Note on azeotropic systems and indifferent states

We must mention however, that in certain special cases—called indifferent states—the choice of variables T and p is not convenient in the sense that for these systems these two variables do not suffice to calculate all the others. We indicate below the way in which this state of affairs arises, but a detailed examination is deferred until chap. XXIX. 

Let us consider, to fix our ideas, a mixture of water and alcohol in the presence of the two vapours. This system, of two phases and two components, is divariant. Suppose we choose some fixed pressure (say 1 atm.) and study the composition of the system at equilibrium as a 

The state represented by M is that in which the two states, vapour and Uquid have the same composition on the mole fraction scale. Because of the special properties associated with systems in this state, the point M is called an azeotropic point, and the system is said to form an azeotrope. 

Now we consider a system, at a pressure of 1 atm., and at a tempera ture T. The compositions of the two phases at equilibrium are given 

We see therefore, that for values of T and p for which the liquid and vapour compositions are equal, there are an infinite number of equilibrium states which differ from one another only in the amounts of liquid and vapour which are present. In an azeotropic system, one phase may be transformed to the other at constant temperature, pressure and composition without affecting the equilibrium state.  

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