Page 388 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.3 Polymerization 2159

If we continue in this way we would find that the net rate of formation of the
PI is
m
= -2kP1 1 (E7-3.4)
Pj
IPl j= 1
m
However, we note that P, is just the total concentration of functional groups of
I= I
[ 1
either A or B, which is M M = J'1 PI .

rp, = -2kP1M (E7-?I .5)
Similarly we can generalize reactions (1) through (4) to obtain the net rate of for-
mation of the j-mer, for j ? 2 .

I
j -
r,i = k 1 Pi Pj-; - 2kPjM (E7-3.6)
i= 1
For a batch reactor the mole balance on PI and using Equation (7-23) to eliminate
M gives
(E7-3.7)

which solves to

2
P,=M, ~ (E7-3.8)
(I 1 +hoki)
Having solved for P, we can now use rj to solve successively for PI

5 r2 = kP:- 2kP,M (E7-3.9)
=
dt
(E7-3. II 0)

with P2 = 0 at t = 0

(E7-3.11)

continuing we find, that in general'

(E7-3.12)

' N. A. Dotson, R. GalvBn, R. L. Lawrence, and M. Tirrell, Polymerization Process
Modeling, VCH Publishers, New York, NY (1996).