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At certain temperature, \( 1.6 \% \) solution of an unknown substance is isotonic with \( 2.4 \% \) solution of urea. If both the solutions have the same solvent and both the solution have same density \( 1 g m / c m^{3}, \) what will be the molecular mass of unknown substance in \( \boldsymbol{g} \boldsymbol{m} / \boldsymbol{m} \boldsymbol{o l} \) (Molecular mass of urea 60 gm / mol)

1. 30
2. 40
3. 80
4. 90

Correct answer: 80

Solution

For isotonic solutions at the same temperature, osmotic pressures are equal, so their molar concentrations must be equal. Using the given density, the 2.4% urea solution gives the molarity, and the unknown solution must have the same molarity; solving for its molar mass gives 80 g/mol.

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