Chapter 13, Problem 13.21P

The following is a rule of thumb: For a binary system in VLE at low pressure, the equilibrium vapor-phase mole fraction y₁corresponding to an equimolar liquid mixture is approximate

$y_1=\frac{P_1^{sat}}{P_1^{sat}+P_2^{sat}}$

where $P_i^{sat}$ is a pure-species vapor pressure. Clearly, this equation is valid if Raoult's law applies. Prove that it is also valid for VLE described by Eq. (13.19), with $In{\gamma }_1=A{x}_2^2$ and $In{\gamma }_2=A{x}_1^2$ .