Question:
If pure liquids A and B have vapour pressures of 55 kPa and 15 kPa respectively. If in a solution of A and B, mole fraction of A in vapour is 0.8, then find mole fraction of A in liquid phase.
If pure liquids A and B have vapour pressures of 55 kPa and 15 kPa respectively. If in a solution of A and B, mole fraction of A in vapour is 0.8, then find mole fraction of A in liquid phase.
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Vapour phase is always richer in the more volatile component.
Updated On: Jan 25, 2026
- 0.813
- 0.5217
- 0.407
- 0.363
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The Correct Option is B
Solution and Explanation
Step 1: Apply Dalton’s law of partial pressures.
\[ y_A = \frac{p_A}{p_A + p_B} \]
Step 2: Apply Raoult’s law.
\[ p_A = x_A P_A^0 \] \[ p_B = x_B P_B^0 \]
Step 3: Substitute given values.
\[ 0.8 = \frac{x_A \times 55}{x_A \times 55 + (1 - x_A) \times 15} \]
Step 4: Solve the equation.
\[ 0.8 (55x_A + 15 - 15x_A) = 55x_A \] \[ 0.8 (40x_A + 15) = 55x_A \] \[ 32x_A + 12 = 55x_A \] \[ 23x_A = 12 \]
\[ x_A = \frac{12}{23} = 0.5217 \]
\[ y_A = \frac{p_A}{p_A + p_B} \]
Step 2: Apply Raoult’s law.
\[ p_A = x_A P_A^0 \] \[ p_B = x_B P_B^0 \]
Step 3: Substitute given values.
\[ 0.8 = \frac{x_A \times 55}{x_A \times 55 + (1 - x_A) \times 15} \]
Step 4: Solve the equation.
\[ 0.8 (55x_A + 15 - 15x_A) = 55x_A \] \[ 0.8 (40x_A + 15) = 55x_A \] \[ 32x_A + 12 = 55x_A \] \[ 23x_A = 12 \]
\[ x_A = \frac{12}{23} = 0.5217 \]
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