The Effect of Temperature on Mutual Solubility

We have considered so far the effect of nonideality on the mixing of the two liquids, at a specified temperature of 300 K, by varying the value of A in Eq. 12.10.1. We examine next the effect that temperature has on the mixing of the two liquids. To this purpose we keep, for simplicity, A independent of temperature and equd to 4 kJ/mol, a value that leads to complete miscibility at 300 K. 

At this temperature the two liquid phases merge into one, i.e. their properties become identical, and it is referred to as the critical solution (or consolute) temperature. 

The maximum temperature at which phase separation is possible independent of composition, occurs at Xj = 2 = 0.5  

We conclude that at temperatures higher than 240.5 K a single liquid is the equilibrium state at lower ones, two liquid phases at equilibrium are present. This is demonstrated in the following Example. 

Equations 12.10.5 through 12.10.12 are based on the use of the two-suffix (one-parameter) Margules expression for the excess Gibbs free energy (Eq. 12.10.1). It is a very simple model which, even with a temperature dependent A, is applicable to a very limited number of systems where is a symmetric function of a i, mainly hydrocarbons of similar size. 

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