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

3.6 Oscillating reactions* 68
• Both reactions (1) and (2) are autocatalytic.
• The Lotka mechanism illustrates the principle, but it does not correspond to an
existing chemical reaction system.
• A real oscillating reaction is the Belousov-Zhabotinsky reaction; this reaction may
be described using a more complicated mechanism (see below).
In order to model the resulting chemical oscillations, we assume that the reaction takes
place in a flow reactor, which is constantly supplied with new A such that the concentration
of A stays constant ([A] = [A] 0
), while the product Z is constantly removed.
I
Rate equations and steady-state solutions:
[X]
[Y]
=+ 1 [A] 0
[X] − 2 [X] [Y] (3.176)
=+ 2 [X] [Y] − 3 [Y] (3.177)
Steady-state solutions:
[X]
[Y]
=+ 1 [A] 0
[X] − 2 [X] [Y] = 0 (3.178)
=+ 2 [X] [Y] − 3 [Y] = 0 (3.179)
Dividing these equations by [X] and [Y], respectively, we find
2 [Y]
= 1 [A] 0
(3.180)
2 [X]
= 3 (3.181)
Since [A] = [A] 0
, the steady state solutions for [X] and [Y] are independent of time!
I Displacements from steady-state solutions: What happens if the concentrations
are displaced from the steady-state values by small amounts and ?
(1) Ansatz:
[X] = [X]
+ (3.182)
[Y] = [Y]
+ (3.183)