Benzene and toluene form nearly ideal solution. At `20^(@)C` the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at `20^(@)C` for a solution containing 78g of benzene and 46 g of toluene in torr is-

Options

A. 25
B. 50
C. `53.5`
D. `37.5`

Explanation

To find the partial vapor pressure of benzene in a solution containing 78 g of benzene and 46 g of toluene at 20°C, we can follow these steps:

### Step 1: Calculate the number of moles of benzene and toluene.
- **Molecular weight of benzene (C6H6)** = 78 g/mol
- **Molecular weight of toluene (C7H8)** = 92 g/mol

**Moles of benzene:**
\[ \text{Moles of benzene} = \frac{\text{mass of benzene}}{\text{molecular weight of benzene}} = \frac{78 \text{ g}}{78 \text{ g/mol}} = 1 \text{ mol} \]

**Moles of toluene:**
\[ \text{Moles of toluene} = \frac{\text{mass of toluene}}{\text{molecular weight of toluene}} = \frac{46 \text{ g}}{92 \text{ g/mol}} = 0.5 \text{ mol} \]

### Step 2: Calculate the total number of moles in the solution.
\[ \text{Total moles} = \text{Moles of benzene} + \text{Moles of toluene} = 1 \text{ mol} + 0.5 \text{ mol} = 1.5 \text{ mol} \]

### Step 3: Calculate the mole fraction of benzene.
\[ \text{Mole fraction of benzene} = \frac{\text{Moles of benzene}}{\text{Total moles}} = \frac{1 \text{ mol}}{1.5 \text{ mol}} = \frac{2}{3} \]

### Step 4: Use Raoult's Law to calculate the partial vapor pressure of benzene.
Raoult's Law states that the partial vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.

**Given:**
- Vapor pressure of pure benzene, \( P^0_{\text{benzene}} = 75 \text{ torr} \)

**Partial vapor pressure of benzene:**
\[ P_{\text{benzene}} = P^0_{\text{benzene}} \times \text{Mole fraction of benzene} = 75 \text{ torr} \times \frac{2}{3} \]

Calculating this gives:
\[ P_{\text{benzene}} = 75 \times \frac{2}{3} = 50 \text{ torr} \]

### Final Answer:
The partial vapor pressure of benzene at 20°C for the solution containing 78 g of benzene and 46 g of toluene is **50 torr**.

---