The vapour pressure of two pure liquids (A) and (B) are 100 and 80 torr respectively. The total pressure of solution obtained by mixing 2 mole of (A) and 3 mole of (B) would be :-

Options

A. 20 torr
B. 36 torr
C. 88 torr
D. 180 torr

Answer

To find the total pressure of the solution obtained by mixing 2 moles of liquid A and 3 moles of liquid B, we can use Raoult's Law, which states that the vapor pressure of a solution is equal to the sum of the partial pressures of each component.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Vapor pressure of pure liquid A (P0A) = 100 torr
- Vapor pressure of pure liquid B (P0B) = 80 torr
- Moles of A (nA) = 2 moles
- Moles of B (nB) = 3 moles

2. **Calculate Total Moles:**
- Total moles (n_total) = nA + nB = 2 + 3 = 5 moles

3. **Calculate Mole Fraction of A (xA):**
- Mole fraction of A (xA) = nA / n_total = 2 / 5 = 0.4

4. **Calculate Mole Fraction of B (xB):**
- Mole fraction of B (xB) = nB / n_total = 3 / 5 = 0.6

5. **Calculate Partial Pressure of A (PA):**
- PA = P0A * xA = 100 torr * 0.4 = 40 torr

6. **Calculate Partial Pressure of B (PB):**
- PB = P0B * xB = 80 torr * 0.6 = 48 torr

7. **Calculate Total Pressure (P_total):**
- P_total = PA + PB = 40 torr + 48 torr = 88 torr

### Final Answer:
The total pressure of the solution obtained by mixing 2 moles of A and 3 moles of B is **88 torr**.

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