Question

The polymer has a following molar mass distribution

Number of molecules Molar mass ($g/mol$)

$50$ $5000$

$75$ $6000$

Calculate the weight average molecular (approximate) weight (${\stackrel{-}{M}}_w$) .

Answer 1

Given,

$n_1=50$

$n_2=75$

$M_1=5000g/mol$

$M_2=6000g/mol$

The weight average molecular weight is given as:

${\stackrel{-}{M}}_w=\frac{\sum n_i{M}_i^2}{\sum n_i{M}_i}$

Thus by putting all the values we get,

${\stackrel{-}{M}}_w=\frac{n_1{M}_1^2+n_2{M}_2^2}{n_1{M}_1+n_2{M}_2}=\frac{50\times (5000{)}^2+75\times (6000{)}^2}{50\times 5000+75\times 6000}=5642g/mol$