J . Phys. Chem. 1989, 93, 210-214
270
Controverslal Interpretations of Ag' Perturbation of the Belousov-Zhabotinsky Reaction Richard M. Noyes,* Department of Chemistry, University of Oregon, Eugene, Oregon 97403
Richard J. Field,* Department of Chemistry, University of Montana, Missoula, Montana 5981 2
H. D. Forsterling, Fachbereich Physikalische Chemie, Philipps-Universitat Marburg, 0 - 3 5 5 0 MarburglLahn, Federal Republic of Germany
Endre Koros, Institute of Inorganic and Analytical Chemistry, L. Eotvos University, H- 1443 Budapest, Hungary
and Peter Ruoff Department of Chemistry, Rogaland University Center, Ullandhaug, N-4004 Stavanger, Norway (Received: June 14, 1988; I n Final Form: October 6, 1988)
Addition of silver ion to a Belousov-Zhabotinsky (BZ) system affects the rate at which bromide ion is being removed and thereby influences the observed processes. Noszticzius and McCormick on the basis of potentiometric measurements have concluded that the precipitation of AgBr can be described with a second-orderrate constant of about lo9 M-' s-', corresponding to virtual diffusion control. Varga and Kcirb and also Ruoff have used more indirect methods and modeling computations to conclude that the rate constant for the same process is approximately lo4 M-I s-'. The resulting disagreement may be resolved by the spectrophotometric studies of the precipitation by Kshirsagar, Field, and Gycirgyi. These authors conclude that Ag+ and Br- react very rapidly homogeneously to form complex ions and small oligomers of AgBr; these reactions rapidly reduce the activities of silver and of bromide ions as shown by the potentiometric studies. However, bromide ion in or from these complexes is 'still available for reaction with HBrOz in the BZ reaction. The subsequent precipitation of AgBr on the surface of growing crystals is a much slower process consistent with the other measurements. This resolution of the disagreement is supported by model computations that indicate that silver-induced oscillationsare still controlled by free or lightly complexed bromide ion much as are other Belousov-Zhabotinsky oscillations.
I. Introduction The mechanism of the oscillatory Belousov-Zhabotinsky (BZ) reaction is normally considered to be based on switching between two sets of component reactions, one involving radical chemistry and the other involving nonradical chemistry. The concentration of Br- determines which process is dominant, and BZ oscillations are thus referred to as bromidscontrolled. That control is effected by influencing the relative net rates of processes 0 2 and 0 3 , which Br- + HBr02 + H+ 2HOBr (02)
-
Br03-
+ H B r 0 2 + H+ s 2Br0,' + H 2 0
(03)
compete for HBr02. Reaction 0 2 (high [Br-1) leads to dominance by the set of nonradical reactions, and reaction 0 3 (low [Br-1) leads to dominance by radical reactions. Reagents such as Ag+ or T13+which affect the activity of Br- can be expected to influence the relative importance of the two sets of processes. That influence may be quite complex. In 1979, Noszticzius' reported that addition of silver ion to an oscillatory BZ system induced a different kind of oscillation in the potential of a platinum electrode. These induced oscillations tended to be of smaller amplitude and of higher frequency than those in the absence of silver ion. N o significant simultaneous oscillatidns were observed in the potential of an electrode specific to bromide ion, and the potential of such an electrode indicated a bromide concentration that was less than the concentration of silver ion. Noszticzius interpreted his observations to mean that the oscillations induced by silver ion were not controlled by bromide ion in the way other BZ oscillations are controlled. That inter-
pretation was disputed by Ruoff and by Koros in references cited below. The differences of opinion subsequently expressed have been much affected by the question as to the rate of the reaction often designated as 0 6 : Ag'
(06) Thus Noszticzius has maintained that the appropriate rate constant for this reaction from left to right is of the order of lo9 M-'s-', while Ruoff and Koros have alleged that a value of the order of io4 is more appropriate. The present paper attempts to resolve this controversy by examining the existing experimental evidence and the interpretations that have been applied to that evidence. As is so often the case in such situations, the protagonists appear to be reasonably well agreed with regard to the experimental facts, while the disagreements revolve around how those facts should be interpreted. 11. Direct Observations of AgBr Precipitation
Basic Principles. If Ag+ is added to a solution of Br- or vice versa, there will certainly be local regions in which the ion product [Ag'] [Br-] exceeds the equilibrium solubility product of AgBr at least for brief periods. If the system is well stirred and if the ion product exceeds the solubility product by several orders of magnitude, a precipitate will be observed to form rapidly and the ion product in the solution will decrease toward the solubility product. If a subscript eq denotes the ultimate equilibrium concentration of an ion, then vo6, the rate of approach to the equilibrium, can probably be described at sufficiently long times by an expression of the form of eq 1. "06
(1) Noszticzius, 2.J . Am. Chem. SOC.1979,101, 3660-3663.
