Question

For an ideal binary liquid solution with $P_A^0>P_B^0$ which relation between $X_A$ (mole fraction of A in liquid phase) and $Y_A$ (mole fraction of A in vapour phase) is correct? if $X_B$ 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

The correct option is C $\frac{X_A}{X_B}<\frac{Y_A}{Y_B}$

$Y_A=\frac{P_A}{P_{Total}}=\frac{X_A{P}_A^o}{P_{Total}}$

$Y_B=\frac{X_B{P}_B^o}{P_{Total}}$

$\therefore \frac{Y_A}{Y_B}=\left(\frac{X_A}{X_B}\right)\left(\frac{P_A^o}{P_B^o}\right)$

$\because P_A^o>P_B^o\Rightarrow \frac{Y_A}{Y_B}>\frac{X_A}{X_B}$

Hence, the correct option is C.