J . Phys. Chem. 1986, 90, 5407-5409 presented here on this work is not yet clear. New experimental r e s ~ l t s ~on* ,the ~ ~organic chemistry of the BZ reaction also need to be fitted quantitatively into the framework presented here.
Conclusion A revised set of rate constants for the oxybromine chemistry portion of the Belousov-Zhabotinskii reaction has been developed at 20 “ C in about 1 M H2S04. The suggested values are based on new experiments, recently reported direct rate constant determinations, and a critical reevaluation of previous results. The values AGfo (HBr02) z -0.4 kJ/mol and pK, (HBr02) GZ 4.9 are deduced and used in the generation of the suggested rate constants. A major conclusion is that HBr02 is considerably more stable than previously thought, causing the reaction H B r 0 2 Br0,- + H+
+
( 5 8 ) Forsterling, H.-D.; Idstein, H.; Pachl, R.; Schreiber, H.Z . Naturforsch. A: Phys., Phys. Chem., Kosmophys. 1984, 39A, 993. (59) Brusa, M. A.; Perissinotti, L. J.; Colussi, A. J. J . Phys. Chem. 1985, 89, 1572.
+
==2Br02’ H 2 0 to be significantly reversible under the conditions of the BZ reaction. The suggested rate constants are able to simulate well data on [Ce(IV)] and [Br02’] during the overall reaction of Ce(II1) with bromate even when the reactant concentrations are varied by factors up to 500. The suggested rate constants are very significantly smaller than the FKN values and quite close to the Tyson “Lo” values. Appropriate propagation of the new rate constants into the Oregonator model is discussed. Acknowledgment. This work was partially supported by the National Science Foundation under Grants CHE80-23755 and CHE85 18879, by the Deutsche Forschungsgemeinschaft, by the Stiftung Volkswagenwerk, and by the Fonds der Chemischen Industrie. Most useful discussions with F. Ariese, Z. NagyUngvBrai, Z. Noszticzius, and J. J. Tyson are acknowledged. R.J.F. thanks Professor F. W. Schneider of the Institut fur Physikalische Chemie der Universitat Wurzburg for discussions and hospitality. Registry No. Ce, 7440-45-1; BrOC, 15541-45-4; HBrO,, 37691-27-3.
Comparison of the Field-Koros-Noyes and Field-Forsterllng Parameterizations of the Bromate-Cerous Reaction Richard M. Noyes Department of Chemistry, University of Oregon, Eugene, Oregon 97403 (Received: April 9, 1986)
In 1972, Field, Koros, and Noyes assigned all of the rate constants for the oxidation of cerous ion by bromate. The assignment was based on the minimum permissible number of independent observations, and there was no possibility to test for internal consistency. Field and Farsterling have now developed an alternative assignment based on more recent experimental observations. Numerous tests indicate that the FF assignment is internally consistent to within about a factor of 2, but several rate constants in the FF set differ from the FKN set by factors of up to lo4. These discrepancies have led some people to question the validity of the FKN mechanism itself. A reexamination of the original arguments notes that FKN used the Pauling model for strength of oxyacids in order to assign a pK to bromous acid different by almost 3 units from the value selected by FF. When the FKN set is recalculated with the use of the new pK, the deviations from the FF set are not important. Apparently all of the experimental observations used by FKN were valid and consistent with subsequent measurements. The bromatecerous component of the oscillatory Belousov-Zhabotinsky reaction now appears to be well understood.
Introduction In 1972, Field, Koros, and Noyes’ (FKN) proposed a detailed mechanism for the dramatic Belousov-Zhabotinsky oscillations. Although much of the explanation had to be qualitative, FKN developed an involved argument that permitted them to assign numerical values to all of the kinetic parameters explaining the oxidation of cerous ion by bromate. This oxidation exhibits unusal features such as an induction period followed by very rapid autocatalysis, and it has even been used to generate sustained oscillations in a flow r e a ~ t o r . ~ - ~ Although subsequent computations simulated many of these features, evidence began to accumulate suggesting that some of the FKN rate constants might be in error by several orders of magnitude. Such large discrepancies even led some people to question the validity of the FKN mechanism itself. Tyson5 then made a careful analysis that showed that many different parameter assignments might be equally effective at (1) Field, R. J.; Koros, E.; Noyes, R. M. J. Am. Chem. SOC.1972, 94, 8649-8664. (2) Bar-Eli, K. In Nonlinear Phenomena in Chemical Dynamics; Vidal, C., Pacault, A., Eds.; Springer-Verlag: Berlin, 1981; Springer Series in Synergetics, Vol. 12, pp 228-239. (3) Orbiin, M.; De Kepper, P.;Epstein, I. R. J. Am. Chem. Soc. 1982,104, 2657-2658. (4) Geiseler, W. Ber. Bunsen-Ges. Pkys. Chem. 1982, 86, 721-724. (5) Tyson, J. J. In Oscillations and Traveling Waues in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley: New York, 1985; pp 93-144.
