Question

The vapour pressure of a pure liquid $A$ is $70$ torr at ${27}^{o}C$. It forms an ideal solution with another liquid $B$. The mole fraction of $B$ is $0.2$ and total vapour pressure of the solution is $84$ torr at ${27}^{o}C$. The vapour pressure of pure liquid $B$ at ${27}^o$C is:

• A. $14$
• B. $56$
• C. $140$
• D. $70$

Answer 1

Answer: (C)

$140$

We know Raoult's law,

For an ideal solution,

Partial pressure in solution $=$ mole fraction $\times$ Vapour pressure in pure state

Given,

$P_A^0=70$ torr at ${27}^{0}C$ $X_B=0.2$

then $X_A=1-X_B=1-0.2=0.8$ $P_B^0=?$

$P_{total}$ or $P_{solution}$ $=84$ torr

By, Raoult's law

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

$84=0.8\times 70+0.2P_B^0$

$P_B^0=\frac{84-56}{0.2}$

$P_B^0=140$ torr

$\therefore$ Vapour pressure of pure liquid $B$ at ${25}^{0}C$ is $140$ torr.

Hence, the correct option is $\text{C}$