Calculate the molar mass of solute when 4 g of it dissolved in $1 \mathrm{dm}^3$. solvent has osmotic…

Calculate the molar mass of solute when 4 g of it dissolved in $1 \mathrm{dm}^3$. solvent has osmotic pressure 2 atm at $300 \mathrm{~K} .\left[\mathrm{R}=0 . \hat{0} 82 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$
  1. $49.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $44.5 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $54.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $56.4 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \mathrm{M}_2 & =\frac{\mathrm{W}_2 \mathrm{RT}}{\pi \mathrm{V}} \\ & =\frac{4 \mathrm{~g} \times 0.082 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \times 300 \mathrm{~K}}{2 \mathrm{~atm} \times 1 \mathrm{dm}^3} \\ & =49.2 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2024 (04 May Shift 2)

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