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

2.6 Kinetics of simple composite reactions 29
2.6 Kinetics of simple composite reactions
2.6.1 Consecutive first-order reactions
A −→ 1
B (2.102)
B −→ 2
C (2.103)
I
Coupled differential equations:
[A]
= − 1 [A] (2.104)
[B]
=+ 1 [A] − 2 [B] (2.105)
[C]
=+ 2 [B] (2.106)
In this case, since the DE’s are linear, there is an exact solution which we will examine
first. We will also look at an approximate solution which can be obtained with the
quasi steady-state approximation and at methods to obtain numerical solutions, which
we have to use for complex non-linear inhomogeneous DE systems.
I
Mass balance:
[A] + [B] + [C] = [A] 0
(2.107)
I
Initial conditions:
[A ( =0)] = [A] 0
(2.108)
[B ( =0)] = 0 (2.109)
[C ( =0)] = 0 (2.110)
I
Exact solution:
• First-order decay of [A]:
y
[A]
= − 1 [A] (2.111)
[A] = [A] 0
− 1
(2.112)
• Inhomogeneous DE for [B]:
[B]
=+ 1 [A] − 2 [B] (2.113)