Question

If two substances A and B have $P_A^0:P_B^0=1:2$ and have mole ratio in solution 1:2, then mole fraction of A in vapours is:

• A. 0.33
• B. 0.25
• C. 0.52
• D. 0.2

Answer 1

Answer: (D)

0.2

$\frac{P_A^o}{P_B^o}=\frac{1}{2}$

Let, $P_A^o=1$

$P_B^0=2$

Similarly, $n_A=1and{n}_B=2$

By Raoult's law,

$P_A=X_A{P}_A^o$

$\therefore P_A=\frac{1}{3}\times 1=\frac{1}{3}$

$\&P_B=X_B{P}_B^o$

$=\frac{2}{3}\times 2=\frac{4}{3}$

$P_A=X_A\times P_T\therefore \frac{1}{3}=X_A\times (\frac{1}{3}+\frac{4}{3})\therefore X_A=\frac{1/3}{5/3}=\frac{1}{5}=0.2$

Hence, option D is correct.