Bivariant Systems.—As the first examples of the equilibria between a substance and its products of dissociation, we shall consider very briefly those cases in which there is one solid phase in equilibrium with vapour. Reference has already been made to such systems in the case of ammonium chloride. On being heated, ammonium chloride dissociates into ammonia and hydrogen chloride. Since, however, in that case the vapour phase has the same total composition as the solid phase, viz. NH3 + HCl = NH4Cl, the system consists of only one component existing in two phases; it is therefore univariant, and to each temperature there will correspond a definite vapour pressure (dissociation pressure).[[146]]
If, however, excess of one of the products of dissociation be added, the system becomes one of two components.
In the first place, analysis of each of the two phases yields as the composition of each, solid: NH4Cl (= NH3 + HCl); vapour: mNH3 + nHCl. Obviously the smallest number of substances by which the composition of the two phases can be expressed is two; that is, the number of components is two. What, then, are the components? The choice lies between NH3 + HCl, NH4Cl + NH3, and NH4Cl + HCl; for the three substances, ammonium chloride, ammonia, hydrogen chloride, are the only ones taking part in the equilibrium of the system.
Of these three pairs of components, we should obviously choose as the most simple NH3 and HCl, for we can then represent the composition of the two phases as the sum of the two components. If one of the other two possible pairs of components be chosen, we should have to introduce negative quantities of one of the components, in order to represent the composition of the vapour phase. Although it must be allowed that the introduction of negative quantities of a component in such cases is quite permissible, still it will be
better to adopt the simpler and more direct choice, whereby the composition of each of the phases is represented as a sum of two components in varying proportions (p. [12]).
If, therefore, we have a solid substance, such as ammonium chloride, which dissociates on volatilization, and if the products of dissociation are added in varying amounts to the system, we shall have, in the sense of the Phase Rule, a two-component system existing in two phases. Such a system will possess two degrees of freedom. At any given temperature, not only the pressure, but also the composition, of the vapour-phase, i.e. the concentration of the components, can vary. Only after one of these independent variables, pressure or composition, has been arbitrarily fixed does the system become univariant, and exhibit a definite, constant pressure at a given temperature.
Now, although the Phase Rule informs us that at a given temperature change of composition of the vapour phase will be accompanied by change of pressure, it does not cast any light on the relation between these two variables. This relationship, however, can be calculated theoretically by means of the Law of Mass Action.[[147]] From this we learn that in the case of a substance which dissociates into equivalent quantities of two gases, the product of the partial pressures of the gases is constant at a given temperature.
This has been proved experimentally in the case of ammonium hydrosulphide, ammonium cyanide, phosphonium bromide, and other substances.[[148]]
Univariant Systems.—In order that a system of two components shall possess only one degree of freedom, three phases must be present. Of such systems, there are seven possible, viz. S-S-S, S-S-L, S-S-V, L-L-L, S-L-L, L-L-V, S-L-V; S denoting solid, L liquid, and V vapour. In the present chapter we shall consider only the systems S-S-V, i.e. those systems in which there are two solid phases and a vapour phase present.