Question

Two liquids A and B form an ideal solution. The solution has a vapor pressure of 700 torr at ${80}^{o}C$. It is distilled till $2/3^{rd}$ of the solution is collected as condensate. The composition of the condensate is $X_A^{\prime }=0.75$ and that of the residue is $X_A^{\prime \prime }=0.30$. If the vapor pressure of the residue at ${80}^{o}C$ is 600 Torr, which of the following is /are true?

• A. The composition of the original liquid was $X_A=0.6$
• B. The composition of the original liquid was $X_A=0.4$
• C. $P_A^0=\frac{2500}{2}Torr$
• D. $P_B^0=500Torr$

Answer 1

Answer: (A), (C), (D)

The correct options are
A The composition of the original liquid was $X_A=0.6$
C $P_A^0=\frac{2500}{2}Torr$
D $P_B^0=500Torr$

The vapour pressure of solution is 700 torr.

Hence, $X_A{P}_A^o+X_B{P}_B^o=700$

The vapour pressure of the residue is 600 torr.

Hence, $X{"}_A{P}_A^o+X{"}_B{P}_B^o=0.30P_A^o+0.70P_B^o=600......\left(ii\right)$.

Let x and y represent initial moles of A and B respectively.

$x=0.75\times \frac{2}{3}(x+y)+0.30\times \frac{1}{3}(x+y).....\left(iii\right)$

And $X_A=\frac{x}{x+y}=0.6$

These equations are solved.

$X_A=0.6,X_B=0.4,P_A^o=\frac{2500}{3}torr;P_B^o=500torr$