Question

What is the boiling point of 0.200 m lactose in water?

Short answer

The boiling point of the given solution is $100.1°C$.

Step-by-step solution

Elevation in boiling point

A solution’s boiling point is greater than its pure solvent.

The elevation in a boiling point can be determined by${\mathrm{\Delta T}}_{\mathrm{b}}={\mathrm{iK}}_{\mathrm{b}}\mathrm{m},$where the$K_b$is the molal boiling point elevation constant and its value is equal to$0.512{}^{°}C/m$for aqueous solutions, the i is the van’t Hoff factor, and its value for lactose is 1 because lactose is a non-electrolyte substance and it does not dissociate in a solution.

Calculate elevation in boiling point for lactose (ΔTb)

$$\begin{gathered} ∆T_b=i{K}_{b}m \\ =1.0512{}^{°}C/m\times 0.200m \\ =0.1024{}^{°}C \end{gathered}$$

Boiling point of solution

The boiling point of pure water is $100{}^{°}C$.

The formula of the elevation in a boiling point is:

$\Delta T_b=T_{solution}-T_{pure solvent}$

The boiling point of a solution is the sum of the boiling point of a pure solvent and the elevation in a boiling point.

Therefore, the boiling point of the given solution will be:

$$\begin{gathered} Boilingpoint=100{}^{°}C+0.1024{}^{°}C \\ =100.1{}^{°}C \end{gathered}$$