solidify to a mixture of ice and hydrate, and there will be obtained the univariant system ice—hydrate—vapour. The vapour pressure of this system has been determined down to a temperature of -9.5°, at which temperature the pressure amounts to 15 cm. The pressures for this system are represented by the curve BC. If at the point B the volume is diminished, the pressure must remain constant, but the relative amounts of the different phases will undergo change. If suitable quantities of these are present, diminution of volume will ultimately lead to the total condensation of the vapour phase, and there will remain the univariant system ice—hydrate—solution. The temperature of equilibrium of this system will alter with the pressure, but, as in the case of the melting point of a simple substance, great differences of pressure will cause only comparatively small changes in the temperature of equilibrium. The change of the cryohydric point with the pressure is represented by the line BE; the actual values have not been determined, but the curve must slope towards the pressure axis because fusion is accompanied by diminution of volume, as in the case of pure ice.
A fourth univariant system can be formed at B. This is the system hydrate—solution II.—vapour. The conditions for the existence of this system are represented by the curve BF, which may therefore be regarded as the vapour-pressure curve of the saturated solution of sulphur dioxide heptahydrate in water. Unlike the curve for iodine trichloride—solution—vapour, this curve cannot be followed to the melting point of the hydrate. Before this point is reached, a second liquid phase appears, and an invariant system consisting of hydrate—solution I.—solution II.—vapour is formed. We have here, therefore, the phenomenon of melting under the solution as in the case of succinic nitrile and water (p. [122]). This point is represented in the diagram by F; the temperature at this point is 12.1°, and the pressure 177.3 cm. The range of stable existence of the hydrate is therefore from -2.6° to 12.1°; nevertheless, the curve FB has been followed down to a temperature of -6°, at which point ice formed spontaneously.
So long as the four phases hydrate, two liquid phases, and vapour are present, the condition of the system is perfectly defined. By altering the conditions, however, one of the phases can be made to disappear, and a univariant system will then be obtained. Thus, if the vapour phase is made to disappear, the univariant system solution I.—solution II.—hydrate, will be left, and the temperature at which this system is in equilibrium will vary with the pressure. This is represented by the curve FI; under a pressure of 225 atm. the temperature of equilibrium is 17.1°. Increase of pressure, therefore, raises the temperature at which the three phases can coexist.
Again, addition of heat to the invariant system at F will cause the disappearance of the solid phase, and there will be formed the univariant system solution I.—solution II.—vapour. In the case of this system the vapour pressure increases as the temperature rises, as represented by the curve FG. Such a system is analogous to the case of ether and water, or other two partially miscible liquids (p. [103]). As the temperature changes, the composition of the two liquid phases will undergo change; but this system has not been studied fully.
The fourth curve, which ends at the quadruple point F, is
that representing the vapour pressure of the system hydrate—solution I.—vapour (FH). This curve has been followed to a temperature of 0°, the pressure at this point being 113 cm. The metastable prolongation of GF has also been determined. Although, theoretically, this curve must lie below FH, it was found that the difference in the pressure for the two curves was within the error of experiment.
Bivariant Systems.—The different bivariant systems, consisting of two phases, which can exist within the range of temperature and pressure included in Fig. 45, were given on p. [170]. The conditions under which these systems can exist are represented by the areas in the diagram, and the fields of the different bivariant systems are indicated by letters, corresponding to the letters on p. [170]. Just as in the case of one-component systems (p. [29]), we found that the field lying between any two curves gave the conditions of existence of that phase which was common to the two curves, so also in the case of two-component systems, a bivariant two-phase system occurs in the field enclosed[[252]] by the two curves to which the two phases are common. As can be seen, the same bivariant system can occur in more than one field.
As is evident from Fig. 45, three different bivariant systems are capable of existing in the area HFI; which of these will be obtained will depend on the relative masses of the different phases in the univariant or invariant system. Thus, starting with a system represented by a point on the curve HF, diminution of volume at constant temperature will cause the condensation of a portion of the vapour, which is rich in sulphur dioxide; since this would increase the concentration of sulphur dioxide in the solution, it must be counteracted by the passage of a portion of the hydrate (which is relatively poor in sulphur dioxide) into the solution. If, therefore, the amount of hydrate present is relatively very small, the final result of the compression will be the production of the system f, solution I.—vapour. On the other hand, if the vapour is present in relatively small amount, it will be the first phase to disappear,
and the bivariant system a, hydrate—solution I., will be obtained. Finally, if we start with the invariant system at F, compression will cause the condensation of vapour, while the composition of the two solutions will remain unchanged. When all the vapour has disappeared, the univariant system hydrate—solution I.—solution II. will be left. If, now, the pressure is still further increased, while the temperature is kept below 12°, more and more hydrate must be formed at the expense of the two liquid phases (because 12° is the lower limit for the coexistence of the two liquid phases), and if the amount of the solution I. (containing excess of sulphur dioxide) is relatively small, it will disappear before solution II., and there will be obtained the bivariant system hydrate—solution II. (bivariant system b).