Part 1 (2/2)
It might be supposed, now, that this behaviour would be shown by other dissociating substances, _e.g._ ammonium chloride. When this substance is heated it dissociates into ammonia and hydrogen chloride, and at any given temperature the pressure of these gases is constant,[3] and is independent of the amounts of solid and gas present. So far, therefore, ammonium chloride behaves like calcium carbonate. If, however, one of the {4} products of dissociation be added to the system, it is found that the pressure is no longer constant at a given temperature, but varies with the amount of gas, ammonia or hydrogen chloride, which is added. In the case of certain dissociating substances, therefore, addition of one of the products of dissociation alters the equilibrium, while in other cases it does not.
With the help of the Phase Rule, however, a general interpretation of this difference of behaviour can be given--an interpretation which can be applied not only to the two cases cited, but to all cases of dissociation.
Again, it is well known that sulphur exists in two different crystalline forms, octahedral and prismatic, each of which melts at a different temperature. The problem here is, therefore, more complicated than in the case of ice, for there is now a possibility not only of one solid form, but of two different forms of the same substance existing in contact with liquid. What are the conditions under which these two forms can exist in contact with liquid, either singly or together, and under what conditions can the two solid forms exist together without the presence of liquid sulphur? To these questions an answer can also be given with the help of the Phase Rule.
These cases are, however, comparatively simple; but when we come, for instance, to study the conditions under which solutions are formed, and especially when we inquire into the solubility relations of salts capable of forming, perhaps, a series of crystalline hydrates; and when we seek to determine the conditions under which these different forms can exist in contact with the solution, the problem becomes more complicated, and the necessity of some general guide to the elucidation of the behaviour of these different systems becomes more urgent.
It is, now, to the study of such physical and chemical equilibria as those above-mentioned that the Phase Rule finds application; to the study, also, of the conditions regulating, for example, the formation of alloys from mixtures of the fused metals, or of the various salts of the Sta.s.sfurt deposits; the behaviour of iron and carbon in the formation of steel and the {5} separation of different minerals from a fused rock-ma.s.s.[4] With the help of the Phase Rule we can group together into cla.s.ses the large number of different isolated cases of systems in equilibrium; with its aid we are able to state, in a general manner at least, the conditions under which a system can be in equilibrium, and by its means we can gain some insight into the relations existing between different kinds of systems.
h.o.m.ogeneous and Heterogeneous Equilibrium.--Before pa.s.sing to the consideration of this generalization, it will be well to first make mention of certain restrictions which must be placed on its treatment, and also of the limitations to which it is subject. If a system is uniform throughout its whole extent, and possesses in every part identical physical properties and chemical composition, it is called _h.o.m.ogeneous_. Such is, for example, a solution of sodium chloride in water. An equilibrium occurring in such a h.o.m.ogeneous system (such as the equilibrium occurring in the formation of an ester in alcoholic solution) is called _h.o.m.ogeneous equilibrium_. If, however, the system consists of parts which have different physical properties, perhaps also different chemical properties, and which are marked off and separated from one another by bounding surfaces, the system is said to be _heterogeneous_. Such a system is formed by ice, water, and vapour, in which the three portions, each in itself h.o.m.ogeneous, can be mechanically separated from one another. When equilibrium exists between different, physically distinct parts, it is known as _heterogeneous equilibrium_. It is, now, with heterogeneous equilibria, with the conditions under which a heterogeneous system can exist, that we shall deal here.
Further, we shall not take into account changes of equilibrium due to the action of electrical, magnetic, or capillary forces, or of gravity; but shall discuss only those which are due to changes of pressure, temperature, and volume (or concentration).
Real and Apparent Equilibrium.--In discussing equilibria, also, a distinction must be drawn between real and {6} apparent equilibria. In the former case there is a state of rest which undergoes continuous change with change of the conditions (_e.g._ change of temperature or of pressure), and for which the chief criterion is that _the same condition of equilibrium is reached from whichever side it is approached_. Thus in the case of a solution, if the temperature is maintained constant, the same concentration will be obtained, no matter whether we start with an unsaturated solution to which we add more solid, or with a supersaturated solution from which we allow solid to crystallize out; or, in the case of water in contact with vapour, the same vapour pressure will be obtained, no matter whether we heat the water up to the given temperature or cool it down from a higher temperature. In this case, water and vapour are in _real_ equilibrium. On the other hand, water in contact with hydrogen and oxygen at the ordinary temperature is a case only of _apparent_ equilibrium; on changing the pressure and temperature continuously within certain limits there is no continuous change observed in the relative amounts of the two gases. On heating beyond these limits there is a sudden and not a continuous change, and the system no longer regains its former condition on being cooled to the ordinary temperature. In all such cases the system may be regarded as undergoing change and as tending towards a state of true or real equilibrium, but with such slowness that no change is observed.
Although the case of water in contact with hydrogen and oxygen is an extreme one, it must be borne in mind that the condition of true equilibrium may not be reached instantaneously or even with measurable velocity, and in all cases it is necessary to be on one's guard against mistaking apparent (or false) for real (or true) equilibrium. The importance of this will be fully ill.u.s.trated in the sequel.
