Chemistry - Liquid Solution Question with Solution | TestHub

The elevation in boiling point is given by the relation:

$\Delta {\mathrm{T}}_{\mathrm{b}}={\mathrm{K}}_{\mathrm{b}}\times m$

where $m$ is the molality of the solution.

Molality is defined as the number of moles of solute dissolved per $1000\text{ g}$ of solvent:

$m=\frac{{\mathrm{W}}_2\times 1000}{{\mathrm{M}}_2\times {\mathrm{W}}_1}$

where ${\mathrm{W}}_2$ is the mass of the solute, ${\mathrm{M}}_2$ is the molar mass of the solute, and ${\mathrm{W}}_1$ is the mass of the solvent.

Substituting the expression for molality into the boiling point elevation equation:

$\Delta {\mathrm{T}}_{\mathrm{b}}={\mathrm{K}}_{\mathrm{b}}\times \frac{{\mathrm{W}}_2\times 1000}{{\mathrm{M}}_2\times {\mathrm{W}}_1}$

Rearranging the equation to solve for the molar mass of the solute ${\mathrm{M}}_2$:

${\mathrm{M}}_2=\frac{1000\times {\mathrm{K}}_{\mathrm{b}}\times {\mathrm{W}}_2}{\Delta {\mathrm{T}}_{\mathrm{b}}\times {\mathrm{W}}_1}$

Answer: ${\mathrm{M}}_2=\frac{1000\times {\mathrm{K}}_{\mathrm{b}}\times {\mathrm{W}}_2}{\Delta {\mathrm{T}}_{\mathrm{b}}\times {\mathrm{W}}_1}$