+ Br- @ AgBr(s)
= k06{[Ag'l [Br-l - [Ag+lq[Br-lq~
(1)
The value of ko6 may be a complicated function of the surface
Belousov-Zhabotinsky Reaction: Ag+ Perturbation area of the solid phase, of the aging of that surface since it was formed, and perhaps even of which ion is in excess for the system being considered. Even though there is general agreement concerning the form to be anticipated for eq 1, a reliable evaluation of a numerical value for koa is very difficult with currently available technology. All of the values that have been claimed in the present controversy either were based on systems far removed from equilibrium or else were derived from model calculations on systems in which reactions other than 0 6 were taking place. The measurements directly applicable have been either potentiometric or spectrophotometric. Studies with Bromide-Specific Electrodes. Electrodes referred to as specific to bromide ion involve membranes impregnated with silver bromide and silver sulfide. If the solution in which the electrode is placed contains an excess of either Ag+ or Br-, the concentration of this excess ion in the pores of the membrane will be close to that in the bulk solution, while the concentration of the other ion in the pore will be such that the product of concentrations is equal to the equilibrium solubility product, Ksp,of AgBr. If the concentration in the bulk solution of the ion in excess is significantly more than K,p1/2,it can be calculated from the potential of the electrode by use of the customary Nernst equation. If the concentration of the excess ion is a factor of 5 or less greater than Kspllz,the application of the Nernst equation will have to be modified.2 Although the concentration in the bulk solution of the ion in excess can be measured very well from the potential of the ionspecific electrode, the concentration of the ion in deficiency is not directly related to that potential. If the bulk solution is indeed saturated with AgBr, then the concentration of the deficient ion can be calculated with the use of Kp If the bulk solution is underor supersaturated, the potential of the electrode will not provide any information on that fact. A further complication for dynamic interpretation is that diffusive penetration of the pores of the electrode membrane is a comparatively slow process. We therefore agree that the electrode specific to bromide ion will be so slow to establish its potential that the rate of change of that potential may not provide useful indication concerning the value of ko6 in eq 1. A good discussion of such electrodes and of their times of response has been prepared by Pungor and T t ~ t h . ~ Studies with Silver Electrodes. The potential of a bare silver wire will respond much more rapidly to changes in [Ag+] than will that of an ion-specific electrode. Noszticzius and McCormiclP (NM) show the trace for the potential of a silver electrode when bromide ion and then silver ion were added to a rapidly stirred solution that initially contained a known concentration of silver ion. Each addition was such that the added ion attained an excess concentration of about 5 X lo" M. Figure 1 in their paperS shows that immediately after each addition the potential changed at a rate of the order of 600 mV s-l. The authors point out that their measurements indicate that Ag+ and Br- ions must react initially with a rate constant of at least lo6 M-' s-l. Furthermore, any effects of slow mixing rate or sluggish electrode response would have rendered that figure a minimum value for the rate constant associated with the initial reaction. In some unpublished observations, Ruoff and Vestvik6 (RV) repeated the experiments of Noszticzius and McCormick and also observed an extremely rapid response when the silver electrode was immersed to about 5 cm in the vortex created by the rapid stirring. The response was much slower when the electrode was only immersed about 5 mm into the solution, and RV first asserted that this was the correct response to relate to ka. An alternative (2) Ganapathisubramanian, N.; Noyes, R. M. J . Phys. Chem. 1982,86, 32 17-3222. (3) Pungor, E.; Tbth, K. In Ion-Selective Electrodes in Analytical Chemistry; Freiser, H., Ed.; Plenum Press: New York, 1978; Vol. I, pp 143-210. (4) Noszticzius, 2.;McCormick, W. D. J. Phys. Chem. 1988,92,374-376. ( 5 ) The arrows designated a and b in their figure must obviously be opposite to the directions shown. (6) Ruoff, P.; Vestvik, J. J . Phys. Chem., in press.
