Question

Liquids A and B form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids A and B has a vapour pressure of 45 Torr. At the same temperature, a new solution of A and B having mole fractions $x_A$ and $x_B$, respectively, has a vapour pressure of 22.5 Torr. The value of $\frac{x_A}{x_B}$ in the new solution is. (given that the vapour pressure of pure liquid A is 20 Torr at temperature T)

Answer 1

$X_A=\frac{1}{2},X_B=\frac{1}{2}$
$P_T=P_A^0\times \frac{1}{2}+P_B^0\times \frac{1}{2}$
(Given $P_A^0=20)$
$90=45\times 2=P_A^0+P_B^0.....\left(1\right)$
$P_B^0=90-20=70$
$22.5=p_A^0{X}_A+P_B^0(1-X_A)$
$=20X_A+70(1-X_A)$
$22.5=20X_A+70-70X_A=70-50X_A$
$X_A=\frac{47.5}{50}=\frac{19}{20}$
$X_B=\frac{1}{20}$
$\frac{X_A}{X_B}=\frac{\frac{19}{20}}{\frac{1}{20}}=19$