J. Phys. Chem. 1983, 87, 1204-1208
1204
symmetrical Eckart potential and the potential parameters) as that used in the previous paper.12 The relative rate constants calculated for the reactions of H, D, and T atoms with ethane are given in Table 111. Though the previous calculation12suggests a remarkably large difference in the rate constants for the H, D, and T atoms, the revised calculation in this work shows only a slight difference among the rate constants of H, D, and T atoms. Therefore, it can be expected that T atoms react with ethane by the quantum-mechanical tunneling as easily as H atoms do. Willard et al. reported that the tunneling rate constant for abstraction from 3-methylpentane-d14 or 3-methylheptane-d,, is similar for H and D atoms.', The calculated kinetic isotope ratios (kGh/kczD,) for the reactions of H, D, and T atoms with ethane are also shown in Table IV. Though the previous calculation12suggests a large dependence (4.3 X lo2-3.0 X lo4) of the kinetic isotope ratios on the mass of the reactant, there is only a (18)Wang,
H.Y.;Willard, J. E. J. Phys. Chem. 1979, 83, 2585.
little difference (7.6 X 104-l.Z X lo5) in the ratios for the H, D, and T atoms in the revised calculation in this work. The experimental isotope effect ratio (3.5-6) for T atoms in the 0.2 mol % ethane is much smaller than the predicted ratio (1.2 X lo5) in Table IV. This difference may be due to the following two reasons. The first important reason is that the reaction of the thermal T atoms at 77 K may be diffusion controlled. Second, only part of the T atoms react with ethane as thermalized atoms. The experimental isotope effect represents the isotope effect on the hot T atom reaction in addition to the effect on the thermal T atom reaction. Acknowledgment. This work was done under the Collaboration Program between the Japan Atomic Energy Research Institute and Nagoya University. This work was partially supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science, and Culture. Registry No. T,15086-10-9;C2H6, 74-84-0;C2D6,1632-99-1; HT, 14885-60-0; DT, 14885-61-1.
Sensitivity Analysis of Proposed Mechanisms for the Briggs-Rauscher Oscillating Reaction Davld Edelson Be//Laboratories, Murray Hi//, New Jersey 07974 (Receive& September 2, 1982)
Recently proposed reaction mechanisms for the iodate-peroxide-manganese-malonic acid system (commonly referred to as the Briggs-Rauscher (BR) reaction) have been studied through computer simulation and sensitivity analysis. Both the static and CSTR (continuously stirred tank reactor with flow) cases have been studied. Rate constants and initial conditions most strongly affecting the period of oscillations have been identified, as well as the effect of flow rate in the CSTR. It is found that this reaction system is much more tightly coupled than the related Belousov-Zhabotinsky (BZ) oscillator. Comparisons of the calculated sensitivity of the period to initial concentrationswith available experimental data show discrepancies in both sign and order of magnitude. Suggestions are made regarding some likely deficiencies in the mechanism. In particular, the consideration of a-iodomalonic acid as a stable end product may not be tenable, especially since this species has never been successfully isolated from such a reaction, and there are serious doubts that it even exists. It seems possible that the reaction proceeds to more highly iodinated and oxidized organic species. The stoichiometry of the system might thus be sufficiently altered to account for some of the discrepancies.
Introduction The Briggs-Rauscher (BR) reaction was originally devised to provide a spectacular visual demonstration of the behavior of oscillating reacti0ns.l It is, in a sense, a combination of the iodine analogue of the well-known Belousov-Zhabotinsky (BZ) reaction2 with the BrayLeibhafsky (BL) r e a ~ t i o n . Both ~ these systems have an aqueous oxyhalogen chemistry in common. The BZ system couples this with a metal-ion redox system and provides a feedback mechanism through the halogenation and oxidation of an organic compound having a highly reactive hydrogen atom. The BL system involves the disproportionation of hydrogen peroxide to water and oxygen. One might therefore expect this more complex BR reaction to be explainable in terms of the two separate mechanisms (1) Briggs. T. S.;Rauscher, W. C. J . Chem. Educ. 1973, 50, 496. (2)Zhabotinsky, A. M.Dokl. Akad. Nauk. SSSR 1964,157, 392. (3)Bray, W. C. J . A m . Chem. SOC.1921,43, 1262. 0022-365418312087-1204$01.50/0
that complete with each other for the shared oxyhalogen chemistry. The BZ reaction has been extensively studied experimentally, and the BL system somewhat less so. Mechanistic analysis of the former has covered the gamut from thermochemical kinetic analysis of the possible component reaction steps? and the study of the mathematical properties of the differential equations of lumped analogue^,^ to the numerical simulation and analysis of detailed model mechanisms.&, Although some of the organic chemistry still remains to be resolved, it may be judged that our (4) Field, R. J.; Koros, E.; Noyes, R. M. J.Am. Chem. SOC.1972,94, 8649. (5)Field, R. J.; Noyes, R. M. J. Chem. Phys. 1974, 60, 1877. (6)Edelson, D.; Field, R. J.; Noyes, R. M. Int. J. Chem. Kinet. 1975, 7,417. (7)Edelson, D.;Noyes, R. M.; Field, R. J. Int. J. Chem Kinet. 1979, 11, 155. (8) Edelson, D. Int. J. Chem. Kinet. 1981, 13, 1175.