{7}
CHAPTER II
THE PHASE RULE
Although the fact that chemical reactions do not take place completely in one direction, but proceed only to a certain point and there make a halt, was known in the last quarter of the eighteenth century (Wenzel, 1777; Berthollet, 1799); and although the opening and subsequent decades of the following century brought many further examples of such equilibria to our knowledge, it was not until the last quarter of the nineteenth century that a theorem, general in its application and with foundations weakened by no hypothetical a.s.sumptions as to the nature or const.i.tution of matter, was put forward by Willard Gibbs;[5] a generalization which serves at once as a golden rule by which the condition of equilibrium of a system can be tested, and as a guide to the similarities and dissimilarities existing in different systems.
Before that time, certainly, attempts had been made to bring the different known cases of equilibria--chemical and physical--under general laws. From the very first, both Wenzel[6] and Berthollet[7] recognized the influence exercised by the _ma.s.s_ of the substances on the equilibrium of the system.
It was reserved, however, for Guldberg and Waage, by their more general statement and mathematical treatment of the Law of Ma.s.s Action,[8] to inaugurate the period of quant.i.tative study of equilibria. The law which these investigators enunciated {8} served satisfactorily to summarize the conditions of equilibrium in many cases both of h.o.m.ogeneous and, with the help of certain a.s.sumptions and additions, of heterogeneous equilibrium. By reason, however, of the fact that it was developed on the basis of the kinetic and molecular theories, and involved, therefore, certain hypothetical a.s.sumptions as to the nature and condition of the substances taking part in the equilibrium, the law of ma.s.s action failed, as it necessarily must, when applied to those systems in which neither the number of different molecular aggregates nor the degree of their molecular complexity was known.
Ten years after the law of ma.s.s action was propounded by Guldberg and Waage, Willard Gibbs,[9] Professor of Physics in Yale University, showed how, in a perfectly general manner, free from all hypothetical a.s.sumptions as to the molecular condition of the partic.i.p.ating substances, all cases of equilibrium could be surveyed and grouped into cla.s.ses, and how similarities in the behaviour of apparently different kinds of systems, and differences in apparently similar systems, could be explained.
As the basis of his theory of equilibria, Gibbs adopted the laws of thermodynamics,[10] a method of treatment which had first been employed by Horstmann.[11] In deducing the law of equilibrium, Gibbs regarded a system as possessing only three independently variable factors[12]--temperature, pressure, and the concentration of the components of the system--and he enunciated the general theorem now usually known as the _Phase Rule_, by which he defined the conditions of equilibrium as a relations.h.i.+p between the number of what are called the phases and the components of the system.
Phases.--Before proceeding farther we shall first consider what exactly is meant by the terms _phase_ and _component_. We have already seen (p. 5) that a heterogeneous system is made {9} up of different portions, each in itself h.o.m.ogeneous, but marked off in s.p.a.ce and separated from the other portions by bounding surfaces. These h.o.m.ogeneous, physically distinct and mechanically separable portions are called _phases_. Thus ice, water, and vapour, are three phases of the same chemical substance--water. A phase, however, whilst it must be physically and chemically h.o.m.ogeneous, need not necessarily be chemically simple. Thus, a gaseous mixture or a solution may form a phase; but a heterogeneous mixture of solid substances const.i.tutes as many phases as there are substances present. Thus when calcium carbonate dissociates under the influence of heat, calcium oxide and carbon dioxide are formed. There are then _two_ solid phases present, viz. calcium carbonate and oxide, and one gas phase, carbon dioxide.
The _number of phases_ which can exist side by side may vary greatly in different systems. In all cases, however, there can be but one gas or vapour phase on the account of the fact that all gases are miscible with one another in all proportions. In the case of liquid and solid phases the number is indefinite, since the above property does not apply to them. The number of phases which can be formed by any given substance or group of substances also differs greatly, and in general increases with the number of partic.i.p.ating substances. Even in the case of a single substance, however, the number may be considerable; in the case of sulphur, for example, at least eight different solid phases are known (_v._ Chap. III.).
It is of importance to bear in mind that equilibrium is _independent of the amounts_ of the phases present.[13] Thus it is a familiar fact that the pressure of a vapour in contact with a {10} liquid (_i.e._ the pressure of the saturated vapour) is unaffected by the amounts, whether relative or absolute, of the liquid and vapour; also the amount of a substance dissolved by a liquid is independent of the amount of solid in contact with the solution. It is true that deviations from this general law occur when the amount of liquid or the size of the solid particles is reduced beyond a certain point,[14] owing to the influence of surface energy; but we have already (p. 5) excluded such cases from consideration.
Components.--Although the conception of phases is one which is readily understood, somewhat greater difficulty is experienced when we come to consider what is meant by the term _component_; for the components of a system are not synonymous with the chemical elements or compounds present, _i.e._ with the _const.i.tuents_ of the system, although both elements and compounds may be components. By the latter term there are meant only those const.i.tuents the concentration of which can undergo _independent_ variation in the different phases, and it is only with these that we are concerned here.[15]
To understand the meaning of this term we shall consider briefly some cases with which the reader will be familiar, and at the outset it must be emphasized that the Phase Rule is concerned merely with those const.i.tuents which take part in the state of real equilibrium (p. 5); for it is only to the final state, not to the processes by which that state is reached, that the Phase Rule applies.
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