Question

A polymer sample contains 5 molecules of molar mass 1000, 3 molecules of molar mass 500 and 2 molecules of molar mass 250. What is its weight average molecular weight (Mw)?

• A. 700
• B. 870.35
• C. 839.28
• D. 890.35

Hint:

Weight average molecular weight emphasizes heavier molecules more than number average.

Answer 1

The Correct Option is C

Weight average molecular weight ($M_w$) is given by:
$M_w = \dfrac{\sum n_i M_i^2}{\sum n_i M_i}$
Here,
$M_1 = 1000,\ n_1 = 5$
$M_2 = 500,\ n_2 = 3$
$M_3 = 250,\ n_3 = 2$
$M_w = \dfrac{(5 \times 1000^2) + (3 \times 500^2) + (2 \times 250^2)}{(5 \times 1000) + (3 \times 500) + (2 \times 250)}$
$= \dfrac{5,000,000 + 750,000 + 125,000}{5000 + 1500 + 500} = \dfrac{5,875,000}{7000} \approx 839.28$