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An ideal solution is formed by mixing two volatile liquids A and B. Let X_A, X_B be their mole fractions in the liquid phase and Y_A, Y_B be their mole fractions in the vapour phase. 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

Correct answer: P_B⁰ / P_A⁰

Solution

From Raoult's law, Y_A = X_A*P_A⁰ / (P_B⁰ + X_A*(P_A⁰ - P_B⁰)). Taking the reciprocal and simplifying gives 1/Y_A = (P_B⁰/P_A⁰)*(1/X_A) + (1 - P_B⁰/P_A⁰). The slope is P_B⁰/P_A⁰.

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