Question

The plot of $\frac{1}{X_A}$ vs $\frac{1}{Y_A}$ (where $X_A$ and $Y_A$ are the mole fractions of liquid A in liquid and vapour phase, respectively) is linear. The slope and intercept of this plot are respectively:

• A. $\frac{P_A^0}{P_B^0}$ and $\frac{P_A^0-P_B^0}{P_B^0}$
• B. $\frac{P_A^0}{P_B^0}$ and $\frac{P_B^0-P_A^0}{P_B^0}$
• C. $\frac{P_B^0}{P_A^0}$ and $\frac{P_A^0-P_B^0}{P_B^0}$
• D. $\frac{P_B^0}{P_A^0}$ and $\frac{P_B^0-P_A^0}{P_B^0}$

Answer 1

The correct option is B $\frac{P_A^0}{P_B^0}$ and $\frac{P_B^0-P_A^0}{P_B^0}$

The total pressure P is given by the expression $P=\frac{P_A}{Y_A}=\frac{P_A^o{X}_A}{Y_A}$.
It is also given by the expression $P=\frac{P_B}{Y_B}=\frac{P_B^o{X}_B}{Y_B}$.

Hence, $\frac{P_A^o{X}_A}{Y_A}=\frac{P_B^o{X}_B}{Y_B}$.

Note: $1-X_A=X_B:1-Y_A=Y_B$

$P_B^o(\frac{1}{X_A}-1)=P_A^o(\frac{1}{Y_A}-1)$

$\frac{P_B^o}{X_A}-P_B^o=\frac{P_A^o}{Y_A}-P_A^o$

$\frac{P_B^o}{X_A}=\frac{P_A^o}{Y_A}+P_B^o-P_A^o$

$\frac{1}{X_A}=\frac{P_A^o}{P_B^o}\frac{1}{Y_A}+\frac{P_B^o-P_A^o}{P_B^o}$.

This is an equation of straight line of the type $y=mx+c$.

Thus, in the plot of $\frac{1}{X_A}vs.\frac{1}{Y_A}$ the slope is $\frac{P_A^o}{P_B^o}$ and y intercept is $\frac{P_B^o-P_A^o}{P_B^o}$.

Option B is correct.