Question

A solution containing 10 g per dm³ of urea is isotonic with a 5% solution of non volatile solute. Calculate the molecular mass of this non-volatile solute.

Answer 1

Step 1: Calculating the concentration of urea

The molar mass of urea is $60\mathrm{g}$

$\therefore$The concentration of urea is:

$$\begin{gathered} \frac{10\mathrm{g}{\mathrm{dm}}^3}{\mathrm{Mol}.\mathrm{wt}.\mathrm{of}\mathrm{urea}} \\ =\frac{10}{60} \\ =\frac{1}{6}\mathrm{mol}{\mathrm{dm}}^{-3} \end{gathered}$$

Step 2: Calculating the molecular mass

Let the molar mass of the non-volatile solute be M

$\therefore$The concentration of 5% non-volatile solute is:

$$\begin{gathered} \frac{5}{100}\times \frac{1000}{M} \\ =\frac{50}{M}\mathrm{mol}{\mathrm{dm}}^{-3} \end{gathered}$$

Now for isotonic at the same temperature, we know that the concentration is equal

$\therefore$$\frac{1}{6}=\frac{50}{\mathrm{M}}$

$$\begin{gathered} \Rightarrow \mathrm{M}=50\times 6 \\ \Rightarrow \mathrm{M}=300\mathrm{g}{\mathrm{mol}}^{-1} \end{gathered}$$

Therefore, the molecular mass of this non-volatile solute is $300\mathrm{g}{\mathrm{mol}}^{-1}$.