Question

A liquid has vapour pressure $35 \times {10^3}$ ${\text{N}}{{\text{m}}^{{\text{ - 2}}}}$at 298 K. if the solution contains $0.2$mole fraction of a solute, the vapour pressure of the solution will be
A.$2.8 \times {10^3}$ ${\text{N}}{{\text{m}}^{{\text{ - 2}}}}$
B.$7 \times {10^3}$ ${\text{N}}{{\text{m}}^{{\text{ - 2}}}}$
C.$7.0 \times {10^4}$ ${\text{N}}{{\text{m}}^{{\text{ - 2}}}}$
D. $28 \times {10^3}$ ${\text{N}}{{\text{m}}^{{\text{ - 2}}}}$

Answer 1

To solve this question, the idea of mole fraction and vapour pressure are needed. Both are connected together by Raoult's Law for ideal solutions. The mole fraction of any component in a solution can be defined as the ratio of the number of moles of that solute to the total number of moles of the solutes in a solution.

Formula used: ${{\text{x}}_{\text{i}}}{\text{ = }}\dfrac{{{{\text{n}}_{\text{i}}}}}{{{{\text{n}}_{{\text{total}}}}}}$
Where ${{\text{x}}_{\text{i}}}$ is the mole fraction of the component, ${{\text{n}}_{\text{i}}}$ is the moles of that component and ${{\text{n}}_{{\text{total}}}}$ is the total moles.
${{\text{P}}_{\text{a}}}{\text{ = }}{{\text{X}}_{\text{a}}}{{\text{P}}^{\text{0}}}_{\text{a}}$
${{\text{P}}_{\text{b}}}{\text{ = }}{{\text{X}}_{\text{b}}}{{\text{P}}^{\text{0}}}_{\text{b}}$
Where, a and b are the two components of the solution

Complete step by step answer:
The Raoult’s Law states that in an ideal solution, the partial vapour pressure of a component of the solution is equal to the product of the vapour pressure of the pure component and the mole fraction of the component in the mixture. The total pressure of the system will be:
${{\text{P}}_{{\text{total}}}}{\text{ = }}{{\text{P}}_{\text{a}}}{\text{ + }}{{\text{P}}_{\text{b}}}$
According to the sum, ${P_0}$ = vapour pressure of the liquid at 298 K = $35 \times {10^3}$ ${\text{N}}{{\text{m}}^{{\text{ - 2}}}}$
Due to the addition of the solute to the solvent, the resulting partial pressure,
${{\text{P}}_{\text{a}}} = 35 \times {10^3} \times 0.2$
$\Rightarrow {{\text{P}}_a} = 7.0 \times {10^3}$ ${\text{N}}{{\text{m}}^{{\text{ - 2}}}}$

Hence, the correct option is option B.

Note:
1.The solubility of a substance depends on the nature of the solute and the solvent as well as the temperature and the pressure.
2.The pressure does not have any influence on the solubility of solids in liquids. This is because solids and liquids are highly incompressible and unaffected by any changes in pressure.
3.Raoult’s Law of vapour pressure is applicable to an ideal mixture of volatile liquids only, for example: Chloroform and acetone.