Question

Calculate the mole fraction of pure liquid B in solution if total vapour pressure of solution, vapour pressure of pure liquid A and vapour pressure of pure liquid B are 500 mm Hg, 400 mm Hg and 575 mm Hg respectively at given temperature.

• A. 0.43
• B. 0.57
• C. 0.62
• D. 0.38

Hint:

$P_{total} = P_{A}^{\circ} + (P_{B}^{\circ} - P_{A}^{\circ})x_{B}$.

Answer 1

The Correct Option is B

Step 1: Formula
Raoult's Law for binary mixture: $P_{total} = P_{A}^{\circ}x_{A} + P_{B}^{\circ}x_{B}$

Step 2: Analysis
Since $x_{A} + x_{B} = 1$, we can write: $P_{total} = P_{A}^{\circ}(1 - x_{B}) + P_{B}^{\circ}x_{B}$ - $500 = 400(1 - x_{B}) + 575x_{B}$

Step 3: Calculation
- $500 = 400 - 400x_{B} + 575x_{B}$ - $100 = 175x_{B}$ - $x_{B} = \frac{100}{175} = \frac{4}{7} \approx 0.57$

Step 4: Conclusion
Hence, the mole fraction of B is 0.57. Final Answer: (B)