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 of finding the mole fraction of toluene in the vapor phase in contact with an equimolar solution of benzene and toluene, we can follow these steps:

### Step 1: Identify Given Data
- Vapor pressure of pure benzene (P₀B) = 160 torr
- Vapor pressure of pure toluene (P₀T) = 60 torr
- The solution is equimolar, meaning the mole fraction of benzene (X_B) = 0.5 and the mole fraction of toluene (X_T) = 0.5.

### Step 2: Use Raoult's Law
According to Raoult's Law, the partial pressure of each component in the solution can be calculated as:
- Partial pressure of benzene (P_B) = P₀B * X_B
- Partial pressure of toluene (P_T) = P₀T * X_T

### Step 3: Calculate Partial Pressures
- For benzene:
\[ P_B = 160 \, \text{torr} \times 0.5 = 80 \, \text{torr} \]
- For toluene:
\[ P_T = 60 \, \text{torr} \times 0.5 = 30 \, \text{torr} \]

### Step 4: Calculate Total Pressure
The total pressure (P_total) in the system is the sum of the partial pressures:
\[ P_{\text{total}} = P_B + P_T = 80 \, \text{torr} + 30 \, \text{torr} = 110 \, \text{torr} \]

### Step 5: Calculate Mole Fraction of Toluene in Vapor Phase
The mole fraction of toluene in the vapor phase (Y_T) can be calculated using the formula:
\[ Y_T = \frac{P_T}{P_{\text{total}}} \]
Substituting the values:
\[ Y_T = \frac{30 \, \text{torr}}{110 \, \text{torr}} \approx 0.2727 \]
Rounding to two decimal places, we find:
\[ Y_T \approx 0.27 \]

### Final Answer
The mole fraction of toluene in the vapor phase is approximately **0.27**.

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