Margules equations asymmetric solutions

To show that the Margules equations have the form of a virial equation, rearrange (15.33) for the total excess free energy of a real, asymmetric solution, remembering that Xi = I — X2 ... 

The Margules equations such as those in Table 15.1 can be fitted by standard least-squares regression analysis to data for real solutions. For example, if data for the total free energy of a binary asymmetric solution is available over a range of compositions at different T and P, you could fit equation (15.41) for Greai (or the equation for in Table 15.1) and obtain Wq, and ITcj as regression parameters. The same could be done with the equations for excess enthalpy, entropy, and so on. This permits construction of phase diagrams and determination of thermodynamic properties based... 

Comparison of equations (26) and (ij) shows immediately that the functional properties of the model described by (l8) and those deriving from (l ), expanded to j=3, are identical. These equations comprise the two-parameter (asymmetric) Margules model for a binary solution. To complete the analogy it is necessary only to equate the coefficients in the expressions for chemical potential,... 

Saxena (1973). A general account of the mixing properties of crystalline solutions, with detailed discussions of the van Laar, regular (one coefficient, symmetric), "sub-regular" (two-coefficient, asymmetric) and quasi-chemical models. Margules and other equations for i presented for binary... 

---