We’re being asked to calculate the vapor pressure of water at 338K (64.85^{o}C) above a solution of a nonvolatile solute in water having a boiling point of 380.4K. (107.25^{o}C).

The vapor pressure of pure water at this temperature is 0.2467 atm.

Recall that the boiling point of a solution is higher than that of the pure solvent and the change in boiling point (ΔT_{b}) is given by:

$\overline{){\mathbf{\u2206}}{{\mathbf{T}}}_{{\mathbf{b}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{T}}}_{\mathbf{b}\mathbf{,}\mathbf{}\mathbf{solution}}{\mathbf{}}{\mathbf{-}}{\mathbf{}}{{\mathbf{T}}}_{\mathbf{b}\mathbf{,}\mathbf{}\mathbf{pure}\mathbf{}\mathbf{solvent}}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{{\mathbf{T}}}_{{\mathbf{b}}}{\mathbf{=}}{\mathbf{}}{\mathbf{107}}{\mathbf{.}}{\mathbf{25}}{\mathbf{}}{}^{{\mathbf{o}}}{\mathbf{C}}{\mathbf{}}{\mathbf{-}}{\mathbf{100}}{\mathbf{.}}{\mathbf{0}}{\mathbf{}}{}^{{\mathbf{o}}}{\mathbf{C}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{{\mathbf{T}}}_{{\mathbf{b}}}{\mathbf{=}}{\mathbf{}}{\mathbf{7}}{\mathbf{.}}{\mathbf{25}}{\mathbf{}}{}^{{\mathbf{o}}}{\mathbf{C}}$

The **change in boiling point** is also related to the molality of the solution:

$\overline{){\mathbf{\u2206}}{{\mathbf{T}}}_{{\mathbf{b}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{K}}}_{{\mathbf{b}}}{\mathbf{m}}}$

where:

**m** = molality of the solution (in m or mol/kg)

**K _{b}** = boiling point elevation constant (0.512 ˚C/m)

A solution of a nonvolatile solute in water has a boiling point of 380.4 K .

Calculate the vapor pressure of water above this solution at 338 K. The vapor pressure of pure water at this temperature is 0.2467 atm.

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