Page 33 - Enzymes in Tropical Soils

Enzymes in Tropical Soils 21

where x is the concentration of the converted substrate.

2.5 First Order Enzyme Reaction

Unlike that at high concentration of substrate, the rate of an enzymatic
reaction at any time at lower concentration of substrate is dependent on the
concentration of substrate following the first order enzyme reaction. The rate of a
reaction increases with the increase in substrate concentration as shown in Fig. 2.3.
The rate of the biochemical reaction at low substrate concentration is controlled by
Eq. 2.7 as follows (Tabatabai, 1982; Sparks, 1989).

( ) ....... Eq. 2.7

where a is the initial concentration of substrate, x is the concentration of converted
substrate, t is the unit of time (in minutes), and k is the rate constant. The value of
a is higher than or equals to x. The concentration of a decreases while that of x
increases with time. The value of x increases with time approaching the value of a,
at which the reaction will cease.
By integrating Eq 2.7, Eq 2.8 and Eq. 2.9 are obtained (Tabatabai, 1982).

....... Eq. 2.8

or

....... Eq. 2.9

These equations clearly show that the rate of an enzymatic reaction is dependent
on the concentration of substrate and that of the converted substrate as well as
time. The rate constant increases with time approaching V max in relation to the
decrease in the substrate left in the system.
Rearranging Eq. 2.9 results in Eq 2.10 as follows (Sparks, 1989).

( ) ....... Eq. 2.10

Abdul Kadir Salam - 2014