Question

Aminoheptanoic acid is step polymerized to a polyamide and the reaction has a second order dependence on the amino acid concentration. The following rate constants are known: k= 1.0x10-3 kg/(mol min) at 150 °C and k= 2.74x10-2 kg/(mol min) at 180 °C.

a) Write the balanced reaction equation for formation of the polyamide with molar mass of 12 737 g/mol.

b) Calculate the activation energy E and the collision frequency factor A for the reaction.

c) What conversion is needed to produce polymer with number average molar mass of 4240 g/mol?

Answer 1

a) Esters of 7 aminoheptanoic acid is monomer for nylon-7 (polyamide). They are prepared from E-caprolactone

n(H2N - (CH2)6 - COOC2H5) (monomer) -------->    [- NH - CO - (CH2)6 -]n   (polymer) (Nylon-7)

                               

b) formula for calculating activation energy is:

T1=120 +273 = 423K

T2 = 180 +273 =453K

R= 8.314 J/K MOL

ln(k2/k1) = -Ea / R (1/T2 -1/T1)

ln(2.74 x 10^-2 / 1 x 10^-3 ) = -Ea / R [ 1/453K - 1/423K]

3.31054 = -Ea / R (-1.5656 x 10^-4 K^-1)

Ea = (3.31054 x (8.314 J / K MOL ))/(1.5656 x 10^-4 K^-1)

Ea = 1.7580 x 10^5 J/MOL (activation energy)

Formula for calculating collision frequency factor A:

K = Ae ^ -Ea/RT

(1.0 x 10^-3 kg / Mol Min ) = A exp { - ( 1.7580 x 10^5 J / Mol ) / (8.314 J / K Mol ) (423 K) }

(1.0 x 10^-3 kg / Mol Min ) = A exp (-49.98831)

(1.0 x 10^-3 kg / Mol Min ) = A (1.951 x 10^-22)

A = 0.5125 x 10^19 kg / Mol min