Representation in Space.
Space Model for Carnallite.—Interesting and important as the isothermal solubility curves are, they are insufficient for the purpose of obtaining a clear insight into the complete behaviour of the systems of two salts and water. A short description will, therefore, be given here of the representation in space of the solubility relations of potassium and magnesium chlorides, and of the double salt which they form, carnallite.[[365]]
Fig. 113 is a diagrammatic sketch of the model for carnallite looked at sideways from above. Along the X-axis is measured the concentration of magnesium chloride in the
solution; along the Y-axis, the concentration of potassium chloride; while along the T-axis is measured the temperature. The three axes are at right angles to one another. The XT-plane, therefore, contains the solubility curve of magnesium chloride; the YT-plane, the solubility curve of potassium chloride, and in the space between the two planes, there are represented the composition of solutions containing both magnesium and potassium chlorides. Any surface between the two planes will represent the various solutions in equilibrium with only one solid phase, and will therefore indicate the area or field of existence of bivariant ternary systems. A line or curve formed by the intersection of two surfaces will represent solutions in equilibrium with two solid phases (viz. those belonging to the intersecting surfaces), and will show the conditions for the existence of univariant systems. Lastly, points formed by the intersection of three surfaces will represent invariant systems, in which a solution can exist in equilibrium with three solid phases (viz. those belonging to the three surfaces).
We shall first consider the solubility relations of the single salts. The complete equilibrium curve for magnesium chloride and water is represented in Fig. 113 by the series of curves ABF1 G1 H1 J1 L1 N1. AB is the freezing-point curve of ice in contact with solutions containing magnesium chloride, and B is the cryohydric point at which the solid phases ice and MgCl2,12H2O can co-exist with solution. BFG is the solubility curve of magnesium chloride dodecahydrate. This curve shows a point of maximum temperature at F1, and a retroflex portion F1G1. The curve is therefore of the form exhibited by calcium chloride hexahydrate, or the hydrates of ferric chloride (Chapter VIII.). G1 is a transition point at which the solid phase changes from dodecahydrate to octahydrate, the solubility of which is represented by the curve G1H1. At H1 the octahydrate gives place to the hexahydrate, which is the solid phase in equilibrium with the solutions represented by the curve H1J1. J1 and L1 are also transition points at which the solid phase undergoes change, in the former case from hexahydrate to tetrahydrate; and in the latter case,
from tetrahydrate to dihydrate. The complete curve of equilibrium for magnesium chloride and water is, therefore, somewhat complicated, and is a good example of the solubility curves obtained with salts capable of forming several hydrates.
The solubility curve of potassium chloride is of the simplest form, consisting only of the two branches AC, the freezing-point curve of ice, and CO, the solubility curve of the salt. C is the cryohydric point. This point and the two curves lie in the YT-plane.
On passing to the ternary systems, the composition of the solutions must be represented by points or curves situated between the two planes. We shall now turn to the consideration of these. BD and CD are ternary eutectic curves (p. [284]). They give the composition of solutions in equilibrium with ice and magnesium chloride dodecahydrate (BD), and with ice and potassium chloride (CD). D is a ternary cryohydric point. If the temperature is raised and the ice allowed to disappear, we shall pass to the solubility curve for MgCl2,12H2O + KCl (curve DE). At E carnallite is formed and the potassium chloride disappears; EFG is then the solubility curve for MgCl2,12H2O + carnallite (KMgCl3,6H2O). This curve also shows a point of maximum temperature (F) and a retroflex portion. GH and HJ represent the solubility curves of carnallite + MgCl2,8H2O and carnallite + MgCl2,6H2O, G and H being transition points. JK is the solubility curve for carnallite + MgCl2,4H2O. At the point K we have the highest temperature at which carnallite can exist with magnesium chloride in contact with solution. Above this temperature decomposition takes place and potassium chloride separates out.
If at the point E, at which the two single salts and the double salt are present, excess of potassium chloride is added, the magnesium chloride will all disappear owing to the formation of carnallite, and there will be left carnallite and potassium chloride. The solubility curve for a mixture of these two salts is represented by EMK; a simple curve exhibiting, however, a temperature maximum at M. This maximum point corresponds with the fact that dry carnallite melts at this temperature with separation of potassium chloride. At all temperatures