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 equimolar solution of benzene and toluene is:

Options

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

Answer

To solve the problem, we need to find the mole fraction of toluene in the vapor phase when it is in contact with an equimolar solution of benzene and toluene. Here are the steps to find the solution:

### Step-by-Step Solution

1. **Identify Given Data**:
- Vapor pressure of pure benzene (P_B) = 160 torr
- Vapor pressure of pure toluene (P_T) = 60 torr
- Mole fraction of benzene in the solution (X_B) = 0.5
- Mole fraction of toluene in the solution (X_T) = 0.5

2. **Calculate Partial Pressures**:
- The partial pressure of toluene (P_T') in the solution can be calculated using Raoult's Law:
\[ P_T' = P_T \times X_T = 60 \, \text{torr} \times 0.5 = 30 \, \text{torr} \]
- The partial pressure of benzene (P_B') in the solution can also be calculated using Raoult's Law:
\[ P_B' = P_B \times X_B = 160 \, \text{torr} \times 0.5 = 80 \, \text{torr} \]

3. **Calculate Total Pressure (P_total)**:
- The total pressure (P_total) of the system is the sum of the partial pressures:
\[ P_{\text{total}} = P_B' + P_T' = 80 \, \text{torr} + 30 \, \text{torr} = 110 \, \text{torr} \]

4. **Calculate Mole Fraction of Toluene in Vapor Phase (Y_T)**:
- The mole fraction of toluene in the vapor phase (Y_T) can be calculated using the formula:
\[ Y_T = \frac{P_T'}{P_{\text{total}}} = \frac{30 \, \text{torr}}{110 \, \text{torr}} \approx 0.2727 \]

5. **Final Result**:
- The mole fraction of toluene in the vapor phase is approximately 0.27.

### Summary
The mole fraction of toluene in the vapor phase in contact with an equimolar solution of benzene and toluene is approximately **0.27**.