The Phase Rule and Its Applications. Alexander Findlay
shown in Figs. 13 and 14 (p. 57). A glance at these figures will show that increase of volume (diminution of pressure) will lead ultimately to the system S-V, for at pressures lower than that of the triple point, the liquid phase cannot exist. Decrease of volume (increase of pressure), on the other hand, will lead either to the system S-L or L-V, because these systems can exist at pressures higher than that of the triple point. If the vapour phase disappears and we pass to the curve S-L, continued diminution of volume will be accompanied by a fall in temperature in the case of systems of the first type (Fig. 13), and by a rise in temperature in the case of systems of the second type (Fig. 14).
Lastly, if the temperature is maintained constant, i.e. if heat can pass into or out of the system, then on changing the volume the same changes in the phases will take place as described above until one of the phases has disappeared. Continued increase of volume (decrease of pressure) will then cause the disappearance of a second phase, the system passing along the dotted line OE′ (Figs. 16, 17), so that ultimately there remains only the vapour phase. Conversely, diminution of volume (increase of pressure) will ultimately lead either to solid (Fig. 16) or to liquid alone (Fig. 17), the system passing along the dotted line OE.
In discussing the alterations which may take place at the triple point with change of temperature and pressure, we have considered only the triple point S-L-V. The same reasoning, however, applies, mutatis mutandis, to all other triple points, so that if the specific volumes of the phases are known, and the sign of the heat effects which accompany the transformation of one phase into the other, it is possible to predict (by means of the theorem of Le Chatelier) the changes which will be produced in the system by alteration of the pressure and temperature.
In all cases of transformation at the triple point, it should be noted that all three phases are involved in the change,[107] and not two only; the fact that in the case, say, of the transformation from solid to liquid, or liquid to solid, at the melting point with change of temperature, only these two phases appear to be affected, is due to there generally being a large excess of the vapour phase present and to the prior disappearance therefore of the solid or liquid phase.
In the case of triple points at which two solid phases are in equilibrium with liquid, other arrangements of the curves around the triple point are found. It is, however, unnecessary to give a general treatment of these here, since the principles which have been applied to the triple point S-L-V can also be applied to the other triple points.[108]
Triple Point Solid—Solid—Vapour.—The triple point solid—solid—vapour is one which is of considerable importance. Examples of such a triple point have already been given in sulphur and tin, and a list of other substances capable of yielding two solid phases is given below. The triple point S-S-V is not precisely the same as the transition point, but is very nearly so. The transition point is the temperature at which the relative stability of the two solid phases undergoes change, when the vapour phase is absent and the pressure is 1 atm.; whereas at the triple point the pressure is that of the system itself. The transition point, therefore, bears the same relation to the triple point S-S-V as the melting point to the triple point S-L-V.
In the following table is given a list of the most important polymorphous substances, and the temperatures of the transition point.[109]
| Substance. | Transition temperature. |
| Ammonium nitrate— | |
β-rhombic  |
35° |
|
α-rhombic |
83° |
|
Rhombohedral |
125° |
| Mercuric iodide | 126° |
| Potassium nitrate | 129° |
| Silver iodide | 145° |
| Silver nitrate | 160° |
| Sulphur | 95.5° |
| Tetrabrommethane | 46.8° |
| Thallium nitrate— | |
|
Rhombic |
80° |
|
Rhombohedral |
142.5° |
| Thallium picrate | 46° |
| Tin | 20° |
Sublimation and Vaporization Curves.—We have already seen, in the case of ice and liquid water, that the vapour pressure increases as the temperature rises, the increase of pressure per degree being greater the higher the temperature. The sublimation and vaporization curves, therefore, are not straight lines, but are bent, the convex side of the curve being towards the temperature axis in the ordinary pt-diagram.
In the case of sulphur and of tin, we assumed vapour to be given off by the solid substance, although the pressure of the vapour has not hitherto been measured. The assumption, however, is entirely justified, not only on theoretical grounds, but also because the existence of a vapour pressure has been observed in the case of many solid substances at temperatures much below the melting point,[110] and in some cases, e.g. camphor,[111] the vapour pressure is considerable.
As the result of a large number of determinations, it has been found that all vapour pressure curves have the same general form alluded to above. Attempts have also been made to obtain a general expression for the quantitative changes in the vapour pressure with change of temperature, but without success. Nevertheless, the qualitative changes, or the general direction of the curves, can be predicted by means of the theorem of Le Chatelier.
As we have already learned (p. 16), the Phase Rule takes no account of the molecular complexity of the substances participating in an equilibrium. A dissociating substance, therefore, in contact with its vaporous products of dissociation (e.g. ammonium chloride in contact with ammonia and hydrogen chloride), will likewise constitute a univariant system of one component, provided the composition of the vapour phase as a whole is the same as that of the solid or liquid phase (p. 13). For all such substances, therefore, the conditions of equilibrium will be represented by a curve of the same general form as the vapour pressure curve of a non-dissociating substance.[112] The same behaviour is also found in the case of substances which polymerize on passing into the solid or liquid state (e.g. red phosphorus). Where such changes in the molecular state occur, however, the time required