The osmotic pressure of solutions of PVC in cyclohexanone at 300   K are plotted on the graph. The…

Using osmotic pressure in ideal gas equation:
$\pi ={\mathrm{M}}^{\text{'}}\mathrm{RT}=\left(\frac{\mathrm{W}/\mathrm{M}}{\mathrm{V}}\right)\mathrm{RT}$

$\Rightarrow \pi =\left(\frac{\mathrm{W}}{\mathrm{V}}\right)\left(\frac{1}{\mathrm{M}}\right)\mathrm{RT}=\mathrm{C}\left(\frac{\mathrm{RT}}{\mathrm{M}}\right)$

$\Rightarrow \frac{\pi }{\mathrm{C}}=\frac{\mathrm{RT}}{\mathrm{M}}$

If we assume given graph between $\frac{\pi }{C}$ and $\mathrm{C}$

Slope $=\frac{\mathrm{RT}}{\mathrm{M}}=\frac{0.083\times 300}{\mathrm{M}}=6\times {10}^{-4}$

$\therefore \mathrm{M}=\frac{0.083\times 300}{6\times {10}^{-4}}=\frac{830\times 300}{6}$

$=41,500\mathrm{gm}/\mathrm{mole}$