Problem: 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.

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

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:     

$$\begin{gathered} \boxed{\mathbf{∆}{\mathbf{T}}_{\mathbf{b}}\mathbf{ }\mathbf{=}\mathbf{ }{\mathbf{T}}_{\mathbf{b}\mathbf{,}\mathbf{ }\mathbf{solution}}\mathbf{ }\mathbf{-}\mathbf{ }{\mathbf{T}}_{\mathbf{b}\mathbf{,}\mathbf{ }\mathbf{pure}\mathbf{ }\mathbf{solvent}}} \\ \mathbf{∆}{\mathbf{T}}_{\mathbf{b}}\mathbf{=}\mathbf{ }\mathbf{107}\mathbf{.}\mathbf{25}\mathbf{ }{}^{\mathbf{o}}\mathbf{C}\mathbf{ }\mathbf{-}\mathbf{100}\mathbf{.}\mathbf{0}\mathbf{ }{}^{\mathbf{o}}\mathbf{C} \\ \mathbf{∆}{\mathbf{T}}_{\mathbf{b}}\mathbf{=}\mathbf{ }\mathbf{7}\mathbf{.}\mathbf{25}\mathbf{ }{}^{\mathbf{o}}\mathbf{C} \end{gathered}$$

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

$\boxed{\mathbf{∆}{\mathbf{T}}_{\mathbf{b}}\mathbf{ }\mathbf{=}\mathbf{ }{\mathbf{K}}_{\mathbf{b}}\mathbf{m}}$

where: 

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

K_b = boiling point elevation constant (0.512 ˚C/m)