The vapour pressure of two liquids 'P' and 'Q' are 80 and 60 torr respectively. The total vapour pressure of solution obtained by mixing 3 mole of P and 2 mol of Q would be

Options

A. 140 torr
B. 20 torr
C. 68 torr
D. 72 torr

Explanation

To solve the problem of finding the total vapor pressure of a solution obtained by mixing two liquids 'P' and 'Q', we can use Raoult's Law. Here's a step-by-step solution:

### Step 1: Identify Given Data
- Vapor pressure of pure liquid P, \( P_P^0 = 80 \) torr
- Vapor pressure of pure liquid Q, \( P_Q^0 = 60 \) torr
- Moles of liquid P, \( n_P = 3 \)
- Moles of liquid Q, \( n_Q = 2 \)

### Step 2: Calculate Total Moles
Total moles in the solution:
\[ n_{\text{total}} = n_P + n_Q = 3 + 2 = 5 \text{ moles} \]

### Step 3: Calculate Mole Fractions
- Mole fraction of P, \( X_P \):
\[ X_P = \frac{n_P}{n_{\text{total}}} = \frac{3}{5} = 0.6 \]
- Mole fraction of Q, \( X_Q \):
\[ X_Q = \frac{n_Q}{n_{\text{total}}} = \frac{2}{5} = 0.4 \]

### Step 4: Calculate Partial Pressures
Using Raoult's Law, the partial pressure of each component in the solution can be calculated as follows:
- Partial pressure of P, \( P_P \):
\[ P_P = X_P \times P_P^0 = 0.6 \times 80 \text{ torr} = 48 \text{ torr} \]
- Partial pressure of Q, \( P_Q \):
\[ P_Q = X_Q \times P_Q^0 = 0.4 \times 60 \text{ torr} = 24 \text{ torr} \]

### Step 5: Calculate Total Vapor Pressure
The total vapor pressure of the solution, \( P_{\text{total}} \), is the sum of the partial pressures:
\[ P_{\text{total}} = P_P + P_Q = 48 \text{ torr} + 24 \text{ torr} = 72 \text{ torr} \]

### Final Answer
The total vapor pressure of the solution is **72 torr**.

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