If Pa and Pb are 108 and 36 torr respectively. What will be the mole fraction of A is vapour phase if B has mole fraction in solution 0.5:

Explanation

To solve the problem, we need to find the mole fraction of component A in the vapor phase, given the partial pressures of A and B and the mole fraction of B in the solution.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Partial pressure of A, \( P^0_A = 108 \) torr
- Partial pressure of B, \( P^0_B = 36 \) torr
- Mole fraction of B in the solution, \( x_B = 0.5 \)

2. **Calculate Mole Fraction of A in the Solution:**
- The mole fraction of A, \( x_A \), can be calculated using the relationship:
\[ x_A + x_B = 1 \]
- Therefore,
\[ x_A = 1 - x_B = 1 - 0.5 = 0.5 \]

3. **Calculate the Total Vapor Pressure (P):**
- The total vapor pressure \( P \) can be calculated using Raoult's Law:
\[ P = x_A P^0_A + x_B P^0_B \]
- Substituting the values:
\[ P = (0.5 \times 108) + (0.5 \times 36) \]
- Calculate each term:
\[ P = 54 + 18 = 72 \text{ torr} \]

4. **Calculate the Mole Fraction of A in the Vapor Phase:**
- The mole fraction of A in the vapor phase, \( y_A \), is given by:
\[ y_A = \frac{P_A}{P} \]
- Where \( P_A \) (partial pressure of A) is given by:
\[ P_A = x_A P^0_A = 0.5 \times 108 = 54 \text{ torr} \]
- Now substituting into the equation for \( y_A \):
\[ y_A = \frac{54}{72} \]
- Simplifying this gives:
\[ y_A = 0.75 \]

5. **Final Result:**
- The mole fraction of A in the vapor phase is \( y_A = 0.75 \).