Q. Consider a binary solution of two volatile liquid components 1 and 2. $x_1$ and $y_1$ are the mole fractions of component 1 in liquid and vapour phase, respectively. The slope and intercept of the linear plot of $\frac1{x_1}$ vs $\frac1{y_1}$ are given respectively as:
A) $\frac{P_2^0}{P_1^0},\ \frac{P_2^0-P_1^0}{P_2^0}$
B) $\frac{P_1^0}{P_2^0},\ \frac{P_2^0-P_1^0}{P_2^0}$
C) $\frac{P_1^0}{P_2^0},\ \frac{P_1^0-P_2^0}{P_2^0}$
D) $\frac{P_2^0}{P_1^0},\ \frac{P_1^0-P_2^0}{P_1^0}$
Explanation
[Solution by Dr. Abubacker] $y_1=\frac{x_1P_1^0}{x_1P_1^0+x_2P_2^0}\Rightarrow\frac1{y_1}=1+\frac{P_2^0}{P_1^0}\left(\frac1{x_1}-1\right)$. Solving for $\frac1{x_1}$: $\frac1{x_1}=\frac{P_1^0}{P_2^0}\cdot\frac1{y_1}+\frac{P_2^0-P_1^0}{P_2^0}$. So the slope is $\frac{P_1^0}{P_2^0}$ and the intercept is $\frac{P_2^0-P_1^0}{P_2^0}$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.