- stant r, has been shown to be variable with pressure and tempera- ture, and therefore our original choice, by which we gave up proportionality between gas density and combining weight, is justified. We have retained the other principle by which combin- ing weights of compounds are made up as the sum of the combining weights of their elements, premising in this that no fraction of com- bining weights shall appear in our formula?. In order to express the law of gas volumes conveniently and simply, we have introduced a new concept to represent the weight of equal gas volumes, indicating their close relation to combin- ing weights. The weights of equal gas volumes are called molar weights. Molar weights are chosen as nearly like combining weights as possible. It follows from the relations just discussed that the molar weights of those elements which form gaseous compounds of greater volume must be chosen greater than the combining weights in the same proportion, i. e. the molar weight of the ele- ment will be to the combining weight of the element as the com- bining volume is to the volume of the element. Experiment has shown that this proportion is equal to two for many elements. COLLIGATIVE PROPERTIES 260 These elements never form gaseous compounds whose volume is greater than twice that of their own volume. It is therefore sufficient to make the molar weight of such elements twice the combining weight in order to avoid fractions in the writing of formulae. This settles the question concerning freedom of choice of the rational factor for the combining weights. The molar weight is by definition proportional to the gaseous density under normal condi- tions of pressure and temperature. The proportionality factor has been so chosen that the molar weight of a compound is the same as its combining weight, while for the elements mentioned above the molar weight is twice the combining weight. There are a few elements in which this relation does not hold. Some of them form gaseous compounds whose volume is, at the most, equal to the volume of the element, or in some cases a rational fraction of it. The molar weight of such elements is chosen equal to the combining weight. There are also elements which enter combination in four times the elementary volume. Their molar weight is therefore four times their combining weight. In all these cases, however, the relation once chosen holds for all gaseous compounds of the same element. An element which enters com- pounds with four times its elementary volume does not form com- pounds in which a triple volume or one five times the elementary volume is active. The deviations observed are cases in which, a rational fraction of the larger combining volume is found. For example, these same elements form occasional compounds whose gas volumes are only twice that of the elementary volume instead of four times. In these cases we must assume that two combin- ing weights of the element must be used in writing the molar formula for the compound. If m represents the greatest multiple of the elementary volume in which an element enters into com- bination, any other volume relation of this element can be repre- sented by the fraction , n being a whole number, showing the n 270 FUNDAMENTAL PRINCIPLES OF CHEMISTRY number of combining weights of the element which enter the compound in question. Our choice of a combining weight is limited by the considera- tions just mentioned. We must choose for it the greatest value which can be chosen without contradiction of our principle of integral coefficients. This fundamental principle could evidently be maintained if we assumed any rational fraction of this greatest value as the combining weight of the element, for then all co- efficients would be multiples in the corresponding proportion, and they would therefore still remain integral. For the sake of sim- plicity it is necessary to add one more condition, and this we do by choosing the greatest value as the value for the combining weight. In other words, the combining weight is so chosen that the coefficients necessarily applied to the element in the molar formulae of its compounds have no common factor. It is not possible to carry this out for all elements, for there are several which form no gaseous compounds within the limits of our experimental knowledge. Not only the volumes of gas, but also several other properties of substances, are brought into simple connection by the concept of molar weight. These regularities open other ways of making a definite choice of a combining weight. It has also been found that these various principles all lead to the same numerical re- sult, as far as the choice of a combining weight is concerned. At the present time we have a generally accepted system of these con- stants, and the old question about the best choice of a combining weight has completely disappeared. It is customary at the present time to write most of our chemical formulae so that they indicate, not only the combining weight, but also the molar weight of the substances involved. To do this a mol of one of the elements of Sec. 173, whose gaseous compounds have double volume, must be indicated as containing two com- bining weights. The chemical symbol for such an element will therefore have the form A 2 . The elements forming compounds COLLIGATIVE PROPERTIES 271 of fourfold volume are written B, etc. Chemical equations written in this molar form show immediately by definition the volume relations in which the substances should take part, com- bine with, or form from one another, as gases. Finally, we have found that the general chemical relations are most evidently and logically represented by molar formulae. This method of writ- ing equations is therefore based upon facts much more general than those representing gaseous volumes. 174. NUMERICAL VALUES. Molar weights correspond to amounts of the different gases occupying the same volume under the same conditions of temperature and pressure. In a strict system of units we would be obliged to choose the molar quantity having unit volume under unit temperature and unit pressure. Unit temperature would be 1 in the absolute system or 272 C., or what amounts to the same thing, in view of the gas law, ?fa of the volume at 0, the melting point of ice. Unit volume is 1 cubic centimetre. Unit pressure in absolute measures is , or 1 ccm. about the millionth of an atmosphere. If these values are sub- PV stituted in the gas equation, r = , amounts of the various gases so defined would give in each case r = l. Absolute units have, however, been considered only in late years, and by an historical development an entirely different and much larger unit than the one mentioned above has been developed and has come into general use. This means, of course, merely that molar amounts have been increased in a definite proportion, but it means also that the constant r of the gas equation has a different numerical value. At the same time it has remained equal for molar amounts of the various gases. We have arranged to so choose our molar quantities that their weight in grammes is equal to the numerical value of the molar weight, and therefore equal to the sum of the combining weights in the molar formula. In order that this may hold, the constant r 272 FUNDAMENTAL PRINCIPLES OF CHEMISTRY must be made equal to 82.1, the volume being measured in ccm. and the pressure in atmospheres.* If pressure is measured in absolute units, which are about a million times smaller, the constant becomes 83.2 x 10 6 . By definition this constant has the same value for molar quan- tities of all gases and vapours. It is therefore of very frequent occur- rence in chemical calculations. The. symbol R is generally given to it, and the gas equation containing it has the form PV = RT. All calculations which involve pressure, volume, density, and spe- cific volume of a gas can be carried out by the aid of this equation if the molecular weight of the gas is known. If M is this molecular * The relations between the unit of combining weight and that of molar weight have come down to us slightly complicated because of their remark- able historical development. Dalton, who developed the law of combining weights on the basis of a hypothesis concerning the atomic structure of matter, chose hydrogen as his unit, because this substance has the smallest atomic weight or combining weight. Because of the low value of the combining weight of hydrogen, compounds of this element are difficult to analyze, and Dalton made errors of about 20 per cent in his determinations. Berzelius made the first exact determinations of combining weights, and he chose oxygen as his standard, giving to it the combining weight 100 instead of 1 , in order to avoid using very small numbers. Later a reform was undertaken with respect to the rational factor of the combining weights (Sec. 173), and this reform took place in connection with the development of organic chemistry when it be- came evident that it was desirable to differentiate the new system as clearly as possible from the old one. The hydrogen unit of Dalton was therefore in- troduced again, since the relation between the combining weights of oxygen and hydrogen was thought to be accurately known. Later results showed, however, that this relation had been determined with much less accuracy than the relation of other combining weights, and oxygen was therefore made the standard element again for the same reasons as led Berzelius to choose it. The second time, however, the combining weight of oxygen was not taken equal to 100 as before, but equal to 16. This latter number is the combining weight of oxygen based on hydrogen as unit, and this ratio was assumed to be correct for many years. The relation is, however, more exactly 1 : 15.87 or 1.008 : 16. At the present time the combining weight of hydrogen is 1.008, and if changes in this number become necessary, this one element alone will be affected and not the other combining weights. If a change of this sort were to be made in oxygen it would be necessary to recalculate all the other com- bining weights, as they all depend directly or indirectly on the analysis of oxygen compounds. This basis for the calculation of combining weights has been reached by international agreement, and this insures the greatest pos- sible unanimity. COLLIGATIVE PROPERTIES 273 M MP M . weight we have, for example, = . is the weight of a ccm. of the gas, i. e. it is its density under the given conditions of tem- perature and pressure. If we make T=273 and P = l atmos- phere, we obtain the density under normal conditions. By inserting the normal values of pressure and temperature in RT the gas equation PV = RT, or V = -=j-, we obtain the molar volume of all gases, that is, the volume which is occupied by a mol in grammes of any gas, assuming normal conditions for pressure and temperature. This volume is 22,412 ccm. The specific volume of a gas under the same conditions may be found by dividing this volume by the molar weight. The molar weight in grammes is of frequent use in chemical calculations, and it is customary to use the name " mol" for it. A solution of 1 mol per litre indicates a solution containing a number of grammes per litre equal to the number of units in the molar weight of the substance in question. Such a solution is called a molar solution, and another solution containing ^ of a mol per litre is called a tenth molar solution. The name " millimol," the thousandth part of a mpl, or a molar weight in milligrammes, is used when small quantities of substance and dilute solutions are required. 175. THE PROPERTIES OF DILUTE SOLUTIONS. Attention has already been called to the fact that the equilibrium between a liquid and its vapour, or between a liquid and its solid phase, is changed when another substance is dissolved in the liquid. This change increases from zero as small amounts of dissolved substance are added, and is proportional to the content of dis- solved substance. All properties of a solution are functions of its composition, and these effects and the effect just mentioned are equal for solutions of equal composition. The effects just mentioned are always in a definite sense. The vapour pressure of the solvent is always lowered by dissolving the 18 274 FUNDAMENTAL PRINCIPLES OF CHEMISTRY other substance in it, and the freezing point of the solvent is also lowered in the same way. The first statement holds for the vapour pressure of the sub- stance which is present in excess, and which we have therefore called the solvent, and it does not hold for the total vapour pres- sure of the solution. In other words, the partial pressure of the solvent is decreased. It follows from this that a corresponding statement cannot be made for the boiling point, for the boiling point of a solution is higher than that of the solvent only when the dissolved substance is not measurably volatile. If the dis- solved substance has an influence on the composition of the vapour, the sense in which the boiling point will be changed depends upon this composition. If only .a very little of the dissolved substance is present in the vapour, compared with the amount in the liquid, the boiling point will rise, but by a less amount than would be the case if none of the dissolved substance went over into the vapour, If, on the other hand, a relatively large amount of the dissolved substance is present in the vapour, as compared with the amount in the liquid, the boiling point will be lower than that of the sol- vent. Finally, if the proportion is the same in vapour and solution no change in, the boiling point will occur. Proof of these state- ments may be drawn from a consideration of the boiling point lines of solutions, especially where we have a maximum or mini- mum boiling point (see Sections 106 and 109). Similar reasoning holds for the freezing point. It has just been said that ice * separates from a solution at a lower temperature than from the solvent. This holds, however, only under the as- sumption (usually fulfilled) that the ice itself is the pure substance. If a solid solution is formed, a set of conclusions precisely similar to those drawn for boiling points will hold. The freezing point sinks when less of the solid substance is present in the solid solu- tion than in the liquid one. If the inverse is true, the freezing * By ice is meant in general a hylotropic solid phase corresponding to a liquid. COLLIGATIVE PROPERTIES 275 point rises, and it will remain unchanged if the composition of both is the same. Solid solutions occur only rarely, and we will therefore leave out this possibility except in cases where it is spe- cially mentioned. 176. MOLAR LOWERING OF THE VAPOUR PRESSURE. All dissolved substances lower the vapour pressure, and within fairly wide limits they do so in proportion to the content of dissolved substance in the solution. The question therefore arises what property determines the amount of this lowering for a given con- tent of dissolved substance, or, it might be asked, what amounts produce the same lowering. The answer which experiment has taught us is that equimolar solutions correspond to the same lowering of vapour pressure. Equimolar solutions have been explained in the previous para- graph to be those which contain an equal number of mols of the dissolved substance in a given amount of solvent, or, what amounts to the same thing, they are solutions which contain an equal amount of solvent to a mol of various substances. It follows that a definite parallelism exists between the gase- ous state and the state of a dilute solution with reference to the dissolved substance. Equal volumes of different gases contain amounts which are in simple relations to the combining weights. In the same way an equal lowering of the vapour pressure corre- sponds to amounts of different substances which have the same simple relation to the combining weights. The amounts deter- mined in these two ways are, in the majority of cases, propor- tional to one another (or equal to one another if units are properly chosen). The determination of molar weights, which has so far been possible only in the gaseous state, can now be extended to apply to all substances which can be dissolved in any volatile solvent. Properties like this, which have the same value for equimolar amounts of different substances, are called colligative properties, and there are several of these beside gas volume and lowering of vapour pressure. 276 FUNDAMENTAL PRINCIPLES OF CHEMISTRY 177. OSMOTIC PRESSURE. The relation between the vapour pressure of a solution and that of the pure solvent depends, as do the other colligative properties which belong to solutions, on energy changes which become active when solutions are made. It has already been mentioned that a solution which has once been formed does not separate of its own accord into its original con- stituents without the expenditure of external work. It follows that when solutions are produced from their constituents work is given out which can be made useful by proper experimental arrangement. The same holds true when a gas is produced by any process. If P is the pressure under which it is evolved, and V the volume which it occupies, then, if the gas is to form, the pressure P must be overcome through the volume V. The work to be done is the product of pressure and volume, and is therefore PV. If a mol of each gas is produced, the numerical value for the work PV will be the same for each gas, and it will be PV = RT. This work is independent of the pressure P, for since pressure is inversely proportional to volume the product PV always has the same value no matter what the pressure may be. It will be noticed that this work is also proportional to the absolute temperature T, as will be seen in the formula. Conversely an amount of work PV must be expended when a gas disappears, that is, whenever it is changed into a solid or a liquid. The relation expressed as above, and including the concept of a mol, declares in other words that molar quantities of different gases are quantities such that the same amount of external work or volume energy is given out during their formation (assuming the same temperature in each case). These same quantities of different gases are also in simple proportion to their combining weights. Similar relations hold for solutions. If we permit a layer of pure solvent to flow over a solution the process of diffusion begins immediately. The dissolved substance spreads of its own accord into the solvent, and this continues until the concentration is equal in all parts of the solution. In the same way a gas spreads out into COLLIGATIVE PROPERTIES 277 a vacant space, and this process only stops when the concentra- tion of the gas is the same throughout the entire space. In the two cases we mean precisely the same thing by concentration, that is, the amount of the substance in question contained in the unit of volume, whether a dissolved substance or gas. Here con- centration by weight must be kept separate from molar concen- tration; the former is given by the weight in grammes which is contained in a cubic centimetre, the latter by the number of mols in the same volume. In gases the definition of concentration by weight is synonymous with density. Among solutions concentra- tion by weight gives the partial density of the dissolved substance in the volume occupied by the solution. Among solutions the pure solvent plays the same part that a vacuum plays for a gas. If a gas is bounded by empty space it can be prevented from spreading into it by interposing a solid partition. This partition will experience a pressure which depends upon the volume and the temperature of the gas. If these two factors are kept constant, molar quantities of various gases exercise the same pressure, and the numerical value of this pressure is given by P= . If a solution is bounded by a pure solvent, the dissolved sub- stance can be prevented from spreading into it by interposing a diaphragm. If this diaphragm is to experience a measurable pres- sure it must be able to move in such a way that the dissolved sub- stance can assume a larger volume, and in order that this should take place the dissolved substance must spread into a larger volume of the solvent. The partition must therefore be able to move through the solvent unhindered, that is to say, it must permit the solvent to pass through it, but not the dissolved substance. Such partitions may be found in plant cells. In a living state certain substances remain dissolved in the cell liquid, and these substances cannot leave the cell, even though it is in contact with pure water. The water itself passes through the cell wall without hindrance. 