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  4. 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

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Q. 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

Polymers

Solution:

$\bar{M}_{w}=\frac{\sum N_{i} M_{i}^{2}}{\sum N_{i} M_{i}}$

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

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

$\bar{M}_{n}=\frac{\sum N_{i} M_{i}}{\sum N_{i}}=\frac{(10 \times 1000)+(50 \times 2000)+(40 \times 4000)}{10+50+40}$

$=2700$

P.D.I. $=\frac{\bar{M}_{w}}{\bar{M}_{n}}=\frac{850}{729}$