A non-volatile solute (A) is dissolved in a volatile solvent (B). The vapour pressure of the resultant solution is ${\mathrm{P}}_{\mathrm{s}}$. The vapour pressure of pure solvent is ${\mathrm{P}}_{\mathrm{B}}^0$. If$\text{'} \mathrm{X} \text{'}$ is mole fraction, which of the following is correct?

From Raoult's Law we know that the partial pressure of each component of the solution is directly proportional to its mole fraction present in solution.

${\mathrm{P}}_{\mathrm{A}}={\mathrm{P}}_{\mathrm{A}}^0 {\mathrm{X}}_{\mathrm{A}}$

${\mathrm{P}}_{\mathrm{B}}={\mathrm{P}}_{\mathrm{B}}^0 {\mathrm{X}}_{\mathrm{B}}$

Now, By Dalton’s law of partial pressure,

${\mathrm{P}}_{\mathrm{s}}={\mathrm{P}}_{\mathrm{A}}+{\mathrm{P}}_{\mathrm{B}}$

But A is a non-volatile solute, So ${\mathrm{P}}_{\mathrm{A}}=0$

Then 

${\mathrm{P}}_{\mathrm{s}}={\mathrm{P}}_{\mathrm{B}}^0 {\mathrm{X}}_{\mathrm{B}}$

Hence, option(c) is correct.