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

Answer

To solve the problem of finding the total vapor pressure of a solution obtained by mixing two liquids P and Q, we can follow these steps:

### Step 1: Identify the given data
- Vapor pressure of liquid P (P₁) = 80 torr
- Vapor pressure of liquid Q (P₂) = 60 torr
- Moles of liquid P = 3 moles
- Moles of liquid Q = 2 moles

### Step 2: Calculate the total number of moles in the solution
Total moles = Moles of P + Moles of Q
Total moles = 3 + 2 = 5 moles

### Step 3: Calculate the mole fraction of each component
- Mole fraction of P (X₁) = Moles of P / Total moles
\[ X₁ = \frac{3}{5} = 0.6 \]

- Mole fraction of Q (X₂) = Moles of Q / Total moles
\[ X₂ = \frac{2}{5} = 0.4 \]

### Step 4: Apply Raoult's Law to find the total vapor pressure
According to Raoult's Law, the total vapor pressure (P_total) of the solution is given by:
\[ P_{total} = (X₁ \cdot P₁) + (X₂ \cdot P₂) \]
Substituting the values:
\[ P_{total} = \left(\frac{3}{5} \cdot 80\right) + \left(\frac{2}{5} \cdot 60\right) \]

### Step 5: Calculate each term
- For P₁:
\[ \frac{3}{5} \cdot 80 = 48 \text{ torr} \]

- For P₂:
\[ \frac{2}{5} \cdot 60 = 24 \text{ torr} \]

### Step 6: Add the contributions to find the total vapor pressure
\[ P_{total} = 48 + 24 = 72 \text{ torr} \]

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

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