278 FUNDAMENTAL PRINCIPLES OF CHEMISTRY It is also experimentally possible to produce such walls artificially, at least for certain substances. Such membranes are said to be semi-permeable, and they play the same part toward dissolved sub- stances that solid walls would for gases. All the operations which can be carried out for gases by means of solid walls can be repeated in solutions with semi-permeable ones. It has been shown experimentally that the pressure experienced by such a semi-permeable membrane, when placed between solu- tions of different concentration, can be described by the same laws as those which describe pressure in gases. The pressure of a solution on such a semi-permeable membrane is called the osmotic pressure. Van't Hoff showed that this osmotic pressure is repre- sented by the gas law PV = RT. The osmotic pressure is inversely proportional to the volume, or, what amounts to the same thing, directly proportional to concentration or partial density. It is furthermore proportional to the absolute temperature, and, finally, under given conditions of volume and pressure, its numerical value is the same as that of the gaseous pressure which would be ex- hibited by the same substance if it occupied the same space at the same temperature in the form of a gas. It follows from this that the constant R has the same value for equal molar amounts of dis- solved substances and that this value is the same as for gases. If the pressure is measured in atmospheres, the equation PV = 82.lT holds for the osmotic pressure of dissolved substances. A dissolved substance therefore gives out or takes in work during a change of concentration just as a gas does during a change of pressure. It is, in general, possible to produce a change in the density of a gas (aside from the effect of temperature) only by the use of some mechanical means, such as a cylinder and piston. Changes in the concentration of solutions can, however, be brought about by any process by which solvent can be added or withdrawn. A semi-permeable membrane affords one means. Evaporating the solution so that the solvent escapes is another. A third con- sists in separating the solvent in the form of a solid phase, by par- COLLIGATIVE PROPERTIES 279 tial freezing, for example. From this point of view the necessity of the relation explained in Sec. 175 will be evident. A rise in boiling point, corresponding to an increased amount of work ex- pended on the solution, only appears when the vapour which sepa- rates contains less of the dissolved substance than the solution itself. If it contains the same amount no expenditure of work is necessary for the separation and therefore no change in the boiling point takes place. If the vapour contains more of the dissolved substance the opposite effect is to be expected. The solution is diluted by boiling, and the boiling point is lowered by a corresponding amount. Corresponding changes in the freezing point are directly con- nected with the boiling point changes just described by the rela- tions which exist between the vapour pressure of the solution and that of ice. They can therefore be deduced directly from them, as will be shown immediately. 178. NUMERICAL RELATIONS. The conclusions just reached can be expressed in formulae by the application of a principle which we have frequently used. That which is in equilibrium in one sense is in equilibrium in every sense. Let us imagine a solu- tion separated from a pure solvent by a semi-permeable membrane and held in equilibrium with it by the application of a hydrostatic pressure equal to the osmotic pressure. If such a system is in equilibrium we may be sure that it is in equilibrium for any process whatever, and, what especially interests us, for any process by which the maintenance of a definite concentration in the solution might be influenced. In other words, the determining quantities on which such a change would depend must have values such that the change is impossible. Fig. 64 represents a vessel of pure solvent, and standing in it a cylinder containing a definite solution and closed at the bottom with a semi-permeable membrane. The height of the cylinder is to be so chosen that its hydrostatic pressure is just sufficient to maintain equilibrium against the osmotic pressure on the semi- 280 FUNDAMENTAL PRINCIPLES OF CHEMISTRY -fl FIG. 64. permeable membrane. The system is then in equilibrium as far as osmotic pressure is concerned, that is to say, solvent will not leave the solution and pass out through the semi-permeable membrane, ^^_^^ producing a more concentrated jf "*^\ solution, nor can solvent enter the ' " cylinder, increasing the height of the liquid column and making the solution more dilute. One possibility, however, still remains open. The solution may become more dilute or more concen- trated by the transport of solvent through the vapour. If the solvent evaporated at the open end of the cylinder and condensed in the dish below the solution might become more concentrated, and vice versa. The principle we have just stated demands that both of these possibilities should be excluded. It might be reasoned at first sight that the vapour pressure of the solution must be the same as that of the solvent, and that therefore no effect should be produced on the vapour pressure of the volatile liquid by dissolving a substance in it. This conclusion contradicts experience, for it has been known for a century and more that the boiling point of water is raised when a salt is dissolved in it. In making this first conclusion we have overlooked the fact that the two vessels containing the same liquid, but having different levels, are by no means in equilibrium. If the two are connected by a tube the upper liquid will flow into the lower vessel by gravity, and if they are connected merely by a common atmosphere con- taining vapour the upper liquid will distil into the lower one for the same reason. For anything which is not in equilibrium in one sense cannot be in equilibrium in any sense. As a matter of fact there exists in this case a difference of pres- COLLIGATIVE PROPERTIES 281 sure between the upper and lower free surfaces of the liquid, and this difference is equal to the hydrostatic pressure of the vapour which fills the space. If then equilibrium is to exist in our apparatus with the semi-permeable membrane and the liquid column, the vapour pressure of the solution must be less than that of the pure solvent by an amount equal to the hydrostatic pressure of a column of va- pour as long as the column of liquid in the cylinder. The lowering of the vapour pressure stands in the same relation to the osmotic pressure as the density of the vapour does to that of the liquid. If we wish to express this in a formula, the height of the liquid and vapour column may be called h and the density of the liquid D. The hydrostatic pressure of the liquid, which is equal to the osmotic pressure P Q , will have the value P Q hD. The osmotic pressure has the same value as that of the gas pressure which would be experienced by the dissolved substance if it were present in gaseous form and with the same molar weight occupying the same volume as the solution. This pressure is given by the gas equation P^V^ RT We therefore have PQ = -=- . In this expression we must replace the volume V by a proper value for the solution. Suppose the solution contains N mols of the solvent to each mol of the dis- solved substance, and that M is the molar weight of the solvent, then the weight of solvent for each mol of dissolved substance is NM NM and the volume is - . Let us assume that the solution is so dilute that its density and volume are equal to that of the pure RTD solvent. We obtain for osmotic pressure the value PQ = AT ,,, and RT since P = hD the height of the liquid column h = We can now make use of this value to calculate the hydrostatic pressure of the vapour column. This pressure is kd, where d is the density of the vapour, and it represents the lowering of the vapour pressure produced in the solvent by the solution of the dissolved 282 FUNDAMENTAL PRINCIPLES OF CHEMISTRY substance. Let us designate this lowering by A, and we then have A = hd. To find the unknown d we may again make use of the gas equation as applied to the vapour. In the expression pv=RT p is the vapour pressure of the pure solvent and v the volume of a mol of the pure solvent at the pressure p. The density d is equal to the weight of a mol M of the solvent divided by the volume, and since v = - , d = = . Multiplying this value by the value of h, h = , we obtain A = hd = - , or = N. It will be seen that our final formula contains neither R, T, nor M, and that it is therefore exceedingly simple. The number of mols of solvent for each mol of dissolved substance is equal to the ratio of the vapour pressure of the solvent to the lowering of vapour pressure in the solution. Calling the molar concentra- A tion and the relative lowering of vapour pressure, we have the simple statement: the relative lowering of the vapour pressure is equal to the molecular concentration. 179. INTERPRETATION. The above result is remarkable for its simplicity. It contains neither the temperature nor any factor involving the nature of the substances concerned. The change in vapour pressure is referred exclusively to the ratio between the number of mols of dissolved substance to the number of mols of solvent. It is easy to see why the effect of temperature disappears. A rise in temperature corresponds to an increased osmotic pressure, since the latter is proportional to the absolute temperature, and we may assume that the volume of the solution remains constant because of the small coefficient of expansion which is characteristic of liquids. The density of the vapour will, however, decrease in direct proportion to the absolute temperature if the pressure re- mains the same. The column of vapour which determines the COLLIGATIVE PROPERTIES 283 lowering of the vapour pressure will therefore be higher at higher temperatures, but at the same time it will have a correspondingly lower density. The hydrostatic pressure will remain constant, and the effect of temperature disappears. The vapour pressure does not, however, remain the same, since it increases in accordance with laws which depend upon the nature of the liquid ; but the hydrostatic pressure of the column of vapour increases in the same proportion as the density of the vapour, and it has therefore under all circumstances a value which is the same fraction of the vapour pressure. It follows from this that, while the absolute lowering of the vapour pressure is not independent of temperature, the propor- tional lowering of the vapour pressure is quite independent of it, and this fact is expressed by the formula. The gas equation applies to both parts of the relation, the osmotic pressure, and the condi- tion of the vapour in the vessel. Factors which depend upon it cancel one another, and this leads to great simplicity in the result. The same reasons determine the fact that the molar proportion determines the relative lowering of the vapour pressure. The osmotic column h = is affected by the molecular weight M and the temperature T in the opposite sense from the effect due to the density of the vapour d = ^ . These two effects therefore HI cancel one another in the product, and there remains only the relation between molar proportion, vapour pressure, and lowering of vapour pressure, as given above. The osmotic pressure always has a positive value, and the column of liquid in this apparatus can only be raised and never lowered by its action. It follows necessarily that dissolved substances which exert an osmotic pressure can only decrease the vapour pressure of the solvent, and can never under any circumstances increase it. We know of some solutions which cannot be distinguished from ordinary solutions so far as their mechanical and optical proper- ties are concerned, but which exhibit no osmotic pressure. Solu- 284 FUNDAMENTAL PRINCIPLES OF CHEMISTRY tions of this kind are called colloidal solutions, and they have no measurable effect on the vapour pressure of the solvent. 180. THE EFFECT ON FREEZING POINT. The laws which describe the lowering of the freezing point can be deduced most directly by considering the vapour pressure of solution and ice. The same principle which enables us to deduce the laws describ- ing the lowering of vapour pressure from those of osmotic pressure leads to the conclusion that ice and solution can only be in equilib- rium at a temperature such that their vapour pressures are equal ; for if the vapour pressures are different, solvent distils over to form more ice and the concentration of the solution increases, or the reverse process takes place and ice distils into the solution, de- creasing the concentration of the latter. It is evident first of all that the solution cannot be in equilibrium with ice at the melting point of the pure solvent, for at that point the solid phase has the same vapour pressure as the liquid, while the solution certainly has a lower vapour pressure. The difference between the vapour pressure of the solid and liquid phases is such that the vapour pressure of the ice is greater above the melting point and smaller below this point than that of the liquid phase. The vapour pressure of ice and solution can therefore be equal only at a point which lies below the melting point of the pure solvent. In Fig. 65 the vapour pressure line of the pure solvent is labelled " water," and the vapour pressure line of the hylotropic solid phase is indicated by the line marked "ice." At the melting point / the two vapour pressures are equal, and below this point the vapour pressure of ice lies below that of the water. For the small differences which need to be considered the vapour pressure line FIG. 65. COLLIGATIVE PROPERTIES 285 of the solution is approximately parallel to that of the solvent, in agreement with the laws developed in the previous paragraph, and the distance between these two lines is proportional to the molar concentration of the solution. The freezing point of the solution is given as the point where the vapour pressure curves for solution and ice cut each other, and this follows from the general conditions of equilibrium. It will be noticed that it lies at a lower temperature than the freezing point of the pure solvent. If the vapour pressure lines are taken as straight lines throughout the region in question, and if we as- sume that the lines for water and solution are parallel, it is evident that the lowering of the freezing point is proportional to the lower- ing of vapour pressure. Their numerical ratio depends upon the angle at which the curves for ice and water cross. It follows immediately that equimolar solutions of various sub- stances in the same solvent must cause the same lowering of the freezing point, and experience proved this long before any relation to the laws of osmotic pressure was recognised. It is evident also that the lowering of the freezing point will be proportional to the molar concentration, and since the latter is proportional to the concentration by weight, the lowering of the freezing point must also be in the same proportion. This principle has been known for more than a century as an experimental fact. In various solvents the lowering of the freezing point must depend upon factors which determine the angle between the vapour pressure curves of ice and water. The development of the latter relation will not be taken up in this book, and its appli- cation will therefore not be considered. It may be stated, however, that this angle (or rather its tangent) increases proportionately with the latent heat of melting of the solid phase. It follows that the lowering of the freezing point will vary inversely as the heat of fusion, for the point of contact of the two curves will be farther from the melting point as the angle between them is made smaller and smaller. Experiment confirms this result also. 286 FUNDAMENTAL PRINCIPLES OF CHEMISTRY It may be asked in conclusion why the change in freezing point cannot be stated with the same simplicity as the lowering of the vapour pressure. The reason for this is that comparisons of the lowering of vapour pressures are made at constant temperature while the effect of the freezing point involves the use of different temperatures. It may also be asked what relation exists between the lowering of vapour pressure and the corresponding rise of the boiling point, since in this case also differences of temperature enter. A precisely similar set of conclusions leads in this case to a formula exactly similar to that for the lowering of the freezing point. 181. THE IMPORTANCE OF THE SOLUTION LAWS. The solu- tion laws enable us to determine the quantities of energy which correspond to the formation of solutions and also those which correspond to any change of concentration in solutions. They offer us the means of setting up conditions of equilibrium for all processes in which changes of concentration take place. They give us therefore a foundation for the study of chemical equilibrium in solution, for the theory of the electromotive force of a voltaic cell, etc. We shall not, however, take up these applications at present. The solution laws enable us to reach a theoretically complete solution of another problem which has already been mentioned. In Sec. 173 it was stated that the choice of combin- ing weights from among the possible values, with the aid of molar weights and the rule that no fractional combining weights should appear in the molar weights, is limited to a considerable degree. Gaseous compounds of many of the elements are either not known or exist under conditions which make measurement impossible, but with the aid of the laws of solutions molar weights can be determined for all soluble substances. Scarcely a substance exists for which a solvent cannot be found, and this means that it is generally possible to determine the molar weights of all the com- pounds of the elements. The probability that substances exist whose molar weight con- COLLIGATIVE PROPERTIES 287 tains only a fraction of the combining weight of one of its elements is therefore exceedingly small, and the combining weights now in use, which are based upon these extended determinations, must be considered as being sufficiently definite for all purposes. If this conclusion is to be used with complete scientific certainty, the question as to the relation between molar weights determined from the properties of solutions and those calculated from the properties of gases remains to be answered. The reasoning of Sec. 178 is applicable here. It was shown at that point that the law of the lowering of vapour pressure (which was originally an experimental fact) assumes on the one hand the law of gas pres- sure, and on the other hand that of osmotic pressure. These two laws are therefore supported by the experimental confirmation of the law of the lowering of vapour pressure. In the majority of cases experiment has confirmed the fact that the same molar weights are found whether they are determined from the gas pressure or the osmotic pressure. In individual cases larger values have been found for molar weights in solution than for the same substances in the state of vapour, but in these cases it can be shown with certainty that in the particular solutions in question multiples of the other molar weight are active. The nature of the solvent is an important factor. The same substance dissolved in various solvents is comparable with a substance under investigation at various temperatures, and even among the elements there are a few whose molar weight in the gaseous state is different at different temperatures. Another special case where the molar weight is too small in solutions will