Chemistry - Liquid Solution Question with Solution | TestHub

According to Raoult's law, the total vapour pressure of the solution is given by:

$P_T=P_A^0{X}_A+P_B^0{X}_B$

Since $X_A+X_B=1$, substituting $X_A=1-X_B$ gives:

$P_T=P_A^0(1-X_B)+P_B^0{X}_B$

$P_T=P_A^0+(P_B^0-P_A^0)X_B$

Substituting the given values $P_T=500\text{ mmHg}$, $P_A^0=400\text{ mmHg}$, and $P_B^0=575\text{ mmHg}$:

$500=400+(575-400)X_B$

$100=175X_B$

$X_B=\frac{100}{175}=\frac{4}{7}\approx 0.57$

The mole fraction of liquid B in the solution is $0.57$.

Answer: 0.57