Question

Insulin is dissolved in a suitable solvent and the osmotic pressure $\left(\pi \right)$ of solutions of various concentration $C$ (g/cc) is measured at ${20}^{o}C$. The slope of a plot of ($\pi$) against $C$ is $4.65\times {10}^{-3}$. The molecular weight of insulin is:

• A. $4.8\times {10}^5$
• B. $9\times {10}^5$
• C. $3\times {10}^5$
• D. $5.7\times {10}^6$

Answer 1

Answer: (D)

$5.7\times {10}^6$

The expression for the osmotic pressure is $\pi =CRT$

Here, the osmotic pressure is in atm and the concentration is in mol/L.

When the concentration is expressed in g/cc, the expression for the osmotic pressure becomes $\pi =\frac{1000CRT}{M}$

Here, M is the molar mass.

When a graph of the osmotic pressure vs concentration (g/cc) is plotted, the slope is $\frac{1000RT}{M}$

Substitute values in the above expression.

$4.65\times {10}^{-3}=\frac{0.0821\times 293\times 1000}{M}$

$M=5.17\times {10}^6$ g/mol.

Hence, the correct option is $D$