Question

The plots of osmotic $\pi($ in $atm$ ) vs. concentration (in $g /$ $cm ^{3}$ ) of a polymer at $300 \,K$ gives a straight line having slope $2 \times 10^{-3}$. The molar mass of polymer is :

• A. $1.23 \times 10^{6}$
• B. $1.23 \times 10^{7}$
• C. $4 \times 10^{7}$
• D. $4 \times 10^{6}$

Answer 1

Answer: (B)

$\pi =\frac{C R T}{V}=\frac{w R T}{m \cdot V_{i n} L}$

$=\frac{w \times R T \times 1000}{m \times V_{i n} m L}$

$\pi =\frac{1000 R T}{m} \times C_{g / cm ^{3}}$

$\therefore$ slope $=\frac{1000 R T}{m}=2 \times 10^{-3}$

$\therefore m =\frac{1000 \times 0.0821 \times 300}{2 \times 10^{-3}}$

$=1.23 \times 10^{7} \,g \,mol ^{-1}$