4394
J. Phys. Chem. 1982, 8 6 , 4394-4399
Multiplicity, Stability, and Oscillations in the Stirred Flow Oxidation of Manganese( I I ) by Acidic Bromate W. Gelseler Institut fur Technische Chemie, Technische Universltai Berlin, P 1000 Berlin 12, FRG (Received: December 30, 198 I; In Final Form: July 7, 1982)
The present paper is concerned with the autocatalytic oxidation of manganese(I1) ions by acidic bromate in the presence of bromide inhibitor. We demonstrate that in an isothermal continuously stirred tank reactor (CSTR) this reaction exhibits nearly the same variety of dynamical behavior as the celebrated BelousovZhabotinsky reaction, namely, steady-state multiplicity,sustained oscillations,excitability, and hysteresis. The regions of multiplicity and oscillations are measured in some planes of constraints and the responses of the steady states to perturbations are investigated in some detail. The experimental observations and data provide a first check of the Noyes-Field-Thompson (NFT) mechanism for manganese(I1)ions as the weak one-electron reducing agent and can be used for further tests of available and future models. The flow system described here seems to be the best understood bromate oscillator presently known.
Introduction During the past few years several papers concerned with steady-state multiplicity of isothermal reactive flow systems have been published. Evidently, this is a consequence of the close relationship between bistable and oscillatory reactions, which have attracted attention since Belousovl reported oscillations during the reaction of citric acid with acidic bromate and ceric ions. The first example of bistability has been described by Degn,2who investigated the oxidation of NADH by O2 catalyzed by horseradish peroxidase. Horak et aL3studied steady-state multiplicity in the reaction of bis(trichloromethy1) trisulfide (BTT) with aniline in methanol. DeKepper et observed bistability during CSTR studies of the Belousov-Zhabotinsky (BZ) reacti0n.l Similar behavior was reported to occur in the Briggs-Rauscher system by Boissonade and DeKepper.6 Recently, Papsin et al.'j and DeKepper et al.' independently investigated the iodate oxidation of arsenous acid in a CSTR and observed steady-state multiplicity over a significant range of input concentrations and flow rates. Some other examples of kinetic bistability have been reported very recently by Reckley and Showaltd (oxidation of oxalate by permanganate) and Epstein et al.9 (flow systems of arsenite-iodate-chlorite-iodide and ferrous nitrate). At present the only bistable system understood in terms of elementary chemical reaction steps is the oxidation of cerium(II1) by acidic bromate. This reaction represents the inorganic part of the BZ system.l Working with a CSTR Geiseler and Follner'O discovered multiplicity of steady states over a wide range of flow rates. The sta(1)(a) Belousov, B. P. Sb. Ref.Radiat. Med. (Moscow) 1959,1958,145. (b) Zhabotinsky, A. M. DokE. Akad. Nauk SSSR 1964,157,392. (2)Degn, H. Nature (London) 1968,217, 1047. (3)Horak, J.; Jiracek, F.; Krausova, L. Chem. Eng. Sci. 1971,26,1. (4)DeKepper, P.; Roasi, A.; Pacault, A. C. R. Hebd. Seances Acad. Sei. Ser. C 1976,283, 371. (5)Boissonade, J.; DeKepper, P. J . Chem. Phys. 1981,75,189. (6)Papsin, G. A.;Hanna, A.; Showalter, K. J. Phys. Chem. 1981,85, 2575. (7) DeKepper, P.; Epstein, I. R.; Kustin, K. J . Am. Chem. SOC.1981, 103,6121. (8)Reckley, J. S.; Showalter, K. J. Am. Chem. SOC.1981,103,7012. (9)Epstein, I. R.; Dateo, C. E.; DeKepper, P.; Kustin, K.; Orban, M. In 'Synergetics"; Vidal, C., Pacault, A., Eds.; Springer-Verlag: Berlin, 1981;Vol. 12,p 188. (10)Geiseler, W.;Follner, H. H. Biophys. Chem. 1977,6 , 107. 0022-3654/82/2086-4394$0 1.2510
tionary concentrations of certain intermediate species differed considerably in each steady state (SS). After a perturbation introduced to the reactor, the system either returned to its previous SS or moved to the other one. Bar-Eli and Noyes"J2 succeeded in explaining these observations by use of the mechanism of Noyes, Field, and Thompson (NFT).13 Their further computational predictions for various experimental conditions were verified recently by Geiseler and Bar-Eli.14 In a subsequent paperI5 they also studied a system consisting of two coupled CSTRs of equal size and detected switching effects and hysteresis phenomena. In the present article we extend our investigations to the flow system with manganese(I1) as the weak one-electron reducing agent. The early papers of Thompson16 and Noyes et al.13suggest that in a flow reactor manganese(I1) will behave similarly to cerium(II1); however, up to now an experimental proof has not been given. We report the various hysteresis loops, which can be observed in the CSTR when one of the constraints is scanned over a certain range and thus demonstrate experimentally that in addition to residence time the CSTR provides some other bifurcation parameters, namely, the inflow concentration of each reactant. We measure the hysteresis loop limits (transition points) and determine the regions of multiplicity in some planes of constraints. Moreover, we report on the verification of sustained oscillations which have been p r e d i ~ t e d 'to ~ occur near the critical point, where multiplicity disappears, and investigate the responses of the bistable CSTR to perturbations regarding the inhibitor. The main intention of this paper, however, is to point out that the flow reaction under study, being only part of the BZ flow s y ~ t e mexhibits ,~ nearly the same variety of nonlinear phenomena, namely, multiplicity, excitability, hysteresis, and oscillations, while both reactions differ considerably under batch conditions (the former one behaves like a clock reaction, the BZ reaction is still oscil(11)Bar-Eli, K.;Noyes, R. M. J. Phys. Chem. 1977,81,1988. (12)Bar-Eli, K.; Noyes, R. M. J. Phys. Chem. 1978,82,1352. (13)Noyes, R. M.;Field, R. J.; Thompson, R. C. J. Am. Chem. SOC. 1971,93,7315. (14)Geiseler, W.;Bar-Eli, K. J . Phys. Chem. 1981,85, 908. (15)Bar-Eli, K.; Geiseler, W. J . Phys. Chem. 1981,85,3461. (16)Thompson, R. C.J . Am. Chem. SOC.1971,93,7315. (17)Bar-Eli, K. In "Synergetics";Vidal, C., Pacault, A,, Eds.; Springer-Verlag: Berlin, 1981;Vol. 12,p 228.
