Now, suppose that isomeric transformation takes place with measurable velocity. If the pure α-modification is heated to a temperature t′ above its melting point, and the liquid maintained at that temperature until equilibrium has been established, a certain amount of the β-form will be present in the liquid, the composition of which will be represented by the point x′. The same condition of equilibrium will also be reached by starting with pure β. Similarly, if the temperature of the liquid is maintained at the temperature t″, equilibrium will be reached, we shall suppose, when the solution has the composition x″. The curve DE, therefore, which passes through all the different values of x corresponding to different values of t, will represent the change of equilibrium with the temperature. It will slope to the right (as in the figure) if the transformation of α into β is accompanied by absorption of heat; to the left if the transformation is accompanied by evolution of heat, in accordance with van't Hoff's Law of movable equilibrium. If transformation occurs without heat effect, the equilibrium will be independent of the
temperature, and the equilibrium curve DE will therefore be perpendicular and parallel to the temperature axis.
We must now find the meaning of the point D. Suppose the pure α- or pure β-form heated to the temperature t′, and the temperature maintained constant until the liquid has the composition x′ corresponding to the equilibrium at that temperature. If the temperature is now allowed to fall sufficiently slowly so that the condition of equilibrium is continually readjusted as the temperature changes, the composition of the solution will gradually alter as represented by the curve x′D. Since D is on the freezing point curve of pure α, this form will be deposited on cooling; and since D is also on the equilibrium curve of the liquid, D is the only point at which solid can exist in stable equilibrium with the liquid phase. (The vapour phase may be omitted from consideration, as we shall suppose the experiments carried out in open vessels.) All systems consisting of the two hylotropic[[281]] isomeric substances α and β will, therefore, ultimately freeze at the point D, which is called the "natural" freezing point[[282]] of the system; provided, of course, that sufficient time is allowed for equilibrium to be established. From this it is apparent that the stable modification at temperatures in the neighbourhood of the melting point is that which is in equilibrium with the liquid phase at the natural freezing point.
From what has been said, it will be easy to predict what will be the behaviour of the system under different conditions. If pure α is heated, a temperature will be reached at which it will melt, but this melting point will be sharp only if the velocity of isomeric transformation is comparatively slow; i.e. slow in comparison with the determination of the melting point. If the substance be maintained in the fused condition for some time, a certain amount of the β modification will be formed, and on lowering the temperature the pure α form will be deposited, not at the temperature of the melting point, but at some lower temperature depending on the concentration of the β modification in the liquid phase. If isomeric transformation
takes place slowly in comparison with the rate at which deposition of the solid occurs, the liquid will become increasingly rich in the β modification, and the freezing point will, therefore, sink continuously. At the eutectic point, however, the β modification will also be deposited, and the temperature will remain constant until all has become solid. If, on the other hand, the velocity of transformation is sufficiently rapid, then as quickly as the α modification is deposited, the equilibrium between the two isomeric forms in the liquid phase will continuously readjust itself, and the end-point of solidification will be the natural freezing point.
Similarly, starting with the pure β modification, the freezing point after fusion will gradually fall owing to the formation of the α modification; and the composition of the liquid phase will pass along the curve BC. If, now, the rate of cooling is not too great, or if the velocity of isomeric transformation is sufficiently rapid, complete solidification will not occur at the eutectic point; for at this temperature solid and liquid are not in stable equilibrium with one another. On the contrary, a further quantity of the β modification will undergo isomeric change, the liquid phase will become richer in the α form, and the freezing point will rise; the solid phase in contact with the liquid being now the α modification. The freezing point will continue to rise until the point D is reached, at which complete solidification will take place without further change of temperature.
The diagram also allows us to predict what will be the result of rapidly cooling a fused mixture of the two isomerides. Suppose that either the α or the β modification has been maintained in the fused state at the temperature t′ sufficiently long for equilibrium to be established. The composition of the liquid phase will be represented by x′. If the liquid is now rapidly cooled, the composition will remain unchanged as represented by the dotted line x′G. At the temperature of the point G solid α modification will be deposited. If the cooling is not carried below the point G, so as to cause complete solidification, the freezing point will be found to rise with time, owing to the conversion of some of the β form into the α form
in the liquid phase; and this will continue until the composition of the liquid has reached the point D. From what has just been said, it can also be seen that if the freezing point curves can be obtained by actual determination of the freezing points of different synthetic mixtures of the two isomerides, it will be possible to determine the condition of equilibrium in the fused state at any given temperature without having recourse to analysis. All that is necessary is to rapidly cool the fused mass, after equilibrium has been established, and find the freezing point at which solid is deposited; that is, find the point at which the line of constant temperature cuts the freezing point curve. The composition corresponding to this temperature gives the composition of the equilibrium mixture at the given temperature.
It will be evident, from what has gone before, that the degree of completeness with which the different curves can be realised will depend on the velocity with which isomeric change takes place, and on the rapidity with which the determinations of the freezing point can be carried out. As the two extremes we have, on the one hand, practically instantaneous transformation, and on the other, practically infinite slowness of transformation. In the former case, only one melting and freezing point will be found, viz. the natural freezing point; in the latter case, the two isomerides will behave as two perfectly independent components, and the equilibrium curve DE will not be realised.