An ideal solution is formed by mixing two volatile liquids $A$ and $B . X_A$ and $X_B$ are the mole

Question

An ideal solution is formed by mixing two volatile liquids $A$ and $B . X_A$ and $X_B$ are the mole fractions of $A$ and $B$ respectively in the solution and $Y_A$ and $Y_B$ are the mole fractions of $A$ and $B$ respectively in the vapour phase. A plot of $\frac{1}{Y_A}$ along $y$-axis against $\frac{1}{X_A}$ along $x$-axis gives a straight line. What is the slope of the straight line ?

Professor PC Thomas Classes · Answer

(a)
$
\begin{aligned}
y_A=\frac{P_A^{\circ} x_A}{P_A^{\circ} x_A+P_B^{\circ} x_B} & =\frac{P_A^{\circ} x_A}{P_B^{\circ}+\left(P_A^{\circ}-P_B^{\circ}ight) x_A} \
\frac{1}{y_A}=\frac{P_B^{\circ} x_B+P_A^{\circ} x_A}{P_A^{\circ} x_A} & =1+\left(\frac{P_B^{\circ}}{P_A^{\circ}}ight)\left(\frac{1-x_A}{x_A}ight) \
& =1-\frac{P_B^{\circ}}{P_A^{\circ}}+\frac{1}{x_A}\left(\frac{P_B^{\circ}}{P_A^{\circ}}ight) \
	herefore 	ext { Slope } & =\frac{P_B^{\circ}}{P_A^{\circ}}
\end{aligned}
$