Question

Molecular weight data for a polymer is tabulated here.

(a) Compute the number-average molecular weight

(b) Compute the weight-average molecular weight

(c) If it is known that this material's degree of polymerization is 710, which one of the polymers listed in Table 4.3 is this polymer? Why?

(d) After you do the calculations, consider whether you would consider this material a high molecular weight polymer and why or why not.

(e) Give one property that tends to increase with increasing molecular weight.

Molecular Weight Range g/mol	xi	wi
15,000–30,000	0.04	0.01
30,000–45,000	0.07	0.04
45,000–60,000	0.16	0.11
60,000–75,000	0.26	0.24
75,000–90,000	0.24	0.27
90,000–105,000	0.12	0.16
105,000–120,000	0.08	0.12
120,000–135,000	0.03	0.05

Answer 1

a and b

Molecular Weight	xi	wi
Range g/mol			Mean Mi	xiMi	wiMi
15,000–30,000	0.04	0.01	22500	900	225
30,000–45,000	0.07	0.04	37500	2625	1500
45,000–60,000	0.16	0.11	52500	8400	5775
60,000–75,000	0.26	0.24	67500	17550	16200
75,000–90,000	0.24	0.27	82500	19800	22275
90,000–105,000	0.12	0.16	97500	11700	15600
105,000–120,000	0.08	0.12	112500	9000	13500
120,000–135,000	0.03	0.05	127500	3825	6375
		Number average molecular weight = sum of xiMi = 73800
		Weight average molecular weight = Sum of wiMi = 81450

c) Degree of polymerisation = Number average molecular weight / Molecular weight of monomer

Molecular weight of monomer = 73800 / 710 = 103.94

So you can match with the said table

d) we can calculate the polydispersity index as

PDI = weight average molecular weight / Number average molecular weight = 1.1

So this is average molecular weight

e) the strength of polymer increases with increase in molecular weight.