CHAPTER IV
GENERAL SUMMARY
In the preceding pages we have learned how the principles of the Phase Rule can be applied to the elucidation of various systems consisting of one component. In the present chapter it is proposed to give a short summary of the relationships we have met with, and also to discuss more generally how the Phase Rule applies to other one-component systems. On account of the fact that beginners are sometimes inclined to expect too much of the Phase Rule; to expect, for example, that it will inform them as to the exact behaviour of a substance, it may here be emphasized that the Phase Rule is a general rule; it informs us only as to the general conditions of equilibrium, and leaves the determination of the definite, numerical data to experiment.
Triple Point.—We have already (p. 28) defined a triple point in a one-component system, as being that pressure and temperature at which three phases coexist in equilibrium; it represents, therefore, an invariant system (p. 16). At the triple point also, three curves cut, viz. the curves representing the conditions of equilibrium of the three univariant systems formed by the combination of the three phases in pairs. The most common triple point of a one-component system is, of course, the triple point, solid, liquid, vapour (S-L-V), but other triple points[99] are also possible when, as in the case of sulphur or benzophenone, polymorphic forms occur. Whether or not all the triple points can be experimentally realized will, of course, depend on circumstances. We shall, in the first place, consider only the triple point S-L-V.
As to the general arrangement of the three univariant curves around the triple point, the following rules may be given. (1) The prolongation of each of the curves beyond the triple point must lie between the other two curves. (2) The middle position at one and the same temperature in the neighbourhood of the triple point is taken by that curve (or its metastable prolongation) which represents the two phases of most widely differing specific volume.[100] That is to say, if a line of constant temperature is drawn immediately above or below the triple point so as to cut the three curves—two stable curves and the metastable prolongation of the third—the position of the curves at that temperature will be such that the middle position is occupied by that curve (or its metastable prolongation) which represents the two phases of most widely differing specific volume.
Now, although these rules admit of a considerable variety of possible arrangements of curves around the triple point,[101] only two of these have been experimentally obtained in the case of the triple point solid—liquid—vapour. At present, therefore, we shall consider only these two cases (Figs. 13 and 14).
An examination of these two figures shows that they satisfy the rules laid down. Each of the curves on being prolonged passes between the other two curves. In the case of substances of the first type (Fig. 13), the specific volume of the solid is greater than that of the liquid (the substance contracts on fusion); the difference of specific volume will, therefore, be greatest between liquid and vapour. The curve, therefore, for liquid and vapour (or its prolongation) must lie between the other two curves; this is seen from the figure to be the case. Similarly, the rule is satisfied by the arrangement of curves in Fig. 14, where the difference of specific volumes is greatest between the solid and vapour. In this case the curve S-V occupies the intermediate position.
As we see, the two figures differ from one another only in that the fusion curve OC in one case slopes to the right away from the pressure axis, thus indicating that the melting point is raised by increase of pressure; in the other case, to the left, indicating a lowering of the melting point with the pressure. These conditions are found exemplified in the case of sulphur and ice (pp. 29 and 35). We see further from the two figures, that O in Fig. 13 gives the highest temperature at which the solid can exist, for the curve for solid—liquid slopes back to regions of lower temperature; in Fig. 14, O gives the lowest temperature at which the liquid phase can exist as stable phase.[102]
Theorems of van't Hoff and of Le Chatelier.—So far we have studied only the conditions under which various systems exist in equilibrium; and we now pass to a consideration of the changes which take place in a system when the external conditions of temperature and pressure are altered. For all such changes there exist two theorems, based on the laws of thermodynamics, by means of which the alterations in a system can be qualitatively predicted.[103] The first of these, usually known as van't Hoff's law of movable equilibrium,[104] states: When the temperature of a system in equilibrium is raised, that reaction takes place which is accompanied by absorption of heat; and, conversely, when the temperature is lowered, that reaction occurs which is accompanied by an evolution of heat.
The second of the two theorems refers to the effect of change of pressure, and states:[105] When the pressure on a system in equilibrium is increased, that reaction takes place which is accompanied by a diminution of volume; and when the pressure is diminished, a reaction ensues which is accompanied by an increase of volume.
The demonstration of the universal applicability of these two theorems is due chiefly to Le Chatelier, who showed that they may be regarded as consequences of the general law of action and reaction. For this reason they are generally regarded as special cases of the more general law, known as the theorem of Le Chatelier, which may be stated in the words of Ostwald, as follows:[106] If a system in equilibrium is subjected to a constraint by which the equilibrium is shifted, a reaction takes place which opposes the constraint, i.e. one by which its effect is partially destroyed.
This theorem of Le Chatelier is of very great importance, for it applies to all systems and changes of the condition of equilibrium, whether physical or chemical; to vaporization and fusion; to solution and chemical action. In all cases, whenever changes in the external condition of a system in equilibrium are produced, processes also occur within the system which tend to counteract the effect of the external changes.
Changes at the Triple Point.—If now we apply this theorem to equilibria at the triple point S-L-V, and ask what changes will occur in such a system when the external conditions of pressure and temperature are altered, the general answer to the question will be: So long as the three phases are present, no change in the temperature or pressure of the system can occur, but only changes in the relative amounts of the phases; that is to say, the effect on the system of change in the external conditions
