concentration is low, the intermediate-producing pathway is favored; and when
the intermediate’s concentration is high, the intermediate-consuming pathway
is favored. Eventually, the reaction comes to equilibrium as final products are
formed (ultimately in accordance with thermodynamics).
In 1910–1920, the American biophysicist Alfred Lotka* proposed two sim-
ple mechanisms for oscillating reactions. Using hypothetical reactants and
products, the two mechanisms are as follows:
A→B
B C→2C (mechanism 1)
C→DA B→2B
BC →2C (mechanism 2)
C→D
In both cases, the overall reaction is simply A →D, with B and C as interme-
diate species. Each individual step in a mechanism has a rate law based on the
stoichiometry of the individual elementary process. Lotka showed that if [A]
is assumed to be constant (that is, it is present in a large excess), the differen-
tial equations that relate the concentrations of A, B, C, and D have mathemat-
ical solutions that predict oscillations in the concentrations of intermediates B
and C if the rate constants have the appropriate values. In mechanism 1, [B]
and [C] follow damped oscillations, and for mechanism 2 the intermediate
concentrations oscillate more evenly. Figure 20.21 shows the concentration be-
haviors of the intermediates versus time.
At the time of Lotka’s work, no chemical reaction was known to follow his
two mechanisms. In 1921, W. C. Bray reported an oscillation in a liquid-phase
reaction between hydrogen peroxide and potassium iodate (H 2 O 2 KIO 3 ), but
this report was treated with some skepticism. In 1951, the Russian biophysicist
Boris Belousov discovered another example of an oscillating reaction, which
was studied in detail by his fellow Russian biophysicist Anatol M. Zhabotinsky.
Despite initial resistance to the thought of oscillating reactions (Belousov’s ini-
tial work wasn’t published until 1959, and Zhabotinsky’s detailed studies
weren’t done until the mid 1960s), the Belousov-Zhabotinsky(or BZ) reaction
is now the best-known example of an oscillating chemical reaction.
The reaction is actually a group of reactions that have some common in-
gredients. Generally, a BZ reaction is the metal-ion-catalyzed oxidation of cer-
tain carboxylic acids by bromate (BrO 3 ) ions. A common catalyst is the
cerium(IV) ion, Ce^4 . One example of an overall reaction is
Ce^4
2HBrO 3 (aq) 3 malonic acid →
2 bromomalonic acid 4H 2 O 3CO 2 (g) (20.69)
The steps in the mechanism of the BZ reaction are complex (an 18-step mech-
anism has been proposed!), but the two pathways can be summarized as
BrO 3 Br→HBrO 2 Br→products (path I)
BrO 3 HBrO 2 →HBrO 2 →Brproducts (path II)718 CHAPTER 20 Kinetics
*Lotka’s models have also been applied to the understanding of animal populations in
ecology. Although animals aren’t molecules, the “kinetics” of their populations follows
similar differential equations!Time[B] [C][B][C]Concentration(a)
TimeConcentration(b)
Figure 20.21 (a) In Lotka’s first mechanism
for an oscillating reaction, the concentrations of
intermediates B and C oscillate in a damped fash-
ion (that is, the oscillations get less and less ex-
treme). (b) In Lotka’s second mechanism, the
concentrations of the intermediates oscillate in a
more regular fashion—at least in the short term.