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

8.7 References 203
9. Explosions
9.1 Chain reactions and chain explosions
9.1.1 Chain reactions without branching
I
Reaction scheme:
(1) A → X chain initiation
(2) X+B→ P+X chain propagation
(4) X → A chain termination
I
Rate laws:
[X]
= 1 [A] − 4 [X] (9.1)
[P]
= 2 [B] [X] (9.2)
As we see, reaction (2) does not appear in the rate law because → !
I Solutions of Eq. 9.1 for two limiting cases (cf. Fig. 9.1):
(1) Solution for → 0 and [A] ≈ const by substitution, using
= 1 [A] − 4 [X]
y
y
y
y
=0:
y
[X] = − 5 y [X] = −
4
− 1 4
= y
= − 4
= − 4 = 1 [A] − 4 [X] (9.3)
[X] = 1
4
[A] − − 4
(9.4)
[X] = 0 y = 1
[]
4
(9.5)
[X] = 1 [A]
³ ´
1 − − 4
4
(9.6)