Chapter 15, Problem 15.35P

The spinodal curve for a binary liquid system is the locus of states for which

$\frac{d^2\left(\Delta G/RT\right)}{d{x}_1^2}=0(constT,P)$

Thus it separates regions of stability from instability with respect to liquid/liquid phase splitting. For a given T. there are normally two spinodal compositions (if any). They are the same at a consolute temperature. On curve II of Fig. 12.13 they are a pair of compositions between $x_1^{\alpha }$ and $x_1^{\beta }$ , corresponding to zero curvature.

Suppose a liquid mixture is described by the symmetrical equation

$\frac{G^E}{RT}=A\left(T\right)x_1{x}_2$

(a)Find an expression for the spinodal compositions as a function of A(T).

(b)Assume that A(T) is the expression used to generate Fig. 15.2. Plot on a single graph the solubility curve and the spinodal curve. Discuss.