Question

A solution containing $4\, g$ of polyvinyl chloride polymer in one litre of dioxane was found to have an osmotic pressure of $4.1 \times 10^{-4} atm$ at $27^{\circ} C$. The approximate molecular weight of the polymer is

• A. $1500$
• B. $10,000$
• C. $2.4 \times 10^{5}$
• D. $2 \times 10^{12}$

Answer 1

Answer: (C)

Given, weight of $PVC,\, w=4\, g$
Volume of solution, $V=1\, L$
Osmotic pressure, $\pi=4.2 \times 10^{-4}$
Temperature, $T=27^{\circ} C =27+273=300\, K$
$\Rightarrow \pi V=n R T$ or $\pi V=\frac{w}{M} R T$
( $M=$ molecular weight)
$4.1 \times 10^{-4} \times 1=\frac{4}{M} \times 0.0821 \times 300$
$M=\frac{4 \times 0.0821 \times 300}{4 \times 10^{-4} \times 1}$
$\therefore M=2.4 \times 10^{5}$