Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

2.3 Kinetics of reversible first-order reactions (relaxation processes) 22
I Solution for [A(t)] (Fig. 2.8):
or
( 1 + −1 )[A]− −1 [A] 0
( 1 + −1 )[A] 0
− −1 [A] 0
=exp[− ( 1 + −1 ) ] (2.72)
−1
[A] − [A]
1 + 0
−1
[A] 0
−
=exp[− ( 1 + −1 ) ] (2.73)
−1
[A]
1 + 0
−1
This expression is not so easy to memorize, but we may recast it in a simple way:
Using
1
= [B] ∞
= [A] 0 − [A] ∞
(2.74)
−1 [A] ∞
[A] ∞
which gives
[A] ∞
=
−1
[A]
1 + 0
(2.75)
−1
we obtain
[A ()] − [A] ∞
=exp[− ( 1 + −1 ) ] (2.76)
[A] 0
− [A] ∞
With ∆ [A]
=[A()]−[A] ∞
and ∆ [A] 0
=[A] 0
−[A] ∞
, we write this result in compact
form as
∆ [A]
∆ [A] 0
=exp[− ( 1 + −1 ) ] (2.77)
I
Figure 2.8: Kinetics of reversible first-order reactions.