be considered more at length in the chapter on ions. 182. COLLIGATIVE PROPERTIES. J Those properties which are related to molar quantities are called colligative properties, and they have equal values for equimolar amounts of various sub- stances, wholly independent of the other properties of the sub- stances involved. Among these we find first of all the volume of gases, or, in more general terms, the R value in the equation of 288 FUNDAMENTAL PRINCIPLES OF CHEMISTRY condition for a gas, and the corresponding value in the equation for solutions. A second set of properties, including the lowering of the freezing point, lowering of the vapour pressure, and rise of the boiling point, all of which are determined by the equation of condition for solutions, also come under this head. The question arises whether other properties of the same sort exist, and if so what relation they exhibit to those already mentioned. It was shown in Sec. 169 that many properties assume values which are either equal or in simple rational proportion if they are based upon the combining weight of the substance in ques- tion. These will only be colligative properties in the sense of our definition if the rational factors, which must be used to make the values of the properties based on the combining weights equal, are the same for all properties (as they are for gases and solu- tions). This is not the case in general. Equal amounts of electricity do not appear during electrolysis with equal molar amounts of various substances. The rational factors in this case are wholly different. It is therefore necessary to introduce another idea, that of chemical equivalents. In the same way equal heat capacities correspond among the elements to amounts which are in the proportion of the combining weights. Among compounds heat capacities are proportional to the number of combining weights of the element in the compound. One other property, which is called molar surface energy, is, however, very nearly a colligative one. This holds for pure liquids, and we can determine molar composition with its aid if we assume that it is a colligative property. This assumption is supported by the far-reaching agreement between molar weights determined by this and the other methods. Even the singularities which corre- spond to differences of molar weight in solutions in various solvents find their corresponding expression in differences in molar surface energy. The molar concept has so far attained no importance among solids in the sense in which it is here used. No satisfactory method has yet been developed for measuring the amount of COLLIGATIVE PROPERTIES 289 work corresponding to the formation of solid solutions or to changes in them. There is, however, no fundamental reason why such a process should not be discovered, and if it is, all of our reasoning would be applicable to solid solutions. It would also be possible to make use of the same set of relations for pure solids if colliga- tive properties were known among them. No extension of the law of the equality of molar surface energy (at constant temperature) to include solid substances has yet been made, because measurement of surface tension among solids is still accompanied by very great difficulties. Other difficulties arising from the crystalline structure must also be overcome.* * It is necessary to differentiate carefully between conclusions like these and hypothetical investigations of so-called molecular size among gaseous, liquid, and solid substances. By this is meant the size of the hypothetical molecules, which are denned as the smallest amounts of substances which can exist independently. Various considerations, all of which contain a larger or smaller number of arbitrary assumptions, or other uncertainties, have been applied with the hope of reaching conclusions about molecular sizes. Such processes lead to the assumption that the weights of the molecules must be proportional to the molar weights, as calculated from the laws for gases and solutions. 19 CHAPTER IX REACTION VELOCITY AND EQUILIBRIUM 183. REACTION VELOCITY. A definite time may be said to be a function of every physical process. So far in our discussion we have made the assumption that time has no effect on the factors considered. This includes another assumption, which is that the phenomena in which time is a factor have already taken place, and that we have arrived at a condition which is no longer variable with time. Every system, so far as we know, tends toward this condition. Every unequalized difference in energy is a reason for something happening, the differences tend to equalize each other, and such a change is necessarily coupled with changes in the condition of the system considered. Changes in the amount of energy present, by a decrease in such differences, determine everything that happens in the light of final analysis, or at any rate they determine something which is so nearly related to what happens that it may be considered as the actual thing itself. Such occurrences result in the equalization of energy differences, that is to say, the difference decreases towards zero, and therefore every occurrence produces by its very nature a decrease in the cause of the occurrence, and so limits itself. When the energy difference is equalized there is no longer any cause for the occurrence of any further process. It follows from this that every process proceeds more and more slowly as it approaches its end, and therefore if we are dealing with continuous phenomena the end itself can only be reached after unlimited time. The chemical reactions which we call homogeneous, those which take place in a single phase, are repre- 290 REACTION VELOCITY AND EQUILIBRIUM 291 sentative of this, since no discontinuities have ever been observed in them. Our appliances for testing and measuring substances are, however, exceedingly limited in their sensitiveness, and in every such reaction a definite time can be observed, after which no further changes can be observed in the system. This time increases as our experimental methods improve, but nevertheless remains finite. The assumption which we have used, i. e. that the systems ex- amined are in equilibrium and unaffected by changes in time, may be regarded as fundamentally justifiable, and as being attainable under proper conditions. Anything which lies outside of our powers of measurement and observation is not an object of ex- perience. It is not the duty of science to make any statements about such things, and moreover science has no right to discuss such objects. We certainly do not know whether the processes which we assume to be continuous remain continuous in regions where we cannot follow them. If they do not, our assumption concerning the unlimited course of such processes has no value. Processes which take place in time are characterized by a velocity. There are as many kinds of velocity as there are differ- ent kinds of processes which take place in time, and for chemical processes we need to define chemical velocity. Chemical processes depend upon the appearance and disappearance of substances, and changes in the amount of the substances involved can be measured. Chemical velocity is therefore the ratio of this change in amount to the time which elapses during the change. The unit of time in this case, as in science in general, is the second, and there are 24x60x60 = 86,400 of this unit in a mean solar day. The unit in which the chemical change is to be measured requires some consideration. Relative and not absolute amounts of substances are used in this measurement, and therefore chemical velocity, or reaction velocity, as it is called, is calculated in terms of the change in relative amounts of the substances involved. Various substances 292 FUNDAMENTAL PRINCIPLES OF CHEMISTRY are not to be measured by weight, but in terms of some chemically comparable unit. The most convenient unit has been found in the molar weight (not the combining weight), and it is therefore usual to use molar formulae in expressing results. Suppose that we are considering a chemical reaction which is described by the general equation m 1 ^4 1 + m 2 ^4 2 + m 3 v4 3 + . . . =n 1 B 1 +n 2 B 2 + n 3 B 3 + . . . The reaction velocity of this process will be expressed in terms of changes in the relative amounts of A L , A 2 , A 3 . . . or B lf B 2 , B 3 . . . . Various methods of expression are possible, but the most usual one is to define chemical equilibrium in terms of the molar con- centration of the substances which take part in the reaction. By molar concentration is to be understood the reciprocal of the volume in which a mol of substance is contained, and this value is to be found by dividing the number of mols of the substance in a given system by the total volume. This method of calculation only leads to simple relations when the volume of the system remains constant during the reaction. In the majority of experiments which have been made in this field this assumption is realized (at least very closely), and we can therefore retain this method of calculation. It is of great advantage, for the law which relates reaction velocity to concentration is so simple that the correspond- ing theoretical considerations take on an especially simple and evident form. It should be kept in mind that the reaction velocity for a process may have different values depending on the sub- stance used as basis for the calculation, provided the molar co- efficients m lt m 2 , ra 3 , . . . . n lt n 2 , n s . . . in the general equation do not happen to be all equal to unity. But because of this very equation the values for the velocity based upon different sub- stances will necessarily be in simple rational proportion, and this proportion will be determined by the reciprocals of the molar coefficients. Reaction velocities based upon the formation of substances are usually termed positive; those based upon the disappearance of substances are termed negative. All velocities which are based REACTION VELOCITY AND EQUILIBRIUM 293 on substances appearing on the same side of the reaction equa- tion will therefore have the same sign. 184. VARIABLE VELOCITY. We have now given definitions for the two quantities which determine a reaction velocity, con- centration and time. We may next define reaction velocity in any given case as the change in the molar concentration which takes place in one second. Such a definition as this is not clear, however, because the velocity of chemical reaction is in general variable. If the reaction is investigated at various stages wholly different values for the velocity, as defined above, will be obtained. The velocity is itself a function of the time or of the other variable, the concentration, which changes with time. Furthermore the velocity is different at the beginning and the end of the second during which the change is to be measured, and different results will be obtained for the velocity at any time, the results varying with the duration of the observation. In such cases the velocity cannot be based upon a finite duration, but must be calculated for a time which is immeasurably short. If we call such a short time dt, and call the change of concentration which takes place in this time dc (this must also be immeasurably small), the definition of a variable velocity is given by the expres- dc sion . Small values of this kind cannot be measured, and we dt must therefore fix them by indirect means. This can be done either by calculation, in case we know velocity as a function of the concentration, or by experiment. W^e can replace the im- dc measurably small values in the expression by finite ones which dt can be observed and measured, and which we will designate with ^^(* (],(* Ac and A/ ; then the value of approaches the value of as Ac * Xf ( / / /\f* and A are made smaller and smaller. may be determined for finite and easily measurable values, and then for values one half as large. If the two quotients show a considerable difference^ 294 FUNDAMENTAL PRINCIPLES OF CHEMISTRY smaller intervals must be chosen. An approximate value for the velocity has at any rate been obtained, and this can be improved in various ways, which will not be described at this point. 185. THE LAW OF REACTION VELOCITY. The convenience attained by relating reaction velocities to the concentrations of the substances involved is immediately evident, for it leads us to the expression of a very simple law. Under similar conditions the velocity is proportional to the concentration of the substances which take part in the reaction. If only a single substance is changing its concentration this law, as stated, is quite sufficient. If several substances take part in the reaction the velocity is proportional to the concentration of all of these substances and therefore to their product. These concentrations may decrease during the process, or, if the quantities consumed are replaced from another phase, they may . remain practically constant. Differences of this kind affect the detail of the course of the reaction, but do not affect the general character of the phenomena. The history of the discovery of this law is a complicated one with chapters lying very far apart. The fact that under otherwise equal conditions reaction velocity is proportional to concentration was expressed by C. F. Wenzel in the second half of the 18th century, but without any experimental support. About the middle of the 19th century Wilhelmy investigated the course of a typical chemical reaction of the simplest sort both experimentally and theoretically, and in a completely convincing manner. Cases in which several substances react w r ere considered by Wilhelmy, but these cases were only subjected to thorough treatment about 1860 by Harcourt and Esson and by Guldberg and Waage. Berthelot and Pean de St. Gilles had made measurements on a more compli- cated case previous to this time but their treatment of the case was not wholly correct. The characteristic or normal course of a chemical reaction fol- lows the general law that reaction velocity is proportional to the product of the concentrations of all the substances involved. The REACTION VELOCITY AND EQUILIBRIUM 295 concentration of the original substances always decreases and never increases during the reaction. Under certain circumstances it may remain practically constant. It follows that the product on which the calculation is based has its greatest value at the begin- ning of the reaction, and that it either decreases or, at most, re- mains constant during the progress of the reaction. Every normal chemical process which takes place under constant conditions of temperature and pressure, and therefore in such a way that only the concentrations change, begins with its greatest velocity, and the velocity decreases during the process, finally approaches zero asymptotically. Theoretically it requires infinite time for the reaction to reach completion; practically a limit is set by the limited accuracy of our methods of determining small changes. Deviations from this typical course appear when the conditions just mentioned are not satisfied. Suppose that heat is developed by the reaction, and that this collects in the system and results in a rise of temperature. The velocity will be increased, and the pro- cess may take place in such a way that it begins slowly and then increases in rapidity. Finally, however, the reacting substances will become exhausted and the reaction will proceed more slowly. The asymptotic end of all reactions is therefore a general rule. The case is similar when a substance which accelerates the course of the reaction is produced during the reaction. In this case also the reaction velocity will first increase, then decrease, and finally drop to an infinitely slow rate. 186. CATALYSERS. The velocity with which various chemical processes take place varies in different cases between the extreme limits of measurement. In other words, chemical processes are known which proceed so rapidly, and others which proceed so slowly, that we are quite unable to determine their duration. Two wholly different things must be kept separate in this connection. If we cause a chemical process to take place between two sub- stances two liquids, for example by bringing them in contact, the reaction will at first take place only where the different sub- 296 FUNDAMENTAL PRINCIPLES OF CHEMISTRY stances come in contact. The reaction takes place at the surface where the substance A is in contact with the substance B. A layer made up of the product of the reaction forms between the two masses. This layer must be removed in some way if the process is to continue. Removal takes place by diffusion and convection. The first of these effects depends upon the fact that all the sub- stances within a phase tend to distribute themselves equally through- out it. If an inequality is present the substances are set in motion automatically to restore the equality. Such processes take place rapidly only through very small distances, and the time required becomes large if the distance to be passed over be only a few mil- limetres. Convection or mechanical mixing is of assistance. By stirring, beating, and similar movements the surfaces at which the various substances are in contact are increased and moved into hitherto inactive portions of the liquid. After this, diffusion has only to take place through very short distances. The mechanical hindrance to a chemical process can be very greatly reduced in this way. These things are of great practical importance, but they have no direct bearing on the velocity in the chemical sense of the term. In many cases it is possible to complete this mechanical mixing between various substances before an appreciable, or at any rate considerable, fraction has reacted chemically, and from this point on the true reaction velocity shows itself. The chemical process takes place slowly in the homogeneous solution, and may be fol- lowed by measurement of the corresponding change in its proper- ties. Slow and rapid processes may be differentiated now without difficulty; some of them are so rapid that the reaction is complete as soon as mixture is complete. In this case it is only the end products which are open to investigation. Other reactions are so slow that the properties of the unchanged original solution can be determined at leisure before the chemical process has exerted any appreciable influence upon them. We must of course assume that, theoretically, a portion of the substances involved has been trans- REACTION VELOCITY AND EQUILIBRIUM 297 formed in this case as well as in others, and all that we can state is that this portion is, under some circumstances, quite inappreci- able. This can be proven by repeating the measurements after an interval to see whether the same result is obtained. The factors which determine the velocity in any given case are still to a large extent unknown to us. Temperature has a very great effect on reaction velocity, the latter increasing rapidly with rising temperature. Chemical reaction velocity is the most variable of all the things which vary with temperature; in round numbers it doubles for a temperature increase of 10.* One of the properties which varies most rapidly with temperature is the viscos- ity of liquids and this changes by about 2 per cent per degree, doubling its value for a temperature change of about 50. The increase in reaction velocity is an exponential function of the temperature. An increase of 10 in temperature doubles it; for 20 it is multiplied by 4, for 30 by 8, etc. It will be seen from this that a rise in temperature of 100, a very moderate one practically, corresponds to an increase of a thousandfold in reaction velocity. Reaction velocity shows a similar sensitiveness to other effects. A change of solvent in which given substances react under other- wise constant conditions of concentration and temperature may produce a change in velocity within the most extreme limits. The same substances may react stormily or appear practically indiffer- ent to each other, so that no apparent change takes place after hours and days, and this variation may be produced by changing the medium in which they are dissolved. Nothing very definite is known of this effect, but it may be stated broadly that those sol- vents which contain oxygen usually exhibit more rapid reactions than those which are free from oxygen. There are also a large number of substances which affect the velocity of a given reaction even when they are present only in * The change in vapour pressure of a liquid is a function of the temperature of about the same order. 