CHEM3210: Chemical Kinetics of Complex Systems
Professor S.K. Scott 
Lecture 4: Oscillations- the BZ reaction
4.1 Oscillations in batch reactors
Although the combined effects of the 2nd Law of Thermodynamics and the Principle of
Detailed Balance require that any thermodynamically-closed system must have a single
chemical equilibrium state, that chemical systems cannot oscillate about that equilibrium state
and, that the overall free energy of the system Gtot must decrease as a function of time, it is
still possible to observe oscillations in batch reactors.
Typically, such oscillations occur in the concentrations of intermediate species rather than in
those of the initial reactants or the final products. For all such systems, oscillatory behaviour
may be long- or short-lived, but it cannot last forever: oscillations in a closed system are a
strictly transient phenomenon and must eventually give way to a final, undamped approach to
the chemical equilibrium state.
The most widely studied solution-phase oscillatory reaction in batch systems is the BelousovZhabotinsky (BZ) reaction - named after its Russian discoverers. This system may oscillate in
a closed system for several hours undergoing hundreds of oscillations before these cease.
4.2 The BZ reaction
The BZ reaction involves the oxidation of an organic species such as citric or malonic acids
(malonic acid, MA = HO2CCH2CO2H) with a solution of acidified bromate (H+/BrO3) in the
presence of a 1-electron transfer redox catalyst. The redox catalyst can be, for instance, an
Fe2+/Fe3+ couple - the metal ion being appropriately complexed such that the reduction
potential is compatible with the bromate chemistry. Other catalysts systems include the
Ce3+/Ce4+ and Mn2+/Mn3+ couples.
We may represent the catalyst system generally as an Mred/Mox couple.
In many cases, the two oxidation states have different colours, allowing the change of
oxidation state to be observed visually. Complexation of Fe2+ with the 1,10-phenanthroline
ligand gives the species known as ferroin which as a red colour. The oxidised ferriin form is
blue. This complex is a model for biological molecules such as haemoglobin.
4.3 Oscillatory responses
Over a relatively wide range of initial reactant concentrations, the behaviour exhibited by the
BZ system has the following main characteristic features:
 there is an initial pre-oscillatory phase during which various intermediate species
concentrations build up (or decay);
 this is followed by an oscillatory phase during which oscillations in the concentrations of
several intermediate species are observed, typically with a period between oscillations of
1-2 minutes - this phase of the reaction may last for, perhaps, 2-3 hours allowing of the
order of 100 oscillations;
 finally, the oscillations cease and there is a monotonic evolution towards the final,
equilibrium state during the post-oscillatory phase.
In some situations, the final part of the oscillatory phase is accompanied by relatively
complex oscillatory responses, but for most of this period the oscillations have a relatively
simple form. Example experimental records from (a) a Pt-electrode and (b) a bromide-ion
specific electrode are reproduced below:
The Pt-electrode responds to the oxidation state of redox catalyst: in the diagram, a low
potential corresponds to the oxidised form and a high potential to the reduced form. From the
waveform from this electrode, we see that there is a sharp oxidation - which is accompanied
visually by a sharp redblue colour change - followed by a slower ‘recovery’ back to the
reduced state. Over the 14 oscillations shown in this trace, there is little observable variation
in either the amplitude or the period of the oscillation in this species.
The Br selective electrode responds primarily to the concentration of bromide ion (although
there is interference from HOBr when [Br] becomes very low). Bromide ion in an
intermediate in the BZ reaction and there is usually some non-zero initial concentration of
this species due to impurities in the bromate source.
The experimental record indicates a waveform for Brthat shows several distinct parts:
 there is a decrease in the bromide ion concentration between points A and B: this portion
of the trace is approximately linear, indicating an exponential decay in [Br] from its
maximum value (remember, the electrode potential E varies as the logarithm of the
concentration through the Nernst equation);
 there is then a sharp, large drop in the bromide ion concentration to a minimum value at C;
 there is recovery from C to D followed by a growth from D back to the maximum value A.
Oscillations are also found in the concentration of other intermediate species, in particular in
the concentration of bromous acid (HBrO2) and the brominated from of the organic species,
bromomalonic acid (BrMA).
4.4 FKN Mechanism of the BZ reaction
The fundamental features of the chemical mechanism underlying the oscillations in the BZ
system were determined by Field, Koros and Noyes at the University of Oregon. Their
mechanism can be introduced through a set of three component ‘processes’.
Process A: removal of inhibitor Br with steady state HBrO2
The important stoichiometric steps, with their empirical rate laws in this part of the reaction
are as follows:
(4.1)
(4.2)
BrO3 + Br + 2H+  HBrO2 + HOBr
HBrO2 + Br + H+  2HOBr
rate = k1[BrO3][Br][H+]2
rate = k2[HBrO2][Br][H+]
Both reactions remove bromide ion: the first produces HBrO2, the second removes it so this
species has the role of a ‘reactive intermediate’ within the overall process.
