Question

Vapour pressure of pure benzene is $119$ torr and that of toluene is $37.0$ torr at the same temperature. Mole fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of toluene $0.50$, will be :

• A. $0.137$
• B. $0.237$
• C. $0.435$
• D. $0.205$

Answer 1

Answer: (B)

$P_{A}=P^{0}_{A}\times x_{A}=$ total pressure $\times y_{A}$
$P_{B}=P^{0}_{B}\times x_{B}=$ total pressure $\times y_{B}$
where $x$ and $y$ represents mole fraction in liquid and vapour phase respectively.
$\frac{P^{0}_{B}x^{0}_{B}}{P^{0}_{A}x_{A}}=\frac{y_{B}}{y_{A}} ; \frac{P^{0}_{B}\left(1-x_{A}\right)}{P^{0}_{A}x_{A}}=\frac{1-y_{A}}{y_{A}}$
on putting values $\frac{119\left(1-0.50\right)}{37\times0.50}=\frac{1-y_{A}}{y_{A}}$
on solving $y_{A} = 0.237$