Solutions Question 385
Question: A mixture of A and B, which are two miscible liquids, is distilled under equilibrium conditions at atmospheric pressure. The mole fraction of A in solution is 0.3 and in vapour phase is 0.6. If the solution behaves ideally the ratio of $ P, _A^{o} $ to $ P, _B^{o} $ is
Options:
A) 4.0
B) 2.5
C) 3.5
D) 1.5
Show Answer
Answer:
Correct Answer: C
Solution:
In solution $ X_{A}=0.3 $
$ \therefore $ $ X_{B}=0.7 $
In vapours $ Y_{A}=0.6\therefore Y_{B}=0.4 $
Using Dalton’s law
$ Y_{A}=\frac{p_{A}}{p_{T}} $
i.e., $ Y_{A}=\frac{p_A^{o}\times X_{A}}{P_A^{o}X_{A}+p_B^{o}X_{B}} $
$ \therefore $ $ Y_{B}=\frac{p_B^{o}X_{B}}{p_A^{o}X_{A}+p_B^{o}X_{B}} $
$ \therefore $ $ \frac{Y_{A}}{Y_{B}}=\frac{p_B^{o}X_{B}}{p_B^{o}X_{B}} $
$ \therefore $ $ \frac{p_{{}}^{o}A}{p_{{}}^{o}B}=\frac{Y_{A}}{Y_{B}}\times \frac{X_{B}}{X_{A}}=\frac{0.6}{0.4}\times \frac{0.7}{0.3}=3.5 $
