HW 4
ENME 382
4.3
Below, molecular weight data for a polytetrafluoroethylene material are tabulated. Compute (a) the number-
average molecular weight, (b) the weight-average molecular weight, and (c) the degree of polymerization.
Molecular Weight
Range
(
g/mol
)
x
i
w
i
10,000–20,000
0.03
0.01
20,000–30,000
0.09
0.04
30,000–40,000
0.15
0.11
40,000–50,000
0.25
0.23
50,000–60,000
0.22
0.24
60,000–70,000
0.14
0.18
70,000–80,000
0.08
0.12
80,000–90,000
0.04
0.07
Solution
(a)
From the tabulated data, we are asked to compute
M
n
, the number-average molecular weight.
Using
Equation 4.5a, this is computation is carried out below.
Molecular wt
Range
Mean
M
i
x
i
x
i
M
i
10,000-20,000
15,000
0.03
450
20,000-30,000
25,000
0.09
2250
30,000-40,000
35,000
0.15
5250
40,000-50,000
45,000
0.25
11,250
50,000-60,000
55,000
0.22
12,100
60,000-70,000
65,000
0.14
9100
70,000-80,000
75,000
0.08
6000
80,000-90,000
85,000
0.04
3400
____________________________
M
n
=
x
i
M
i
∑
= 49,800 g/mol