0022-3654/86/2090-5407$01 Sb/O
TABLE I: Rate Constants Exhibiting Major Discrepancies between FKN and FF Assignments constant FKN value FF Value k2/(M-, s-I) L3/(M-I s-l) k4/(M-’ s-l) k_4/(M-, S-’) / c ~ / ( M -SKI) ~ k6/(M-2 S-I) k+,/(M-’ 5-l)
2 x 109 1 x 104 4 x 107 2 x 10-10 1 x 104 6.5 X los 2.4 X 10’
3 x 106 3.2 3 x 103 1 x 10-8 42 ’ 8 x 104 8.9 x 103
interpreting most of the observations as long as certain key ratios of rate constants were maintained. Field and Forsterling6 (FF) have now analyzed the accumulated experimental information and have developed a revised set of rate constants for 1 M H2S04medium at 20 OC. They believe that these rate constants can simulate all known behavior in this system and that any further refinements probably will not need to be by more than a factor of about 2. Because of the interest in this system and because of the doubts caused by the large discrepancies in the values claimed for some rate constants, it may be useful to summarize the arguments leading to the original FKN set. The reexamination validates all of those arguments and the experimental observations on which (6) Field, R. J.; Forsterling, H.-D. J. Phys. Chem., preceding paper in this issue.
0 1986 American Chemical Society
5408 The Journal of Physical Chemistry, Vol. 90, No. 21 1986
Noyes
~
they are based; almost all of the discrepancies can be traced to a mistaken inferential assignment of the ionization constant of bromous acid.
TABLE I 1 Ratios of FKN and FF Quantities Expected To Differ by Factors of 800
Basis of the FKN Assignments FKN proposed that the oxidation of cerium(II1) by bromate could be explained by means of the six7 steps in Scheme I. SCHEME I
value/(800 X FF value) 0.8 0.3 3.9
+ HOBr + H + F? Br, + H 2 0 Br- + HBrOz + H + F? 2HOBr Br- + BrO,- + 2H+ = HOBr + HBrO, HBrO, + HBrO, F? HOBr + BrO,- + H+ HBrOZ + BrO,- + H+ 2BrOZ' + H,O Ce(II1) + BrOz' + H+ F? Ce(1V) + HBr0, Br-
F?
(R2) (R4) (R5) (R6)
+ Br2 9 BrO,- + *BrBr
+ 4Ce(III) + 5H+ s HOBr + 4Ce(IV)+
2H20
1.5 X 10" 3.2 1.7 55 5.5 x 10' 42 1 x 10-6 9 x 103 0.1 1
(R3)
in equilibrium. The rather involved kinetics indicated that step R5 was rate determing for reaction A, and the data then evaluated kS[HBrOzlW,where [HBrO& was in simultaneous equilibrium with [BrO,-] and [Br2]. v. A value of k-, could be extracted from the pulse radiolytic studies of bromine oxides by Buxton and Dainton.I3 The independent availability of expressions involving kS and k-* generated necessary information about the free energy of formation of Br0;. vi. Thompson14 studied the kinetics of reaction B and found that at sufficiently high concentrations of cerous ion the rate was Br03-
FF value 3 x 106
(R1)
If this mechanism were to be made the basis of model computations, it would be necessary to assign numerical values to all forward and reverse rate constants. At that time, free energies of formation were available for all species appearing in Scheme I except HBr0, and Br0,'. If a rate constant in one direction were also measured for each step, a minimum of eight independent pieces of dynamic or thermodynamic information would be needed: i. The values of k, and k-, for the hydrolysis of bromine were available from the classic study of Eigen and K ~ s t i n . ~ ii. The value of k-, was estimated from the study by Betts and MacKenzie'O of the disproportionation of hypobromous acid. Thermodynamic arguments then evaluated k2[HBr02],and k2 could be calculated if the free energy formation of H B r 0 2 were known. iii. The value of k3 was estimated from the study by Bray and Liebhafsky" of the reduction of bromate by bromide. Thermodynamic arguments then evaluated k3[HBrO,] . iv. Betts and MacKenzieI2 also studied the rate of isotopicexchange reaction (A) when all bromine-containing species were *BrO,-
FKN
(B)
zero order in [Ce(III)]. Then step R5 was rate determining for reaction B and k5,/k4 could be evaluated by combining data on reactions A and B. vii. The data of Thompson14 did not permit an evaluation of k,, and this parameter was unassigned in the original FKN paper, although a minimum value could have been calculated. Edelson et aLi5subsequently used the best information available to obtain (7) The oxidation of BrO,' by cerium(1V) was originally included as a seventh step in order to explain the slowing of the rate long before equilibrium was approached. Subsequent consideration* has revealed that this (R7)step is not necessary to explain the observations and that it must be too slow to be of significance to the dynamics of the overall system. (8) Barkin, S . ; Bixon, M.; Noyes, R. M.; Bar-Eli, K. Int. J . Chem. Kiner. 1977, 11, 841-862. (9)Eigen, M.; Kustin, K. J . A m . Chem. SOC.1962,84, 1355. (10) Betts, R.H.; MacKenzie, A. N. Can. J. Chem. 1951,29, 666-677. (11) Bray, W.C.;Liebhafsky, H. A. J. Am. Chem. SOC.1935,57,51-56. (12) Betts, R. H.; MacKenzie, A. N. Can. J . Chem. 1951,29, 655-665. (13) Buxton, G.V.; Dainton, F. S. Proc. R. Soc., London, A 1968,A304, 427-439. (14) Thompson, R. C. J. Am. Chem. SOC.1971, 93, 7315. (15) Edelson, D.;Field, R.J.; Noyes, R.M. Inr. J. Chem. Kine?. 1975,7, 417-432.
