Page 409 - Elements of Chemical Reaction Engineering Ebook

380 Nonelementary Reaction Kinetics Chap. 7

Solution
R. = Io- @j-1 e-@ (7-66)
(j- I)!
We recall that the zero moment is just the total radical concentrations:
m
Rj
Xo = 1 = Io (E7-5.1)
j=l
The first moment is
m m j@j- le-@
jRj = Io 2 (E7-5.2)
Xl = (j- l)!
j= 1 j=l
Letk=j- 1:

m @ke-@
A, = J, 1 (k+ 1)- (E7-5.3)
k=O k!
Expanding the (k + 1) term gives

(E7-5.4)

Recall that

(E7-5.5)

Therefore,

(E7-5.6)

Letl=k- 1:

(E7-5.7)

The first moment is
I A, = Zo(l+@) 1 (E7-5.8)

The number-average length of growing polymer radical (i.e., live polymer) is

(E7-5,9)

m
A, = io 2 j2Rj = l0.1 @j-1 (E7-5.10)
W
J2-
j=O (j- l)!
j=O