The average and endtoend distance L of a chain of an amorph

The average and end-to-end distance (L ) of a chain of an amorphous polymer can be

expressed as L =l*sqrt(m) , where l is the interatomic distance (1.54 Å for C–C) and m is

the number of bonds. If the average molecular weight of a polystyrene is 20,800

g/mol, what is the average end-to-end distance (L ) of a chain?

Solution

In that given polymer there are 200 molecules of styrene.

And in each molecule there are 5 C-C bonds.So there are 1000 total C-C bonds in the polymer.

1. For single bonded carbons

L= 1.54*sqrt(1000)

L= 1.54*31.6227

L= 48.699 A°

2. For double bonded carbons

Number of bonds are 600 because there are 3 in each polymer

L= 1.33*sqrt(600)

L= 1.33*24.495

L= 32.5782 A°

3. Now carbon hydrogen bonds there are 8 in a molecule.

And. There are 1600 in total number of bonds.

L= 1.09*sqrt(1600)

L= 1.09*40

L= 43.6A°

Total average end-to-end distance (L) of a chain =124.8772A°