Estimation of partial excess properties

Example 1.14 Estimation of partial excess properties The heat of mixing (excess enthalpy) for a binary mixture is 

a is the parameter in J/mol. Derive relations for /IE and HE in terms of x,. The partial properties are 

Therefore, Eqs. (1.205) and (1.206) yield partial molar excess enthalpies 

Azeotrope mixtures reach a point at which liquid and vapor compositions become the same at a certain temperature and pressure. Some azeotropes show a maximum boiling temperature, while others show a minimum boiling temperature. Table 1.8 shows some examples of binary and ternary azeotropes. Azeotrope mixtures cannot be separated into their pure species by a single distillation column. 

For a binary vapor-liquid system, the Gibbs-Duhem relations are 

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