J. Phys. Chem. 1996, 100, 16441-16442
16441
COMMENTS Mechanism of the Oscillatory Bromate Oxidation of Sulfite and Ferrocyanide in a CSTR
TABLE 1: Oscillatory Model for the BrO3--HSO3--Fe(CN)64- System reaction 3HSO3 + BrO3 f 3SO42- + Br- + 3H+ (2)a 3H2SO3 + BrO3- f 3SO42- + Br- + 6H+ (3) H+ + SO32- h HSO3(4) H+ + HSO3- h H2SO3 (5)a BrO3- + 6Fe(CN)64- + 6H+ f Br- + 6Fe(CN)63- + 6H2O (1)a
Gyula Ra´bai* Institute of Physical Chemistry, Kossuth Lajos UniVersity, H-4010 Debrecen, Hungary
Akiko Kaminaga and Ichiro Hanazaki*
a
-
-
constant 5.97 × 10-2 M-1 s-1 18 M-1 s-1 1.0 × 107 M-1 60 M-1 k5 ) 1.5 × 10-5 M s-1, k5′ ) 2.5 × 10-4 M
Rate laws are shown in the text as eqs R1, R2, and R5.
react with S(IV) rapidly.
Institute for Molecular Science, Myodaiji, Okazaki 444, Japan ReceiVed: March 5, 1996 Edblom et al. have discovered oscillations and bistability during simultaneous oxidations of sulfite and ferrocyanide by bromate in a CSTR.1 To explain their results, they considered but discarded an old mechanism suggested by Williamson and King2 for the component reaction between BrO3- and sulfur(IV) (S(IV)). They proposed a new scheme to simulate the observed dynamical behavior. Despite the success of their simulations, the mechanism would seem to deserve further considerations. New findings3 and old results4 on the kinetics of the component reactions are not consistent with it, but they are in full agreement with Williamson and King’s early proposal. In Edblom’s mechanism simproportionations and disproportionations of bromine species of different oxidation states (reactions B2, B3, B4, and B5 in ref 1) provide the positive feedback pathway necessary for oscillations. Direct reactions between the intermediate bromine species and S(IV) are not considered. However, the rate of HOBr oxidation of S(IV) is near the diffusion limit (k ) 5 × 109 M-1 s-1, at 25 °C and I ) 0.5 M).3 The oxidation of S(IV) by BrO2- is also much faster than the disproportionation of Br(III) (B5). An extrapolation from a measurement carried out in alkaline solutions4 gives a value of 2.95 × 106 M-1 s-1 at 39.1 °C and pH ) 7 for the second-order constant of the S(IV)-BrO2- reaction. The slower indirect pathway (reactions B2-B6 with the rate constants listed in ref 1) is obviously not competitive with the fast direct oxidations in the pH range of oscillations. From this it is concluded that the reaction proceeds more likely through the direct oxidations of S(IV) by BrO2- and HOBr. The question is how one can explain the nonlinearity without the autocatalytic indirect pathway. According to Williamson and King,2 the BrO3--S(IV) reaction proceeds via two pathways:
HSO3- + BrO3- f {HSO3-‚BrO3-‚H2O} f SO42- + BrO2- + H+ (1a) H2SO3 + BrO3- f {SO2‚BrO3-‚H2O} f SO42- + BrO2- + 2H+ (2a) It is the first step in the six-equivalent reduction of bromate that is the rate-determining one. The bromine intermediates which are produced in the breakup of the transition states further S0022-3654(96)00670-3 CCC: $12.00
HSO3- + BrO2- f SO42- + HOBr
(1b)
HSO3- + HOBr f SO42- + Br- + 2H+
(1c)
H2SO3 + BrO2- f SO42- + HOBr + H+
(2b)
H2SO3- + HOBr f SO42- + Br- + 2H+
(2c)
