Activity Coefficients in Asymmetric Systems

We can find the activity coefficient of one component in a solution described by (15.33) using the same reasoning as above for solutions that fit the single-parameter equation (15.22). First, as with (15.28), we need to write out the expression for the total free energy per mole of such a solution  

Next we find the chemical potential of either component as before by applying equation (15.27) to (15.41), then using relationships (15.16) and (15.18), rearranging, and remembering that Xi - I — X2  

This is convenient because, like equations (15.30) it gives the activity coefficient (or excess free energy) of a non-ideal solution for different concentrations in terms 

Equation (15.42) also shows the interesting fact that when X = 1 (Xj = 0), RT nj2 = Wg2- The same is true in the symmetrical case, equation (15.30). But 

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