Question

Liquid $A$ and $B$ form an ideal solution at temperature $T$. Mole fraction of $A$ in liquid and vapor phase are $0.4$ and $\frac{4}{13}$ respectively, when total pressure is $130\text{torr}$. The vapor pressure (in torr) of $A$ and $B$ in pure state at temperature $T$ are respectively

• A. $100,200$
• B. $200,100$
• C. $100,150$
• D. $150,100$

Answer 1

The correct option is C $100,150$

Given $A$ and $B$ are ideal solution at temp, $T$
$\text{Mole fraction of A in liquid phase},{\chi }_A=0.4$
$\text{Mole fraction of A in vapour phase},Y_A=\frac{4}{13}$
$\text{Mole fraction of B in liquid phase},{\chi }_B=0.6$
$\text{Mole fraction of B in vapour phase},Y_B=\frac{9}{13}$
$\text{Total pressure},P_T=130\text{torr}$
$P_A\text{and}{P}_B=?$
We know,
$P_T=P_A^o{X}_A+P_B^o{X}_B$
$P_A=P_A^o\cdot X_A=Y_A{P}_T=\frac{4}{13}\times 130=40\text{torr}$
$\Rightarrow P_A^o=\frac{P_A}{{\chi }_A}=\frac{40}{0.4}=100\text{torr}$
Similarly,
$P_B=P_B^o\times X_B=P_T\times Y_B=\frac{9}{13}\times 130=90\text{torr}$
$\Rightarrow P_B^o=\frac{P_B}{{\chi }_B}=\frac{90}{0.6}=150\text{torr}$
$\therefore P_A^o=100,P_B^o=150$
Option (C) is correct answer.