What mass of solute (molar mass $58 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is to be dissolved in $2.5…

What mass of solute (molar mass $58 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is to be dissolved in $2.5 \mathrm{dm}^3 \mathrm{H}_2 \mathrm{O}$ to generate osmotic pressure of 0.245 atm at 300 K ? $\left(\mathrm{R}=0.0821 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K} \mathrm{~mol}^{-1}\right)$.
  1. 1.0 gram
  2. 0.72 gram
  3. 1.44 gram
  4. 1.75 gram

Solution

$\begin{aligned} & \Pi=C R T \\ & \Pi=\frac{\mathrm{W}_2 \times \mathrm{R} \times \mathrm{T}}{\mathrm{M}_2 \times \mathrm{V}} \\ & \mathrm{W}_2=\frac{\Pi \times \mathrm{M}_2 \times \mathrm{V}}{\mathrm{R} \times \mathrm{T}} \\ & \quad \mathrm{W}_2=\frac{0.245 \mathrm{~atm} \times 58 \mathrm{~g} \mathrm{~mol}^{-1} \times 2.5 \mathrm{dm}^3}{0.0821 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \times 300 \mathrm{~K}} \\ & \therefore \quad \text { Mass of solute }=1.44 \mathrm{~g}\end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 2)

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