Question

Calculate the number average degree of polymerization and the number average molecular weight of an equimolar mixture of adipic cid and methylene diamond for the extents of reaction 0.5; 0.8; 0.9; 0.95 and 0.995.

Answer 1

The number average degree of polymerization () can be expressed as shown below.

= 1/(1-p), where p = extent of reaction or extent of polymerization

The number average molecular weight (M_n) of an equimolar mixture of adipic acid and hexamethylene diamine can be represented as shown below.

M_n = M₀*, where M₀ = molecular weight of repeating monomer unit, i.e. 226 g mol^-1

(The repeating monomer unit: -C(=O)-(CH₂)₄-C(=O)-NH-(CH₂)₆-NH-)

(i) p = 0.5

= 1/(1-0.5)

i.e. = 1/0.5, i.e. 2

i.e. M_n = 226*2, i.e. 452 g mol^-1

(ii) p = 0.8

= 1/(1-0.8)

i.e. = 1/0.2, i.e. 5

And M_n = 226*5, i.e. 1130 g mol^-1

(iii) p = 0.9

= 1/(1-0.9)

i.e. = 1/0.1, i.e. 10

i.e. M_n = 226*10, i.e. 2260 g mol^-1

(iv) p = 0.95

= 1/(1-0.95)

i.e. = 1/0.05, i.e. 20

i.e. M_n = 226*20, i.e. 4520 g mol^-1

(v) p = 0.995

= 1/(1-0.995)

i.e. = 1/0.005, i.e. 200

i.e. M_n = 226*200, i.e. 45200 g mol^-1