Question

Molecular weight data for some polymer are tabulated. Determine:
a) The number-average molecular weight
b) The weight-average molecular weight
c) What is the number-average degree of polymerization for this polymer?
d) What is the weight-average degree of polymerization for this polymer?

Molecular Weight

Range (g/mol)	xi	wi
8,000-16,000	0.05	0.02
16,000-24,000	0.20	0.10
24,000-32,000	0.20	0.25
32,000-40,000	0.25	0.25
40,000-48,000	0.23	0.20
48,000-56,000	0.07	0.18

Answer 1

(a) The number-average molecular weight,

This is carried out below:

Range (g/mol)	Mean Mi	xi	Mixi
8,000-16,000	12,000	0.05	600
16,000-24,000	20,000	0.20	4000
24,000-32,000	28,000	0.20	5600
32,000-40,000	36,000	0.25	9000
40,000-48,000	44,000	0.23	10120
48,000-56,000	52,000	0.07	3640

Thus,

(b) The weight-average molecular weight,

This is carried out below:

Range (g/mol)	Mean Mi	wi	Miwi
8,000-16,000	12,000	0.02	240
16,000-24,000	20,000	0.10	2000
24,000-32,000	28,000	0.25	7000
32,000-40,000	36,000	0.25	9000
40,000-48,000	44,000	0.20	8800
48,000-56,000	52,000	0.18	9360

Thus,

(c) Name of the polymer or the monomer is required to calculate this.

(d) Name of the polymer or the monomer is required to calculate this.