298 FUNDAMENTAL PRINCIPLES OF CHEMISTRY very small amount. In the majority of cases these substances do not take part in the chemical process, or at least they are found practically unchanged in amount in the reacting mixture before, during, and after the reaction. It does not necessarily follow from this that they take no part in the reaction. We need only to assume that their activity is a transient one, and that they are formed in unchanged amount from the products of reaction in case they do react with any of the substances present. They may, for example, be constituents of intermediate products of the reaction, and as the process goes on these intermediate products are broken up, setting the original substance free. Such substances are called catalysers, and they show the same remarkable versatility in their quantitative effects as has been already observed in reaction velocities in general. The very smallest amounts of substance sometimes show very considerable effects, and of all our methods of detecting very small amounts those which depend upon catalytic action are by far the most sensitive. Sometimes our ordinary means of detecting a definite substance fail completely, and a. given object may appear to be completely free from that substance. In these conditions it is sometimes possible to prove the actual presence of the substance by measuring the catalytic effect of the other substance in which it is supposed to be contained. The greatest dilution in which a particular element has been determined in this way is about one mol in a billion litres. A catalytic effect is, in the majority of cases, an acceleration of a reaction, that is, an increase in reaction velocity. It is not yet completely decided whether or not there are any negative catalysers, or whether the actually observed decrease in reaction velocity is a secondary effect due to small amounts of foreign substances. These would act by destroying the effect of accelerating catalysers which might be present. However this may be, negative catalysers are comparatively much rarer than positive ones, of which there are a very great number. REACTION VELOCITY AND EQUILIBRIUM 299 Catalysers are all more or less specific in their action, and each special reaction shows its own individual peculiarity with respect to foreign substances which affect its velocity. There are, to be sure, some substances which catalyse many different reactions, but their effect cannot be reduced to two factors, one of which depends only on the catalyser and the other on the reaction. In- fluences are active which differ from case to case, and no relation with other properties or factors has as yet been recognised. The predominance of positive catalysers is connected with the fact that very pure substances often react extremely slowly with each other. The active amounts of catalytic substances are often very much smaller than anything we can detect by other means. It would therefore be impossible to refute the statement that pure substances do not react at all with appreciable velocity, and that all our actual reactions are caused by the presence of extremely small amounts of catalytically active, foreign substances. If this statement cannot be refuted it is also, and for the same reasons, impossible of proof. It can, however, in general be concluded that an unknown catalyser is active whenever the velocity of a certain reaction is found to vary under apparently constant con- ditions, the concentration or some other peculiarity of the catalyser constituting a variable among conditions which we are assuming constant. 187. IDEAL CATALYSERS. The existence of catalysers is of importance in the general theory of chemistry, for they enable us to carry out idealized simplifications of actual processes. Every science makes use of these idealizations. In mechanics, for ex- ample, absolutely stiff bodies, absolutely mobile liquids, etc., play an important part. In other divisions of physics we use absolutely perfect gases, which obey the gas equation exactly, absolutely per- fect insulators for heat and electricity, absolutely black bodies, perfectly reflecting mirrors, etc. None of these things exist as a matter of fact, and their assumption constitutes a conscious devia- tion from the true conditions. They are, however, limiting cases 300 FUNDAMENTAL PRINCIPLES OF CHEMISTRY toward which actual things approximate more or less perfectly, and they also permit of simple numerical treatment because of the simplicity in the assumptions made in treating them. Results of calculations based on them are therefore never absolutely cor- rect, but these ideal cases have been so chosen that the result approaches accuracy in the same measure that the actual con- ditions approach those assumed. This permits of a corresponding predetermination of actual conditions. A further advantage is afforded by these limiting cases. They teach us the aspect of actual phenomena which are best suited to lead us toward the ideal limiting case. For example, the formula for the ideal pendulum indicates immediately the best way to construct an actual pendu- lum which will possess the most important property of the ideal one, equal time of swing. In this sense catalysers afford a theoretical means of producing ideal chemical conditions. Suppose that we are examining a sys- tem in which a reaction is taking place very slowly indeed. If we add an exceedingly active accelerator the system becomes free from changes in time, that is, it enters a state of equilibrium. All the investigations which we have carried out up to now can be con- sidered as having been carried out in this ideal way. All these chemical processes might have taken place under the influence of such an ideal accelerator, for we have invariably started with the assumption that complete equilibrium existed. Or, on the other hand, we might assume ideal negative catalysers, or the equivalent assumption that no reaction takes place without an accelerator and that no accelerator is present. Every system in process of chemical change could then be fixed firmly in its condition, and the substances present considered as exerting no further effect on each other. None of these things can be carried out actually, and this is in agreement with the physical ideals considered above. Our method shares with them the advantage that it permits of far- reaching simplification and of arriving at conclusions which ap- proximate the actual facts more or less closely. REACTION VELOCITY AND EQUILIBRIUM 301 In making use of any such idealization the question must always be raised whether the assumptions do not conflict with any actual relations, for, if they do, conclusions drawn will no longer be limit- ing values but false ones. It is, in general, impossible to answer such a question exhaustively, but it is possible to show a contra- diction with the most general of all laws, the laws of energy, if any such contradiction exists. In the case of the ideal catalysers it does not exist. The assumption of these accelerators presupposes that the velocity of a chemical process may have any value between zero and infinity without a proportional variation in the energy involved. It is a physical fact that catalysers do exist which permit of variations in reaction velocity between very wide finite limits, though not, of course, between infinite limits. With their aid it has been proven that very large finite variations in reaction velocity can be brought about without expenditure of energy, and the transition to ideal catalysers is therefore justified. As far as energy is concerned, only the final condition of a system is determined when the conditions affecting it are stated. Nothing need be given about the time within which this final condition is to be reached. As among mechanical, electrical, thermal, and other systems, other factors are effective in chemical systems also, and these factors are not definitely determined by the two laws of energetics. A corresponding freedom remains in the matter of reaction velocity. Reaction velocities can vary from zero to infinity, and this corre- sponds to a degree of complexity among chemical systems far greater than any which could be foreseen from our previous dis- cussion. Systems which are by no means in equilibrium, but in which the reaction velocity is infinitesimal, appear to us as systems in equilibrium. It means also that substances and solutions which would have been for ever unknown to us, if all earthly chemical processes took place within unlimitedly high velocities, are open to our observation and demand our consideration. New problems, especially those of isomerism and constitution, are presented to us as a result, and they will be taken up later. 302 FUNDAMENTAL PRINCIPLES OF CHEMISTRY 188. CHEMICAL EQUILIBRIA. Suppose we have a reaction equation of the form m l A 1 +m 2 A 2 + m 3 A 3 + . . .=n 1 B 1 +n 2 B 2 + n 3 B 3 + . . ., the substances at the left being transformed into those at the right. It is often possible to find conditions of temperature and pressure such that the reaction takes place in the opposite direction, the substances at the right disappearing and those at the left being formed. It will be remembered that it requires an unlimited number of operations to separate the two constituents of a solution completely. The converse of this would be that the first traces of substances would appear with unlimited intensity in systems where these substances do not exist, but in which they can be produced from other substances which are present. As a matter of fact we would be very nearly in agreement with observed facts if we should assume that all the substances which are possible under given conditions are really present, though they are often present in concentrations lying more or less below the limit of detection. There is good reason for this assumption, for, as our analytical methods advance, more and more processes are found which are actually limited by an opposing process in just the way that has been mentioned above. The number of processes which belong to this class is being constantly increased by these discoveries, and processes once placed in this class always remain there. It follows that the class must always increase and never decrease. No characteristic has ever been discovered which differentiates these balanced reactions from the others, which we are obliged to consider as one-sided for lack of proof that the opposed reaction takes place. We are in agreement with the general inductive methods of science if we assume that all reactions belong in the class of balanced ones, at least until proof is given that this is not true. This conclusion is limited by the assumptions involved in it. Our reasoning is based upon a general property of solutions, and its application must therefore be limited to solutions. If there- REACTION VELOCITY AND EQUILIBRIUM 303 fore a chemical reaction takes place among solids which are not mutually soluble in appreciable amount, it is not necessary to assume a chemical equilibrium in which all possible substances are actually represented. It may still be doubted whether this new assumption of mutual insolubility is fulfilled even among solids, and it seems possible that our general reasoning may be applicable to them also; but if the limit of solubility is beyond experimental investigation it has no practical interest, and these cases may be treated as though the substances involved were per- fectly insoluble in each other. This conclusion, which was reached experimentally, is in no way different from the one which might be drawn from the assumption that the solubility among solids is finite but small beyond the limits of measurement. Under the given conditions each reaction will, in general, take place in both directions, but the final result of the reaction will depend upon the velocity of each of the two opposed reactions. The observed change will be made up of the difference of the two opposed reactions. Let us suppose to begin with that one of the two processes predominates, and that this is the direct one. The concentration of the substances which are in transformation will be constantly decreased by the reaction, and the concentration of the products, that is to say, of the substances which produce the opposed reaction, will increase simultaneously. Both causes will act in slowing down the direct action and in accelerating the op- posed one, and this will continue until both processes are taking place with the same velocity. From. this point on there will be formed in unit time an amount of the products of the direct re- action equal to the amount used up, and the condition of the system will no longer change with time. This is the definition of a chemical equilibrium, and it is characterized as such in a system containing several substances in one homogeneous phase by the fact that all possible substances are present in definite concentrations which vary with pressure, temperature, and the nature of the substances involved. 304 FUNDAMENTAL PRINCIPLES OF CHEMISTRY It happens very often that these concentrations are immeasur- ably small for substances which lie on one side of the reaction equation, and in this case the reaction is practically unidirectional. Such cases have always been of special interest in experimental and technical chemistry, since they permit of the preparation of pure substances with the greatest ease, and pure substances are, and always have been, of great interest both in science and in technical affairs. The idea that such unidirectional processes were normal or typical ones, while chemical equilibrium with its finite concentrations of the substances involved was an exception, has been handed down to us from earlier times. As our knowledge of chemical reactions became more complete and extended it was found that these finite equilibria were not by any means rare, and they are of much greater theoretical interest at the present time than other reactions. 189. MORE THAN ONE PHASE. The appearance of a new phase beside the original one produces a very great effect upon the equilibrium of a given chemical system. As we have already seen, the concentration of the individual substances existing side by side in several phases affect each other mutually, and the result is a condition of " saturation." If we have a gas in contact with a liquid its concentration in the liquid can never be greater than that given by Henry's Law (Sec. 98). If the gaseous substance in question is produced in the liquid phase until the solution contains a larger amount than is permissible by Henry's Law, the excess escapes in the form of gas. As this takes place further amounts of the same substance are produced, and the equilibrium in the liquid phase is shifted more and more in the sense which permits of the formation of more gas. Finally, saturation equilibrium with the gas phase is attained in addition to any other chemical equi- librium which may exist in the liquid. If the saturation equilibrium corresponds to a very small amount of dissolved gas, because of low pressure and slight solubility, then the reaction within the liquid will go on until equilibrium is reached as the result of this REACTION VELOCITY AND EQUILIBRIUM 305 small concentration. This means that the reaction by which the gas is formed will be greatly predominant over the opposed reaction, and it may often appear to be a practically com- plete one. This peculiarity among chemical equilibria was noticed more than a century ago by C. L. Berthollet. He recognised that the tendency of a substance to take on gaseous form (he called it " elas- ticity") was a circumstance which favoured the almost exclusive formation of this particular substance by chemical reactions in which it could appear. Similar conditions are applicable when one of the substances in question possesses the property of separating as a solid phase of slight solubility. Here again the greatest concentration which this substance can have in the liquid is given by the concentration of its saturated solution, and the equilibrium will therefore shift as the solid phase separates until the concentration of saturation in the solution is sufficient to maintain equilibrium against the concentration of the other substances. The formation of such a difficultly soluble solid will, under these circumstances, take place so easily that the reaction will often appear to take place exclusively for the benefit of its formation. Berthollet understood this case also and called it the effect of " cohesion." We have developed this case for the liquid phase made up of a solution of the substances taking part, and a precisely similar conclusion may be drawn for the case where the solution phase is gaseous. The great rarity of solid solutions practically excludes the third probability. 190. THE LAW OF MASS ACTION. Our conclusions concerning the setting up of a chemical equilibrium by the equalization of op- posed reaction velocities leads directly to a mathematical expression in which the equilibrium is expressed as a function of the concen- trations of the substances which take part. It is only necessary to set down the velocities of the two opposed reactions as being 20 306 FUNDAMENTAL PRINCIPLES OF CHEMISTRY equal. If m^A v + m 2 A 2 + m 3 A 3 +..-= n l B l + n 2 B 2 + n 3 B 3 + . . and a 1} a 2 , a 3 and b lt b 2} b s are the concentrations of the substances on the two sides of the reaction equation, then the velocity of the first reaction is given by the expression (^ = & 1 o 1 mi a a " l a i w , and that of the second by c 2 = k^b^b^bs 713 . The two velocities are to be equal, and therefore k l aj n *aj n *aj n * - = kjb^b.pbj 1 * - , or writing ^_ a^a^a^^ &i ' b^b^bsn,..