The vapour pressure of two pure liquids A and B are 50 and 40 torr respectively. If 8 moles of A is mixed with x moles of B , then vapour pressure of solution obtained is 48 torr. What is the value of x.

Answer

To solve the problem, we will use Raoult's law, which states that the vapor pressure of a solution is equal to the sum of the partial vapor pressures of each component in the solution.

### Step-by-Step Solution

1. **Identify Given Values:**
- Vapor pressure of pure liquid A, \( P_A^0 = 50 \) torr
- Vapor pressure of pure liquid B, \( P_B^0 = 40 \) torr
- Moles of A, \( n_A = 8 \)
- Moles of B, \( n_B = x \)
- Vapor pressure of the solution, \( P_{solution} = 48 \) torr

2. **Calculate Mole Fractions:**
- The mole fraction of A, \( X_A = \frac{n_A}{n_A + n_B} = \frac{8}{8 + x} \)
- The mole fraction of B, \( X_B = \frac{n_B}{n_A + n_B} = \frac{x}{8 + x} \)

3. **Apply Raoult's Law:**
\[ P_{solution} = X_A \cdot P_A^0 + X_B \cdot P_B^0 \]
Substituting the values:
\[ 48 = \left(\frac{8}{8 + x}\right) \cdot 50 + \left(\frac{x}{8 + x}\right) \cdot 40 \]

4. **Simplify the Equation:**
Multiply through by \( (8 + x) \) to eliminate the denominators:
\[ 48(8 + x) = 8 \cdot 50 + x \cdot 40 \]
Expanding both sides:
\[ 384 + 48x = 400 + 40x \]

5. **Rearrange the Equation:**
Move all terms involving \( x \) to one side and constant terms to the other:
\[ 48x - 40x = 400 - 384 \]
This simplifies to:
\[ 8x = 16 \]

6. **Solve for \( x \):**
Divide both sides by 8:
\[ x = 2 \]

### Final Answer:
The value of \( x \) is **2 moles** of liquid B.