3.5 0.14 1 .o
0.3 0.6 3.3 0.4
a preliminary estimate of k,, and that value is included in what is now called the FKN set of rate constants. viii. The above measurements provided all six of the necessary pieces of dynamic information and one of the two pieces of thermodynamic information. The keystone to the arch was the free energy of formation of HBrO,. Lee and Lister], had estimated the equilibrium constant of reaction C by measuring BrO,-
+ Br- s Br02- + BrO-
(C)
forward and reverse rates in strongly alkaline solution; this information generated AGfo for BrO,-. The only missing piece of the puzzle was then the equilibrium constant for ionization reaction D. Unfortunately this ionization HBr0, s Br02-
+ H+
(D) constant can not be measured by conventional methods because solutions of HBrO, rapidly disproportionate by step R4. FKN failed to discover a paper by Massagli et al.I7 that suggested reaction D had a pK of about 6. The argument was based on the pH region in which the order of the bromite decomposition reaction changed between 1 and 2. Massagli et al. were apparently looking at the competition of steps R2 and R4 as a function of pH. The work could not have been regarded as a pK measurement, but it might have given pause to the FKN decision to select a much smaller pK. That decision was based on an argument by PaulingI8 that an oxyacid of empirical formula HXO, should have a pK of about 2. Information was then in hand to derive the entire set of rate constants now known as FKN. It was a tightly reasoned argument with precisely the minimum number of pieces of independent information necessary to evaluate the desired parameters. There were no redundancies and no possible tests for internal consistency. Any mistake in logic or in interpretation of experiment could undermine the whole structure. Table I lists those FKN rate constants that differ by more than a factor of about 3 from the new F F assignments. Anybody looking at the major discrepancies in Table I could reasonably question whether FKN had even selected a viable mechanism on which to base their superstructure. Resolution of the Discrepancies F F have now built an alternative structure using many independent experimental studies that were not available in 1972. Numerous redundancies can be used to test for internal consistency. The structure seems to be sound. The best estimate for the pK of HBrO, is 4.9. Therefore, anywhere that the FKN treatment generates a k,[HBrO,] value in a rate expression, that k, should differ by a factor of about 800 from the same k, derived by the methods of FF. Table I1 shows how ratios of rate and equilibrium constants in the two parameter sets differ from the amounts expected be(16) Lee, C.L.; Lister, M. W. Can. J. Chem. 1971,49, 2822-2826. (17)Massagli, A,; Indeli, A,; Pergola, F. Inorg. Chim. Acta 1970, 4 , 593-596. (18)Pauling, L. General Chemirtry, 3rd ed.; W. H. Freeman: San Francisco, 1970;p 501,
Parameterizations of the Bromate-Cerous Reaction TABLE III: pK Values of HXOz Acids
acid
DK
HC102 HNOZ HC02H
2.0 3.3 3.7
CH3COzH
4.7
cause of the 2.9 pK unit difference in the assumed strength of HBrO,. The smoothing is dramatic with the biggest deviation from unity the factor of 7 in k4’I2. It was the independent estimate of this rate c ~ n s t a n t that ’ ~ first cast serious doubt on the FKN set of parameters. Of course even this pK correction does not bring the F K N set into exact concordance with the improved FF set, but the discrepancies are now of a magnitude to be anticipated from 14 years of new data on these systems. Apparently there were no other serious mistakes that impacted the complicated reasoning leading to the F K N mechanism and assignments. It is appropriate to wonder about reasons for the apparent failure of the Pauling’* rule. Pauling proposed that oxyacids of empirical formula H X 0 2 or H 2 Y 0 3will all have about the same pK for ionization of the first proton. A number of H 2 Y 0 3acids do indeed have pK values of about 2. Table I11 lists the available data for HXO, acids. The range of values suggests that acids with smaller total numbers of oxygens are more sensitive to properties like electronegativity and polarizability of the central atom. Consistent with this interpretation is the observation that pK values of HOZ range from 7.5 for Z = C1 to 11.O for Z I with 8.7 for Z = Br. It is not easy to rationalize why the pK of HBrO, should be as large as 4.9, but this is a situation where it is well to remember that chemistry is ultimately an experimental rather than a theoretical science!
