Question

For an ideal binary liquid solution with $P_{A}^{\circ}>P_{B}^{\circ}$ in which relation between $X_{A}$ (mole fraction of $A$ in liquid phase) and $Y_{A}$ (mole fraction of $A$ in vapour phase) is correct, $X_{B}$ and $Y_{B}$ are mole fraction of $B$ in liquid and vapour phase respectively

• A. $X_{A}=Y_{A}$
• B. $X_{A}>Y_{A}$
• C. $\frac{X_{A}}{X_{B}}<\frac{Y_{A}}{Y_{B}}$
• D. $X_{A}, Y_{A}, X_{B}$ and $Y_{B}$ cannot be correlated

Answer 1

Answer: (C)

$P_{A}'=P_{A}^{\circ} \cdot X_{A}=P_{T} \cdot Y_{A}$

$P_{B}'=P_{B}^{\circ} \cdot X_{B}=P_{T} \cdot Y_{B}$

$\therefore \frac{P_{A}^{\circ}}{P_{B}^{\circ}} \cdot \frac{X_{A}}{X_{B}}=\frac{Y_{A}}{Y_{B}} $

$\because \frac{P_{A}^{\circ}}{P_{B}^{\circ}} > 1$

$ \therefore \frac{X_{A}}{X_{B}}<\frac{Y_{A}}{Y_{B}}$