The vapour pressure of a certain pure liquid A at 298 K is 40 mbar. When a solution of B is prepared in A at the same temperature, the vapour pressure is found to be 32 mbar. The mole fraction of A in the solution is

Options

A. `a.) 0.5`
B. `b.)0.3`
C. `c.)0.4`
D. `d.)0.8`

Explanation

To solve the problem, we will use Raoult's Law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent in the solution.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- The vapor pressure of pure liquid A, \( P_A^0 = 40 \) mbar.
- The vapor pressure of the solution, \( P_t = 32 \) mbar.

2. **Apply Raoult's Law:**
According to Raoult's Law, the total vapor pressure of the solution (\( P_t \)) can be expressed as:
\[ P_t = P_A^0 \cdot X_A \]
where \( X_A \) is the mole fraction of component A in the solution.

3. **Substitute the Known Values:**
Substitute the known values into the equation:
\[ 32 \text{ mbar} = 40 \text{ mbar} \cdot X_A \]

4. **Solve for \( X_A \):**
Rearranging the equation to solve for \( X_A \):
\[ X_A = \frac{32 \text{ mbar}}{40 \text{ mbar}} \]
\[ X_A = 0.8 \]

5. **Conclusion:**
The mole fraction of A in the solution is \( X_A = 0.8 \).

### Final Answer:
The mole fraction of A in the solution is \( 0.8 \).