0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Briggs-Rauscher Oscillating Reaction
present understanding of this system is quite good. The situation for the BL reaction is rather less satisfactory; it may also require the inclusion of some heterogeneous phase transformations (precipitation of iodine; supersaturation and release of oxygen) whose kinetics are poorly understood.1° The BR system has attracted a good deal of recent attention and mechanistic proposals have begun to appear.11J2 As expected, these incorporate several features of its predecessors, while omitting much of the complexity of the organic chemistry as well as the heterogeneous components. Numerical simulation of subsets of these mechanisms has given oscillatory behavior, and their authors have therefore concluded that their proposals are a tenable explanation of the system. The study of these mechanisms is extended in this paper by the technique of sensitivity analysis.13 The extent to which these results are supported by experimental data is outlined. Qualitative conclusions are drawn with respect to remaining uncertainties in these mechanisms.
Mechanisms Furrow and Noyes14studied the reaction possibilities in the separate chemical systems that combine to make up the BR reaction, and include 36 of these, divided into 6 subgroups, in a proposed mechanism.l' Further arguments result in assigning many of these a zero rate constant, leaving only 14 in the final mechanism. This could be made to oscillate over a range of initial conditions, and the authors therefore accept it as a feasible mechanism. De Kepper and Epstein12studied a similar mechanism in the context of a continuously-stirred tank reactor (CSTR) in which spent reaction mixture was continuously replaced by fresh solution at the initial concentrations. The system is thus characterized by an additional parameter, the flow rate, or its inverse, the residence time. Furrow15 used his previous mechanism to study a BR system in which a-methylmalonic acid was used as the organic reactant, which supposedly obviated complexities that could arise from the reaction of the second a-hydrogen in malonic acid. The rate constants of the organic reactions were appropriately modified, but the rest of the mechanism remains the same. These three mechanisms were studied as presented by their authors; the reactions are essentially the same, and they differ only in the assignment of rate constants. The sets of reactions are given in Table I, and the initial conditions in Table 11. A very fast replenishment term was substituted for the constraint of constant concentration of some of the reactants. Water is considered a reactant with a molarity of 55. The steady-state formulation of the malonic acid-enol-iodine reaction subset used by De Kepper and Epstein was changed to the kinetic formulation used by Noyes and Furrow in order to maintain a consistent ODE representation of the problem and to simplify the analysis; this was observed to cause no change in the mechanistic behavior. One of the rate constants in the Noyes and Furrow mechanism (k33)was found to lie extremely close to a stability boundary of the system (Figure 1) and was modified slightly to move the operating point of the system away from a region of damped oscil(9)Odutola, J. A.; Bohlander, C. A.; Noyes, R.M . J. Phys. Chem. 1982, 86, 818.
(10) Edelson, D.; Noyes, R. M . J . Phys. Chem. 1979, 83, 212. (11) Noyes, R. M.; Furrow, S. D. J. Am. Chem. SOC.1982, 104, 45. (12) De Kepper, P.; Epstein, I. R.J . Am. Chem. SOC.1982, 104, 49. (13) Rabitz, H. Comput. Chem. 1981, 5, 167. (14) Furrow, S. D.; Noyes, R. M. J. Am. Chem. SOC.1982, 104, 38. (15) Furrow, S. D . J . Phys. Chem. 1981,85, 2026.
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lation which would give misleading results.
