Page 387 - Elements of Chemical Reaction Engineering Ebook

358 Nonelementary Reaction Kinetics Chap. 7

The number average molecular weight, a,, is just the average molecular
weight of a structural unit as, times the average number of structural unit per
chain, x,, plus the molecular weight of the end groups, Meg

a, xniTs + Meg
=
Since Meg is usually small (1 8 for the polyester reaction), it is neglected and

(7-26)

In addition to the conversion of the functional groups, the degree of poly-
merization, and the number average molecular weight we are interested in the
distribution of chain lengths, n, (i.e. molecular weights M,).

Example 7-3 Determining the concentrations of polymers
for step polymerization

Determine the concentration and mole fraction of polymers of chain length j in
terms of initial concentration of ARB, M,,, the concentration of unreacted functional
groups M, the propagation constant k and time t.
Solution
Letting P, = A-R-B, P, = A-R,-B, ... P, = A-R,-B and omitting the
water condensation products AB for each reaction we have
Reaction Rate Laws
rlP
kP:
=
2
(1) 2p1 +pz -rlPI = 2kP:, rlpz = -1
(2) p1 + P24P3 -rzpl = -r2p2 = rZp3 = 2kPlP2
-
(3) p1 + p3 +p4 -r3p, - -rjP3 = r3p4 = 2kPlP3

The factor of 2 in the disappearance term (e.g. -r3p3 = 2kP,P,) comes about
because there are two ways A and B can react.
x
A-R,-B

A-R,-B

The net rate of reaction of P, , P2 and P, for reactions (1) through (4) are
rl = rp, = - 2kP: - 2kPlP, - 2kP,P3 (E7-3.1)
r2 rp2 = kP~-2kPlP2-2kP~ (E7-3.2)

r3 rp3 = 2kPlP, - 2kPlP, - 2kP2P3 (E7-3.3)