The molecular weight of the acrylonitrile monomer is
The weight average molecular weight is given by
where fi is the weight fraction
of the polymer. If we use xi (the number fraction) instead of
fi, we get the number average molecular weight (see page 478).
I need the average molecular weight to determine these items and the degree
of polymerization, so I'll make the table (N/A = not applicable):
| number of chains | mean MW of chains Mi | number fraction xi | xiMi | molecular weight | weight fraction fi | fiMi |
| 10,000 | 3,000 | 0.137 | 411 | 30 x 106 | 0.0442 | 133 |
| 18,000 | 6,000 | 0.247 | 1479 | 108 x 106 | 0.159 | 956 |
| 17,000 | 9,000 | 0.233 | 2096 | 153 x 106 | 0.226 | 2031 |
| 15,000 | 12,000 | 0.205 | 2466 | 180 x 106 | 0.265 | 3186 |
| 9,000 | 15,000 | 0.123 | 1849 | 135 x 106 | 0.199 | 2987 |
| 4,000 | 18,000 | 0.0548 | 986 | 72 x 106 | 0.106 | 1912 |
| sums are below: | ||||||
| 73,000 | N/A | N/A | 9287 | 678 x 106 | N/A | 11,205 |
To get the number fraction, I divided the number of chains by the sum. For example, 10000/73000 = 0.137. (Please note: while the values in column 3 are rounded, I used the unrounded values to compute successive columns.) To get the molecular weight, I multiplied columns 1 and 2. The weight fraction was obtained by dividing values in column 5 by the sum; e.g., 30/678 = 0.0442.
a) Thus, the weight average MW is 11,205 g/mol. The degree of polymerization is 11205/53 = 211.
b) The number average MW is 9287 g/mol and the degree of polymerization using this number is 9287/53 = 175.