Question

2. Calculate the number-average molecular weight of a random poly (isobutylene-isoprene) copolymer in which the fraction of isobutylene repeat units is 0.25; assume that this concentration corresponds to a degree of polymerization of 1500.

Answer 1

Answer : The number-average molecular weight is, 97500 g/mol

Explanation :

First we have to calculate the molecular weight of isobutylene and isoprene.

The molecular formula of isobutylene and isoprene is, $C_4H_8$ and $C_5H_8$

Molecular weight of $C_4H_8$ = 4(12 g//mol) + 8(1 g/mol) = 56 g/mol

Molecular weight of $C_5H_8$ = 5(12 g//mol) + 8(1 g/mol) = 68 g/mol

Now we have to calculate the average repeat molecular weight.

Average repeat molecular weight = $0.25\times (56g/mol)+(1-0.25)\times (68g/mol)$

Average repeat molecular weight = 65 g/mol

Now we have to calculate the number-average molecular weight.

Number-average molecular weight = Average repeat molecular weight × Degree of polymerization

Number-average molecular weight = (65 g/mol) × (1500)

Number-average molecular weight = 97500 g/mol

Thus, the number-average molecular weight is, 97500 g/mol