Question

An equimolar mixture of 'A' and 'B' is prepared. The total vapour pressure of this mixture as a function of mole fraction of B is found to be $P_T=300+600X_B$.

(i) Calculate the composition of vapour of this mixture (Assume that the number of moles going into the vapour phase is negligible in comparison to the number of moles present in the liquid phase).

(ii) If the vapours above the liquid in part (i) are collected and condensed into a new liquid, calculate the composition of vapours of this new liquid.

• A. $\left(i\right)\Rightarrow Y_A=25\%,Y_B=75\%\left(ii\right)\Rightarrow Y_A=30\%,Y_B=70\%$
• B. $\left(i\right)\Rightarrow Y_A=30\%,Y_B=70\%\left(ii\right)\Rightarrow Y_A=25\%,Y_B=75\%$
• C. $\left(i\right)\Rightarrow Y_A=10\%,Y_B=90\%\left(ii\right)\Rightarrow Y_A=25\%,Y_B=75\%$
• D. $\left(i\right)\Rightarrow Y_A=25\%,Y_B=75\%\left(ii\right)\Rightarrow Y_A=10\%,Y_B=90\%$

Answer 1

The correct option is D $\left(i\right)\Rightarrow Y_A=25\%,Y_B=75\%\left(ii\right)\Rightarrow Y_A=10\%,Y_B=90\%$

(i)
$\text{Total vapour pressure,}{P}_T=300+600X_B$
where, $X_B$ is mole faction of B.
When $X_B=1$,
$\text{Pure vapour pressure of B,}{p}_B^{\circ }=300+600=900$
When $X_B=0$,
$\text{Pure vapour pressure of A,}{p}_A^{\circ }=300$
We know, it is a equimolar solution
$\therefore$
$\text{Mole fraction of A,}{X}_A=\frac{1}{2}\text{Mole fraction of B,}{X}_B=\frac{1}{2}\text{Total vapour pressure,}{P}_T=300+600X_B{P}_T=300+600\times \frac{1}{2}{P}_T=600$
By raoults law,
$p_A=X_A\times p_A^{\circ }=Y_A\times P_T$
$\Rightarrow Y_A=\frac{X_A\times p_A^{\circ }}{P_T}$
where,
$Y_A\Rightarrow \text{Composition of A at vapour phase}\text{Also,}{Y}_B\Rightarrow \text{Composition of B at vapour phase}$
$Y_A=\frac{\frac{1}{2}\times 300}{600}{Y}_A=\frac{1}{4}=25\%$
Similary,
$Y_B=\frac{\frac{1}{2}\times 900}{600}{Y}_B=\frac{3}{4}=75\%$

(ii)
Vapours of (A) is condensed to form new liquid with 75% composition of B and 25% composition of A
i.e.,$X_A^{\prime }=\frac{1}{4}$
$X_B^{\prime }=\frac{3}{4}$
Therefore, the new total pressure obtained is,
$\text{Total pressure,}{P}_T^{\prime }=X_A^{\prime }\times p_A^{\circ }+X_B^{\prime }\times p_B^{\circ }$
$P_T^{\prime }=\frac{1}{4}\times 300+\frac{3}{4}\times 900$
$P_T^{\prime }=750$

$Y_A^{\prime }\Rightarrow \text{Composition of A at vapour phase of new liquid}\text{Also,}{Y}_B^{\prime }\Rightarrow \text{Composition of B at vapour phase of new liquid}$
$Y_A^{\prime }=\frac{\frac{1}{4}\times 300}{750}{Y}_A^{\prime }=\frac{1}{10}=10\%$
Similary,
$Y_B^{\prime }=\frac{\frac{3}{4}\times 900}{750}{Y}_B^{\prime }=\frac{9}{10}=90\%$