Chapter 13, Problem 13.59P

Consider the following model for G^E/RT of a binary mixture:

$\frac{G^E}{x_1{x}_{2}RT}={\left(x_1{A}_{21}^k+x_2{A}_{12}^k\right)}^{1/k}$

This equation in fact represents a family of two-parameter expressions for G^E/RT: specification of k it leaves A i; and as the free parameters.

1. Find general expressions for In ${\gamma }_1$ and In ${\gamma }_2$ for any k.

Show that ln ${\gamma }_1^{\infty }=A_{12}$ and In ${\gamma }_2^{\infty }=A_{21}$

Specialize the model to the cases where k equals $-\infty$ , -1, 0, +1. and $+\infty$ . Two of the cases should generate familiar results. What are they?