
29Introduction to Kinetics and Chemical Reactors
Thus, a plot of
1
0
CM
Mx
A
A
A
()
ln
−
−
−
versus t (Figure 2.13) is a straight line with a
slope equal to k.
The half-life period t
1/2
is
t
kC M
M
M
A
12
0
1
1
/
()
ln=
−
(2.67)
Note that for M = 1, Equations 2.66 and 2.67 get reduced to the form of integrated
Equations 2.54 and 2.55 derived for second-order reaction in Section 2.1.7.2.
2.1.7.5 Reversible First-Order Reaction
Consider a reversible rst-order reaction
k
k
1
2
The rate equation is
rk
C
AAB
(2.68)
Let C
Ae
and C
Be
be the concentrations of A and B at equilibrium. Then, the equilibrium
constant K is
K
k
k
C
C
Be
Ae
==
1
2
(2.69)
Let