- ' Expressed in words, equilibrium exists if the product of the con- centrations on one side of the reaction, divided by the correspond- ing product for the other side, is a constant. It should be noticed that this constant is only to be considered as constant with respect to differences of concentration. Its value still depends upon the temperature. The special cases mentioned in the previous paragraph follow directly from this formula. Let us consider the simplest case, - in which only one substance is present. The reaction will be mA=nB, and the equation for equilibrium will be r^- = K. If the concentration b is reduced in any way 4^y the formation of a gas or of a difficultly soluble solid, for example, then a must also decrease in the same proportion if K is to remain constant. This means that a corresponding amount of A will change into B before equilibrium can exist. As far as the formation of B is concerned the reaction is practically complete. Similar conclusions apply when several substances occur on one or both sides of the equation. If one factor of the product is very small the entire product must be small, for it is not usually possi- ble that another factor should be very large at the same time. The concentrations of substances have finite limits because of their finite specific volumes, and it is only possible to compensate for the small value of one factor by an increase in another within a very narrow range. REACTION VELOCITY AND EQUILIBRIUM 307 191. EXPLANATION OF ANOMALOUS CASES. Science is forced to the assumption of chemical equilibrium between opposed re- actions in another way. The assumption is necessary for the ex- planation of certain contradictions between general laws which are characteristic of the properties of pure substances. Gases are known which appear hylotropic throughout a large range of pressures and temperatures. Judged by this criterion they act like pure substances, but these gases by no means obey the general laws of gases. They do not exhibit the normal coefficient of ex- pansion', their volume is not inversely proportional to the pressure, and they do not follow the volume law of Gay-Lussac. These contradictions are removed, and these gases can be arranged under general laws, if we assume that they are mutual solutions of two or, more substances which can react with one another chemically. But we have said that solutions of gases behave like pure sub- stances as far as obedience to the general equation is concerned, and the assumption just made cannot therefore explain these deviations. If we make the further assumption that the ratio of the constituents in the solution changes with temperature and pressure, it is possible to explain the anomalies in question, pro- vided the volume changes during reaction. Suppose a reaction of the form A 2 = 2A, A being either an element* or a compound. A solution of these substances A and A 2 would behave in the man- ner just described, provided the proportion of the two constituents changed with pressure and temperature. If a decrease of pressure causes A 2 to change into A the gas will behave normally under very small or very large pressures, for in the first case it will con- tain almost wholly A and in the second almost wholly A 2 , in either case with only a minute amount of the other substance. Consider- able changes of temperature must produce the same effect if the equilibrium is variable with temperature. These peculiarities correspond very closely with those actually observed. All of these irregular gases become normal at high temperatures and low pres- sures, and under these conditions they obey Gay-Lussac's Law. 308 FUNDAMENTAL PRINCIPLES OF CHEMISTRY This idea has also other applications. Let us apply the law of mass action, as given in Sec. 190, to these chemical equilibria, and especially to their dependence upon pressure, which is, in this case, proportional to concentration. With the aid of this law it is possible to represent quantitatively, not only the limiting con- ditions, but also all the intermediate states of this system. Sup- pose we have 1 mol of the substance A 2 , and we will assume that a fraction x of this mol has been transformed into A. The state of the gas solution can now be determined by the statement that its r value must be made up of the sum of the corresponding partial values of the constituents A and A 2 . 2x mols of A are present and l-x mols of B. We have therefore r=(l-x)R+2xR = (l+x)R and the equation pv(l+x)RT will hold for the solution. If # = 0, pv = RT; if x = l, pv = 2RT, and these are the two limiting cases. If p, v, and T are measured for an amount of gas correspond- ing to 1 mol of A 2 , x can be determined for any given condition. From r = (I + x)R we obtain x = . r has been measured and R R has a constant value (see Sec. 174), and the value of x is thus determined. Applying the law of mass action to this case we obtain the equilibrium equation ^| = K from the reaction equation A 2 = 2A. The concentrations a and a 2 are proportional to their amounts 2x and 1 x, since the two gases form a solution and therefore n x} 2 both occupy an equal volume. It follows that ^-75 - = K, K 2i3C being a constant, and from this that the concentration of A must change in the proportion of the inverse square of the concentration of A 2 under the influence of a change of pressure, provided the law of mass action holds. Experiment has confirmed this deduction. 192. THE QUANTITATIVE INVESTIGATION OF EQUILIBRIA. - What facts lead us to assume a condition of chemical equilibrium in a liquid phase ? Let us assume the most general case. Two or REACTION VELOCITY AND EQUILIBRIUM 309 more substances are brought together which can not only form a solution, but which can also react chemically to form new sub- stances, which in turn form solutions with each other and with the unchanged residue. What phenomena force us to the assumption that a reaction has taken place and that new substances have been formed ? It has been already shown by general reasoning that when no new phase separates it is theoretically impossible to dis- criminate in the case of liquids between a solution and a chemical reaction. If, however, we caused separation and removed a phase by distillation we found that the most volatile substance would be the first to separate. The chemical equilibrium will, under these circumstances, be shifted in such a way that this particular sub- stance will be formed. These new amounts will continue to distil over, and we will finally obtain not only an amount of this substance equal to the amount originally present, but as much as could pos- sibly be produced from the substances in the system. The other constituents remain in the residue. The substance so removed by distillation may either be one of the original substances or a prod- uct of the reaction. In the first case we must conclude that no chemical process has taken place; in the second, that a complete reaction has been carried out. In neither case could we conclude anything about an equilibrium involving the presence of all possible substances. This is in fact the condition of things in many cases where the assumption of chemical equilibrium in the presence of all possible substances depends upon more or less indirect conclusions. This is the case when the velocity with which equilibrium (as measured by the concentrations in the system) is restored after being dis- turbed, is very great in proportion to the velocity with which the distillation or other operation is carried out. Equilibrium either continues unchanged during such an operation or else it is attained immediately after the separation of one or the other of the con- stituents. It is never possible to isolate a group of substances which belongs on one side or the other of the reaction equation. 310 FUNDAMENTAL PRINCIPLES OF CHEMISTRY This condition of things is reversed when the velocity relation is of the opposite sort. If separation can be carried out by causing new phases to form before the new equilibrium is attained as a result of a change in concentration, then the system behaves as though no mutual reaction whatever took place between the sub- stances. The ordinary operations of separation yield the substances which take part in the equilibrium in approximately the same pro- portions as those in which they were originally present. In this way it is possible to show whether or not a chemical reaction has taken place, and in the latter case it is possible to determine the proportions corresponding to equilibrium. The assumption of ideal catalysers (see Sec. 187) enables us to set up ideal conditions. We will first add to the system a catalyser which results in producing equilibrium instantly. Then we will suppose this catalyser to be removed, or, still better, re- placed by an absolutely negative catalyser. Analysis can then be carried out at leisure, since no further change can take place under our assumptions. It is possible to approximate this ideal condition of things when a gas reaction is under investigation at high temperatures. Under these conditions (see Sec. 186) equilibrium is very rapidly reached. If the gas is now suddenly cooled by leading it from the vessel in which the reaction has taken place through a narrow, well-cooled tube, it will remain fixed in its condition, since the reaction velocity at the low temperature is practically zero. The nature of the gases in question can then be determined by ordinary analytical methods. In liquid systems it is also sometimes pos- sible to greatly retard a reaction by suddenly cooling the liquid, and in this case also an approximate analysis can be carried out. 193. Is EQUILIBRIUM AFFECTED BY A CATALYSER ? The method just described only leads to correct results if the chemical equilibrium is not shifted by the addition of the catalyser. The latter has a great effect on the reaction velocity, and it has been shown that equilibrium is determined by the ratio of the opposed REACTION VELOCITY AND EQUILIBRIUM 311 reaction velocities. It might therefore be supposed that a catalyser would have a decided influence on equilibrium. As a matter of fact our assumptions are correct, and a catalyser cannot affect equilibrium in spite of the fact that it may have so great an influence on the reaction velocity. This conclusion may be drawn from general reasoning. A chemical equilibrium cannot be changed without the expenditure of a corresponding amount of work, for equilibrium is that condi- tion in which the system has already given up the whole of its avail- able energy. If any work is still available a corresponding change in the system would take place of its own accord, that is, the system is not in equilibrium. On the other hand, if the condition of a system in equilibrium is to be changed, work must be furnished from without. Addition of the catalyser does not correspond to furnishing work, for, by our definition, the catalyser is in the same condition at the end of the reaction as at the beginning, and it can therefore have furnished no work. A shift of equilibrium, due to the catalyser, would therefore be in contradiction to the second law, and it is a matter of experience that we know of no such contradiction. These two .effects, influence on reaction velocity and lack of influence on equilibrium, are the basis for the conclusion that a catalyser which influences a reaction must also influence the op- posed reaction in the same sense and in the same proportion. If it accelerates the direct process it must accelerate the reverse one in the same way. Only when this is true can the ratio of the two velocities remain unchanged, so that equilibrium is not disturbed. In any other case the equilibrium would be affected. Experiment confirms this theoretical conclusion. 194. INDUCTION AND DEDUCTION. The relations considered in the last few paragraphs have a special character. They have been first developed from other laws and then tested by experi- ment. The laws used in their development have, most of them, been discovered directly as generalizations from corresponding 312 FUNDAMENTAL PRINCIPLES OF CHEMISTRY experience. The process of deducing other laws from those already known is called deduction, in distinction from induction, which is the term used to indicate the direct process. Deduced laws are less certain than induced ones, for they involve not only uncertainty in the laws on which they are based, but also the possibility of error due to incorrect or incomplete derivation. They must therefore be subjected to experimental proof by induction just as the direct laws are proven, that is, they must be confirmed by generalizations from a finite number of observations or measurements before they can take their place as scientific laws. A well justified question arises here. How is it possible to derive a law from another given law which is different from it ? A law can only include those cases for which it holds, quite aside from the question of its correctness or exactness. The answer is that deduced laws are nothing more than special cases of the laws from which they are derived. If our interest is directed to the question how a special case or group of cases, which we know to be described by certain assumptions, can be brought under a general law, the answer frequently comes in such a way that the results obtained appear to be completely new ones, and this is because it is quite impossible to include in the first statement and first study of the general law all the special cases which fall within it. As we become accustomed to apply such a general law to each special case belonging under it, we become so confident of its value that we apply it to new cases, which have not yet been investigated, without any difficulty, and in fact quite unconsciously. The truth of the law becomes so " self-evident" that its application does not attract our attention, and it is only when the law appears to be " broken" that our special interest is awakened. This state of things holds for the majority of scientists at the present time, as far as the mechanical laws, and especially the law of the conservation of energy, are concerned. We are not yet so thoroughly accustomed to the manifold applications of the second law of energetics, and this is shown by the fact that opinions are REACTION VELOCITY AND EQUILIBRIUM 313 occasionally still put forward in scientific literature, which would, if correct, indicate a breach of the second law. On the other hand, familiarity with the application of this law in certain fields, and especially in general chemistry, has made many scientists so thoroughly familiar with its consequences that in any special case, whether it has been treated by previous investigation or not, the correct conclusion comes almost as a matter of intuition. The history of the development of those laws which have been derived by deduction shows that they refer to regions in which two or more laws are simultaneously applicable. Both Boyle's Law and Gay-Lussac's Law were discovered by induction. The general gas law PV=RT was never expressed in this form as a result of empirical reasoning. It was built up by a combination of the other two laws and afterwards subjected to experimental proof. In this case the regions covered by the two individual laws are of the same extent, Boyle's Law holding for all temperatures and Gay-Lussac's for all pressures within which a gas remains an approximately perfect one. The realm of the combined law is of the same extent. In the majority of cases, however, the regions described by laws which are combined for purposes of deduction only partially coin- cide, and under these circumstances the application of the deduced law is correspondingly limited. The law that catalysers cannot change equilibrium is confined to cases where chemical equilib- rium is possible and where we have catalysers for the reaction. We derived it, however, from the second law, which has application in numberless regions where neither chemical equilibrium nor catalysers appear. While it is true that laws obtained by deduction are narrower, as far as the region of their application is concerned, it is also true that in any case such a law expresses more than either of the laws from which it is deduced. In the region where it holds the state- ments which can be made on a basis of the separate laws hold simultaneously, and therefore the phenomenon in question is much more exactly described or determined than it could be by either of 314 FUNDAMENTAL PRINCIPLES OF CHEMISTRY the separate laws alone. Each new derivation of such a deduced law opens the way to a new proof which shows whether or not the more general laws hold for the special case in question. It is of course possible that special laws of this kind, which result from the simultaneous application of more general laws, should be found directly by experiment instead of being derived by deduction. Every individual phenomenon which we observe and measure is the subject of an unknown and very large number of different laws. We express as the result of study a general rela- tion between a number of individual phenomena, and our expres- sion of these phenomena determines how many general laws are included. The boundary between general and special laws must therefore be a somewhat indefinite one. It may easily happen that a general law and a narrower one included within it may be dis- covered experimentally and completely independent of each other. It is even possible that the mutual dependence may remain unrec- ognised : no one may combine them consciously with the intention of deducing a special law from them. It is, however, an important task for science to clear up all such relations, and to determine what general laws are necessary and sufficient to include all the special laws involved. Investigations of this sort have been under- taken in late years in mathematics and geometry, and they have been found difficult. In physics such a task can only be taken up systematically after individual investigations along the same line have been at hand for a long period. The present book is an ex- periment of the same sort in chemistry, or rather a preliminary step in this direction. CHAPTER X ISOMERISM 195. THE RELATION BETWEEN COMPOSITION AND PROPERTIES. During an earlier period in chemistry, which lasted until about the end of the 18th century, it was possible to uphold the statement that equality or difference of properties and composition were mutually determining facts definitely connected in every case. In other words, if substances were observed which had different properties, it was to be concluded that they would show differ- ences in composition under elementary analysis. These differences might consist in differences in the nature of the elements involved, or at least in differences in the proportions by weight in which they were found. In the same way the converse could be asserted, that difference in composition corresponds necessarily to difference in properties. Properties were recognised as definite functions of composition. One exception to this statement was known, but because of its very generality it was not felt to be an exception. This was the set of facts included in what we call differences of state. Water, ice, and steam are certainly substances having different properties, and they just as certainly have the same composition, since they can be transformed into one another without residue. Hypotheti- cal aid was made use of in escaping from this exception, and it was assumed that the final particles of these different forms were alike, but that they were arranged in different ways with respect to each other. The name " state of aggregation" as applied to these dif- ferences is an expression of this assumption. This is, of course, no explanation in the scientific sense. It merely transfers the fact 315 316 FUNDAMENTAL PRINCIPLES OF CHEMISTRY to be explained into a region of hypothetical cases which are in- capable of proof. If it were possible, however, to draw other conclusions which were in agreement with experience from this assumption, it would immediately become of scientific value, but this has so far not been done in this particular case. If it could be done this assumption would be in its effect equal to a natural law, since it would connect a set of different facts in a single common expression. Until this is done it is better in every way to give up such a hypothesis. What is, then, the general difference between different forms of the same substance? The answer is that their energy content is different. The difference is always in such a sense that gases contain the most energy and solids the least, the liquid state being intermediate between them. As a matter of form this case can be described by considering energy as like a chemical element differ- ing from all other elements in having no weight. As far as applica- tion of stochiometric laws is concerned, we might in this case also differentiate between solutions and pure substances. We might then combine the various kinds of energy, heat, volume energy, etc., in continuously varying proportions with a given amount of substance by varying temperature, pressure, and, in general, the intensity of the various energies freely and continuously in the sub- stances in question. We could also state a definite set of relations with respect to capacity factors of various kinds of energy, and these relations would be similar to the stochiometric ones (see Sec. 170). When we come to the question of differences of energy between the various states it is necessary to consider whether it is not possible, by overstepping the limits of equilibrium, to produce substances having the same energy content but differing in prop- erties. We may, for example, imagine water to be subcooled so far that its content of energy is reduced to a value equal to that of ice. This does not seem to be possible, at least in the simpler cases. Water cannot be subcooled below about -25; beyond ISOMERISM 317 that point it freezes. On the other hand, it gives out so much heat when it freezes that it could be cooled to 80 without reaching the condition desired. In those regions where we can investigate subcooling we have not yet succeeded in producing water which contains less energy than ice at 0, where the latter form has its greatest energy content. The matter is still less hopeful if condi- tions