
49Introduction to Kinetics and Chemical Reactors
()−=
+
r
kC
KC
A
A
A
1
2
2
1
(2.123)
In this section, we present a method for the estimation of parameters k
1
and K
2
using
the experimental readings on variation of C
A
with time recorded in a batch reactor experi-
ment. The differential equation for variation of C
A
with time is written as
dC
dt
kC
KC
A
=
+
1
2
2
1
(2.124)
Integrating this equation, we get
1
2
1
2
0
+
()
=
KC
kC
dC dt
A
A
A
C
C
t
A
A
(2.125)
On integration, Equation 1.125 gets reduced to
t
k
x
Cx
K
A
AA A
=
−
+
−
1
1
1
1
10
2
1
()
ln
(2.126)
This equation can be written in linear form as
ya
x
11
(2.127)
where
x
x
A
1
0
1
=
−
x
x
A
2
1
1
=
−
ln
a
k
1
1
1
=
a
k
2