Since step 2a is faster than step 1a and H+ is produced when H2SO3 or HSO3- gets oxidized to sulfate, the reaction accelerates in an unbuffered solution due to the protonation of an increasing fraction of HSO3- with increasing [H+]. This claim is supported by the experiment shown in Figure 1a of ref 1, where a sharp ending is seen on the pH-time curves. The sharp break point is not reflected in the curve calculated with Edblom’s mechanism (Figure 1b of ref 1). As other evidence of selfacceleration, we observed a substantial increase in the rate of the bromide ion formation and an acceleration in the production of the reaction heat in the final stage. All these features of the reaction can be understood and quantitatively simulated by Williamson and King’s mechanism. The main question, however, is whether the oscillatory kinetics of the BrO3--SO32--Fe(CN)64--H+ system can be understood in this way. Shown in Table 1 is a simplified scheme drawn from Williamson and King’s mechanism. Reactions 1 and 2 are stoichiometries of reactions 1a-1c and 2a2c having rate laws (R1) and (R2), respectively:
V1 ) -d[BrO3-]/dt ) k1[BrO3-][HSO3-]
(R1)
V2 ) -d[BrO3-]/dt ) k2[BrO3-][H2SO3]
(R2)
Since the conditions of the oscillator system differ from those applied by Williamson and King, we could not use their numerical values in the simulations. The values determined from our batchwise experiments are k1 ) 5.97 × 10-2 M-1 s-1 and k2 ) 18 M-1 s-1. Other constants are K3 ) 1 × 107 M-1 and K4 ) 60 M-1 at 35 °C and at I ) 0.5 M.5 Reaction 5 is the negative feedback for oscillations as it removes some H+ when the pH is low. Its rate practically does not depend on [Fe(CN)64-] but approaches a limiting value with increasing [H+] and [BrO3-].6 Since [BrO3-] hardly varies during oscillations, the rate can be approximated by eq R5
V5 ) -d[BrO3-]/dt ) k5[H+]/(k5′ + [H+]) © 1996 American Chemical Society
(R5)
16442 J. Phys. Chem., Vol. 100, No. 40, 1996
Comments Figure 1. Experimental curve shown in ref 1 can also be simulated with some deviation in the periodic time. The calculated region of oscillations and bistability in the bromatesulfite subsystem fit to their measured counterpart. The same results were obtained when a detailed mechanism consisting of reactions 1a-1c and 2a-2c as well as steps given in ref 6 for reaction 5 were used instead of (R1), (R2), and (R5). We conclude that Williamson and King’s proposal is in agreement with all the known experimental results and can, at the very least, equally well describe the oscillatory kinetics as Edblom’s scheme does. Since the latter contradicts some new findings, Williamson and King’s mechanism keeps its ground more firmly.
Figure 1. Measured (solid line) and calculated (dashed line) pH oscillations. Reactions 1-5 were used for the calculation. [BrO3-]0 ) 0.0650 M, [SO32-]0 ) 0.0750 M, [H+]0 ) 0.020 M, k0 ) 1.25 × 10-3 s-1, T ) 35 °C.
Acknowledgment. We acknowledge financial support from the Hungarian Science Foundation (OTKA No. T14440) and the Japan Society for Promotion of Science.
with k5 ) 1.5 × 10-5 M s-1 and k5′ ) 2.5 × 10-4 M at 35 °C if [Fe(CN)64-]0 ) 0.020 M and [BrO3-]0 ) 0.065 M. Equilibria 3 and 4 were taken into account using mass action kinetic laws for both the forward and reverse reactions with k3 ) 5 × 1010 M-1 s-1, k-3 ) 5 × 103 s-1, k4 ) 6 × 1010 M-1 s-1, and k-4 ) 1 × 109 s-1. Our calculations have proved that the measured oscillations can be simulated by the model shown in Table 1. Typical calculated and measured oscillatory curves are presented in
References and Notes (1) Edblom, E. C.; Luo, Y.; Orba´n, M.; Kustin, K.; Epstein, I. R. J. Phys. Chem. 1989, 93, 2722. (2) Williamson, F. S.; King, E. L. J. Am. Chem. Soc. 1957, 79, 5397. (3) Troy, R. C.; Margerum, D. W. Inorg. Chem. 1991, 30, 3538. (4) Lee, C. L.; Lister, M. W. Can. J. Chem. 1979, 57, 1524. (5) Gaspar, V.; Showalter, K. J. Am. Chem. Soc. 1987, 109, 4873. (6) Rabai, G.; Epstein, I. R. Inorg. Chem. 1989, 28, 732.
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