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 relationship 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
up of different portions, each in itself homogeneous, but marked off in space and separated from the other portions by bounding surfaces. These homogeneous, 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 homogeneous, need not necessarily be chemically simple. Thus, a gaseous mixture or a solution may form a phase; but a heterogeneous mixture of solid substances constitutes 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 participating 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
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 constituents of the system, although both elements and compounds may be components. By the latter term there are meant only those constituents 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 constituents 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.
Consider now the case of the system water—vapour or ice—water—vapour. The number of constituents taking part in the equilibrium here is only one, viz. the chemical substance, water. Hydrogen and oxygen, the constituents of water, are not to be regarded as components, because, in the first place, they are
not present in the system in a state of real equilibrium (p. [6]); in the second place, they are combined in definite proportions to form water, and their amounts, therefore, cannot be varied independently. A variation in the amount of hydrogen necessitates a definite variation in the amount of oxygen.