For an ideal binary liquid solution with $P_A^{\circ}P_B^{\circ}$, which relation between $X_A$ (mo

Question

For an ideal binary liquid solution with $P_A^{\circ}>P_B^{\circ}$, which relation between $X_A$ (mole fraction of $A$ in liquid phase) and $Y_A$ (mole fraction of $A$ in vapour phase) is correct ?

Professor PC Thomas Classes · Answer

$y_A=\frac{P_A^{\circ} 	imes x_A}{P_A^{\circ} x_A+P_B^{\circ} x_B}=\frac{x_A}{x_A+x_B\left(\frac{P_B^{\circ}}{P_A^{\circ}}ight)}$
$\left[\because P_A^{\circ}>P_B^{\circ}ight]$
$	herefore \frac{y_A}{x_A}=\frac{1}{x_A+x_B\left(\frac{P_B^b}{P_A^o}ight)}>1 \Rightarrow y_A>x_A$

Similarly, $y_B=\frac{P_B^{\circ} 	imes x_B}{P_A^{\circ} x_A+P_B^{\circ} x_B}=\frac{x_B}{x_B+x_A\left(\frac{P_A^{\circ}}{P_B^{\circ}}ight)}$
$\begin{array}{ll}	herefore & y_B<x_B \ 	herefore & \frac{y_A}{y_B}>\frac{x_A}{x_B}\end{array}$