A $5.25 %$ solution of a substance is isotonic with a $1.5 %$ solution of urea (molar mass= $60 g m o l^{- 1}$ ) in the same solvent. If the densities of both the solutions are assumed to be equal to $1.0 g c m^{- 3},$ molar mass of the substance will be:

210.0 g m o l^{- 1}

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90.0 g m o l^{- 1}

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115.0 g m o l^{- 1}

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105.0 g m o l^{- 1}

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Solution

The correct option is A $210.0 g m o l^{- 1}$
When two solutions are isotonic, then, the osmotic pressure of one solution is equal to the osmotic pressure of the other, i.e., $π_{1} = π_{2}$

$⟹ C_{1} R T = C_{2} R T$

$⟹ \frac{5.25}{M . w t} \times \frac{1000}{100} = \frac{1.5}{60} \times \frac{1000}{100}$

$⟹ M . w t = \frac{5.25 \times 60}{1.5}$

$= 210 g m o l^{- 1}$ .

Hence, the correct option is $A$

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A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass= 60g mol−1) in the same solvent. If the densities of both the solutions are assumed to be equal to 1.0g cm−3, molar mass of the substance will be:

The correct option is A 210.0g mol−1When two solutions are isotonic, then, the osmotic pressure of one solution is equal to the osmotic pressure of the other, i.e., π1=π2⟹C1RT=C2RT⟹5.25M.wt×1000100=1.560×1000100⟹M.wt=5.25×601.5=210g mol−1.Hence, the correct option is A

A $5.25 %$ solution of a substance is isotonic with a $1.5 %$ solution of urea (molar mass= $60 g m o l^{- 1}$ ) in the same solvent. If the densities of both the solutions are assumed to be equal to $1.0 g c m^{- 3},$ molar mass of the substance will be: