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An ideal solution of two volatile liquids A and B obeys Raoult's law. Let X_A, X_B be mole fractions in the liquid phase and Y_A, Y_B in the vapour phase, with P_A⁰ and P_B⁰ as the pure-component vapour pressures. A graph of 1/Y_A (y-axis) versus 1/X_A (x-axis) is a straight line. What is the slope of this line?

1. P_B⁰ / P_A⁰
2. P_A⁰ / P_B⁰
3. P_B⁰ - P_A⁰
4. (P_A⁰ - P_B⁰) / P_A⁰

Correct answer: P_B⁰ / P_A⁰

Solution

From Raoult's law: Y_A = X_A P_A⁰ / (X_A P_A⁰ + (1-X_A) P_B⁰). Taking reciprocal: 1/Y_A = [X_A P_A⁰ + (1-X_A) P_B⁰] / (X_A P_A⁰) = 1 + (P_B⁰/P_A⁰)(1-X_A)/X_A = 1 + (P_B⁰/P_A⁰)(1/X_A - 1) = (P_B⁰/P_A⁰)(1/X_A) + (1 - P_B⁰/P_A⁰). So 1/Y_A = (P_B⁰/P_A⁰)*(1/X_A) + constant. Slope = P_B⁰/P_A⁰.

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