are compared at the same temperature ; for each degree below zero we must take away from water about double as much heat as from ice. If the two are to have the same energy content at the same temperature the subcooling would have to be carried to about 160, assuming that the values of the specific heats are inde- pendent of temperature. For other substances the difference in specific heat in the solid and liquid states is, in general, still smaller, and calculation will show that a still greater degree of subcooling would be necessary to produce the desired result. On the other hand, the latent heat of melting is often less than for water. The case discussed is one that has been so far scarcely examined at all, either experimentally or theoretically, and it can therefore not be stated that it is in gen- eral impossible to prepare two substances having the same com- position and the same energy content, but exhibiting different properties. It might perhaps be possible to attain this result in such a way that the total energy would be the same, but made up of various fractions of partial energies so combined that the sums are equal. In this case, however, differences in the substances could be referred to differences in energy content, but we should be obliged to consider qualitative differences in energy in place of quantitative ones, or in connection with them. 196. POLYMORPHISM. Beside differences of state among sub- stances of the same composition, we know also of differences in the properties of such substances in the same state. These va- riations were first noticed among solid substances, and they have been given the name of polymorphism because of the fact that they are most noticeable in differences in crystalline form. 318 FUNDAMENTAL PRINCIPLES OF CHEMISTRY Cases in which amorphous solids also show this relation were afterwards added to the class. At the present time we understand by the term " polymorphism " that solid substances can have the same composition but different forms, amorphous or crystalline. In these cases the other properties density, index of refraction, colour, elasticity, etc. are also different. Among these forms we find that the difference in energy content, mentioned above, always exists. A definite quantity of energy, which usually appears as heat, is developed or absorbed in every case when a substance passes from one of these solid forms to another. Another general peculiarity holds here. Under given conditions of temperature and pressure only one of these forms is, in general, stable ; all the others are unstable, and can only be produced with the aid of phenomena explained in Sec. 63, and by avoiding the presence of the stable phase. In this case also there will be found a corresponding series of temperatures and pressures at which two phases can exist together, and the appear- ance of a system of three phases is confined to single values of temperature and pressure. This latter conclusion may be drawn directly from the phase law. These various solid forms behave, in general, like the different states of a substance, and they can best be tabulated by adding them directly to those states. The usual idea that substances can only exist in three states must be replaced by another permitting of an unlimited number. Among these will usually be found one gaseous, one liquid, but several solid forms. When a gas- eous substance, stable at high temperatures, changes into a liquid stable at lower temperatures, and in the corresponding change from liquid to solid, heat is always given out, and a similar rela- tion holds for changes among the different solid forms of a sub- stance. Heat is always generated during a transformation resulting from decreasing temperature, and vice versa. The sense of the energy change is governed in any case by the law of Sec. 67. Ac- cording to this law that heat change takes place which resists the ISOMERISM 319 imposed conditions. Heat is absorbed during a rise of tempera- ture and developed when temperature is lowered in all cases of polymorphic transformation. The fact that a form with greater energy content is produced by a rise of temperature is a special case of this general law. The fact that an increasing indefiniteness in properties accompanies a change of form which involves an absorption of energy has not yet been expressed in any general law (the indefiniteness men- tioned corresponds to the fact that liquids have no shape of their own and gases no characteristic volume). In place of such a general law we have, so far, only the hypothesis concerning " state of aggregation." 197. THE DETERMINATION OF THE STABILITY OF POLYMOR- PHIC FORMS. It will be seen from the above considerations that within the limits of the solid state only one form can exist which is stable for any given values of temperature and pressure. If a transition point happens accidentally to fall upon one of these values then two solid forms can exist together in any proportions. It might therefore be supposed that only one of the possible poly- morphic forms would exist ; only the one, for instance, which is stable at ordinary temperatures. Experience shows the opposite to be true. Many substances exist in various forms under the same conditions, and even if they are brought in contact in such a way that any strain which might be present would be released, the unstable one often remains unaffected for a longer or shorter period of time. The reason for this is to be sought in the fact that the velocity of such reactions among solid substances is usually extremely small, and in many cases it is beyond the limit of observation. Even when an unstable phase is brought in contact with a stable one they can only touch each other in a few points because of their nature as solids, and the contact is far from being as perfect as would be the case between liquid and gaseous phases in con- tact with solids and with each other. In these cases it is very -j 320 FUNDAMENTAL PRINCIPLES OF CHEMISTRY difficult to decide by direct observation which form is the stable one. In this connection we make use of the reasoning applied in Sec. 70 to the mutual transformation of the states. We found that the unstable form always exhibits the greater vapour pres- sure, provided it can be changed hylotropically into the gaseous state. In the cases in question it would only rarely be possible to measure vapour pressure directly. It is, however, evident that a similar law must apply to the solubility of these substances, independent of the solvent used. Imagine each of the solid forms to be placed beside a drop of the solvent at the same temperature. Each drop of solvent would then dissolve the vapour of the solid in proportion to its pressure until equilibrium was obtained. The solution near the form having the greater vapour pressure will therefore be the most concentrated in the porportion of the vapour pressures. The principle that a system which is in equi- librium in one sense must be in equilibrium in every sense can now be applied. The solutions which are saturated with respect to vapour must also be saturated with respect to the solid phase, that is, they would remain unchanged in direct contact with it, and the above principle follows directly. We may expand this to show that the ratio of the concentrations of the two solutions must be the same as the ratio of the vapour pressures, at least within the range through which Henry's Law holds for the sub- stances in question. The principle is evidently quite independent of the nature of the liquid used as a solvent. The method indicated is of general applicability in the deter- mination of the comparative stability of the polymorphic forms of a substance, even when the extreme slowness of transitions of one state into another prevents direct determination. 198. ISOMERISM. In the majority of cases the distinction be- tween polymorphic forms of a given substance disappears when they are changed by fusion or solution into the liquid state, or by vaporization into the gaseous state. This behaviour is, however, ISOMERISM 321 n^t general, and substances are known, which are liquids under ordinary conditions, which have the same elementary composition, and which still exhibit very great differences in properties. The study of the carbon compounds, which began about the middle of the last century, brought to light a very great number of such substances, and the systematic arrangement of the phenomena involved was of great importance in the historical development of chemical theory. Substances having the same composition but different proper- ties, and in which the difference in properties persists in spite of a change of form, are called isomers. Polymorphic substances are only found among solids, and the various forms of a poly- morphic substance take on identical properties when they are transformed into gases or liquids. Isomers, on the other hand, exhibit their characteristic differences in spite of such changes of state. This statement holds only for the two extremes which are possible. A number of isomeric substances are known which behave in the way mentioned within moderate limits of tem- perature and time, but in which mutual transformation takes place at higher temperatures and after longer times. The result is finally a liquid or a gas of definite properties, and the same sub- stance is produced from any of the isomeric substances chosen as starting point. If the substance is then brought back into its original condi- tion, in which the mutual transformation takes place so slowly that it may be regarded as practically non-existent, it will be found to be a solution of two or more different substances, and it may be separated into its constituents by the ordinary means (diffusion, distillation, crystallization, etc.). It is evident that this is a case of chemical equilibrium, and one of those in which it is possible to arbitrarily arrange for 'con- ditions in which the reaction will take place in a reasonable time. It is also possible to return to other conditions, such that the re- 21 322 FUNDAMENTAL PRINCIPLES OF CHEMISTRY action velocity is practically zero. The case is different in one important point from polymorphism. Among isomers the normal condition, or equilibrium, is characterized by the fact that the various possible substances are all present in mutual solution, while among polymorphic substances one form appears to the exclusion of the others, because of the very limited solubility of solids. At the transition points for polymers two forms can exist together, but here also we find an important difference. At the transition points two polymorphous forms can exist together in any proportion whatever. In a case of equilibrium between liquid isomers equilibrium is in any case only possible at a definite proportion between the concentrations of the substances involved, and in any case where this ratio is not present transformation takes place until it is reached. Cases of isomerism are found in very great numbers among carbon compounds, and this is because of two reasons: first, carbon compounds are very numerous and varied; second, they almost always exhibit an extremely small reaction velocity. This means that we are able to prepare and observe forms which could not be characterized as individual substances if other conditions held. The result of this condition has been that investigators have studied these individual substances, unstable of themselves, but easy of isolation because of their very small reaction velocities. At the same time only very slight attention has been paid to their mutual transformations. General reasons suggest that all of these isomers can be mutually transformed so that a single substance, under the influence of an accelerator, would finally give us a solu- tion of all the possible isomers. This view is, however, unsupported by the results of any extended experience, and it must be con- sidered as a deduction which still requires confirmation by ex- periment. In other words, we have sufficient scientific grounds for the assumption that these substances are subject to the general laws of chemical equilibrium. In only a very few cases, however, have actual equilibrium conditions been investigated, and proof ISOMERISM 323 is therefore still necessary which will show that no other causes are active which might affect the application of this law. 199. METAMERISM AND POLYMERISM. - Two substances hav- ing the same chemical composition may differ in molar weight. It is only necessary that their molar weights should be in rational proportion. If A a , B b , C c , . . . is the simplest formula which ex- presses the composition of a substance, the molar weight of any isomeric substance must be expressible by a formula m(A a B b C c ), in which m is a whole number, and the molar weights of two such substances must be in the proportion m:m l , that is to say, in a rational proportion. One of these numbers is frequently unity, and then the molar weight of the other isomeric substance is a multiple of the molar weight of the simple one. Because of this relation such substances are called polymers, and this name has been extended to include isomers having different molar weights, although it is not strictly applicable in this case as far as its derivation is concerned. In contradistinction to these, isomers which have the same molar weight are called metameric substances, but this name is not in general use, and the broader term " isomerism " is usually applied to cases of metamerism to distinguish them from those of polymerism. The same general relations of equilibrium exist be- tween polymers and metamers, and there is no particular distinc- tion between them. Isomers share with polymorphous solids the property of differ- ences in energy content. Heat changes accompany their mutual transformation, and even in the numerous cases where the trans- formation takes place with such difficulty that the corresponding heat change cannot be directly measured, there are general methods of determining it. These depend on the transformation of isomers into a final state which is the same for all of them (for example, by complete combustion). Differences in the amounts of heat so determined are equal to the differences in the energy content in the isomers under investigation, for the total energy difference, 324 FUNDAMENTAL PRINCIPLES OF CHEMISTRY corresponding to a given original and final condition of a system, is only dependent on this condition and is not dependent on the way by which we pass from one condition to another. This is an immediate consequence of the law of the conservation of energy, and if it were not true it would be possible to create or destroy any amount of energy by causing the process to take place in one direction and in another way in the opposite direction. We can suppose the transformation of the isomers into their common, final condition to be so carried out that the first of the isomeric sub- stances passes directly into the final state. The second, how- ever, might be first transformed into the original condition of the other isomer and then into the final condition, and the same way with the third, if one existed. Then the heat change, correspond- ing to the transformation of the second and third isomers into the final condition, will be made up of the heats of transformation of those substances corresponding to a change into the first isomer, and added to these in each case equal quantities of heat corre- sponding to the transformation from the first into the final condi- tion. The differences between these sums must be equal to the heat of transformation of the other isomers into the first one. This reasoning can be expressed in symbols as follows: Sup- pose the heats corresponding to the transformation of the various isomers into the final condition are E lf E 2 , E 3 , that the transfor- mation of the second into the first produces an amount of heat equal to w 2 , that of the third into the first produces w 3 , etc., then E 2 = u 2 +E 1 ; E 3 = u s +E 19 etc., and E z -E l = u 1 ; E 3 -E l = u 39 which was to be proven. It follows that isomeric substances can be defined as substances having the same composition but different energy content, and it will be noticed that this definition holds for polymorphous substances also. 200. CONSTITUTION. Let us consider a special property, with respect to which isomeric substances may differ. This is their tendency to form new substances by chemical interactions of all kinds. Different products result when the same reactions are ISOMERISM 325 carried out on isomeric substances under the same conditions. In this way each individual substance of an isomeric group (there may be three or more different substances of the same composition) is connected with a special family of derivatives which are char- acteristic of this particular substance. These facts have led to the concept of constitution. We can consider that a part of the elements present in the various members of such a family are the same in each derivative, while the other elements are either removed by the chemical changes involved, or else replaced by others. The portions which remain constant are termed radicals, and we try to express all the reactions of a sub- stance by saying that it is made up of the corresponding radicals. If two substances are built up in this way from different radicals, so that the sum total of the combining weights of the individual elements is the same in each, the result is two substances of the same composition as far as the elements are concerned, but dif- fering in the radicals contained in them. This affords a so-called explanation for the facts of isomerism, especially for the fact that substances having the same composition may possess different properties. Such a method of procedure has one disadvantage. As our knowledge of the reactions which a substance can enter is extended, it becomes necessary to increase the number and complexity of the radicals which we assume to be present in the compound in question. Chemists have therefore endeavoured to make the formulation of such cases as general as is compatible with the aim before them. The result is the so-called structural theory, in which a distinct difference is assumed between elements which are directly bound to each other and those which are indirectly bound, that is, by means of other elements. All those radicals which can be built up from the directly bound elements are assumed to persist in the compound, at least potentially, and this permits of very general application in a great many reactions. As our knowledge of re- actions becomes more complete it is found that this auxiliary fails 326 FUNDAMENTAL PRINCIPLES OF CHEMISTRY in many cases. Especially where substances have been investi- gated with great minuteness it has been found that the constitution, as based on the above assumptions, becomes less and less certain instead of more definite. The definition of isomers as substances having the same com- position but different constitution offers no contradiction to our previous definition, in which they were said to be substances of the same composition but differing in energy content. It is very reasonable to assume that differences in constitution will corre- spond to differences in energy. The two definitions are, however, different, for the one based on energy content is a purely experi- mental one and quite free from doubt. It predicts, however, nothing whatever about the chemical reactions which are to be expected, and is therefore not applicable as an aid to building up a system. Energy in the sense in which the word is used here is expressible by a mere number; it has no further properties, and is therefore not of value in expressing the qualitative differences belonging to chemical reactions. The concept of chemical con- stitution was created for this latter use, and one of the aims of science will be to give to it a sharper and more exactly defined meaning without in any way decreasing the manifoldness of its applications. These will at the same time be extended and enlarged. 