Question

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

• A. $Y_A=Y_B$
• B. $\frac{Y_A}{Y_B}=\frac{X_A}{X_B}$
• C. $\frac{Y_A}{Y_B}>\frac{X_A}{X_B}$
• D. $\frac{Y_A}{Y_B}<\frac{X_A}{X_B}$

Answer 1

Answer: (C)

$P_A=P_A^0{X}_A$ (Raoult's law)

$P_A=P_{\text{total }}{Y}_A$ (Daltons law)

$\therefore P_A^0{X}_A=P_{\text{total }}{Y}_A$

$P_A^0=\frac{P_{\text{total }}{Y}_A}{X_A}\dots \dots$(1)

(2) Similarly, $P_B^0=\frac{P_{\text{total }}{Y}_B}{X_B}\dots \dots$(2)

Now, $P_A^0>P_B^0$

$\therefore P_{\text{Total }}\frac{Y_A}{X_A}>P_{\text{Total }}\frac{Y_B}{X_B}$

$\frac{Y_A}{X_A}>\frac{Y_B}{X_B}$