Chapter 13, Problem 13.33P

If Eq. (13.24) is valid for isothermal VLE in a binary' system, show that

$\left(\frac{dP}{d{x}_1}\right)x_1=0\ge -P_2^{sat}\left(\frac{dP}{d{x}_1}\right)x_1=1\le P_1^{sat}$

13.24. Flash calculations are simpler for binary systems than for the general multicomponent case because the equilibrium compositions for a binary are independent of the overall composition. Show that, for a binary system in VLE,

$x_1=\frac{1-K_2}{K_1-K_2}{y}_1=\frac{K_1\left(1-K_2\right)}{K_1-K_2}$

$\mathcal{V}=\frac{z_1\left(K_1-K_2\right)-\left(1-K_2\right)}{\left(K_1-1\right)\left(1-K_2\right)}$