The Phase Rule and Its Applications

CHAPTER III

TYPICAL SYSTEMS OF ONE COMPONENT 21

A. Water. Equilibrium between liquid and vapour. Vaporization curve, 21. Upper limit of vaporization curve, 23. Sublimation curve of ice, 24. Equilibrium between ice and water. Curve of fusion, 25. Equilibrium between ice, water, and vapour. The triple point, 27. Bivariant systems of water, 29. Supercooled water. Metastable state, 30. Other systems of the substance water, 32. B. Sulphur, 33. Polymorphism, 33. Sulphur, 34. Triple point--Rhombic and monoclinic sulphur and vapour. Transition point, 34. Condensed systems, 36. Suspended transformation, 37. Transition curve--Rhombic and monoclinic sulphur, 37. Triple point--Monoclinic sulphur, liquid, and vapour. Melting point of monoclinic sulphur, 38. Triple point--Rhombic and monoclinic sulphur and liquid, 38. Triple point--Rhombic sulphur, liquid, and vapour. Metastable triple point, 38. Fusion curve of rhombic sulphur, 39. Bivariant systems, 39. C. Tin, 41. Transition point, 41. {xii} Enantiotropy and monotropy, 44. D. Phosphorus, 46. Enantiotropy combined with monotropy, 51. E. Liquid Crystals, 51. Phenomena observed, 51. Nature of liquid crystals, 52. Equilibrium relations in the case of liquid crystals, 53.

CHAPTER IV

GENERAL SUMMARY 55

Triple point, 55. Theorems of van't Hoff and of Le Chatelier, 57. Changes at the triple point, 58. Triple point solid--solid--vapour, 62. Sublimation and vaporization curves, 63. Fusion curve--Transition curve, 66. Suspended transformation. Metastable equilibria, 69. Velocity of transformation, 70. Law of successive reactions, 73.

CHAPTER V

SYSTEMS OF TWO COMPONENTS--PHENOMENA OF DISSOCIATION 76

Different systems of two components, 77. PHENOMENA OF DISSOCIATION. Bivariant systems, 79. Univariant systems, 80. Ammonia compounds of metal chlorides, 82. Salts with water of crystallization, 85. Efflorescence, 86. Indefiniteness of the vapour pressure of a hydrate, 87. Suspended transformation, 89. Range of existence of hydrates, 90. Constancy of vapour pressure and the formation of compounds, 90. Measurement of the vapour pressure of hydrates, 91.

CHAPTER VI

SOLUTIONS 92

Definition, 92. SOLUTIONS OF GASES IN LIQUIDS, 93. SOLUTIONS OF LIQUIDS IN LIQUIDS, 95. Partial or limited miscibility, 96. Phenol and water, 97. Methylethylketone and water, 100. Triethylamine and water, 101. General form of concentration-temperature curve, 101. Pressure-concentration diagram, 102. Complete miscibility, 104. Pressure-concentration diagram, 104.

CHAPTER VII. Solutions of Solids in Liquids, Only One of the Components Being

SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE 106

General, 106. The saturated solution, 108. Form of the solubility curve, 108. A. ANHYDROUS SALT AND WATER. {xiii} The solubility curve, 111. Suspended transformation and supersaturation, 113. Solubility curve at higher temperatures, 114. (1) Complete miscibility of the fused components. Ice as solid phase, 116. Cryohydrates, 117. Changes at the quadruple point, 119. Freezing mixtures, 120. (2) Partial miscibility of the fused components. Supersaturation, 124. Pressure-temperature diagram, 126. Vapour pressure of solid--solution--vapour, 126. Other univariant systems, 127. Bivariant systems, 129. Deliquescence, 130. Separation of salt on evaporation, 130. General summary, 131.

CHAPTER VIII. Solutions of Solids in Liquids, Only One of the Components Being

SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE COMPONENTS BEING VOLATILE 133

B. HYDRATED SALT AND WATER, (1) The compounds formed do not have a definite melting point. Concentration-temperature diagram, 133. Sodium sulphate and water, 134. Suspended transformation, 137. Dehydration by means of anhydrous sodium sulphate, 138. Pressure-temperature diagram, 138. (2) The compounds formed have a definite melting point. Solubility curve of calcium chloride hexahydrate, 145. Pressure-temperature diagram, 149. The indifferent point, 150. The hydrates of ferric chloride, 151. Suspended transformation, 155. Evaporation of solutions at constant temperature, 155. Inevaporable solutions, 157. Illustration, 158.

CHAPTER IX

EQUILIBRIA BETWEEN TWO VOLATILE COMPONENTS 161

General, 161. Iodine and chlorine, 161. Concentration-temperature diagram, 162. Pressure-temperature diagram, 165. Bivariant systems, 167. Sulphur dioxide and water, 169. Pressure-temperature diagram, 170. Bivariant systems, 173.

CHAPTER X

SOLID SOLUTIONS. MIXED CRYSTALS 175

General, 175. Solution of gases in solids, 176. Palladium and hydrogen, 178. Solutions of solids in solids. Mixed crystals, 180. Formation of mixed crystals of isomorphous substances, 182. I. The two components can form an unbroken series of mixed crystals. (a) The freezing points of all mixtures lie between the freezing points of the pure components. Examples, 183. Melting-point curve, 183. (b) The freezing-point curve passes through a maximum. Example, 186. (c) The freezing-point curve passes through a minimum. Example, 188. Fractional {xiv} crystallization of mixed crystals, 188. II. The two components do not form a continuous series of mixed crystals. (a) The freezing-point curve exhibits a transition point, 190. Example, 190. (b) The freezing-point curve exhibits a eutectic point, 191. Examples, 192. Changes in mixed crystals with the temperature, 192.

