Part 1 (1/2)

The Phase Rule and Its Applications.

by Alexander Findlay.

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 a.n.a.lysis; 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--pota.s.sium 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._

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 cla.s.sification 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 relations.h.i.+ps 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 ill.u.s.trate their application to the cla.s.sification 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 a.s.sistance in reading the proof-sheets.

A. F.

_November, 1903._

THE PHASE RULE

CHAPTER I

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 s.p.a.ce, 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,[1] 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.[2] Ice, water, and vapour, therefore, can be in equilibrium with one another only at one definite temperature and one definite pressure.

In the case of a solution of common salt, however, we may have ice in contact with the solution at different temperatures and pressures. Further, it is possible to have a solution in equilibrium not only with anhydrous salt (NaCl), but also with the hydrated salt (NaCl, 2H_{2}O), as well as with ice, and the question, therefore, arises: Is it possible to state in a general manner the conditions under which such different systems can exist in equilibrium; or to obtain some insight {3} into the relations which exist between pure liquids and solutions? As we shall learn, the Phase Rule enables us to give an answer to this question.

The preceding examples belong to the cla.s.s of so-called ”physical”

equilibria, or equilibria depending on changes in the physical state. More than a hundred years ago, however, it was shown by Wenzel and Berthollet that ”chemical” equilibria can also exist; that chemical reactions do not always take place completely in one direction as indicated by the usual chemical equation, but that before the reacting substances are all used up the reaction ceases, and there is a condition of equilibrium between the reacting substances and the products of reaction. As an example of this, there may be taken the process of lime-burning, which depends on the fact that when calcium carbonate is heated, carbon dioxide is given off and quicklime is produced. If the carbonate is heated in a closed vessel it will be found, however, not to undergo entire decomposition. When the pressure of the carbon dioxide reaches a certain value (which is found to depend on the temperature), decomposition ceases, and calcium carbonate exists side by side with calcium oxide and carbon dioxide. Moreover, at any given temperature the pressure is constant and independent of the amount of carbonate or oxide present, or of the volume of the gas; _nor does the addition of either of the products of dissociation, carbon dioxide or calcium oxide, cause any change in the equilibrium_. Here, then, we see that, although there are three different substances present, and although the equilibrium is no longer due to physical, but to chemical change, it nevertheless obeys the same law as the vapour pressure of a pure volatile liquid, such as water.