States of uniform composition

Azeotropic transformations in systems in which chemical reactions may take place in addition to transfers from one phase to another, or which have more than two phases, are not necessarily associated with states of uniform composition but with the more general class of indifferent states. A study of systems of uniform composition is a natural introduction to the more general question of indifferent states. 

We shall not repeat here any discussion of the properties already established for states of uniform composition. It will be recalled that a state of uniform composition corresponds to an extreme value (maximum, minimum, or inflexion with a horizontal tangent) of the equilibrium pressure at constant temperature, or of the equilibrium temperature at constant pressure (Gibbs-Konovalow theorems, chap. XVIII, 6 and 9). 

We have shown above that the activity coefficients of the components of an azeotropic mixture may be calculated from a knowledge of the properties of the pure components, and the temperature and pressure of the azeotropic state. In this paragraph we shall investigate the prediction of states of uniform composition from a knowledge of the behaviour of the activity coefficients as functions of temperature and pressure. 

Considerations essentially similar to those above apply also to states of uniform composition in a continuous series of mixed crystals. Equation (21.52 ) can be applied not only to a liquid solution but also to mixed crystals, so that instead of (28.25), we have at all points of uniform composition ... 

From the position of the state of uniform composition, we can calculate a -using (28.28). Thus for Co + Mn we find a value of 1070 cal. /mole. This is very large and indicates that the departure from ideality, measured by the magnitude of a, is very much greater in the solid state than in liquids. 

We are now in a position to study the series of states of uniform composition which are obtained when T,p and a 2 all vary simultaneously. These three variables are always related by the two equatoms (28.17) it follows therefore that only one of them can be varied independently, so that the states of uniform composition fall on a line called the azeotropic line. The differential relations which this line must satisfy are examined below. ... 

In the preceding chapter we studied the properties of states of uniform composition in two-phase binary systems. As was demonstrated by the work of Duhem, Saurel and Jouguet, these states of uniform composition are but a special case of a much larger family of thermodynamic states indifferent states. We shall end this book therefore, with a chapter dealing with the properties of such states. 

Hence for this system to be indifferent, it is necessary and sufficient that the two phases shall have the same composition. We thus find, as a special case of indifferent states, the states of uniform composition discussed in the preceding chapter. 

The inverse of this theorem is clearly not true, for in 5 we have already seen examples of indifferent systems in which no pair of phases has the same composition. In two-phase non-reacting systems all indifferent states are states of uniform composition, for in the case of only two phases (29.19) reduces to... 

We see that the concept of indifferent states is much more general than that of states of uniform composition. All states of uniform composition of two or more phases are indifferent, but by no means all indifferent states involve phases of the same composition. The properties discussed in the previous chapter in connection with states of uniform composition are nearly all a consequence of the fact that these states are indifferent states, and we shall find most of these properties exhibited in the more general case. 

We met these theorems in studying the properties of states of uniform composition (chap. XVIII, 6) we shall now examine them in a more general form as a property of all static indifferent states in a poly variant system. 

This example also shows how indifferent states are a generalization of states of uniform composition. Thus we may compare fig. 29.7 with the phase diagram (fig. 29.8) of vaporization of a binary liquid with an azeotrope. 

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