Generalizations for Ternary Mixtures

So far, we have seen several ways of calculating the Gibbs free energy of a two-component mixture. To extend calculations to ternary and higher-order mixtures, we use empirical combinatory extensions of the binary properties. We summarize here only some of the most popular approaches. An extended comparative appraisal of the properties of ternary and higher-order mixtures can be found in Barron (1976), Grover (1977), Hillert (1980), Bertrand et al. (1983), Acree (1984), and Fei et al. (1986). 

Because the ideal Gibbs free energy of mixing contribution is readily generalized to n-component systems (cf eq. 3.131), the discussion involves only excess terms. 

According to Wohl (1953), the excess Gibbs free energy of mixing for a three-component mixture is represented by 

The activity coefficient of component 1 in a ternary mixture is defined by 

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