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

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

A
$90.0 g {mol}^{- 1}$
B
$115.0 g {mol}^{- 1}$
C
$105.0 g {mol}^{-}$
D
$210.0 g {mol}^{- 1}$

Solution:

Isotonic solutions have the same osmotic pressure. Hence, from $Π = c R T$ , we get

$c_{1} = c_{2} \Rightarrow n_{1} = n_{2}$

$i . e . \frac{5.25 g}{M} = \frac{1.5 g}{60 g {mol}^{- 1}} \Rightarrow M = \frac{5.25 \times 60}{1.5} g {mol}^{- 1} i.e. M = 210 g {mol}^{- 1}$

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