$200 \mathrm{~mL}$ of an aqueous solution of a protein contains its $1.26 \mathrm{~g}$. The osmotic pressure…

$200 \mathrm{~mL}$ of an aqueous solution of a protein contains its $1.26 \mathrm{~g}$. The osmotic pressure of this solution at $300 \mathrm{~K}$ is found to be $2.57 \times 10^{-3}$ bar. The molar mass of protein will be $\left(\mathrm{R}=0.083 \mathrm{~L} \mathrm{bar} \mathrm{mol}^{-1} \mathrm{~K}^{-1}ight)$
  1. $51022 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $122044 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $31011 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $61038 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

Osmotic pressure $(\pi)=\mathrm{CRT}$
$(\pi)=\frac{\mathrm{wt} \times 1000}{\text { Molecular mass } \times \mathrm{V}} \mathrm{RT}$
$=2.57 \times 10^{-3}=\frac{1.26 \times 1000}{\text { Mol.mass } \times 200} \times 0.083 \times 300$
Molecular mass $=61038 \mathrm{~g}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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