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
|
Solution
(a) From the tabulated data, we are asked to compute , the number-average molecular weight. This is carried out below.
Molecular wt.
Range Mean Mi xi xiMi
15,000-30,000 22,500 0.04 900
30,000-45,000 37,500 0.07 2625
45,000-60,000 52,500 0.16 8400
60,000-75,000 67,500 0.26 17,550
75,000-90,000 82,500 0.24 19,800
90,000-105,000 97,500 0.12 11,700
105,000-120,000 112,500 0.08 9000
120,000-135,000 127,500 0.03 3825
_________________________
(b) From the tabulated data, we are asked to compute , the weight-average molecular weight. This determination is performed as follows:
Molecular wt.
Range Mean Mi wi wiMi
15,000-30,000 22,500 0.01 225
30,000-45,000 37,500 0.04 1500
45,000-60,000 52,500 0.11 5775
60,000-75,000 67,500 0.24 16,200
75,000-90,000 82,500 0.27 22,275
90,000-105,000 97,500 0.16 15,600
105,000-120,000 112,500 0.12 13,500
120,000-135,000 127,500 0.05 6375
_________________________
(c) We are now asked if the degree of polymerization is 710, which of the polymers in Table 14.3 is this material? It is necessary to compute m in Equation 14.6 as
The repeat unit molecular weights of the polymers listed in Table 14.3 are as follows:
Polyethylene--28.05 g/mol
Poly(vinyl chloride)--62.49 g/mol
Polytetrafluoroethylene--100.02 g/mol
Polypropylene--42.08 g/mol
Polystyrene--104.14 g/mol
Poly(methyl methacrylate)--100.11 g/mol
Phenol-formaldehyde--133.16 g/mol
Nylon 6,6--226.32 g/mol
PET--192.16 g/mol
Polycarbonate--254.27 g/mol
Therefore, polystyrene is the material since its repeat unit molecular weight is closest to that calculated above.
14.7 Is it possible to have a poly(methyl methacrylate) homopolymer with the following molecular weight data and a of polymerization of 527? Why or why not?
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