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STEREOCHEMISTRY. By A. W. STEWART, D.Sc., Carnegie Research Fellow, Lecturer on Stereochemistry in University College, London. With 87 Illustrations. Crown 8vo. 10s. 6d.

RELATIONS BETWEEN CHEMICAL CONSTITUTION AND PHYSICAL PROPERTIES. By SAMUEL SMILES, D.Sc.

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THERMODYNAMICS. By F. G. DONNAN, M.A., Ph.D.

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LONGMANS, GREEN, AND CO. 39 PATERNOSTER ROW, LONDON NEW YORK, BOMBAY, AND CALCUTTA

* * * * *

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

Longmans, Green, and Co. 39 Paternoster Row, London New York, Bombay, and Calcutta 1908

All rights reserved

DEDICATED

TO

FRANCIS ROBERT JAPP, LL.D., F.R.S.

PROFESSOR OF CHEMISTRY, UNIVERSITY OF ABERDEEN,

IN GRATITUDE FOR EARLY TRAINING

AND ADVICE

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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._

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CONTENTS

PAGE