An ideal solution is formed by mixing two volatile liquids A and B. X_A and X_B are the mole fractions of A and B respectively in the solution and Yo and Y, are the mole fractions of A and B respectively in the vapour phase. A plot of $\frac{1}{Y_{A}}$ along y-axis against, along x-axis gives a $\frac{1}{X_{A}}$ straight line. What is the slope of the straight line ?

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$P_{B}^{\circ} - P_{A}^{2}$

$P_{A}^{\circ} - P_{B}^{\circ}$

$\frac{P_{B}^{\circ}}{P_{A}^{\circ}}$

$\frac{P_{A}^{\circ}}{P_{B}^{\circ}}$

answer is A.

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Detailed Solution

$y_{A} = \frac{P_{A}^{\circ} x_{A}}{P_{A}^{\circ} x_{A} + P_{B}^{\circ} x_{B}} = \frac{P_{A}^{\circ} x_{A}}{P_{B}^{\circ} + (P_{A}^{\circ} - P_{B}^{\circ}) x_{A}} \frac{1}{y_{A}} = \frac{P_{B}^{\circ} x_{B} + P_{A}^{\circ} x_{A}}{P_{A}^{\circ} x_{A}} = 1 + (\frac{P_{B}^{\circ}}{P_{A}^{\circ}}) (\frac{1 - x_{A}}{x_{A}}) = 1 - \frac{P_{B}^{\circ}}{P_{A}^{\circ}} + \frac{1}{x_{A}} (\frac{P_{B}^{\circ}}{P_{A}^{\circ}}) ∴ Slope = \frac{P_{B}^{\circ}}{P_{A}^{\circ}}$

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