Question

The vapour pressure of a liquid decreases by $10torr$ when a non-volatile solute is dissolved. The mole fraction of the solute in solution is $0.1$. What would be the mole fraction of the liquid if the decrease in vapour pressure is $20torr$, the same solute being dissolved?

• A. $0.2$
• B. $0.9$
• C. $0.8$
• D. $0.6$

Answer 1

The correct option is C $0.8$

Answer is option $C.$

According to Rault's law,

$\frac{P^0-P}{P}=X_a⟶\left(1\right)$ Where $X_a=\text{Mole fraction of solute.}$

$\underset{–}{\text{Case 1}:}$ $P^0-P=10$ $torr,$ $X_a=0.1$

$\therefore$ $\frac{10}{P}=0.1$ or $P=\frac{10}{0.1}=100$ $torr$

$\underset{–}{\text{Case 2}:}$ $P^0-P=20$ $torr,$

$\therefore \left(1\right)⟶\frac{20}{100}=X_a⟹X_a=0.2$

We have $X_a+X_b=1,$ where $X_b=\text{Mole fraction of solvent.}$

$\therefore X_b=1-0.2=0.8$