Question

Calculate the mole fraction of toluene in the vapor phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of 0.5 (The vapor pressure of pure Benzene is 119 torr and that of toluene is 37 torr at the same temperature:

• A. 0.5
• B. 0.75
• C. 0.625
• D. 0.237

Answer 1

The correct option is D 0.237

solution:

The partial pressure of toluene in the vapour phase is $P_T=P_T^0$

$X_T=37torr\times 0.5=18.5torr$

.Here, $P_T^0$ is the vapour pressure of pure toluene and $X_T$ is the mole fraction of toluene in the liquid phase.

The partial pressure of benzene in the vapour phase is $P_B=P_B^0{X}_B=119torr\times 0.5=59.5torr$

Here, $P_B^0$ is the vapour pressure of pure benzene and $X_B$ is the mole fraction of benzene in the liquid phase.

The total pressure is $P_T+P_B=18.5torr+59.5torr=78torr$.

The mole fraction of toluene in the vapour phase is $Y_T$ .

It is given by the expression $Y_T=\frac{P_T}{totalpressure}=18.578=0.237$.

Hence, the mole fraction of toluene in the vapour phase is $0.237$

Hence the correct answer is D