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

2.6 Kinetics of simple composite reactions 33
2.6.3 Parallel reactions
A −→ 1
B (2.130)
A −→ 2
C (2.131)
A −→ 3
D (2.132)
y
y
and
[A]
= − ( 1 + 2 + 3 )[A] (2.133)
[A] = [A] 0
−( 1+ 2 + 3 )
(2.134)
[B] =
[C] =
[D] =
1 [A] 0
¡ ¢ 1 −
−( 1 + 2 + 3 )
( 1 + 2 + 3 )
(2.135)
2 [A] 0
¡ ¢ 1 −
−( 1 + 2 + 3 )
( 1 + 2 + 3 )
(2.136)
3 [A] 0
¡ ¢ 1 −
−( 1 + 2 + 3 )
( 1 + 2 + 3 )
(2.137)
Note that the decay of [A] is determined by the total removal rate constant =
1 + 2 + 3
2.6.4 Simultaneous first- and second-order reactions*
A −→ 1
C (2.138)
A+A−→ 2
D (2.139)
y
y
[A]
= − 1 [A] − 2 2 [A] 2
(2.140)
µ
1
[A] = −2 2 22
+ + 1
exp (− 1 )
1 1 [A] 0
(2.141)
I Approximation for k 1 t ¿ 1: Power series expansion of the exponential gives
1
[A] ≈ 1 µ
1
+ +2 2 × (2.142)
[A] 0
[A] 0