Liquid-Phase Activity Coefficients for Ternary Mixtures

1 Liquid-Phase Activity Coefficients for Ternary Mixtures 

For liquids, we use the same equations listed in Table 9.1, in forms that extend to any number of species. Holmes and Van Winkle [5] show the ternary (three species) forms for the common activity coefficient equations. Here we consider only the Margules equation, which seems more intuitive than the others (not necessarily the most accurate, but perhaps with the best product of accuracy times intuitive content). The form shown is 

If we examine this term by term, we will see that it has more intuitive content than appears at first glance. Comparing it to Eq. 9.K we see that it is in log form, while Eq. 9.K is in In form. Then we see that the first term on the right, x [Aab + 2xa Aba — Aab), is the same as the right-hand side of Eq. 9.K, if 

this term represents the behavior of species a and b, in the absence of c. (If we set Xc = 0, all except the first term in Eq. 9.10 disappears, and we have the simple binary form of the Margules equation.) Similarly, the second term on the right represents the behavior of species a and c, in the absence of b, with 

If we set C = 0.00, then Eq. 9.10 allows us to estimate the activity coefficient for species a in mixtures of a, b, and c, using only the mol fractions and the Margules equation constants for the three binary combinations of a, b, and c. To find the activity coefficients for species b and c we rotate the subscripts, a b b c c—ya or simply renumber the species, making the one we are now interested in species a. 

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