Analysis The previously developed method16 for computing the sensitivity of the oscillator period to the rate constants and initial conditions was applied to the mechanisms under consideration. In all cases, the full 36-step mechanism was used despite the fact that many of the rates were zero. It has previously been that this procedure can sometimes give a measure of the importance of these omitted steps, although in the present case, with so many of them zero, these indications can be questionable. Particularly when a reaction is consecutive to one whose rate constant is zero, its sensitivity will necessarily vanish since none of its reactants is ever formed in the process. Similarly, the mechanism will be insensitive to the addition of a species that only appears as a product, e.g., the organic iodide in this system. Calculations were made for only one operating point for each system. The results are given in Tables I and 11. For those reactions whose rates are nonzero the sensitivities are presented in relative form: a In T / a In k. Otherwise, absolute values are listed. The sensitivities with respect to initial conditions are similarly given. Results Upon examination of the rate constant sensitivities in Table I, one is struck by the observation that the values for several of the most sensitive steps all cluster together. It therefore appears that the different types of reaction processes are intimately coupled together in their deter(16) Edelson, D.; Thomas, V. M . J. Phys. Chem. 1981,85, 1555. (17) Edelson, D. Int. J. Chem. Kinet. 1981, 13, 1175.
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mination of the oscillator period. This is in sharp contrast to the case of the BZ reaction,8 where it was possible to identify the halogenation and subsequent oxidation of the organic acid as the period's main determining factor. It is consistent, however, with the altered role of the organic component that is assumed in the BR mechanisms. In the BZ mechanism, bromomalonic acid is considered to be the starting point for the regeneration of bromide ion through a complex oxidation process initiated by the metal redox system. In BR, a-iodomalonic acid is considered a final byproduct in this regeneration and is primarily viewed as a means of disposing of excess iodine. There is no interaction of the metal redox and organic systems. In addition, the hydrogen peroxide system provides a parallel source of I-; the sensitivity is of the same order of magnitude for both sources. For the case of the CSTR,which was run by using a flow (residence time = 156 s), the relative rate of 6.41 X sensitivity to flow rate was found to be 2.7 X 10-l. Although this is about the same as the reaction sensitivities for the static case, the most sensitive reactions, steps 1-3 of the iodine series and step 13 of the "down" steps, are about 9 X 10-1 for these operating conditions. Thus, the CSTR is still being controlled mainly by the chemistry. The methylmalonic acid case gives sensitivities which show an increase over those for the malonic acid system but in general bear about the same relationship to one another. There are some notable exceptions. The sensitivity to the organic system is now about equal to that of reaction 13, and the sensitivity to the manganese redox system is about 1 order of magnitude larger. It is not obvious why the change in only the organic system rates should affect all the sensitivities in this way; some of these changes might also be due to the change in the initial condition operating point. These questions have not been further investigated at this time. Table I1 gives the sensitivity of the period to the initial conditions for the three cases. In general, these values parallel those for the reactions in which the particular species are involved. Note, for example, the identical values obtained for Mn2+and reaction 25, and (RCO0H)H and reaction 23. No conclusions can be drawn by comparing the three cases because of the possible dependencies of the sensitivies on the system operating point which have not been investigated in this work. Note, for example, the change in sign for the H+and IO; sensitivities between the static malonic and methylmalonic systems. Absolute sensitivities for reactions and initial conditions having zero values are also included in these tables. These may be interpreted as the inverse of the value of the parameter required to affect a one-unit change in period of the system (units of moles, liters, seconds), at the particular operating point. The very tight coupling between all processes makes it difficult to conclude very much from these values. For example, the nonzero values for the "up" steps 21, 22, and 24 reflect the result of competition for reactants with the rest of the mechanism. The zero values for the remainder of this class result from the absence of a precursor reaction. Should all these have been assigned nonzero rates, the picture might be substantially changed. Similarly, the inclusion of the organic iodide (RCO0H)I with the initial conditions is of no consequence since this species, here being considered only an end product, could never affect the course of reaction, and the calculated absolute sensitivity bears out this conclusion. Comparison with Experiment Much of the experimental work on the BR system has been concerned with delineating the stability limits of the
1208
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Edelson