The Journal of Physical Chemistry, Vol. 93, No. I, 1989 271 interpretation is that the slow response of the short electrode was associated with less efficient mixing in the surface layer than in the vortex. The evidence presented by Noszticzius and McCormick" (NM) appears to be unequivocal that when silver and bromide ions are rapidly mixed the activity of free silver ion decreases in a reaction whose second-order rate constant must be orders of magnitude greater than the lo4 M-' s-l assigned to koa by Ruoff. However, the ko6 in eq 1 is intended to describe the final approach to equilibrium, while the koa calculated by N M is based on the initial change of potential when free ions are mixed. Their potentiometric measurements are equivocal regarding the ultimate approach to equilibrium. After the first few tenths of a second, the curves in Figure 1 of ref 4 exhibit some irregular steps that are very likely artifacts associated with the finite rate of mixing into a volume of 50 cm3. The curves then exhibit slow but significant drifts that seem to persist for at least as long as the times of several seconds shown in the figure. Those drifts make it clear that dynamic behavior of the electrode potential cannot be described by means of a single-exponential decay during the entire time from initial addition of an ion to equilibrium with the precipitate. It is not clear which features of this Figure 1 are relevant to evaluation of koa as defined in eq 1. Spectrophotometric Studies. An alternative approach to obtaining information about ko6 is to follow the precipitation spectrophotometrically. This approach has been employed by Kshirsagar, Field, and Gyorgyi.' The behavior is complex, but an initial very fast and perhaps diffusion-controlled process leads to formation of complex ions or (AgBr), oligomers, where n is a small integer. These small oligomers then relax to larger ones on a time scale of the order of 10 s, and this relaxation corresponds to the behavior anticipated from the ka favored by Ruoff. When the initial ion product does not greatly exceed the equilibrium solubility product and when the two ions are in approximately equal concentrations, then the formation of a sol of AgBr may take place on a time scale of the order of 10 min. Conclusions about Direct Precipitation. There does not seem to be any reason to question the validity of any of the above experimental observations of direct precipitation of AgBr. The very different interpretations with regard to the value of k a appear to relate to the stage of the precipitation being studied and the rate at which mixing of the solutions is attained. The picture that emerges from the studies of Kshirsagar et a1.7 is that when solutions are mixed there is an extremely rapid homogeneous reaction that reduces the initial activity of silver ion as revealed also by the electrochemical observations of Noszticzius and McCormick.4 The subsequent growth of solid phase apparently involves a much smaller rate constant, and it is this approach to equilibrium that is appropriate to the koa as defined in eq 1. During the silverion-induced oscillations reported by Noszticzius,l a considerable precipitate of AgBr is already present in the system, and efforts at modeling can probably best use the value of kO6 appropriate to the approach to equilibrium. However, it is doubtful that any model computations based on a single value of ko6 can describe the full complexity that may occur. Leubriers has recently discussed some of the factors associated with precipitation of AgBr crystals in connection with the manufacture of photographic film. That discussion makes it clear that it will be impossible to assign a value of ko6 valid under all circumstances. 111. Indirect Studies of AgBr Precipitation Model Computations of Silver-Induced Oscillations. Nosz-
ticzius' interpreted his original experimental observations to mean that Belousov-Zhabotinsky oscillations in the presence of silver ion were not controlled by bromide ion. This contention was challenged by R ~ o f f , ~who . ' ~used computations to generate os(7) Kshirsagar, G.;Field, R. J.; GyBrgyi, L. J. Phys. Chem. 1988, 92, 2472-2419. (8) Leubner, I. H. J . Phys. Chem. 1987, 91, 6069-6073. (9) Ruoff, P. Chem. Phys. Lett. 1982, 92, 239-244. (10) Ruoff, P. 2.Naturforsch, Sect. A . 1983, 38a, 914-919.
Noyes et al.
272 The Journal of Physical Chemistry, Vol. 93, No. 1, 1989
cillations of approximately the observed frequency and amplitude while assuming that ko6 was about lo4 M-' s-l. Those initial computations treated reaction 0 6 as irreversible, but subsequent computations by Ruoff and Schwitters" have reached very similar conclusions with reversibility included. Noszticzius has not yet attempted to counter the Ruoff claims by making computations with the large koa that he believes is more appropriate. Competitive Formation of AgBr and BrMA. Varga and Korijs'2 attempted to estimate koa in eq 1 by measurements on a Belousov-Zhabotinsky malonic acid system perturbed by addition of a known amount of silver ion. In the absence of silver, as bromate is consumed all of the bromine appears as bromomalonic acid, BrMA, or as other brominated organic compounds. In the presence of silver ion the rate of reduction of bromate, 4[BrO
