SolutionHard
Question
Liquids A and B form an ideal solution. The plot of $\frac{1}{X_{A}}$ (Y-axis) versus$\frac{1}{Y_{A}}$ (X-axis) (where XA and YA are the mole fractions of A in liquid and vapour phases at equilibrium, respectively) is linear whose slope and intercept, respectively, are given as
Options
A.$\frac{P_{A}^{o}}{P_{B}^{o}},\frac{\left( P_{A}^{o} - P_{B}^{o} \right)}{P_{B}^{o}}$
B.$\frac{P_{A}^{o}}{P_{B}^{o}},\frac{\left( P_{B}^{o} - P_{A}^{o} \right)}{P_{B}^{o}}$
C.$\frac{P_{B}^{o}}{P_{A}^{o}},\frac{\left( P_{A}^{o} - P_{B}^{o} \right)}{P_{B}^{o}}$
D.$\frac{P_{B}^{o}}{P_{A}^{o}},\frac{\left( P_{B}^{o} - P_{A}^{o} \right)}{P_{B}^{o}}$
Solution
$Y_{A} = \frac{P_{A}}{P_{\text{total}}} = \frac{X_{A}.P_{A}^{o}}{P_{\text{total}}}$
$\frac{1}{X_{A}} = \frac{1}{Y_{A}}.P_{A}^{o}.\left( \frac{Y_{A}}{P_{A}^{o}} + \frac{\left( 1 - Y_{A} \right)}{P_{B}^{o}} \right) = \frac{1}{Y_{A}}.\frac{P_{A}^{o}}{P_{B}^{o}} + \frac{P_{B}^{o} - P_{A}^{o}}{P_{B}^{o}}$
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