Question

The vapour pressure of pure liquids 1 and 2 are $450mmHg$ and $700mmHg$ respectively at $350K$. At a point when total vapour pressure is $600mmHg$, choose the correct option(s) :

• A. Mole fraction of component 2 in vapour phase is 0.3
• B. Mole fraction of component 1 in liquid phase is 0.4
• C. Mole fraction of component 1 in liquid phase is 0.6
• D. Mole fraction of component 2 in vapour phase is 0.7

Answer 1

Answer: (B), (D)

Mole fraction of component 2 in vapour phase is 0.7

By Raoult's Law :
$P_T=p_1^{\circ }{\chi }_1+p_2^{\circ }{\chi }_2$
where
$P_T$ is the total pressure of the solution.
$p_1^{\circ }$ is the vapour pressure of pure component 1
$p_2^{\circ }$ is the vapour pressure of pure component 2
${\chi }_1$ is the mole fraction of component 1 in liquid phase.
${\chi }_2$ is the mole fraction of component 2 in liquid phase.

Putting the values:
$600=450{\chi }_1+700{\chi }_{2}600=450{\chi }_1+700(1-{\chi }_1)600=700-250{\chi }_1{\chi }_1=0.4$
${\chi }_2=1-0.4=0.6$
Hence option (a) is correct and (d) is incorrect.
Also, from dalton's law we can write,
$y_1\times P_T=p_1^{\circ }{\chi }_1$

where,
$y_1=\text{Mole fraction of component 1 in vapour phase}$
Putting values:
$y_1=\frac{450\times 0.4}{600}{y}_1=0.3y_2=1-y_1=0.7$
Hence option (c) is correct and (b) is incorrect.