question_answer

The vapour pressure of two pure liquids A and B which form an ideal solution are 1000 and 1600 torr respectively at 400 K. A liquid solution of A and B for which the mole fraction of A is 0.60 is contained in a cylinder by a piston on which the pressure can be varied. The solution use slowly vapourised at 400 K by decreasing the applied pressure. What is the composition of last droplet of liquid remaining in equilibrium with vapour?

A) \[{{X}_{A}}=0.30,{{X}_{B}}=0.70\]

B) \[{{X}_{A}}=0.40,{{X}_{B}}=0.60\]

C) \[{{X}_{A}}=0.70,{{X}_{B}}=0.30\]

D) \[{{X}_{A}}=0.50,{{X}_{B}}=0.50\]

Correct Answer: C

Solution :

[c] \[p_{A}^{0}=1000\] torr \[p_{B}^{0}=1600\]

\[{{X}_{A}}=0.6\] \[{{Y}_{A}}=0.6\] (from graph)

\[{{Y}_{A}}=\frac{p_{A}^{0}{{X}_{A}}}{p_{A}^{0}{{X}_{A}}+p_{B}^{0}(1-{{X}_{A}})}\]

\[0.6=\frac{1000{{X}_{A}}}{1000{{X}_{A}}+1600(1-{{X}_{A}})}\]

\[X{{X}_{A}}=0.70\,\,X{{X}_{B}}=1-{{X}_{A}}=0.30\]