Question

The mass percentage of urea in an aqueous solution is $30\%$ the molality of urea in solution is

• A. $4.5\mathrm{m}$
• B. $5.2\mathrm{m}$
• C. $6.1\mathrm{m}$
• D. $7.1\mathrm{m}$

Answer 1

The correct option is D

$7.1\mathrm{m}$

Explanation for correct option

(D) $7.1\mathrm{m}$

Step 1: Analyzing the entities given.

• Since the mass percentage of urea in an aqueous solution is $30\%$ ,Weight of Water $=100–30=70\mathrm{g}$
• Mol. wt. of urea $=60\mathrm{g}{\mathrm{mol}}^{-1}$
• Weight of Urea $=30\mathrm{g}$

Step2. Calculation of moles of solute

$$\begin{gathered} \text{Moles of solute}=\frac{30\text{g}}{60{\text{g mol}}^{-1}} \\ =0.5\text{mol} \end{gathered}$$

Step 3: Formula for molality

• $\mathrm{Molality}=\frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}}{\text{Mass of solvent (kg)}}$

Step4. Calculation for molality

• $$\begin{gathered} \mathrm{Molality}=\frac{0.5\text{mol}}{70\text{g×}{\displaystyle \frac{1\text{kg}}{1000\text{g}}}} \\ =7.1{\text{mol kg}}^{-1} \\ \text{=7.1 m} \end{gathered}$$

Explanation for incorrect options

The molality of urea in solution is $7.1\mathrm{m}$. Hence, options (A), (B),(C) are incorrect.

Hence the correct option is (D). The molality of urea in solution is $7.1\mathrm{m}$.