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: Understanding the Question:
For an ideal solution of two liquids, the total vapor pressure is given by Raoult's Law.

Step 2: Key Formula or Approach:
\[ \text{P}_{\text{total}} = \text{P}^{\circ}_{\text{A}}\chi_{\text{A}} + \text{P}^{\circ}_{\text{B}}\chi_{\text{B}} \]
Since \( \chi_{\text{A}} + \chi_{\text{B}} = 1 \), we can write \( \chi_{\text{A}} = 1 - \chi_{\text{B}} \).
\[ \text{P}_{\text{total}} = \text{P}^{\circ}_{\text{A}}(1 - \chi_{\text{B}}) + \text{P}^{\circ}_{\text{B}}\chi_{\text{B}} \]

Step 3: Detailed Explanation:
Given:
\( \text{P}_{\text{total}} = 500 \text{ mm Hg} \)
\( \text{P}^{\circ}_{\text{A}} = 400 \text{ mm Hg} \)
\( \text{P}^{\circ}_{\text{B}} = 575 \text{ mm Hg} \)
Substitute values into the formula:
\[ 500 = 400(1 - \chi_{\text{B}}) + 575\chi_{\text{B}} \]
\[ 500 = 400 - 400\chi_{\text{B}} + 575\chi_{\text{B}} \]
\[ 500 - 400 = 175\chi_{\text{B}} \]
\[ 100 = 175\chi_{\text{B}} \]
\[ \chi_{\text{B}} = \frac{100}{175} = \frac{4}{7} \approx 0.5714 \]

Step 4: Final Answer:
The mole fraction of liquid B is approximately 0.57.