a. Given experimental data either for the excess Gibbs energy, G^ex, or for species activity coefficients from which G^ex can be computed, it is sometimes difficult to decide whether to fit the data to the two constant Margules or van Laar expressions for G^ex and γ_i. One method of making this decision is to plot G^ex/x₁x₂ versus x₁ and x₁x₂/G^ex versus x₁ and determine which of the two plots is most nearly linear. If it is the first, the data are best fit with the two-constant Margules expression; if the second, the van Laar expression should be used. Justify this procedure, and suggest how these plots can be used to obtain the parameters in the activity coefficient equations.

b. The following data have been obtained for the benzene–2,2,4-trimethyl pentane mixture (Illustration 10.1-4). Using the procedure in part (a), decide which of the two solution methods is likely to best fit the data.

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XB Gex (J/mol) XB Gex (J/mol) 0.0819 0.2192 0.3584 83.7 203.8 294.1 0.5256 0.8478 0.9872 351.9 223.8 23.8 0.3831 302.5