201. VALENCE. The concept of chemical constitution in- cludes another important idea. The elements combine not only in the ratio of single combining weights, but also in very manifold proportions for which no complete and regular principles have yet been found, although chemical investigation has been busy with this problem for more than half a century. Let us first call to mind the facts in the case. If a chemical compound is subjected to a transformation by which one element is replaced by another, the remainder of the compound being unchanged, this replacement can be carried out in various ways. The elements may replace each other in the ratio of their combining weights, so that the number of combining ISOMERISM 327 weights remains unchanged, or in place of the ratio 1:1 we may find other ratios, 1:2, 1:3, 2:3, etc. Those elements which are never replaced by more than one combining weight of another element are set aside and said to be univalent. They exhibit, of course, the inverse of this property, and more than one combining weight of one of these elements replaces a single combining weight of certain other elements. The number so determined is used in characterizing the other elements as possessing valences correspond- ing to the number of combining weights of the univalent elements which must be used to replace one combining weight. By this classification we have bivalent, trivalent, quadrivalent, etc., ele- ments. The highest valence which we have so far been obliged to assume is 8, but there is no real reason why we should not go higher if necessary. Valences of the various elements are so chosen that in chemical compounds each valence is active. If two univalent elements are concerned this can only be expressed in one way. The valence of each of the elements is connected with the valence of the other, and the two valences are said to be mutually " saturated." In the same way one combining weight of a bivalent or polyvalent element can only be combined in one way with a corresponding number of combining weights of a univalent element. But where two com- bining weights of a trivalent element combine with three combin- ing weights of a bivalent one, six valences are to be disposed of, and in this case three different arrangements are possible by which the elements are made to appear as combined in three different ways. In order to make this clear we will make use of a method of expression which has become general in chemistry. The number of valences will be indicated by a corresponding number of strokes emanating from the symbol of the element. If A is the bivalent and B the trivalent element, the following structures are possible : /A\ /A A-A-A B-A-B A=B-B | \ / \A B=B 328 FUNDAMENTAL PRINCIPLES OF CHEMISTRY It will be seen that all the valences are active or saturated. Each A has two strokes, and each B has three, and none of these strokes is left unconnected with another element. It is evident that this schematic representation contains a theory of isomerism which is in general agreement with the one given above, for it affords a means of expressing either direct or indirect combination between elements. The three structures given above are all different in a definite sense, and the question arises whether such differences in valence diagrams correspond to constitutional differences in chemical compounds and to related differences in their chemical reactions. The answer is that such a representation of the facts is in general possible, but at the same time a considerable degree of uncer- tainty and incompleteness still remain. Such relations are there- fore to be considered rather as rules with a considerable number of exceptions than as natural laws to which no exceptions exist. It must first be questioned whether the valence concept can be carried out so strictly that a definite valence can be ascribed to each ele- ment, by means of which all of its compounds can be represented. The answer is that this is in general impossible. Each element has, to be sure, a principal valence according to which the majority of its compounds is made up, but almost all elements form com- pounds with univalent elements, in which they are present in vary- ing proportion, and this means that a varying number of valences must be active. In order to show in such a case which valence is to be used in the representation of a given compound, further data is necessary. This data is in many cases available, for the prop- erties of compounds are dependent upon the valences involved, and measurement of properties enables us to determine the valence to be used in describing this particular compound. Different prop- erties usually give the same result when investigated in this way, but apparent contradictions occasionally occur. This fact is to be regarded as a sign that the scientific statement of the facts in question is not given with sufficient accuracy by the ISOMERISM 329 scheme we have used to represent it (in this case the use of valences). It must therefore be inquired whether the experimentally dis- covered cases of isomerism correspond in number and constitution to those which are indicated by the schematic representation em- ployed. In general, the number of experimentally known cases of isomerism is smaller than the theoretically possible number, and this is to be expected, for it is hardly possible that the experi- mental possibilities would already be exhausted. But from time to time cases have appeared where experimental isomers have been found in larger number than would be indicated by the theory. This necessitates the introduction of a new factor into the theory, for example, one involving differences in the spatial arrangement of elements, and in a few cases even this assumption appears insuf- ficient. All of these questions are most important in the study of carbon compounds, for it is in this branch of chemistry that the number and variety of isomers is by far the greatest. In this great group of compounds a systematic arrangement and a theory of isomers, together classed under the name of structure theory, which has been developed on the basis of valence, has proven itself a very important aid. In this system it has been possible to give to carbon a constant valence of 4 in the majority of cases. It has never been found necessary to give it a greater valence, but cases have appeared in which valences of 2 and 3 might lead to a better representation of the actual relations. The relation between the theory of valence and the molar con- cept deserves special mention. It is evident from the following diagram that the valences of a single bivalent element cannot be saturated by those of a trivalent one. If, however, we use polymers, there is no difficulty in taking care of the valences, and this is shown below for the case where the molar weight has double the simple Value " A-B-B-A. An assumption of this sort is demanded by the structural theory, 330 FUNDAMENTAL PRINCIPLES OF CHEMISTRY and it has been agreed that molar formulae are to be used as the basis for structural diagrams. Mutual saturation of the valences is demanded for the corresponding number of combining weights of the various elements. Determination of the molar weight is therefore a matter of the greatest importance for all those questions which involve structural theory, and especially for isomerism and constitution. CHAPTER XI THE IONS 202. SALT SOLUTIONS AND IONS. The majority of substances recognised by chemistry can be described by the laws which we have developed, and they need no further fundamental assumptions in their scientific treatment. There is, however, a large and im- portant group of substances in which regular contradictions to those laws appear, and these are not pure substances but a definite set of solutions. Especially among the aqueous solutions of salts we will find it necessary to extend our general ideas. The con- tradictions mentioned are most apparent in this class of substances, and they can also be most satisfactorily explained in connection with them. First of all we must have an experimental definition of the concept " salt." A salt is a substance whose solutions act as conductors of electricity of the second class. This definition has the advantage of simplicity and clearness, but it has at the same time the disadvantage that it depends upon the application of electrical energy. This form of energy has numerous relations to chemical energy, but it is unquestionably different from the latter. A chemical definition of a salt may be given as follows: A salt is a substance which has the properties of a pure substance in the undissolved condition, while it exhibits the properties of two dif- ferent substances while it is in solution. Both definitions will be considered exhaustively in the following pages. By a conductor of the second class is to be understood a sub- stance in which chemical reaction takes place at the points where the electric current enters and leaves it, and having the further characteristic that the amount of chemical action is proportional 331 332 FUNDAMENTAL PRINCIPLES OF CHEMISTRY to the amount of electricity which passes. In other words, an elec- tric current cannot pass through such a conductor without at the same time causing decomposition. A reasonable description of the facts may be based upon the assumption that the passage of the electric current is accompanied by the simultaneous motion of certain constituents of the solution. These are the ions, and the action takes place in such a way that negative electricity moves with one of the constituents of the salt, while positive electricity moves with the other. The first constituent is called the anion, the second, the cation of the salt. The places where the current enters and leaves are called the electrodes, and a substance which conducts in this way with simultaneous separation of its constitu- ents is called an electrolyte. The simplest case is one in which the salt consists of two elements, neither of which reacts with the solvent in the free state. They are therefore not influenced by the solvent, and the elements appear at the electrodes while the cor- responding quantity of electricity passes on through the circuit. The elements within the electrolyte are in some way connected with this quantity of electricity, and in this condition they exhibit properties quite different from those belonging to their ordinary condition, that is, belonging to their condition after the quantity of electricity has left them. This difference becomes evident when the elements give up their electricity at the electrodes, for at these points they appear in their ordinary condition. It must be con- cluded that they possess other properties as long as they are con- nected with the corresponding quantities of electricity. During the process heat effects are produced at the electrodes, and counter electro-motive forces are produced which can only be overcome by the expenditure of energy from the current. The passage of ions of a salt into the ordinary condition is therefore accompanied by energy changes. We have already given a name to substances having the same composition but exhibiting different properties and different energy contents. These we have called isomers, and in this sense of the word ions and elements having the same com- THE IONS 333 position may be included in the same class. The electrical differ- ences between ions and ordinary neutral substances indicate that this form of isomerism is even more complicated than the other. It may be characterized by the term " electrical," or even better " electrolytic," isomerism to indicate its close connection with elec- trical' phenomena. 203. FARADAY'S LAW. Salts in the solid state behave like neutral, unelectrified substances. It is a well-known principle of physics that only equal amounts of electricity of opposite signs can be produced simultaneously, and it follows from this that the quantities of electricity which are connected with the two ions of a salt in solution must be equal and of opposite sign. If amounts of various salts, each of which contains the same amount of any particular ion, are compared, it follows that the quantity of elec- tricity which is connected with the other ions must be in every case the same, and this reasoning holds for cations and for anions as well. It follows that, in general, equivalent amounts of different ions are connected with the same amount of electricity. When they can combine, those anions will be equivalent which combine with the same amount of any cation, and cations will be equivalent which combine with the same amount of any anion. The quantity of electricity in each of these cases will be the same, and the signs will be found in the proper relation. A cation is equivalent to an anion if it forms a neutral salt with it. Each is connected with the same quantity of electricity of different sign, and the salt will be neutral. The quantities involved are given by the law of the com- bining weights, and the conclusion is that equal quantities of electricity are connected either with one combining weight of any ion, or a rational fraction of the combining weight. This last statement is necessary because elements combine to form a salt not only in the ratios of their combining weights but also in other proportions as 1 : 2, 1 : 3, 2 : 3, etc. This law exhibits itself in a special way when ions separate from the electrolyte during electrolysis. Under these circumstances 334 FUNDAMENTAL PRINCIPLES OF CHEMISTRY chemically equivalent amounts of the different ions are separated in connection with the passage of the same quantity of electricity. While the quantity of electricity is in each case the same, the work required may be very different in different cases, since electrical energy is the product of quantity of electricity by potential differ- ence. Differences in the latter factor determine differences in the amount of work which accompanies the transformation of ions into electrically neutral isomeric substances. This law, which states that chemically equivalent amounts of ions or their transformation products separate from any salt solu- tion, or in general from any electrolyte, in connection with the same quantity of electricity, was discovered by Faraday, and it is called Faraday's Law. Before he arrived at this law Faraday showed that the quantity of substance separated is proportional to the quantity of electricity which passes, and this is of course a necessary premise for the statement of the general law. The derivation which we have just given for Faraday's Law depends upon the fact that electric neutrality is preserved as a mat- ter of experiment throughout all transformations which take place between salts. Measurements on Faraday's Law have also shown that a very large quantity of electricity is connected with a com- paratively small amount of substance in the form of ion, and the fact that no free electricity ever appears when salts react affords an exceedingly sensitive proof of the quantitative accuracy of Faraday's Law. 204. THE CONCEPT OF IONS CONSIDERED CHEMICALLY. Salts were defined above (Sec. 202) as substances which behave like pure substances when in the pure state, but which show reactions of several constituents when in solution. These constituents are the ions, which have just been defined in terms of their electrical properties. Let us consider two salts A 1 B 1 and AJ$^ the constituent A l being the same in each, the other constituent B 1 or B 2 being differ- ent. These two salts are different substances, each possessing its THE IONS 335 own properties. If these salts are dissolved in water a part of the properties of their solutions will be in agreement, while another part will differ. Careful 'investigation shows that the properties of these solutions can be in every case described as a sum, a part of which depends on the constituent A l and another part on the constituent B. These two constituents were combined in the orig- inal salt, but in the limiting case, that of very great dilution of the solution, this fact has no bearing whatever. The two solu- tions, one made of A 1 B 1 and the other of AJE}^ are alike as far as the constituent A l is concerned, and different as far as the other constituent B A or B 2 is concerned. These differences and points of agreement hold for physical properties as well as for chemical ones. If the constituent B^ has a definite colour of its own, the same colour will be characteristic of all dilute salt solutions containing the constituent B lt quite in- dependent of the nature of the other constituent A. Even when A has a colour of its own the colour of the salt solution containing the two coloured constituents will be found to be the sum of the two individual colours, that is to say, each of the constituents ex- hibits its characteristic absorption for light independent of the effect of the other. In the same way any definite chemical property, such as the capacity to form a precipitate with another substance, will be found in all salt solutions which contain a common constituent A or B. Even the physiological and medicinal effects of salts have been found to be independent of one of their constituents, and if the medically active constituent is present in the salt, the other constituent may be anything whatever, provided it exhibits no medicinal effect of its own. This peculiarity is found among salts containing two elements and also among those having more constituents. We may there- fore draw a conclusion similar to that found for composition and electrolytic conductivity. The independent effects found in binary salts belong to the independent constituents of the salt. If more 336 FUNDAMENTAL PRINCIPLES OF CHEMISTRY complicated compounds are in question, these are compared with binary salts having a constituent in common with the more com- plex one. All ions, without exception, combine with each other to form salts, and it is therefore always possible to prepare a salt one of whose ions is familiar. The composition and properties of the other ion can then be determined, and in this way it is possible to investigate salts of any composition whatever. The question arises whether the chemical definition of a salt leads to results which are in agreement with the electrical defini- tion when we apply them both to various substances. The an- swer is in the affirmative. Substances which conduct electrolytically contain constituents which react independently and vice versa. In this case, as in all others, we find cases in which the conductiv- ity is very small, and in which therefore the independent part of the salt is also small. Such cases require more exhaustive treat- ment than can be given here, and they are therefore only mentioned to prevent any tendency to overmuch formal deduction from the laws given. 205. UNIVALENT AND POLYVALENT IONS. Salts are subject to the general rules of valence. Polyvalent elements combine with the corresponding number of univalent ones to form salts, and these salts break up into univalent or polyvalent ions. Measure- ments based on Faraday's Law have shown that 96,540 units of electrical quantity (coulombs) correspond to one combining weight of a univalent ion. With each combining weight of an n-valent ion n X 96,540 coulombs will therefore be connected, and this conclusion depends upon the law of equivalents. It follows in the same way that one combining weight of an w-valent ion combines with n combining weights of any univalent ion to form a salt. This definite relation between quantity of electricity and com- bining weights gives rise to a new kind of isomerism among ions. Composition, molar weight, and, as far as we know, constitution THE IONS 337 also are in agreement among the isomers, but the quantity of electricity which is connected with a mol may be different in different cases. The letter F is used to indicate 96,540 coulombs, and the isomerism just mentioned may be expressed by connect- ing various integral values of F with the same element or complex of elements. Beside this kind of isomerism ions can exhibit the constitutional isomerism already described (Sec. 200), and this differs from electrical isomerism in that ions usually preserve their valence in the different forms. " Those ions which show constitutional isom- erism are portions of salts exhibiting constitutional isomerism, and this condition may appear for both cation's and anions. It is a matter of experience that the great majority of ions are u nivalent or bivalent. Trivalent ions and those of higher valence are comparatively rare, and appear more frequently in complicated compounds than in simple ones. Four valences appears to be the limit among elementary ions, and in fact the existence of quad- rivalent ions is doubtful. 