Question

If \[{{P}^{o}}\] and \[{{P}_{s}}\] are the V.P. of solvent and solution respectively and \[{{N}_{1}}\] and \[{{N}_{2}}\] are the moles of solute and solvent then:
(A) \[({{P}^{o}}-{{P}_{s}})/{{P}^{o}}={{N}_{1}}/({{N}_{1}}+{{N}_{2}})\]
(B) \[({{P}^{o}}-{{P}_{s}})/{{P}_{s}}={{N}_{1}}/{{N}_{2}}\]
(C) \[({{P}^{o}}-{{P}_{s}})/{{P}^{o}}={{N}_{1}}/{{N}_{2}}\]
(D) None of these

Answer 1

Hint: As per Raoult's law, the partial vapour pressure of a solvent of an ideal mixture at the same temperature is the vapour pressure of the pure solvent multiplied by the mole fraction of the solvent present.
According to Raoult’s law:
\[\dfrac{({{P}^{o}}-{{P}_{s}})}{{{P}^{o}}}=\dfrac{n}{n+N}\]
where, \[{{P}^{o}}\] = vapor pressure of a solvent
\[{{P}_{s}}\]= vapor pressure of a solution
n = number of moles of solute
N = number of moles of solvent

Complete step by step solution:
-In the question it is given that \[{{P}^{o}}\] = vapor pressure of a solvent
\[{{P}_{s}}\]= vapor pressure of a solution
\[{{N}_{1}}\]= number of moles of solute
\[{{N}_{2}}\]= number of moles of solvent
-Here we have substitute all the values in Raoults’ law
\[\begin{align}
& \dfrac{{{P}^{o}}-{{P}_{s}}}{{{P}^{o}}}=\dfrac{{{N}_{1}}}{{{N}_{1}}+{{N}_{2}}} \\
& 1-\dfrac{{{P}_{s}}}{{{P}^{o}}}=\dfrac{{{N}_{1}}}{{{N}_{1}}+{{N}_{2}}} \\
& \dfrac{{{P}_{s}}}{{{P}^{o}}}=1-\dfrac{{{N}_{1}}}{{{N}_{1}}+{{N}_{2}}} \\
& \dfrac{{{P}_{s}}}{{{P}^{o}}}=\dfrac{{{N}_{2}}}{{{N}_{1}}+{{N}_{2}}} \\
& {{P}_{s}}={{P}^{o}}\left[ \dfrac{{{N}_{2}}}{{{N}_{1}}+{{N}_{2}}} \right] \\
\end{align}\]
Then\[{{P}_{s}}={{P}^{o}}\left[ \dfrac{{{N}_{2}}}{{{N}_{1}}+{{N}_{2}}} \right]\],

Therefore option A is correct.

Additional information:
Raoult’s law is similar to the ideal gas law. The only exclusion of Raoult’s law is that it is applicable to solutions only. Raoult’s law is also applicable to non-ideal solutions. Though, it can be done by including several factors like interactions between molecules of dissimilar substances.

Note: If a non-volatile is added to a solvent to form a solution, the vapour pressure of the solution is lower than that of the vapour pressure of the solvent. The decrease in vapour pressure of the solution is directly proportional to the mole fraction of solute added to the solvent.