Question

A polymeric sample in which $30\%$ molecules have a molecular mass $20,000$, $40\%$ have $30,000$ and the rest $30\%$ have $60,000$. The $\left({\overline{M}}_n\right)$ and $\left({\overline{M}}_w\right)$ of this sample are, respectively:

• A. $36,000,43,333$
• B. $43,000,36,000$
• C. $72,000,86,000$
• D. $86,000,72,000$

Answer 1

The correct option is A $36,000,43,333$

Number average molecular weight
$\left({\overline{M}}_n\right)=\frac{\Sigma N_i{M}_i}{\Sigma N_i}=\frac{30\left(20000\right)+40\left(30000\right)+30\left(60000\right)}{30+40+30}=36000$

Weight average molecular weight

$\left({\overline{M}}_w\right)=\frac{\Sigma N_i{M}_i^2}{\Sigma N_i{M}_i}=\frac{30(20000{)}^2+40(30000{)}^2+30(60000{)}^2}{30\left(20000\right)+40\left(30000\right)+30\left(60000\right)}=43333$

Hence, the $\left({\overline{M}}_n\right)$ and $\left({\overline{M}}_w\right)$ of this sample are, respectively $36,000$ and $43,333$