Question

The osmotic pressure of solutions of PVC in cyclohexanone at $300 K$ are plotted on the graph.
The molar mass of $PVC$ is ____$g \,mol ^{-1}$ (Nearest integer)

Answer 1

$ \pi= M ^{\prime} RT =\left(\frac{ W / M }{ V }\right) RT$
$ \Rightarrow \pi=\left(\frac{ W }{ V }\right)\left(\frac{1}{ M }\right) RT = C \left(\frac{ RT }{ M }\right) $
$ \Rightarrow \frac{\pi}{ C }=\frac{ RT }{ M } \neq f ( c )$
If we assume graph between $\frac{\pi}{C}$ and $C$

Assuming $\pi$ vs $C$ graph
Slope $=\frac{ RT }{ M }=\frac{0.083 \times 300}{ M }=6 \times 10^{-4}$
$ \therefore M =\frac{0.083 \times 300}{6 \times 10^{-4}}=\frac{830 \times 300}{6} $
$=41,500\, gm / mole$