The overall stoichiometry of Process A is:
(A)
BrO3 + 2Br + 3H+  3 HOBr
Process B: autocatalysis in HBrO2 and oxidation of redox catalyst
The important stoichiometric steps, with their empirical rate laws in this part of the reaction
are as follows:
(4.3)
(4.4)
HBrO2 + BrO3 + H+  BrO2 + H2O
BrO2 + Mred + H+  HBrO2 + Mox
rate = k3[HBrO2][BrO3][H+]
fast reaction
The overall stoichiometric change in Process B is, then:
(B)
HBrO2 + BrO3 + 3H+ + 2Mred  2HBrO2 + 2Mox + H2O
corresponding to a net production of HBrO2 and the oxidation of the redox catalyst (and
hence a colour change). Typically reaction step (4.3) is the rate determining step for this
process, so the rate of increase of HBrO2 is proportional to the concentration of that species;
 d[ HBrO2 ]
  k3[ HBrO2 ][ BrO-3 ][ H + ]



 Pr ocessB
dt
i.e. Process B is autocatalytic in HBrO2. Once the reaction has switched from Process A to
Process B, this autocatalysis will lead to a rapid growth in HBrO2 and an accelerating
oxidation process - the colour change accompanying the transition from Mred to Mox will be
rapid.
Autocatalytic growth in HBrO2 is limited either by the consumption of the reduced form of
the redox catalyst or by the disproportionation reaction
(4.5)
2 HBrO2  BrO3 + HOBr + H+
Process C: clock resetting - reduction of redox catalyst and production of inhibitor Br
Process A removes the inhibitor Br and Process B sees the oxidation of the redox catalyst.
Between them, the form a classic clock reaction - the bromate-ferroin clock (see lecture 2)
which has an induction period controlled by Process A and a sharp red  blue colour change
at the end of this period through Process B.
To ‘reset’ this clock we need to re-establish the concentration of the inhibitor and to reduce
the redox catalyst back to its original state.
The exact mechanism through which this is achieved is still not fully understood, although
much progress has been made recently. In the present context, however, we may confine
ourselves to the simplified representation given by Field-Koros-Noyes. This imagines that
HOBr is converted to Br2 which is then able to brominate the organic species MA to produce
BrMA. At any given instant, the mixture will contain a mixture of MA and BrMA species,
both of which are capable of reacting with, and hence reducing, the oxidised form of the
redox catalyst. In the case of reaction with BrMA, some bromide ions may be liberated.
This chemistry may be represented as:
(C)
2 Mox + BrMA + MA  2 Mred + f Br + other products
The parameter f is known as the stoichiometric factor and represents the number of bromide
ions produced per two redox ions reduced.
The rates of production of Br and of reduction of Mox are given by
(4.6)
d [ M ox ] / dt   kc [ B][ M ox ] , d[ Br  ] / dt 
1
2
fkc [ B][ Mox ]
where [B] = [MA]+[BrMA] represents the total concentration of reducing organic species in
the system.
Because Process C is thought to occur through a chain mechanism involving species such as
the malonyl radical, it is possible to produce many bromide ions for each redox catalyst ion
reduced - so f can have values in excess of 2 - which might seem the obvious upper limit on
this parameter.
4.5 Kinetic analysis of FKN mechanism
Kinetics of Process A
Process A leads to the establishment of a steady-state in HBrO2 and a removal of bromide ion.
An analysis of this part of the reaction has already been given in lecture 2.1, where it was
shown that the steady-state concentration of HBrO2 is independent of the bromide ion
concentration, while the latter undergoes pseudo-first order reaction leading to exponential
decay (and, hence, a linear chenge in EBr as observed experimentally between points A and B
in the experimental record displayed earlier in this lecture.)
Bromide ion is considered to be an inhibitor as reaction (4.2) competes with the autocatalytic
process B for HBrO2. The rate of step (4.2) will exceed that for the autocatalysis (4.3) if [Br]
exceeds the critical bromide ion concentration
(4.7)
[Br]cr = k3[BrO3]/k2
(see lecture 2) at which the rates of the two steps become equal. Using typical values for the
rate coefficients and taking [BrO3] = 0.1 M, gives [Br]cr ~ ?  105 M
The time taken for [Br] to fall to [Br]cr comprises part of the oscillatory period.
The other significant contribution to the oscillatory period comes from the time for Process C
to reset the clock. During this part of the reaction, governed by rate law (4.6), there is
approximately a first-order reduction of the redox catalyst.
The nature of the response of the system depends crucially on the parameter f - the number of
bromide ions produced in Process C.
If f is large, a high concentration of inhibitor will be established and Process A will remain
dominant. The redox catalyst will remain predominantly in its reduced state - we expect to
observe a reduced steady state of high bromide ion concentration.
If f is small, little inhibitor is produced in the system and process B remains dominant. A
steady state with low bromide ion concentration and with the redox catalyst predominantly in
the oxidised state is observed.
Oscillations occur for values of the parameter f in between the above extremes (specifically if
f lies in the range ½ < 1 + 2). The system switches control between the three Processes
giving rise to periodic variations in the intermediate species concentrations.
4.6 Excitability
For conditions just outside those required for spontaneous oscillatory behaviour - for instance
for systems with f slightly larger than 1 + 2 - the BZ system shows a property known as
excitability.
An excitable system is characterised by (i) having a steady state; (ii) the steady state is stable
to small perturbations; (iii) if the perturbation exceeds some critical or threshold value, the
system responds by exhibiting an excitation event. For the BZ system, this excitation event is
the oxidation of the redox catalyst, corresponding to Process B with a local colour change in
the vicinity of the perturbation (initiation) site. This response is typically large compared to
the critical stimulus – so the system acts as a ‘nonlinear amplifier’ of the perturbing signal.
Following the excitation, the system eventually returns to the initial steady state and recovers
its excitability. There is, however, a finite period, the refractory period, between the
excitation and the recovery during which the system is unresponsive to further stimuli. These
basic characteristics are summarised in the figure below:
Excitability is a feature not just of the BZ system, but is found widely throughout physical
and, in particular, biological systems with important examples in nerve signal transmission
and co-ordinated muscle contraction.