CHAPTER XI

EQUILIBRIUM BETWEEN DYNAMIC ISOMERIDES 195

Temperature-concentration diagram, 196. Transformation of the unstable into the stable form, 201. Examples, 203. Benzaldoximes, 203. Acetaldehyde and paraldehyde, 204.

CHAPTER XII

SUMMARY.--APPLICATION OF THE PHASE RULE TO THE STUDY OF SYSTEMS OF TWO COMPONENTS 207

Summary of the different systems of two components, 208. (1) Organic compounds, 212. (2) Optically active substances, 213. Examples, 216. Transformations, 217. (3) Alloys, 220. Iron--carbon alloys, 223. Determination of the composition of compounds without analysis, 228. Formation of minerals, 232.

CHAPTER XIII

SYSTEMS OF THREE COMPONENTS 234

General, 234. Graphic representation, 235.

CHAPTER XIV

SOLUTIONS OF LIQUIDS IN LIQUIDS 240

1. The three components form only one pair of partially miscible liquids, 240. Retrograde solubility, 245. The influence of temperature, 247. 2. The three components can form two pairs of partially miscible liquids, 249. 3. The three components form three pairs of partially miscible liquids, 251.

CHAPTER XV

PRESENCE OF SOLID PHASES 253

A. The ternary eutectic point, 253. Formation of compounds, 255. B. Equilibria at higher temperatures. Formation of double salts, 258. Transition point, 258. Vapour pressure. {xv} Quintuple point, 261. Solubility curves at the transition point, 264. Decomposition of the double salt by water, 267. Transition interval, 270. Summary, 271.

CHAPTER XVI

ISOTHERMAL CURVES AND THE SPACE MODEL 272

Non-formation of double salts, 272. Formation of double salt, 273. Transition interval, 277. Isothermal evaporation, 278. Crystallization of double salt from solutions containing excess of one component, 280. Formation of mixed crystals, 281. Application to the characterization of racemates, 282. Representation in space. Space model for carnallite, 284. Summary and numerical data, 287. Ferric chloride--hydrogen chloride--water, 290. Ternary systems, 291. The isothermal curves, 294. Basic Salts, 296. Bi{2}O{3}--N{2}O{5}--H_{2}O, 298. Basic mercury salts, 301. Indirect determination of the composition of the solid phase, 302.

CHAPTER XVII

ABSENCE OF LIQUID PHASE 305

Iron, carbon monoxide, carbon dioxide, 305.

CHAPTER XVIII

SYSTEMS OF FOUR COMPONENTS 312

Reciprocal salt-pairs. Choice of components, 313. Transition point, 314. Formation of double salts, 315. Transition interval, 315. Graphic representation, 316. Example, 317. Ammonia-soda process, 320. Preparation of barium nitrite, 327. Barium carbonate and potassium sulphate, 328.

APPENDIX

EXPERIMENTAL DETERMINATION OF THE TRANSITION POINT 331

I. The dilatometric method, 331. II. Measurement of the vapour pressure, 334. III. Solubility measurements, 335. IV. Thermometric method, 337. V. Optical method, 338. VI. Electrical methods, 338.

NAME INDEX 341

SUBJECT INDEX 345

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{1}

THE PHASE RULE

CHAPTER I. Introduction

INTRODUCTION

General.--Before proceeding to the more systematic treatment of the Phase Rule, it may, perhaps, be not amiss to give first a brief forecast of the nature of the subject we are about to study, in order that we may gain some idea of what the Phase Rule is, of the kind of problem which it enables us to solve, and of the scope of its application.

It has long been known that if water is placed in a closed, exhausted space, vapour is given off and a certain pressure is created in the enclosing vessel. Thus, when water is placed in the Torricellian vacuum of the barometer, the mercury is depressed, and the amount of depression increases as the temperature is raised. But, although the pressure of the vapour increases as the temperature rises, its value at any given temperature is constant, no matter whether the amount of water present or the volume of the vapour is great or small; if the pressure on the vapour is altered while the temperature is maintained constant, either the water or the vapour will ultimately disappear; the former by evaporation, the latter by condensation. At any given temperature within certain limits, therefore, water and vapour can exist permanently in contact with one another--or, as it is said, be in equilibrium with one another--only when the pressure has a certain definite value. The same law of constancy of vapour pressure at a given {2} temperature, quite irrespective of the volumes of liquid and vapour, holds good also in the case of alcohol, ether, benzene, and other pure liquids. It is, therefore, not unnatural to ask the question, Does it hold good for all liquids? Is it valid, for example, in the case of solutions?

We can find the answer to these questions by studying the behaviour of a solution--say, a solution of common salt in water--when placed in the Torricellian vacuum. In this case, also, it is observed that the pressure of the vapour increases as the temperature is raised, but the pressure is no longer independent of the volume; as the volume increases, the pressure slowly diminishes. If, however, solid salt is present in contact with the solution, then the pressure again becomes constant at constant temperature, even when the volume of the vapour is altered. As we see, therefore, solutions do not behave in the same way as pure liquids.

Moreover, on lowering the temperature of water, a point is reached at which ice begins to separate out; and if heat be now added to the system or withdrawn from it, no change will take place in the temperature or vapour pressure of the latter until either the ice or the water has disappeared. Ice, water, and vapour, therefore, can be in equilibrium with one another only at one definite temperature and one definite pressure.

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