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  4. The vapour pressure of a pure liquid A is 70 torr at 27° 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 in 84 torr at 27° C . The vapour pressure of pure liquid B at 27° C is

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

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Solution:

According to Raoult's law, $p=p_{A}^{o}.X_{A}+p_{B}^{o}.X_{B}$

Here $p_{A}^{o}=70\text{ torr},X_{A}=1-X_{B}=1-0.2=0.8,p=84\text{ torr, }X_{B}=0.2$ and $p_{B}^{o}=?$

So 84 torr $=70\text{ torr}\times \text{0.8+}\text{p}_{B}^{o}\times 0.2$

or $p_{B}^{o}=\frac{84 \text{ torr} - 56 \text{ torr}}{0.2}=140\text{ torr}$ .