A solution containing $10\, g/dm^3$ of urea $(NH_2CONH_2)$ is isotonic with a 10% solution of a non-volatile solute. The molecular mass of the solute is:

$600\, g\, mol^{-1}$

The correct answer is Option (2) → $600\, g\, mol^{-1}$

Isotonic solutions are defined as solutions that have equal osmotic pressure.

$$\pi = CRT$$

Where:

• $\pi = \text{osmotic pressure}$
• $C = \text{molar concentration of the solute (mol/L)}$
• $R = \text{universal gas constant}$
• $T = \text{absolute temperature in Kelvin}$

Since temperature is same,

$C_1 = C_2$

For non-electrolytes, (urea & solute), the van't Hoff factor $i = 1$.

Step 1: Molarity of Urea Solution

Given:

• $10 \text{ g}$ urea per $\text{dm}^3$ ($= 1 \text{ L}$)
• Molar mass of urea $= 60 \text{ g/mol}$

$C_{urea} = \frac{10}{60} = 0.167 \text{ mol/L}$

Step 2: 10% Solution Meaning

$10\% \text{ (w/v)} = 10 \text{ g}$ solute in $100 \text{ mL}$ solution

$\Rightarrow 100 \text{ g}$ in $1 \text{ L}$ solution

Let molar mass of solute $= M$

$C_{solute} = \frac{100}{M}$

Step 3: Isotonic Condition

$0.167 = \frac{100}{M}$

$M = \frac{100}{0.167} \approx 600$