Question

2 moles each of liquids A and B are dissolved to form an ideal solution. What will be the mole fraction of B in the vapour phase?

[$P_A^0=120$ torr and $P_B^0=80$ torr]

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{3}{5}$
• D. $\frac{2}{5}$

Answer 1

Answer: (D)

$\frac{2}{5}$

$X_A=\frac{2}{2+2}=\frac{1}{2}$

$X_B=\frac{2}{2+2}=\frac{1}{2}$

$P_{total}=X_A{P}_A^0+X_B{P}_B^0$

$⟹\frac{1}{2}\times 120+\frac{1}{2}\times 80=100$ torr

Now, the mole fraction of B in vapour phase $=\frac{X_B{P}_B^0}{P_{total}}=\frac{\frac{1}{2}\times 80}{100}$

$=\frac{40}{100}=\frac{2}{5}$.

Hence, the correct answer is option $\text{D}$.