Question

(Note that there are some additional equations and formulas in the last page) 1. A polyethylene sample contains 4000 chains with molecular weights between 0 and 5,000 g/mol, 8000 chains with molecular weights between 5,000 and 10,000 g/mol 7000 chains with molecular weights between 10,000 and 15,000 g/mol, and 2000 chains with molecular weights between 15,000 and 20,000 g/mol. Determine: (1) the number fraction for each molecular weight range, (2) the weight fraction for each molecular weight range, (3) the number average molecular weight of this polyethylene, (4) the weight average molecular weight of this polyethylene, (5) the degree of polymerization of this polyethylene, given its repeat unit molecular weight of 28.05 g/mol." (15 marks)

Answer 1

sl no	initial range g/mole	final range g/mole	Average gm/mol (final-ini)/2	size	Weighted average	fraction of weight	no of fraction
			A	B	A X B
1	0	5000	2500	4000	10000000	5%	19%
2	5000	10000	7500	8000	60000000	31%	38%
3	10000	15000	12500	7000	87500000	45%	33%
4	15000	20000	17500	2000	35000000	18%	10%
			Total	21000	192500000	100%	100%

The above table is the tabular form of all the data given in the question.

1.No of fraction is respectively 19%, 38%, 33% and 10%

2. fraction of weight is respectively 5%, 31%, 45% and 18%

3, the no average molecular weight = (20000-0)/2  = 10000. ( the initial and highest range of polymer)

4.The weighted Average molecular weight = 192500000/21000 = 9167.

5. the degree of polymerisation = 9167/28.05 = 327.