The plot of 1/x_A versus 1/y_A(where x_A and y_A are the mole fraction of A in liquid and vapour phases, respectively) is linear with slope and intercept respectively are given as (y-axis = 1/y_A, x-axis = 1/x_A)

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$P_{A}^{0} / P_{B}^{0}, (P_{A}^{0} - P_{B}^{0}) / P_{B}^{0}$

$P_{B}^{0} / P_{A}^{0}, (P_{B}^{0} - P_{A}^{0}) / P_{B}^{0}$

$P_{B}^{0} / P_{A}^{0}, (P_{A}^{0} - P_{B}^{0}) / P_{A}^{0}$

$P_{A}^{0} / P_{B}^{0}, (P_{B}^{0} - P_{A}^{0}) / P_{B}^{0}$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{P_{A}}{P_{B}} = \frac{P_{A}^{0} \cdot x_{A}}{P_{B}^{0} \cdot x_{B}} = \frac{y_{A}}{y_{B}} \Rightarrow \frac{P_{A}^{0} \cdot x_{A}}{P_{B}^{0} (1 - x_{A})} = \frac{y_{A}}{(1 - y_{A})} \\ \frac{P_{B}^{0}}{P_{A}^{0} x} (\frac{1 - x_{A}}{x_{A}}) = (\frac{1 - y_{A}}{y_{A}}) \\ \Rightarrow \frac{P_{B}^{0}}{P_{A}^{0}} (\frac{1}{x_{A} - 1}) = (\frac{1}{y_{A}} - 1) \\ (\frac{1}{y_{A}}) = (\frac{P_{B}^{0}}{P_{A}^{0}}) (\frac{1}{x_{A}}) + 1 - (\frac{P_{B}^{0}}{P_{A}^{0}}) \\ = (\frac{1}{y_{A}}) = (\frac{P_{B}^{0}}{P_{A}^{0}}) (\frac{1}{x_{A}}) + (\frac{P_{A}^{0} - P_{B}^{0}}{P_{A}^{0}}) \end{array}$
y = mx + c