The Phase Rule and Its Applications

by Alexander Findlay

Non-formation of Double Salts.—In Fig. 102 are shown the solubility curves of two salts, A and B, which at the given temperature do not form a double salt.[^[355]] The ordinates represent the amount of A, the abscissæ the amount of B in a constant amount of the third component, the solvent. The

point A, therefore, represents the solubility of the salt A at the given temperature; and similarly, point B represents the solubility of B. Since we are dealing with a three-component system, one solid phase in contact with solution will constitute a bivariant system (in the absence of the vapour phase and under a constant pressure). At any given temperature, therefore, the concentration of the solution in equilibrium with the solid can undergo change. If, now, to a pure solution of A a small quantity of B is added, the solubility of A will in general be altered; as a rule it is diminished, but sometimes it is increased.[^[356]] The curve AC represents the varying composition of the solution in equilibrium with the solid component A. Similarly, the curve BC represents the composition of the solutions in contact with pure B as solid phase. At the point, C, where these two curves intersect, there are two solid phases, viz. pure A and pure B, in equilibrium with solution, and the system becomes invariant. At this point the solution is saturated with respect to both A and B, and at a given temperature must have a perfectly definite composition. To take an example, if we suppose A to represent sodium sulphate decahydrate, and B, magnesium sulphate heptahydrate, and the temperature to be 18.5° (i.e. below the transition point), the point C would represent a solution containing 2.16 gm.-molecules Na₂SO₄ and 4.57 gm.-molecules MgSO₄ per 100 gm.-molecules of water (p. [268]). The curve ACB is the boundary curve for saturated solutions; solutions lying outside this curve are supersaturated, those lying within the area ACBO, are unsaturated.

Formation of Double Salt.—We have already learned in the preceding chapter that if the temperature is outside[^[357]] the

transition interval, it is possible to prepare a pure saturated solution of the double salt. If, now, we suppose the double salt to contain the two constituent salts in equimolecular proportions, its saturated solution must be represented by a point lying on the line which bisects the angle AOB; e.g. point D, Fig. 103. But a double salt constitutes only a single phase, and can exist, therefore, in contact with solutions of varying concentration, as represented by EDF.

Let us compare, now, the relations between the solubility curve for the double salt, and those for the two constituent salts. We shall suppose that the double salt is formed from the single salts when the temperature is raised above a certain point (as in the formation of astracanite). At a temperature below the transition point, as we have already seen, the solubility of the double salt is greater than that of a mixture of the single salts. The curve EDF, therefore, must lie above the point C, in the region representing solutions supersaturated with respect to the single salts (Fig. 104). Such a solution, however, would be metastable, and on being brought in contact with the single salts would deposit these and yield a solution represented by the point C. At this particular temperature, therefore, the isothermal solubility curve will consist of only two branches.

Suppose, now, that the temperature is that of the transition point. At this point, the double salt can exist together with the single salts in contact with solution. The solubility curve