At `25^(@)C`, the vapour pressure of pure liquid A (mol. Mas = 40) is 100 torr and that of pure Liquid B is 40 torr, (mol. mass = 80). The vapour pressure at `25^(@)C` of a solution containing 20 g of each A and B is :

Options

A. (a) 80 torr
B. (b) 59.8 torr
C. (c) 68 torr
D. (d) 48 torr

Answer

To solve the problem of finding the vapor pressure of a solution containing 20 g of each liquid A and B at 25°C, we will follow these steps:

### Step 1: Calculate the number of moles of each liquid.

For liquid A:
- Given mass of A = 20 g
- Molar mass of A = 40 g/mol

\[ \text{Number of moles of A} (n_A) = \frac{\text{mass of A}}{\text{molar mass of A}} = \frac{20 \, \text{g}}{40 \, \text{g/mol}} = 0.5 \, \text{mol} \]

For liquid B:
- Given mass of B = 20 g
- Molar mass of B = 80 g/mol

\[ \text{Number of moles of B} (n_B) = \frac{\text{mass of B}}{\text{molar mass of B}} = \frac{20 \, \text{g}}{80 \, \text{g/mol}} = 0.25 \, \text{mol} \]

### Step 2: Calculate the total number of moles in the solution.

\[ \text{Total moles} = n_A + n_B = 0.5 \, \text{mol} + 0.25 \, \text{mol} = 0.75 \, \text{mol} \]

### Step 3: Calculate the mole fractions of A and B.

Mole fraction of A (\(x_A\)):
\[ x_A = \frac{n_A}{n_A + n_B} = \frac{0.5}{0.75} = \frac{2}{3} \approx 0.67 \]

Mole fraction of B (\(x_B\)):
\[ x_B = \frac{n_B}{n_A + n_B} = \frac{0.25}{0.75} = \frac{1}{3} \approx 0.33 \]

### Step 4: Apply Raoult's Law to find the partial pressures.

According to Raoult's Law:
- Partial pressure of A (\(P_A\)):
\[ P_A = x_A \cdot P^0_A = 0.67 \cdot 100 \, \text{torr} = 67 \, \text{torr} \]

- Partial pressure of B (\(P_B\)):
\[ P_B = x_B \cdot P^0_B = 0.33 \cdot 40 \, \text{torr} = 13.2 \, \text{torr} \]

### Step 5: Calculate the total vapor pressure of the solution.

Using Dalton's Law, the total vapor pressure (\(P_{total}\)) is the sum of the partial pressures:
\[ P_{total} = P_A + P_B = 67 \, \text{torr} + 13.2 \, \text{torr} = 80.2 \, \text{torr} \]

### Final Answer:
The vapor pressure of the solution at 25°C is approximately **80 torr**.

---