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For a binary ideal liquid solution of A (having vapour pressure $p_{A}^{}$ ) and B (having vapour pressure $p_{B}^{}$ ), $x_{A}$ and $y_{A}$ are the mole fractions of A in liquid and vapour phases, respectively. Which of the following facts holds good?

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$y_{A}$ varies linearly with $x_{A}$

$y_{A}$ varies linearly with $1 / x_{A}$

$1 / y_{A}$ varies linearly with $x_{A}$

$1 / y_{A}$ varies linearly with $1 / x_{A}$

answer is D.

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Detailed Solution

Suppose, $x_{A}$ and $y_{A}$ are the mole fractions of B in liquid and vapour phases, thus,

$\begin{aligned} P_{A}^{'} = P_{A}^{\circ} x_{A} = p_{sol} \times y_{A} \\ P_{B}^{'} = P_{B}^{\circ} x_{B} = p_{sol} \times y_{B} \\ ∴ \frac{Y_{A}}{Y_{B}} = \frac{P_{A}^{\circ}}{P_{B}} \times \frac{X_{A}}{X_{B}} \end{aligned}$

Since

$\begin{array}{l} P_{A}^{\circ} > P_{B}^{\circ} \\ ∴ \frac{Y_{A}}{Y_{B}} > \frac{X_{A}}{X_{B}} \end{array}$

Thus $1 / y_{A}$ varies linearly with $1 / x_{A}$ .

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