Question

A polymer sample has the following composition

No. of molecules	Molecular weight
10	1000
50	2000
40	4000

The polydispersity index $(P.D.I.)$ of the polymer is

• A. $\frac{8500}{20}$
• B. $\frac{85}{81}$
• C. $\frac{850}{729}$
• D. $\frac{729}{850}$

Answer 1

Answer: (C)

${\bar{M}}_w=\frac{\sum N_i{M}_i^2}{\sum N_i{M}_i}$

$=\frac{10\times (1000{)}^2+50\times (2000{)}^2+40\times (4000{)}^2}{(10\times 1000)+(50\times 2000)+(40\times 4000)}$

$=\frac{85\times 10^7}{27\times 10^4}$

${\bar{M}}_n=\frac{\sum N_i{M}_i}{\sum N_i}=\frac{(10\times 1000)+(50\times 2000)+(40\times 4000)}{10+50+40}$

$=2700$

P.D.I. $=\frac{{\bar{M}}_w}{{\bar{M}}_n}=\frac{850}{729}$