Discussion The present paradigm of mechanistic chemistry is the postulate that all chemical change, no matter how complicated, is the consequence of elementary processes, each of which takes place in a single step with net flux in the direction determined by thermodynamics. Failure of observations to conform to predictions for a complex mechanism is regarded as evidence the important steps of the mechanism have not been properly identified. The steps in Scheme I are not truly elementary but are pseudoelementary in that they assume proton transfers between oxygens are equilibrated on a time scale short compared to the scales in Scheme I. Step R5 also assumes the species BrO,’ and Br204 are in rapid equlibrium. As has been minted out, the FKN model was develomd without any redundandies that might have permitted tests for internal consistency. As redundancies did develop, inconsistencieslike those in Table 1 caused some persons to doubt even the validity Of the basic mechanism. Table 11shows that a reassignment Of a single ionization constant that had not even been measured experimentally was enough to reduce those discrepancies sufficiently to provide an impressive confirmation of that same mechanism. (19) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J . Phys. Chem. 1983, 87, 510-524.
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 5409 Field and Forsterling6 have now examined the internal consistencies of the many redundancies that new data have introduced. The remaining inconsistencies are of the order of a factor of 2 or less instead of powers of 10. It is probably unreasonable to expect much better consistency without access to extensive activity coefficient data which are presently unavailable. Although it is early to say, we anticipate that the F F constants will simulate most observed behavior at least as well as the FKN ones did. As Tyson5 has pointed out, occurrence of oscillations is most dependent upon rate constant ratios rather than absolute values. All simulations are in acidic solutions where bromite is completely protonated whether pK is 2.0 or 4.9. Regardless of which set is used, [HBr02] will always be small compared to most other species. FF suggest the change of rate constants will have a positive effect on the modeling of traveling waves. The new rate constants may have more effect on the Oregonator” approximation. As F F point out, the increased reversibility of step R5 will impact on the treatment of step 0 3 , which was always the least satisfactory of the first four steps of the irreversible Oregonator. The new values also impact approximations for modeling the Oregonator with only two variables. I have preferred to use Y and Z (Br- and Ce(IV)), while TysonZ’has preferred X and Z (HBr02 and Ce(1V)). The enhanced thermodynamic stability of HBrOz may better justify the Tyson parameterization. There may also be impacts on studies unrelated to the Belousov-Zhabotinsky reaction. Thus, Thompsonz2 has previously complained that a value of lo9 M-2 s-I for k2 was seriously out of line compared to other known rates of oxygen-atom transfer. The FF constants bring k, more into line. It is gratifying in any area of science when improved internal consistency accompanies increased information. The situation in mechanistic chemistry today is similar to that a century ago when chemists were realizing it was meaningful to discuss the three-dimensional structures of organic molecules. The arguments were involved and indirect, but an internally consistent set of structures evolved. When diffraction techniques were developed decades later, there were few surprises as they confirmed conclusions that were already generally accepted. We can hope the development of mechanistic chemistry will be similar. As spectroscopic or other methods become sensitive enough for quantitative measurements on intermediates at conM, we can undertake more exacting centrations as small as tests than are presently available. Until such a time, we must rely on indirect methods which have already shown that it is possible to understand systems even as complicated as the Belousov-Zhabotinsky reaction.
Acknowledgment. This work was supported in part by a grant from the National Science Foundation. I am indebted to Professor Field for an advance copy of the manuscript of ref 6. This is No. 71 in the series “Chemical Oscillations and Instabilities”. No. 70 is Noyes, R. M., J. Chem. SOC.,Faraday Trans. 1, in press. Registry No. Br03-,15541-45-4; Ce, 7440-45-1. (20) Field, R. J.; Noyes, R. M. J . Chem. Phys. 1974, 60, 1877-1884. (21) Tyson, J. J. J . Phys. Chem. 1982, 86, 3006-3012. (22) Thompson, R. C., personal communication.