62 1982 American Chemical Society
Stirred Flow Oxidation of Mn(I1) by Acidic Bromate
The Journal of Physical Chemistry, Vol. 86, No. 22, 1982 4395
latory). A further intention is to provide critical experimental data for the manganese flow oxidation. Both the transition points and the limits of multiplicity and oscillations, respectively, represent such critical data and cannot be obtained in any other way. They can be used for checking the predictive abilities of available and future models and for obtaining better estimates of the various rate constants used.I4
The Chemical Reaction The essential kinetic features of the oxidation of manganese(I1) ions by bromate in the presence of bromide inhibitor can be described by the NFT me~hanism.'~This mechanism consists of seven reversible reaction steps: BrOC
+ Br- + 2H+ + HBr02 + HOBr
kl = 2.1 M-, HBr02
~3-l
+ Br- + H+
k3 = 8 X BrO,-
(2)
lo9 M-2 s-l
(3)
k-, = 110 s-'
+ HBr02 + H+ + 2Br02. + H 2 0
+
Mn2+ BrO,.
k-4 = 2
X
(4)
lo7 M-l s-l
+ H+ 6 Mn3+ + HBr0,
k , = 6.5 X lo5 M-, s-l
k-, = 2.4
X
lo7 M-'
(5) s-l
+ BrO,. + H,O + Mn2++ BrO,- + 2H+ k , = 1.3 X
k , = 9.6 M-' s-l 2HBr02
k, = 4 X
BrO,-
lo7 M-l s-'
0
600
1200
le00
2L00
3000
3600
(6)
M-, s-l
+ HOBr + H+
Flgure 1. Kinetic features of the Mn2+ oxidation by acidic bromate in a batch reactor with bromide inhibitor initially present. Initial concentrations were [Br03-], = 2 X M, [Br-], = 1 X M, [Mn2+], = 1.5 X M, [H'], = 1.5 M. T = 25 "C. Upper curve: potentiometric trace E,log [Br-1. Lower curve: spectrophotometric trace (absorbance at A = 260 nm).
-
M-' s-l
+ Br- + H++ Br, + H,O
k4 = 1 X lo4 M-2 s-l
Mn3+
2HOBr
F+
k-, = 5 X
1
I t (SI
k-, = 1 X lo4 M-ls-l
kz = 2 x 109 M-2 s-1 HOBr
(1)
(7)
k-, = 2.1 X lo-', M-2 s-l
The rate constants are defined so that solvent water does not enter the rate expressions but is treated as at unit activity. Ratios of forward and reverse rate constants are consistent with free energy assignments of Field, Koros, and Noyesla except those of steps 5 and 6. Mn2+and Mn3+ were assumed to be the only species of manganese participating in the reaction. We tentatively assumed the rate constants of steps 5 and 6 to be equal to those reported for cerium. By doing so we could adopt the computational results published previously11J2J4as reference data without repeating similar calculations. For each chemical species of the mechanism 1-7 a differential equation is obtained. To each equation terms describing the inflow and outflow rates of the species were added in order to model the behavior of the CSTR. The four species BrOg, Br-, Mn2+and H+ were assumed to be added to the reactor at a constant rate and to be perfectly mixed. The rates of the inflow and outflow are described by k,, which is the reciprocal of the mean residence time of the reactor. The stiff differential equation system thus formed was solved numerically by the method of Gear.ls The details of the computations are described elsewhere.11?1%14 (18) Field, R. J.; Koros, E.; Noyes, R. M. J.Am. Chem. SOC.1972,94, 8649. (19) (a) Gear, C. W. 'Numerical Initial Value Problems in Ordinary Differential Equations";Prentice-Hall: Englewocd Cliffs, NJ,1971. (b) Hindmarsh, A. C.; "Gear: Ordinary Differential Equation System Solver", UCID-30001, Rev. 3, Livermore, CA, 1974.
Experimental Section The oxidation of manganese(I1) ions was conducted in an isothermal CSTR which was fed continuously by sulfuric acid solutions of KBrO,, KBr, and MnSO, at 25 "C. The experimental device has been described in detail previ0us1y.l~The oscillations and the transitions between different SS were monitored by recording the emf of a bromide-sensitive galvanic cell (EBr- log [Br-1) consisting of a bromide electrode and a mercurous sulfate reference electrode. At bromide concentrations lower than lo4 M this cell did not follow the Nernst equation but reliably indicated both the temporal oscillations and the transition points. The external constraints besides those which were not changed ([H+], and temperature) were the input concentrations [Br0gI0, [Br-lo, [Mn2+lO, and the input rate k,. In order to find and measure the region of oscillations in the [Br-],-[BrO
