We have a polyethylene (C_2H_4) sample containing 4,000 chains with molecular we

ID: 491715 • Letter: W

Question

We have a polyethylene (C_2H_4) sample containing 4,000 chains with molecular weights between 0 g/mol and 5,000 g/mol, 8,000 chains with molecular weights between 5,000 g/mol and 10,000 g/mol, 7,000 chains with molecular weights between 10,000 g/mol and 15,000 g/mol, and 2,000 chains with molecular weights between 15,000 g/mol and 20,000 g/mol. The atomic mass of hydrogen is 1 g/mol and atomic mass of carbon is 12.01 g/mol. Determine the: (a) Number average molecular weight (b) Weight average molecular weights (c) Number average degree of polymerization (d) Weight average degree of polymerization (e) Polydispersity index.

Explanation / Answer

We have a polyethylene sample containing 4000 chains with molecular weights between 0 and 5000 g/mol, 8000 chains with molecular weights between 5000 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 both the number and weight average molecular weights.

SOLUTION

First we need to determine the number fraction xi and weight fraction fi for each of the four ranges.

Number of chain

Mean M Per chain

X1Mi

Weight

fiMi

4000

2500

0.191

477.5

10x10^6

0.0519

129.75

8000

7500

0.381

2857.5

60x10^6

0.3118

2338.50

7000

12500

0.333

4162.5

87.5 x10^6

0.4545

5681.25

2000

17500

0.095

1662.5

35x10^6

0.1818

3181.5

Sum=21000

Sum=1

=9160

=192.5x10^6

11.331

Mn ==9160 g/mol ---------------answer

Mw ==11331 g/mol ---------------answer

Degree of polymerization -

The average molecular weight of the polymer divided by the molecular weight of the monomer