206. THE MOLAR WEIGHT OF SALTS. Those solutions which conduct electrolytically exhibit remarkable properties when we try to determine the molar weight of the salt in them by the methods of Sections 176 et seq. The molar weight so determined is in all cases too small. Confining ourselves for the present to very dilute solutions (more concentrated ones will be taken up later), it ap- pears that the salts which are made up of two univalent ions give a molar weight one half as great as that which might be expected from their formula?. If the salt is made up of one bivalent and two univalent ions, its molar weight seems to be only one third that given by the formula, and in general it appears as a fraction de- termined by the number of ions into which the salt can break up. These facts may be explained with the aid of the assumption which we made in considering the electrical and chemical prop- erties of salt solutions. This was that ions exist as independent substances in salt solutions. One mol of the salt containing two 22 338 FUNDAMENTAL PRINCIPLES OF CHEMISTRY univalent ions produces two mols of ions, and must therefore exert double the osmotic pressure, etc. If we therefore calculate molar weight with the premise that no separation into ions has taken place, it is found too small by one half. We must in general expect to find that fraction of the molar weight of the salt which is deter- mined by the number of mols of ions which can be produced from the salt, and experiment confirms this. These facts are in complete agreement with the chemical and * electrical ones already mentioned. They form the principal basis for the idea that salts in conducting solutions are subject to elec- trolytic cleavage or dissociation, and this idea was first expressed by Arrhenius in 1887. 207. THE APPLICATION OF THE PHASE LAW. In accordance with the facts and relations just given, a salt solution must be con- sidered a ternary system in the sense of the phase law, even though we made the solution from a single salt and water; that is, from two constituents. If the number of degrees of freedom of such a system be investigated, it will be found to act like a solution which contains two dissolved substances. It has only three degrees of freedom when no other phase except the liquid is present, and a correspondingly smaller number when several phases exist together. If two salts are brought together in a solution further complica- tions result. In some cases the system behaves as though it con- tained three components, and in others as though it contained four. In no case, however, does it appear to contain five constituents, and this would necessarily be the case if any salt added two inde- pendent constituents to the solution. It can be shown that the effective influence may be referred to three constituents or to four, depending on whether or not the two salts contain the same ion. If they do, three constituents are active. If they do not, four constituents appear. In other words, the number of ions present, together with the water, determine the result, but we find one less degree of freedom than would be cal- culated from the number of ions arid the solvent. THE IONS 339 This means that one of the degrees of freedom has already been taken care of under these circumstances, and it is evident that this depends upon the fact that the amounts of the various ions are not independent of each other. Their amounts must be such that the total quantity of anions i$ equivalent to that of cations. If one of the ions were present in excess a corresponding and very large amount of electric charge would appear. Electric neutrality, or, what is the same thing, chemical equivalence, must exist between the anions and the cations. The fulfilment of this condition cor- responds to the disposal of one of the possible degrees of freedom, and one less remains for other changes. Viewed from this standpoint it is possible to show agreement between the behaviour of salt solutions and the statement of the phase law. We may state this in the following rule : The various ions are to be considered as independent constituents, and one is to be subtracted from the sum of freedoms and phases resulting from the corresponding enumeration. This gives us a clue to the fact that a solution of a single salt behaves like a single substance. The solution contains three in- dependent constituents, solvent and two ions. If we have only one phase 3+21=4 degrees of freedom must obtain. As a matter of fact three only will be found in any case, as indicated by the above rule. The actual number of degrees of freedom is in agreement with the number which would belong to the solution of a single substance, and the earlier idea that salts were to be con- sidered as individual substances, even when they were in solution, has its justification in this fact. Deviation from the phase law only appears when several salts are present in a solution, and the ap- pearance of this deviation is a further reason for considering ions as independent constituents of salt solutions. 208. ELECTROLYTIC DISSOCIATION. The transformation of a salt into its ions within a solution is called electrolytic dissocia- tion, and this process is a* chemical reaction coming under the general laws already discussed. A salt solution gives back the 340 FUNDAMENTAL PRINCIPLES OF CHEMISTRY original salt unchanged when it is evaporated, and this proves clearly that the dissociation into ions is reversed when the salt separates. The question arises whether dissociation is complete within the solution or not. In other words, does a quantitative equilibrium exist between the unchanged salt and its ions? The answer is in the affirmative. It is precisely because such a finite equilibrium usually exists that the simple relations of Sec. 206 must be confined to very dilute solutions. When a salt breaks up into its ions, a corresponding increase in osmotic pres- sure accompanies the increase in the molar concentration of the solution, and if the osmotic pressure is forcibly changed by dilu- tion or concentration, reactions will be set up which resist the change. If concentration takes place and the osmotic pressure is forcibly increased, that reaction will take place which tends to diminish the pressure, and if dilution is brought about the re- action will take place which increases the pressure. The first of these reactions consists in the formation of undissociated salt, the second reaction in more complete dissociation. Concentration of a salt solution therefore leads finally to the separation of the salt in the solid, undissociated form, while dilution leads finally to a com- plete dissociation into ions. Between these two limits equilibrium corresponding to the general law of mass action will exist. In the simplest case in which two univalent ions make up a salt, this may be expressed as follows: K is the cation, A the anion, S the salt, and the equation for the reaction will be K + A =S. If k, a, and s are the concentrations of these substances the equili- brium equation is - = C. The equation is based on one mol of s the salt, and we will let x be the fraction of this mol which is broken up into ions; then lx would be the unchanged portion, and we will use v for the total volume. The concentrations are then a = -, k = -, and s = - . Substituting these in the equilibrium x 2 equation, we have = C. THE IONS 341 This equation was first suggested by Ostwald in 1888, and it represents the general behaviour of electrolytes in a qualitative way. In regions of small and medium dissociation it has quantita- tive accuracy. Ir the limiting case of more complete dissociation deviations occur which have not yet been fully cleared up. If v is very large, which is the case for unlimited dilution, x approaches unity and 1 x approaches zero ; that is, the dissociation is com- plete. The constant C has an individual value for each electrolyte or salt, and it frequently shows relations to composition and constitution. In cases where a larger number of different ions are present in a solution the law of mass action is still applicable, and a large number of various phenomena characteristic of ions may be represented by its use. This application does not, however, lead to anything new or of fundamental importance, and the simple example given is therefore sufficient to make the existing relations clear. INDEX A. Absolute temperature, 43 Absolute weight, 10 Absolute zero, 43 Absorption law of, 121 Allotropic forms vapour pressure of, 93 solubility of, 161 Allotropism, 89 Amorphous bodies, 28 Analysis elementary, 172 Analytical chemistry, 245 Analytical processes, 168, 233 Anion, 332 Anomalous behaviour of gases, 307 Arbitrary properties, 3 Atmosphere, 17 Atomic weight, 272 B. Balance, equal arm, 11 BERTHELOT, 294 BERTHOLLET, 305 BERZELIUS, 272 Bodies amorphous, 28 homogeneous, 5 Boiling, 62 Boiling point, 22, 65 constant, 64 curve, 190 BOYLE'S LAW, 40 BUNS EN, 123 C. Calorie, 171 Capacity factor of energy, 19 of chemical energy, 264 Catalyser, 295, 298 ideal, 299 negative, 298 effect on equilibrium, 310 Cation, 332 Centimetre, 9 Centrifuge, 56 Chemical compounds, 200 Chemical energy, 7 capacity factor, 264 Chemical equilibrium, 302 Chemical processes, 5 general criteria, 219 in the narrow sense, 168 of the simplest kind, 61 reversibility of, 171 Chemistry, 4 Coefficient of expansion, 23 of crystals, 31 of gases, 42 of gas solutions, 101 of liquids, 35 of solid bodies, 30 of water, 36 Cohesion, 305 Colligative properties, 265, 275, 287 Colloidal solutions, 284 Combining weights, 247 general meaning and importance of, 263 methods of determination, 260 indefmiteness, 262 of compound substances, 253 343 344 INDEX Complete reaction, 259 Composition, 117 relation to properties, 315 properties, continuous functions of, 120 of ions, 335 of phases, 113 Compounds combining weight of, 253 Compressibility, 23 of liquids, 34 Concentration, 277 molar, 282, 292 Condenser, 135 Conservation of the elements, 173 of energy, 6 of weight, 12 of mass, 14 Constant proportions, Law of, 226, 247 Constitution, 324 Continuity, Law of, 175 Continuous functions, 24 of composition, 245, 293 Continuous phenomena, 291 Convection, 290 Critical line, 130 Critical point, 73 for solutions, 128 Critical pressure, 74 Critical temperature, 74 Critical volume, 74 Crystalline liquids, 40 Crystals, 26 groups of, 28 liquid, 40 expansibility of, 31 Cubic centimetre, 9 Cubic expansion, 31 D. DALTON, 102, 111, 272 Deduction, 311 Density, 15 measurement of, 37 of water, 37 Diaphragms ideal, 104 Diaphragms semi-permeable, 105 Diffusion, 99, 296 Dilute solutions properties of, 273 reactions between, 239 Displacement of equilibrium Law of, 83, 151 Dissociation electrolytic, 339 Dissociation equilibrium in electro- lytes, 340 Distillation, 135 fractional, 136 apparatus for, 137 Double decomposition, 168 E. Elasticity, 28 Elastic limit, 29 Electricity, 7 Electro-chemistry, 7 Electrodes, 332 Electrolyte, 332 Electrolytic dissociation, 339 Elementary analysis, 172 Elements, 169 Emulsion, 58 Energy, 6 as criterion of chemical change, 224 capacity factor of, 19 chemical, 7 conservation of, 7 intensity factor of, 19 Energy changes as criteria of chemical change in solution, 244 Energy content, 224 Entropy, 72 unit of, 73 Equations, chemical, 258 Equilibrium, 63 and catalyse rs, 310 between several phases, 304 between the three states, 85 chemical, 259 effect of pressure on, 112 law of, 85 liquid-gas, 60 INDEX 345 Equilibrium, liquid-solid, 80 quantitative investigation of, 308 solid-solid, 89 with solids t 148 Equimolar solutions, 275 Equivalents, 288 ESSON, 294 Eutectic, 156 Eutectic point, 155 Eutectic solution, 155 Eutectic mixture, 155 Existence of possible substances, 302 Extrapolation, 178 Faraday's Law, 333 Filtration, 55 Foams, 59 Fog, 58 Formulae, chemical, 255 Freedom, degrees of, 76 Freezing, 80 Freezing point, 22, 81 lowering of the, 284 laws of lowering of, 285 G. Gas constant applied to solutions, 101 Gas density, Law of, 266 Gaseous bodies, 26 Gaseous solutions, 97 of two gases, 181 of a gas and a liquid, 186 of a gas and a solid, 186 Gas equation, numerical values, 271 Gases, 40 anomalous, 307 chemical combination between, 202 density of, 266 dissociation of, 235 evolution from solution, 241 fractional separation of, 105 Gas law for solutions, 101 Gas-liquid equilibrium, 60 Gas solutions, 104 Gas solutions, density of, 101 properties of, 103 of liquid substances, 140 separation of the constituents of, 104 with liquids, 120 Gas volume law, 265 GAY-LUSSAC, 42 Gramme, 11 GULDBERG, 294 H. HARCOURT, 294 Heat, 21 expansion caused by, 23 latent, 70 unit of, 71 Heat energy measurement of, 71 quantity of, 71 Heat exchange, 225 HENRY, 122 HOFF, VAN T', 278 Homogeneous bodies, 5 Hylotropic transformation, 166. I. Ideal catalysers, 299 Ideal liquids, 33 Induction, 311 incomplete, 123 Inductive conclusion, 123 Inelastic bodies, 29 Integral reactions, Law of, 249 Intensities, 17 Intensity factor of energy, 19 Intermediate products, 298 Interpolation, 177 Ions, 331 chemical concept of, 334 isomerism of, 332 Isobar, 131 Isobaric change, 60 Isomerism, 315, 320 of ions, 333 electrolytic, 336 theory of, 328 346 INDEX Isothermal change, 60 Isothermal phase diagrams, 190 K. Kilogramme, 11 Kink, characteristic of a chemical compound, 229 Labile condition, 80 Latent heat, 70 Limited solubility among liquids, 126 Limiting solution, 144 Linear expansion, 31 Liquefaction, region of, 133 point of, 81 Liquid bodies, 26 Liquid crystals, 39 Liquid-gas equilibrium, 60 Liquid-liquid solutions, 123 Liquid mixtures, 57 Liquid-solid equilibrium, 80 Liquid solution of a gas and a, 186 Liquid solutions, 53, 97, 118 from solid substances, 152 Liquids, 32 chemical reactions between, 206 crystalline, 39 gaseous solutions from, 140 ideal, 34 separation from solution, 242 solutions of gases in, 120 solutions of solids and, 187 M. Magnetism, 7 Magneto-chemistry, 7 Manometer, 20 Mass, 7, 13 conservation of, 14 Mass action, Law of, 305 Matter, 9, 12 Maxima and minima in solution curves, 125 Measurement of density and specific volume, 37 of quantity of heat, 71 Mechanics, 7 Mechanical properties, 8 Mechano-chemistry, 7 Melting, 80 Melting point, 81 effect of pressure on, 82 curve of, 83 solubility at the, 158 Metamerism, 323 Metastable condition, 80, 92 Metastasis, 168 Metre, 9 Millimol, 273 Mixture, 49 Mixtures eutectic, 155 methods of separating, 51 of liquids and solids, 54 properties of, 52 singular, 147 with gases, 58 Mol, 273 Molar concentration, 292 Molar concept in the case of solid solutions, 288 Molar weight, 267 determination in the case of soluble substances, 286, 287 of salts, 337 Molecular volumes and weights, 289 N. Name, 2 Natural Law, 2, 49, 252 Negative quantities, 116 O. Observation, 3 Optics, 7 Osmotic pressure, 276 P. Partial density, 122 Partial pressure, 100 INDEX 347 Partially soluble liquids the vapour from, 141 PEAN DE ST. GILLES, 294 Phase Law, 77, 113, 114 applied tp salts, 338 Phases, 75 composition of, 113 Photo-chemistry, 7 Physics, 4 Point, triple, 85 eutectic, 155 critical, 73 Polymerism, 323 Polymorphic forms, solubility of, 319, 320' Polymorphism, 317 Polyvalent ions, 336 Porous diaphragms passage of gas solutions through, 105 Potential existence of elements, 257 Prediction, 3 Pressure, 16 critical, 74 effect on equilibrium, 112 effect on melting point, 82 measurement of, 20 Pressure, osmotic, 276 Pressures, scale of, 20 Properties arbitrary, 3 as continuous functions of com- position, 103, 119 colligative, 287 mechanical, 8 of mixtures, 52 as related to composition, 315 Proportions, Law of constant, 226, 247 Q. Quantities, 17 Quantity factor of energy, 19 R. Radical, 325 Rational multiples, Law of, 254 Reactions, Law of integral, 249 Reaction velocity, 290, 291 effect of solvent on, 297 effect of temperature on, 297 Law of, 294 Regular crystals, 32 Relative weight, 9 Retort, 135 Reversible chemical reactions, 171 Reversibility, 62 S. Salts, 331 phase rule applied to, 338 molar weight of, 337 Saturated vapour, 65 Saturation, 64 phenomena of, 149 Saturation equilibrium, effect of tem- perature on, 113 Saturation distribution, 150 Secondary reactions, 298 Semi-permeable diaphragms, 105 Sense impressions, 1 Separation, of liquid solutions into components, 130 of gaseous solutions, 104 Singular mixture, 147, 165 point, 163 solution, 138 value, 126 Solid bodies, 26 chemical reaction between, 208 Solidification, 80 Solid-liquid equilibrium, effect of pressure on, 82 Solid phase, and a solution, 148 Solid, separation from solution, 243 Solid-solid equilibrium, 89 Solid solutions, 54, 97 molar concept in the case of, 289 Solid substance effect of pressure and temperature on the solubility of a, 150 liquid solutions from a, 152 solution of a gas and a, 187 solution of a liquid and a, 186 Solid substances solutions of two, 153 348 INDEX Solubility at the melting point, 158 curve, 124 effect of pressure and temperature on, 150 limited, 126 of allotropic forms, 161 of polymorphic forms, 320 Solute, 120 Solution Law, 286 Solutions, 61, 63, 96 and pure substances as limiting cases, 109 equimolar, 275 from phases in the same state, 181 from phases of unlike states, 186 gas-liquid, 120 liquid, 53, 118 liquid, from solid substances, 152 liquid-liquid, 123 liquid, separation, 130 of higher order, 162 of one gas and one liquid, 186 of one gas and one solid, 186 of one solid and one liquid, 187 of two gases, 181 of two liquids, 182 of two solid substances, 183 properties of dilute, 273 reactions between dilute, 239 singular, 138 solid, 54, 97 vapour of, 131 with a solid phase, 148 Solvent, 120 effect on reaction velocity, 297 Specific gravity, 15 Specific properties, 3 Specific volume, 15 Stability of polymorphic forms, 319 region of, 167 State of aggregation, 315 changes of, 60 States, 26, 47 Structure theory, 325, 329 Sublimation, 78 Substance, 47 Law, 48 Substances, 4 Substances, pure, 61, 63 pure, definition of, 109 undecomposed, 169 Supercooling, 83 Supersaturation, 65, 80 Surface, clean, 57 Surface energy, 29, 32 molar, 288 Surface layer, 56 Surface representing one phase, 189 representing two phases, 189 Surface tension, 32 Suspended transformation, 79, 318 phenomena of, 90 Synthesis, 172 Synthetic processes, 168, 174 Systems of the first order, 117 T. Temperature, 21 absolute, 43 critical, 74 effect on reaction velocity, 297 effect on saturation equilibrium, 113 eutectic, 155 Temperature pressure, 25 Ternary systems, 239 Thermics, 7 Thermo-chemistry, 7, 71 Thermometer, 21 Transition, from one state to another, 60 hylotropic, 166 temperature, 90 Transition point, vapour pressure at, 94 Triaxial crystals, 32 Triple point, 85 U. Undecomposed substances 169 Uniaxial crystals, 32 Unit of volume, 9 Units of combining weights, 272 Univalent ions, 336 Unlimited solubility, 123 INDEX 349 Unsaturated vapour, 64 Unstable forms, 90 V. Valence, 326 Vaporization, 62 change of volume during, 68 heat of, 70 heat of, of water, 72 region of, 133 Vapour, 62 of partially soluble liquids, 141 of solutions, 131 saturated, 64 unsaturated, 64 Vapour pressure, 6,5 and osmotic pressure, 281 molar lowering of, 275 of water, 65 Vapour pressure curves, 67 at the triple point, 88 Vapour pressure of allotropic forms, 9: Velocity, chemical, 291 variable, 293 Viscosity, 29, 33 Volume, 7 critical, 74 Volume, measurement of, 37 specific, 15 unit of, 9 Volume change among solid bodies, 30 Volume energy, 16 Volume expansion, 31 Volumetric analysis, 264 W. WAAGE, 294 Water, density and specific volume of, 37 expansibility of, 36 heat of vaporization of, 72 vapour pressure of, 65 Weight, 7, 10 absolute, 10 conservation of, 12 relative, 10 unit of, 10 WENZEL, 294 WILHELMY, 294 Word, 2 Work, 6 Z. Zero, absolute, 43 OCT FEB .>' N DEC I UNIVERSITY OF CALIFORNIA LIBRARY This book is DUE on the last date stamped below. 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