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For an ideal binary liquid solution with $p_{A}^{o} > p_{B}^{o}, x_{A}$ and $y_{A}$ represent the mole fraction of A in liquid phase and vapor phase, respectively, whereas $x_{B}$ and $y_{B}$ represent the mole fraction of B in liquid phase and vapor phase, respectively. Therefore, which of the following relations is correct?

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$\frac{x_{A}}{x_{B}} > \frac{y_{A}}{y_{B}}$

$x_{A} = y_{A}$

$\frac{x_{A}}{x_{B}} < \frac{y_{A}}{y_{B}}$

$x_{A} > y_{A}$

answer is C.

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Detailed Solution

$P^{'} A = P_{A}^{0} x_{A} = P_{s o l} \times y_{A}$

$P^{'} B = P_{B}^{0} x_{B} = P_{s o l} \times y_{B}$

$\frac{y_{A}}{y_{B}} = \frac{p_{A}^{0}}{p_{B}^{0}} \times \frac{x_{A}}{x_{B}}$ (Since $(p_{A}^{0} > p_{B}^{0})$

$\frac{y_{A}}{y_{B}} > \frac{x_{A}}{x_{B}}$

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