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

3.6 Oscillating reactions* 66
3.6 Oscillating reactions*
The reactant and product concentrations normally approach equilibrium in a smooth
(often exponenential) fashion. Under special circumstances, however, the concentrations
may also show oscillations and/or bistability as they approach equilibrium. Such
behavior can occur only if there is a chemical feedback by autocatalysis.
3.6.1 Autocatalysis
Example for autocatalysis:
A+B → B+B (3.167)
Rate law:
− [A]
= [A] [B] (3.168)
To solve this DE, we substitute for [B ()] using the mass balance relation [A] 0
−[A ()] =
[B ()] − [B] 0
and introduce =[A()] as reaction progress variable:
[B ()] = [A] 0
+[B] 0
− [A ()] (3.169)
=[A] 0
+[B] 0
− (3.170)
This gives the DE
y
Z
−
= ([A] 0 +[B] 0
− ) (3.171)
Z
([A] 0
+[B] 0
) − = − (3.172)
2
Solution:
or
[B ()] =
µ
1 [A]0 [B ()]
ln
= − (3.173)
[A] 0
+[B] 0
[B] 0
[A ()]
[A] 0
+[B] 0
1+([A] 0
[B] 0
)exp[− ([A] 0
+[B] 0
) ]
(3.174)