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

3.6 Oscillating reactions* 71
Here, A and B are reactants, R and S are final products, and X and Y are intermediates.
The autocatalytic reaction is reaction (3).
Rate equations (using “dimensionless time” = 4 ) and steady-state concentrations:
[X]
[X]
Steady-state concentrations:
= ·
[X] = 1 [A] − 2 [B] [X] + 3 [X] 2 [Y] − 4 [X]
4
(3.201)
= ·
[Y] = 2 [B] [X] − 3 [X] 2 [Y]
4
(3.202)
[X]
[Y]
= 1 [A]
4
(3.203)
= 2 4 [B]
1 3 [A]
(3.204)
We now investigate the effect of small displacements from steady-state by [X] and
[Y]. The reaction rates respond to these displacements according to
⎛ ⎞
⎛ ⎞
⎝ [X]
·
⎠ [X] and ⎝ [Y]
·
⎠ [Y] (3.205)
[X]
[Y]
y
• The steady-state is stable if
⎛ ⎞
⎝ [X]
·
⎠
[X]
• The steady-state is unstable if
⎛ ⎞
⎝ [X]
·
⎠
[X]
• Stability criterion:
⎛ ⎞
⎝ [X]
·
⎠
[X]
⎛ ⎞
+ ⎝ [Y]
·
⎠
[Y]
⎛ ⎞
+ ⎝ [Y]
·
⎠
[Y]
⎛ ⎞
+ ⎝ [Y]
·
⎠
[Y]
0 (3.206)
≥ 0 (3.207)
= 2 []
− 2 1 3 [] 2
− 1 (3.208)
4 4
2
c) Belousov-Zhabotinsky reaction
Oxidation of malonic acid to CO 2 by bromate, catalyzed by cerium ions in acidic solution:
2BrO − 3 +3CH 2 (COOH) 2
+2H + −→ 2BrCH(COOH) 2
+3CO 2 +4H 2 O (3.209)
The reaction is probed by addition of the redox indicator ferroin/ferriin: The color varies
between red and blue depending on the concentrations of Ce 4+ and Ce 3+