Question

Two liquids A and B have vapour pressures in the ratio $P_A^o:P_B^o=2:3$ at a certain temperature. Assuming that A and B form an ideal solution and ratio of mole fractions of A to B in the vapour phase is $1:3$, then the mole fraction of A in the solution at the same temperature is?

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

Answer: (A)

$\frac{1}{3}$

Total Vapour Pressure of A and B = 2+3 = 5

Mole fraction of A in vapour phase = $\frac{1}{1+3}=\frac{1}{4}$

Mole fraction of B in vapour phase = $\frac{3}{1+3}=\frac{3}{4}$

According to Dalton's law of partial pressures:

$p_A=X_A\times P_{Tot}=\frac{1}{4}\times 5=1.25$

$p_B=X_B\times P_{Tot}=\frac{3}{4}\times 5=3.75$

Thus, the mole fraction of A:

$\frac{p_A}{p_B}\alpha X_A$

$X_A=\frac{1.25}{3.75}=\frac{1}{3}$