The Phase Rule and Its Applications

by Alexander Findlay

From the example which has just been discussed, it might

appear as if the choice of the components was rather arbitrary. On examining the point, however, it will be seen that the arbitrariness affects only the nature, not the number, of the components; a choice could be made with respect to which, not to how many, constituents were to be regarded as components. As we shall see presently, however, it is only the number, not the nature of the components that is of importance.

After the discussion of the conditions which the substances chosen as components must satisfy, another method may be given by which the number of components present in a system can be determined. Suppose a system consisting of several phases in equilibrium, and the composition of each phase determined by analysis. If each phase present, regarded as a whole, has the same composition, the system contains only one component, or is of the first order. If two phases must be mixed in suitable quantities in order that the composition of a third phase may be obtained, the system is one of two components or of the second order; and if three phases are necessary to give the composition of a fourth coexisting phase, the system is one of three components, or of the third order.[^[16]]

Although the examples to be considered in the sequel will afford sufficient illustration of the application of the rules given above, one case may perhaps be discussed to show the application of the method just given for determining the number of components.

Consider the system consisting of Glauber's salt in equilibrium with solution and vapour. If these three phases are analyzed, the composition of the solid will be expressed by Na₂SO₄, 10H₂O; that of the solution by Na₂SO₄ + xH₂O, while the vapour phase will be H₂O. The system evidently cannot be a one-component system, for the phases have not all the same composition. By varying the amounts of two phases, however (e.g. Na₂SO₄, 10H₂O and H₂O), the composition of the third phase—the solution—can be obtained. The system is, therefore, one of two components.

But sodium sulphate can also exist in the anhydrous form and as the hydrate Na₂SO₄, 7H₂O. In these cases there may

be chosen as components Na₂SO₄ and H₂O, and Na₂SO₄, 7H₂O and H₂O respectively. In both cases, therefore, there are two components. But the two systems (Na₂SO₄, 10H₂O—H₂O, and Na₂SO₄, 7H₂O—H₂O) can be regarded as special cases of the system Na₂SO₄—H₂O, and these two components will apply to all systems made up of sodium sulphate and water, no matter whether the solid phase is anhydrous salt or one of the hydrates. In all three cases, of course, the number of components is the same; but by choosing Na₂SO₄ and H₂O as components, the possible occurrence of negative quantities of components in expressing the composition of the phases is avoided; and, further, these components apply over a much larger range of experimental conditions. Again, therefore, we see that, although the number of the components of a system is definite, a certain amount of liberty is allowed in the choice of the substances; and we also see that the choice will be influenced by the conditions of experiment.

Summing up, now, we may say—

(1) The components are to be chosen from among the constituents which are present when the system is in a state of true equilibrium, and which take part in that equilibrium.

(2) As components are to be chosen the smallest number of such constituents necessary to express the composition of each phase participating in the equilibrium, zero and negative quantities of the components being permissible.