Q. 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 $27℃$ . The approximate molecular weight of the polymer is
A) $1.5 \times 10^{3}$
B) $2.4 \times 10^{5}$
C) $1.0 \times 10^{4}$
D) $2 \times 10^{12}$
Explanation
(b)
Given, weight of PVC, w= 4g
Volume of solution, V = 1 L
Osmotic pressure, $\pi = 4.1 \times 10^{- 4}$
Temperature, T=$27℃\$=27+273=300K
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \pi$V=nRT
Or $\pi$V=$\frac{w}{M}RT$(M=moleclular 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}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.