Question

The molality of an aqueous solution of Urea in which the mole fraction of Urea is $0.18$, is

Answer 1

Step 1 Mole fraction of water:

Mole fraction can be defined as the ratio of one component's moles to the total number of all the components present in the solution.

$\mathrm{Molefraction}\mathrm{of}\mathrm{solvent}\left({\mathrm{\chi }}_{\mathrm{A}}\right)=\frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}\left(\mathrm{n}\right)}{\mathrm{Moles}\mathrm{of}\mathrm{solute}\left(\mathrm{n}\right)+\mathrm{Moles}\mathrm{of}\mathrm{solvent}\left(\mathrm{N}\right)}$

$\mathrm{Molefraction}\mathrm{of}\mathrm{solute}\left({\mathrm{\chi }}_{\mathrm{B}}\right)=\frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}\left(\mathrm{n}\right)}{\mathrm{Moles}\mathrm{of}\mathrm{solute}\left(\mathrm{n}\right)+\mathrm{Moles}\mathrm{of}\mathrm{solvent}\left(\mathrm{N}\right)}$

Here, ${\mathrm{\chi }}_{\mathrm{A}}+{\mathrm{\chi }}_{\mathrm{B}}=1$

The mole fraction of Urea is $0.18$

So the mole fraction of water is $1-0.18=0.82$

Step 2 Molality:

Molality can be explained as the number of moles of solute present in $1000\mathrm{g}$ of the solvent.

That is the relation between mole fraction and morality is;

$\mathrm{Molality}\left(\mathrm{m}\right)=\frac{\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{solute}\times 1000}{\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{solvent}\times \mathrm{Molar}\mathrm{mass}\mathrm{of}\mathrm{solvent}}$

The molar mass of water is $18\mathrm{g}$

By substituting the values,

$$\begin{gathered} \mathrm{Molality}\left(\mathrm{m}\right)=\frac{0.18\times 1000}{0.82\times 18} \\ \mathrm{Molality}\left(\mathrm{m}\right)=\frac{18}{0.82\times 18} \\ \mathrm{Molality}\left(\mathrm{m}\right)=\frac{10}{0.82} \\ \mathrm{Molality}\left(\mathrm{m}\right)=12.19\mathrm{mol}{\mathrm{Kg}}^{-1} \end{gathered}$$

Therefore, the Molality of an aqueous solution is$12.19\mathrm{mol}{\mathrm{Kg}}^{-1}$