APPLICATIONS***


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THE PHASE RULE AND ITS APPLICATIONS

by

ALEX. FINDLAY, M.A., PH.D., D.SC.

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THE PHASE RULE AND ITS APPLICATIONS

BY

ALEX. FINDLAY, M.A., PH.D., D.SC.

Lecturer on Physical Chemistry, University of Birmingham

With One Hundred and Thirty-Four Figures in the Text

Third Impression







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IN GRATITUDE FOR EARLY TRAINING

AND ADVICE



{vii}

PREFACE TO THE SECOND EDITION.

During the two years which have elapsed since the first edition of this
book appeared, the study of chemical equilibria has been prosecuted with
considerable activity, and valuable additions have been made to our
knowledge in several departments of this subject. In view of the scope of
the present work, it has been, of course, impossible to incorporate all
that has been done; but several new sections have been inserted, notably
those on the study of basic salts; the interpretation of cooling curves,
and the determination of the composition of solid phases without analysis;
the equilibria between iron, carbon monoxide, and carbon dioxide, which are
of importance in connection with the processes occurring in the blast
furnace; and the Phase Rule study of the ammonia-soda process. I have also
incorporated a short section on the reciprocal salt-pair barium
carbonate--potassium sulphate, which had been written for the German
edition of this book by the late Professor W. Meyerhoffer. The section on
the iron-carbon alloys, which in the first edition was somewhat
unsatisfactory, has been rewritten.

A. F.

_September, 1906._



{viii}

PREFACE

Although we are indebted to the late Professor Willard Gibbs for the first
enunciation of the Phase Rule, it was not till 1887 that its practical
applicability to the study of Chemical Equilibria was made apparent. In
that year Roozeboom disclosed the great generalization, which for upwards
of ten years had remained hidden and unknown save to a very few, by
stripping from it the garb of abstract Mathematics in which it had been
clothed by its first discoverer. The Phase Rule was thus made generally
accessible; and its adoption by Roozeboom as the basis of classification of
the different cases of chemical equilibrium then known established its
value, not only as a means of co-ordinating the large number of isolated
cases of equilibrium and of giving a deeper insight into the relationships
existing between the different systems, but also as a guide in the
investigation of unknown systems.

While the revelation of the principle embedded in the Phase Rule is
primarily due to Roozeboom, it should not be forgotten that, some years
previously, van't Hoff, in ignorance of the work of Willard Gibbs, had
enunciated his "law of the incompatibility of condensed systems," which in
some respects coincides with the Phase Rule; and it is only owing to the
more general applicability of the latter that the very {ix} important
generalization of van't Hoff has been somewhat lost sight of.

The exposition of the Phase Rule and its applications given in the
following pages has been made entirely non-mathematical, the desire having
been to explain as clearly as possible the principles underlying the Phase
Rule, and to illustrate their application to the classification and
investigation of equilibria, by means of a number of cases actually
studied. While it has been sought to make the treatment sufficiently
elementary to be understood by the student just commencing the study of
chemical equilibria, an attempt has been made to advance his knowledge to
such a stage as to enable him to study with profit the larger works on the
subject, and to follow with intelligence the course of investigation in
this department of Physical Chemistry. It is also hoped that the volume may
be of use, not only to the student of Physical Chemistry, or of the other
branches of that science, but also to the student of Metallurgy and of
Geology, for whom an acquaintance with at least the principles of the Phase
Rule is becoming increasingly important.

In writing the following account of the Phase Rule, it is scarcely
necessary to say that I have been greatly indebted to the larger works on
Chemical Equilibria by Ostwald ("Lehrbuch"), Roozeboom ("Die Heterogenen
Gleichgewichte"), and Bancroft ("The Phase Rule"); and in the case of the
first-named, to the inspiration also of personal teaching. My indebtedness
to these and other authors I have indicated in the following pages.

In conclusion, I would express my thanks to Sir William Ramsay, whose
guidance and counsel have been constantly {x} at my disposal; and to my
colleagues, Dr. T. Slater Price and Dr. A. McKenzie, for their friendly
criticism and advice. To Messrs. J. N. Friend, M.Sc., and W. E. S. Turner,
B.Sc., I am also indebted for their assistance in reading the proof-sheets.

A. F.

_November, 1903._




{xi}

CONTENTS

                                                                       PAGE

  CHAPTER I

  INTRODUCTION                                                            1

  General, I. Homogeneous and heterogeneous equilibrium,
  5. Real and apparent equilibrium, 5.

  CHAPTER II

  THE PHASE RULE                                                          7

  Phases, 8. Components, 10. Degree of freedom. Variability
  of a system, 14. The Phase Rule, 16. Classification of systems
  according to the Phase Rule, 17. Deduction of the Phase
  Rule, 18.

  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
  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
  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