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:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(600\, g\, mol^{-1}\)
Solutions with the same osmotic pressure at the same temperature are isotonic. Since \( \pi = CRT \), isotonic solutions of two non-electrolytes have the same molar concentration:
\( \displaystyle C_1 = C_2 \)
Urea (\( M = 60\ \mathrm{g\,mol^{-1}} \)) at 10 g per dm3:
\( \displaystyle C_1 = \frac{10\ \mathrm{g\,L^{-1}}}{60\ \mathrm{g\,mol^{-1}}} = \frac{1}{6}\ \mathrm{mol\,L^{-1}} \)
A 10% solution of the solute is taken as 10 g in 100 mL of solution, that is 100 g per litre:
\( \displaystyle C_2 = \frac{100\ \mathrm{g\,L^{-1}}}{M} \)
Equating the two:
\( \displaystyle \frac{100}{M} = \frac{1}{6} \)
\( \displaystyle M = 600\ \mathrm{g\,mol^{-1}} \)
The molar mass of the solute is 600 g mol−1.
Shortcut: Equal molar concentrations mean the mass concentration is proportional to the molar mass. The solute is present at 100 g L−1, ten times the 10 g L−1 of urea, so its molar mass is \( 10 \times 60 = 600 \).