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Transcriber's note:
Page numbers enclosed by curly braces (example: {25}) have been
incorporated to facilitate the use of the Table of Contents.
In chemical formulas an underscore is used to indicate that
the following number enclosed by curly braces is a subscript.
For example, the formula of water is indicated by H_{2}O.
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minus 7th power is indicated by 10^{-7}.
A few typographical errors have been corrected and are listed
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THE PHASE RULE AND ITS APPLICATIONS
by
ALEX. FINDLAY, M.A., PH.D., D.SC.
* * * * *
TEXT-BOOKS OF PHYSICAL CHEMISTRY.
EDITED BY SIR WILLIAM RAMSAY, K.C.B., F.R.S., D.SC.
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in the University of Dublin; together with an INTRODUCTION TO THE STUDY
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the Series. Crown 8vo. 7s. 6d.
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CHANGE, CATALYSIS AND EXPLOSIONS. BY J. W. MELLOR, D.Sc. (N.Z.), B.Sc.
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THE PHASE RULE AND ITS APPLICATIONS. By ALEX. FINDLAY, M.A., Ph.D.,
D.Sc., Lecturer and Demonstrator in Chemistry, University of
Birmingham. With 134 Figures in the Text. Crown 8vo. 5s.
SPECTROSCOPY. By E. C. C. BALY, F.I.C., Lecturer on Spectroscopy and
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[_In preparation._
ACTINOCHEMISTRY. By C. E. K. MEES, D.Sc., and S. E. SHEPPARD, D.Sc.
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LONGMANS, GREEN, AND CO.
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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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DEDICATED
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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.