Wilson has proposed that the excess Gibbs energy of a multicomponent system is given by Note

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Wilson has proposed that the excess Gibbs energy of a multicomponent system is given by

where Gex == - RT ;; ; 1n ;4;; i=l = (Xij- Aii) ] exp RT 

Note that this equation contains only the interaction parameters Λij for binary mixtures. Also, the parameters (λij −λii) appear to be insensitive to temperature. Holmes and van Winkle have tested this equation and found it to be accurate for the prediction of binary and ternary vapor–liquid equilibria. They also report values of the parameters VLi and (λij − λii) for many binary mixtures. Use the Wilson equation to

a. Derive Eqs. 9.5-12 and 9.5-13 for the activity coefficients of a species in a binary mixture.

In  = ln(x + x2A12) + x2 In 2 =  ln(x+xA21) - X A12 X1 + xA12 A12 x1 + x2^12 A21 XA21 + x2 A21 XA21 + x2 The

Gex RT = X1X2 T21G21 x1 + x2G21 + T12 G12 x2 + x1G12, (9.5-13)

b. Obtain the following expression for the activity coefficient of species 1 in a multicomponent mixture

C C Inn = 1-1    ; ;1 C ;;; j=1

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