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For a dilute solution containing 2.5 gm of a non-volatile non-electrolyte solute in 100 gm of water, the elevation in the boiling point at 1 atm pressure is \[2{}^\circ \] C. Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure (mm of Hg) of the solution is (\[{{K}_{b}}=0.76\]\[K\]\[kg\]\[mo{{l}^{-1}}\]):
A. 724
B. 740
C. 736
D. 718

Last updated date: 20th Jun 2024
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Hint: Lowering in vapor pressure is due to the reason when solute was added to the pure liquid known as solvent then the liquid surface had molecules of both the solvent and solute. When the number of solvent molecules starts escaping into vapor phase and gets reduced then as a result the pressure exerted by the vapor phase is also reduced which is known as relative lowering of vapor pressure.

Complete step by step solution:
Solution consists of solute and solvent. Solute is that substance which has to be dissolved and solvent is the substance in which solute has dissolved. The presence of a solute leads to a colligative property called the lowering of the vapor pressure of the solution when compared to the vapor pressure of the pure solvent. There is enough difference between the types of volatile and nonvolatile solutes to treat them separately. Volatiles are those substances whose boiling point is lower than \[100{}^\circ \]C while non-volatile have a higher boiling point.
Lowering in vapor pressure is calculated by
= \[\dfrac{{{P}_{o}}-P}{{{P}_{o}}} = \dfrac{n}{n+N}\]
\[{{P}_{o}}\] and P are the vapor pressure of pure solvent and solution respectively and n is number of moles of solute and N describes the number of moles of solution.
Molality = \[\dfrac{\Delta {{T}_{b}}}{{{K}_{b}}}\] = \[\dfrac{2}{0.76}=2.63\]mol/kg:
where \[\Delta {{T}_{b}}\] = elevation in boiling point and \[{{K}_{b}}\] = boiling point elevation constant
And molality of pure water is 55.6 mol/kg
- Now, lowering of vapor pressure
\[\dfrac{{{P}_{o}}-P}{{{P}_{o}}} =\dfrac{n}{n+N}\]
\[\Rightarrow \dfrac{760-P}{760} = \dfrac{2.63}{55.56}\]
By solving the equation value of P is 724 mm Hg.

Therefore, the correct answer is “Option A”.

Note: Solutions with a nonvolatile solute produce a vapor which is pure solvent while solutions with a volatile solute produce a vapor which is a mixture of both solvent and solute. There is another way to express the difference between volatile and nonvolatile is that a nonvolatile solute does not appear as a component of the vapor above the solution while a volatile solute does appear as a component of the vapor above the solution.