Question

A $5.2$ molal aqueous solution of methyl alcohol $\left({\mathrm{CH}}_3\mathrm{OH}\right)$ is supplied. What is the mole fraction of methyl alcohol in the solution?

Answer 1

Step 1: Given data

The concentration of an aqueous solution of methyl alcohol $=5.2\mathrm{mol}$

Step2: Calculating mole fraction

A $5.2$ molal aqueous solution of methyl alcohol indicates that $5.2$ moles of methyl alcohol are present in one kilogram (or $1000\mathrm{g}$) of water.

The molecular weight of water$=18\mathrm{g}$

Moles of water$=\frac{\mathrm{given}\mathrm{weight}\mathrm{of}\mathrm{water}}{\mathrm{molecular}\mathrm{mass}\mathrm{of}\mathrm{water}}$

$=\frac{1000\mathrm{g}}{18\mathrm{g}{\mathrm{mol}}^{-1}}\Rightarrow 55.56\mathrm{mol}$

Mole fraction of methyl alcohol$=\frac{\mathrm{moles}\mathrm{of}\mathrm{methyl}\mathrm{alcohol}}{\mathrm{moles}\mathrm{of}\mathrm{methyl}\mathrm{alcohol}+\mathrm{moles}\mathrm{of}\mathrm{water}}$

$=\frac{5.2\mathrm{mol}}{55.56\mathrm{mol}+5.2\mathrm{mol}}\Rightarrow 0.086$

Therefore, the mole fraction of methyl alcohol in the solution is $0.086$