Page 52 - Modeling of Chemical Kinetics and Reactor Design

22 Modeling of Chemical Kinetics and Reactor Design

Using the Bodenstein steady state approximation for the inter-
mediate enzyme substrate complexes derives reaction rate expressions
for enzymatic reactions. A possible mechanism of a closed sequence
reaction is:

E + [ ES * (1-93)
k 1
S
k 2
r
Enzyme Substrate enzyme-substrate complex

ES → E + P (1-94)

*
k 3
r r
where E = enzyme
S = substrate
*
ES = enzyme-substrate complex
P = product of the reaction
The stoichiometry of the reaction may be represented as:

S → P (1-95)

The net rate of an enzymatic reaction is usually referred to as its
velocity, V, represented by:

dC p
V = = kC * (1-96)
3
dt ES
The concentration of the complex can be obtained from the net rate
of disappearance:

( −r SE * ) net =− dC dt * = kC SE * + k C SE * − k C C E (1-97)
SE
S
3
2
1
Using the steady state approximation,

dC *
SE = kC C − k C − k C ≅ 0 (1-98)
dt 1 S E 2 SE * 3 SE *
or