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Q. Insulin $(C_{2}H_{10}O_{5})_{n}$ is dissolved in a suitable solvent and the osmotic pressure $(\pi)$ of solutions of various concentrations (g/cc) C is measured at $20^{\circ}C$. The slope of the plot of $\pi$ against ‘C’ is found to be $4.65 \times 10^{-3}$ The molecular weight of insulin is

Solutions

Solution:

$\pi V=\frac{w_{B}}{m_{B}} \times RT $
$\pi=\left(\frac{w_{B}}{V}\right) \frac{RT}{m_{B}}$
$\pi=C\times\frac{RT}{m_{B}}\times1000 \ldots\left(i\right)$
where C = concentration in g/cc,
Comparing eqs. (i) and (ii), ...(ii)
Slope $= \frac{RT}{m_{R}}\times1000$
$m_{B}=\frac{RT}{\text{Slope}}\times1000$
$=\frac{0.0821\times293\times1000}{4.65\times10^{-3}}$
$=5.17\times10^{6}\,J$