Question

The vapour pressure of pure benzene and toluene are 160 and 60 torr respectively. The mole fraction of toluene in vapour phase in contact with the equimolar solution of benzene and toluene is

• A. 0.50
• B. 0.6
• C. 0.27
• D. 0.73

Answer 1

Correct option: (C)

Step 1: Calculating the total pressure

Analyzing the given data

Vapor pressure of pure benzene$\left(p_B^o\right)=160torr$

Vapour pressure of pure toluene$\left(p_T^o\right)=60torr$

Since the solution is equimolar which means the number of moles of toluene is equal to the number of moles of benzene.

$X_B+X_T=1$

$2X_B=1$

$X_B=0.5$

$X_B=X_T=0.5$

Now, according to Raoult's law total pressure of an ideal solution is equal to the partial pressure of its component at that composition.

$P_{Total}=P_B+P_T$

$P_{Total}=p_T^0\times X_T+p_B^o\times X_B$

$P_{Total}=160\times 0.5+60\times 0.5=110torr$

Step 2: Calculating the mole fraction of Toluene in vapour phase

$Y_T=\frac{p_T^o\times X_T}{P_T}$

$Y_T=\frac{60\times 0.5}{110}$

$Y_T=0.27$

Hence, the correct option is (C).