Page 53 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 23

S
1
C * = kC C E (1-99)
SE k + k
2 3
Substituting Equation 1-99 into Equation 1-96 gives:

V = kk • 3 • C • C S (1-100)
1
E
k + k 3
2
From the material balance, the total concentration of the enzyme
in the system, C , is constant and equal to the sum of the con-
ET
centrations of the free or unbounded enzyme, C , and the enzyme-
E
substrate complex, C , that is:
SE*
C ET = C + C SE * (1-101)
E
For the substrate C , the total concentration of the substrate in the
S
system, C , is equal to the sum of the concentration of the substrate
ST
and the enzyme substrate complex C
SE*
C ST = C + C SE * (1-102)
S
In laboratory conditions, C k C , since C cannot exceed C .
ST ET SE* ET
This shows that C ≈ C .
ST S
Rearranging Equation 1-101 gives:
C = C ET − C SE * (1-103)
E

Using C ≈ C in Equation 1-102 and substituting Equation 1-103
ST S
into Equation 1-98 gives:

dC *
SE = kC ST( C − C *) − k C − k C ≅ 0
dt 1 ET SE 2 SE * 3 SE *
(1-104)
kC C ET − k C C SE * − k C SE * − k C SE * = 0
1
2
ST
ST
3
1
or
ST
1
C * = kC C ET
SE kC + k + k (1-105)
1 ST 2 3