Part 24 (1/2)
ISOTHERMAL CURVES AND THE s.p.a.cE MODEL
In the preceding chapter we considered the changes in the solubility of double salts and of mixtures of their const.i.tuent salts with the temperature; noting, more especially, the relations.h.i.+ps between the two systems at the transition point. It is now proposed to conclude the study of the three-component systems by discussing very briefly the solubility relations at constant temperature, or the isothermal solubility curves. In this way fresh light will be thrown on the change in the solubility of one component by the addition of another component, and also on the conditions of formation and stable existence of double salts in solution. With the help of these isothermal curves, also, the phenomena of crystallization at constant temperature--phenomena which have not only a scientific interest but also an important bearing on the industrial preparation of double salts--will be more clearly understood.[354]
A brief description will also be given of the method of representing the variation of the concentration of the two salts in the solution with the temperature.
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 abscissae the amount of B in a _constant amount_ of the third component, the solvent. The {273} 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 const.i.tute 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 quant.i.ty 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 Na_{2}SO_{4} and 4.57 gm.-molecules MgSO_{4} 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.
[Ill.u.s.tration: FIG. 102.]
[Ill.u.s.tration: FIG. 103.]
[Ill.u.s.tration: FIG. 104.]
Formation of Double Salt.--We have already learned in the preceding chapter that if the temperature is outside[357] the {274} 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 const.i.tuent 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 const.i.tutes 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 const.i.tuent 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.
[Ill.u.s.tration: FIG. 105.]
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 {275} of the double salt must, therefore, pa.s.s through the point C, as shown in Fig. 105.
From this figure, now, it is seen that a solution saturated with respect to double salt alone (point D), is supersaturated with respect to the component A. If, then, at the temperature of the transition point, excess of the double salt is brought in contact with water,[358] and if supersaturation is excluded, _the double salt will undergo decomposition and the component A will be deposited_. The relative concentration of the component B in the solution will, therefore, increase, and the composition of the solution will be thereby altered in the direction DC. When the solution has the composition of C, the single salt ceases to be deposited, for at this point the solution is saturated for both double and single salt; and the system becomes invariant.
This diagram explains very clearly the phenomenon of the decomposition of a double salt at the transition point. As is evident, this decomposition will occur when the solution which is saturated at the temperature of the transition point, with respect to the two single salts (point C), does not contain these salts in the same ratio in which they are present in the double salt. If point C lay on the dotted line bisecting the right angle, then the pure saturated solution of the double salt would not be supersaturated with respect to either of the single salts, and the double salt would, therefore, not be decomposed by water. As has already been mentioned, this behaviour is found in the case of optically active isomerides, the solubilities of which are identical.
At the transition point, therefore, the isothermal curve also consists of two branches; but the point of intersection of the two branches now represents a solution which is saturated not {276} only with respect to the single salts, but also for the double salt in presence of the single salts.
We have just seen that by a change of temperature the two solubility curves, that for the two single salts and that for the double salt, were made to approach one another (_cf._ Figs. 104 and 105). In the previous chapter, however, we found that on pa.s.sing the transition point to the region of stability for the double salt, the solution which is saturated for a mixture of the two const.i.tuent salts, is supersaturated for the double salt. In this case, therefore, point C must lie above the solubility curve of the pure double salt (Fig. 106), and a solution of the composition C, if brought in contact with double salt, will deposit the latter. If the single salts were also present, then as the double salt separated out, the single salts would pa.s.s into solution, because so long as the two single salts are present, the composition of the solution must remain unaltered.
If one of the single salts disappear before the other, there will be left double salt plus A or double salt plus B, according to which was in excess; and the composition of the solution will be either that represented by D (saturated for double salt plus A), or that of the point F (saturated for double salt plus B).
[Ill.u.s.tration: FIG. 106.]
In connection with the isothermal represented in Fig. 106, it should be noted that at this particular temperature a solution saturated with respect to the pure double salt is no longer supersaturated for one of the single salts (point D); so that at the temperature of this isothermal the double salt is not decomposed by water. At this temperature, further, the boundary curve consists of three branches AD, DF, and FB, which give the composition of the solutions in equilibrium with pure A, double salt, and pure B respectively; while the points D and F represent solutions saturated for double salt plus A and double salt plus B.
On continuing to alter the temperature in the same direction {277} as before, the relative s.h.i.+fting of the solubility curves becomes more marked, as shown in Fig. 107. At the temperature of this isothermal, the solution saturated for the double salt now lies in a region of distinct unsaturation with respect to the single salts; and the double salt can now exist as solid phase in contact with solutions containing both relatively more of A (curve ED), and relatively more of B (curve DF), than is contained in the double salt itself.
[Ill.u.s.tration: FIG. 107.]
Transition Interval.--From what has been said, and from an examination of the isothermal diagrams, Figs. 104-107, it will be seen that by a variation of the temperature we can pa.s.s from a condition where the double salt is quite incapable of existing in contact with solution (supersaturation being excluded), to a condition where the existence of the double salt in presence of solution becomes possible; only in the presence, however, of one of the single salts (_transition point_, Fig. 105). A further change of temperature leads to a condition where the stable existence of the pure double salt in contact with solution just becomes possible (Fig. 106); and from this point onwards, pure saturated solutions of the double salt can be obtained (Fig. 107). _At any temperature, therefore, between that represented by Fig. 105, and that represented by Fig. 106, the double salt undergoes partial decomposition, with deposition of one of the const.i.tuent salts._ The temperature range between the transition point and the temperature at which a stable saturated solution of the pure double salt just begins to be possible, is known as the _transition interval_ (p. 270).
As the figures show, the transition interval is limited on the one side by the transition temperature, and on the other by the temperature at which the solution saturated for double salt and the less soluble of the single salts, contains the component salts in the same ratio as they are present in the double salt. The greater the difference in the solubility of the single salts, the larger will be the transition interval. {278}
Isothermal Evaporation.--The isothermal solubility curves are of great importance for obtaining an insight into the behaviour of a solution when subjected to isothermal evaporation. To simplify the discussion of the relations.h.i.+ps found here, we shall still suppose that the double salt contains the single salts in equimolecular proportions; and we shall, in the first instance, suppose that the unsaturated solution with which we commence, also contains the single salts in the same ratio. The composition of the solution must, therefore, be represented by some point lying on the line OD, the bisectrix of the right angle.
From what has been said, it is evident that when the formation of a double salt can occur, three temperature intervals can be distinguished, viz. the single-salt interval, the transition interval, and the double-salt interval.[359] When the temperature lies in the first interval, evaporation leads first of all to the crystallization of one of the single salts, and then to the separation of both the single salts together. In the second temperature interval, evaporation again leads, in the first place, to the deposition of one of the single salts, and afterwards to the crystallization of the double salt. In the third temperature interval, only the double salt crystallizes out. This will become clearer from what follows.
[Ill.u.s.tration: FIG. 108.]
[Ill.u.s.tration: FIG. 109.]