system12J&20 but there is some work in which the effect measurements of both the kinetics and equilibrium of the of initial conditions on the period has been r e p ~ r t e d . ~ l - ~ ~iodination reaction indicate that only one atom of iodine Only qualitative comparison with the present calculations is substituted on the malonic acid molecule, there are other is warranted since the operating points are not exactly the reports that the kinetics may be of second order.26 It must same. For the static malonic acid oscillator (Table 11) the further be noted that a-iodomalonic acid has never been experimental sensitivities may be summarized as follows: reported to have been isolated as a pure substance and that IO,, somewhat positive to zero; malonic acid, -0.3; HzOz, all the claimed measurements of its concentration in the slightly negative; Mn2+, strongly negative to zero; H+, BR system are based on spectrometric measurements of moderately positive to zero. Discrepancies with the coman otherwise uncharacterized a b ~ o r p t i o n . ~ ’ Reported ,~~ attempts to prepare it have invariably resulted in products putation, in both sign and magnitude, are obvious. of more extensive reaction: diiodomalonic acidzgor triComparison between experiment and model behavior iodoacetic acid.30 The former is even reported to be is more meaningful for the methylmalonic acid oscillator, unstable in aqueous solution and to decompose rapidly where the calculations were done in the middle of the range with the evolution of CO,; it must be prepared and handled of the experimental ~a1ues.l~ Slopes of the experimental in anhydrous solvents. That the iodination kinetics of data were obtained by fitting the points to a quadratic methylmalonic acid is reported to be first order31is more spline and taking the first derivative at the operating point. plausible; however, the preparation of a-iodomethylThese results are given in the last column of Table 11. malonic acid is not mentioned in the literature either. Even though this system is presumably less subject to the complexities possible with malonic acid, it is to be noted The expansion of the organic chemistry certainly apthat similar discrepancies still exist. pears to be warranted. At the very least, the further iodination of the organic substrate should be included to Some CSTR data are available for comparison, but the conform to experimental fact. Furthermore, the presence agreement is no better in this case. of HO. and HOP. radicals (even though the former is not Discussion produced by the mechanisms studied here) must initiate a complex cascade of reaction leading eventually to COz It has only recently become clear that the potential of and other end products. Even though this process may a complex mechanism for exhibiting oscillatory behavior not interact with the oscillating system, its depletion of depends on its network structure.z4 The ability of the the reactant pool upon which the oscillations depend previous authors to assemble a reasonable set of chemical should alter their characteristics. However, the addition reactions and find a range of rate constants over which of the product of iodine uptake by methylmalonic acid (not oscillations do indeed occw indicates that their mechanism otherwise isolated or characterized) is reported to have no is at least structurally correct. Nevertheless, the differeffect on the oscillations.15 Augmentation of the inorganic ences between the simulated behavior and experiment lead set, for example, by the inclusion of I,- and dissolved Oz to the conclusion that many details of the system still as active reactants, could also alter the characteristics of remain to be learned. Whether the deficiency in our the oscillations. What level of additional detail may be knowledge lies in uncertainties in the rate constants, in required to bring the model into acceptable agreement with the participation of the as yet unassigned inorganic reacexperiment is currently open to speculation, but there is tions, with the omitted details of the organic chemistry, a strong probability that the true chemistry is considerably or with a combination of these factors, is not clear at the more complicated than the mechanisms which have been present time. proposed to date. I t is almost certain that the consideration of a-iodomalonic acid as a stable end product is an oversimplifiAcknowledgment. I am grateful to Profs. Richard Noyes cation. Although Leopold and Haim%concluded that their and Irving Epstein for advance copies of their mechanisms and discussions relating to them, and to Prof. Stanley Furrow for his experimental data on these oscillating (18) Pacault, A.; De Kepper, P.; Hanusse, P.; Rossi, A. C. R. Hebd. systems. Seances Acad. Sci.. Ser. C 1975.281. 215. (19) Pacault, A.;’Hanusse,P.f De Kepper, P.; Vidal, C.; Boissonade,
J. Ace. Chem. Res. 1976, 9, 438.
(20) De Kepper, P.; Pacault, A. C. R. Hebd. Seances Acad. Sci., Ser. C 1976,283, 25; (21) De Kemer. P.: Pacault., A.:, Rossi. A. C. R . Hebd. Seances Acad. Sci:, Ser. C 19f6, 282,’ 199. (22) Cooke, D. 0. Inorg. Chem. Acta 1979, 37, 259. (23) Dutt, A. K.; Banerjee, R. S. J.Indian Chem. SOC.1981,58, 546. (24) Feinberg, M. In “Dynamics and Modelling of Reactive Systems”; Stewart, W. E., Ray, W. H., Conley, C. C., Eds.; Academic Press: New York, 1980. (25) Leopold, K. R.; Haim, A. Int. J . Chem. Kinet. 1977, 9, 83.
Registry NO,IO,, 15454-31-6; HzO2,7722-84-1;Mn, 7439-96-5; malonic acid, 141-82-2; a-iodomalonic acid, 84695-78-3. (26) Kappanna, A. N.; Talaty, E. R. J. Indian Chem. Sac. 1951, 28, 675. (27) Row, J. C.; Vidal, C. C. R. Hebd. Seances Acad. Sci., Ser. C 1977, 284, 293. (28) Roux, J. C.; Vidal, C. Now.J . Chim. 1979, 3, 247. (29) Willstatter, R. Ber. 1902, 35, 1374. (30) Cobb, R. L.J. Org. Chem. 1958, 23, 1368. (31) Furrow, S. D. Int. J . Chem. Kinet. 1979, 11, 131.
