J . Phys. Chem. 1984,88, 2844-2847
2844
micelle surface. The value of the rate constant for this process may be contrasted with a similar determination for the reaction of R ~ ( b i p y ) ~and ~ +MV+ on the surface of an SDS micelle16 k = 5.7 X lo6 s-l. It is suggested that the reduced electrostatic repulsion in the case of Ru(bipy)2(CN)2 is responsible for the increased rate.
Conclusion Efficient photoionization of Ru(bipy)z(CN)2by 355-nm laser light has been observed. The hydrated electrons thus formed have been shown to be scavenged by the Ru(bipy)z(CN)z ground state or in the presence of MV2+ by MV2+ to yield MV+. The addition of SDS has the effect of increasing the yield of photoionization and retarding the rate of disappearance of the ions thus formed. Reduced viologen is an important species in potential solar energy conversion systems since it has the capacity under suitable conditions to reduce water (ref 4 and references therein). In such (16) M. A. J. Rodgers and J. C. Becker, J . Phys. Chem., 84,2762 (1980).
systems it is important to prevent or at least retard the reactions leading to loss of MV2+ before water reduction may occur. Although the present system is not useful for solar energy conversion since sunlight does not contain the high-intensity UV radiation required for the reactions to proceed, the mechanisms are interesting and it is tempting to consider molecules which may be efficiently photoionized by sunlight leading to the production of energy-rich species such as MV+. Acknowledgment. Thanks are due to the staff of the C.F.K.R., Mr. J. A. Gurak for help with the preparation of Ru(bipy),(CN),, Dr. M. A. J. Rodgers for helpful suggestions, and Mr. R. M. Hornick for help with the manuscript. The Center for Fast Kinetics Research is supported jointly by the Biotechnology Branch of the Division of Research Resources of N I H (RR00886) and by the University of Texas at Austin. Registry No. SDS, 151-21-3; MV2+, 4685-14-7; MV+, 25239-55-8;
Ru(bipy)2(CN)2, 58356-63-1; Ru(bipy)2(CN)2+,58356-64-2; Ru(bipy)*(CN);, 73746-84-6; Ru(bipy)?+, 15158-62-0; R ~ ( b i p y ) , ~ + , 18955-01-6.
Oscillations and Steady States in the Bromate-Bromide-Cerous System: Comparison of Experimental and Calculated Data of Different Sets of Rate Constants K. Bar-Eli* and J. Ronkin Department of Chemistry, Tel- Aviv University, 69978 Ramat Aviv, Israel (Received: September 19, 1983)
The bistability, hysteresis limits, and oscillations domain of the bromate-bromide-cerous system are calculated by the NFT mechanism and compared to experimental data. The computationsare done on the basis of three sets of plausible rate constants. The best available set of rate constants that best fits most of the experimental data available is the one suggested by Noyes et al. as early as 1972.
Introduction The system of bromate-bromide-cerous ions in sulfuric acid medium in a continuous stirred tank reactor (CSTR) is described quite well by the Noyes-Field-Thompson1 (NFT) mechanism. The system can be in (a) a single steady state (SS), (b) a bistable state (with a possibility of hystereris between the two stable steady states), or (c) an oscillating state. Geiseler and Bar-Eli2 have measured and calculated the single and multiple SS while Bar-Eli,3 Epstein et a1.: Gei~eler,~ and Bar-Eli and Geiseler6 measured and calculated the oscillations of the system, occurring near the critical point. Recently, Tyson7 has questioned the values of some of the rate constants used in the calculations of the previously mentioned authors. The values of rate constants used earlier were estimated by Field, Koros, and Noyes8 by analyzing the available kinetic and thermodynamic data. An estimate of the dissociation constant of bromous acid was taken to be lo-* M. A different estimate of M is given by Massagli, Indeli, and Perg01a.~ This different estimate affects several components of the NFT mech(1) Noyes, R. M.; Field, R. J.; Thompson, R. C. J . Am. Chem. SOC.1971, 93, 7315. (2) Geisler, W.; Bar-Eli, K. J . Phys. Chem. 1981, 85, 908. (3) Bar-Eli, K. In “Nonlinear Phenomena in Chemical Dynamics”; Vidal, C., Pacault, A., Eds.; Springer-Verlag, West Berlin, 1981; pp 228-239. (4) Dateo, C. E.; Orban, M.; DeKepper, P.; Epstein, I. R. J . Am. Chem. SOC.1982, 104, 504. (5) (a) Geiseler, W. Ber. Bunsenges. Phys. Chem. 1982, 86, 721. (b) Geiseler, W. J . Phys. Chem. 1982, 86, 4394. (6) Bar-Eli, K.; Geiseler, W. J. Phys. Chem. 1983, 87, 3769. (7) Tyson, J. J. In “Oscillations and Traveling Waves in Chemical Systems”; Field, R. J., Burger, M., Eds.; Wiley: New York, in press. (8) Field, R. J.; Koros, E.; Noyes, R. M. J. Am. Chem. SOC.1972, 94, 8649. (9) Massagli, A.; Indeli, A.; Pergola, F. Inorg. Chim. Acta 1970, 4, 593.
0022-3654/84/2088-2844$01.50/0
anism. For example, rate constants k-l, kz, and k4 (see Table I) are reduced 1000 times. Experimental data by Rovinskii and Zhabotinski,lo Knight and Thompson,’ Noszticzius et al.,13and Sullivan and Thompson14 are in line with the lower values of the rate constants k-l, k2, and k4; on the other hand, the results of Forsterling et a1.12 support the higher values of these rate constants. Furthermore, the disproportionation of bromous acid (reaction 7) was measured by Noszticzius et al.13 to be a rather slow reaction, while Forsterling et al.12 find its rate to be lo6 faster. In view of these discrepancies we obtain three sets of plausible (for the old set of Noyes et al.I), “Hi” rate constants marked “0” obtained by taking k7 = 2 X lo9 M-’ s-l a nd pK = 2, and “Lo” obtained by taking k7 = 2 X lo3 M-’ s-I a nd pK = 5. The rate constants should also obey the restrictions k4 k5 k6 _ _ _ -- 1
k-4 k-5 k-6
and
(10) Rovinskii, A. B.; Zhabotinskii, A. M. Theor. Exp. Chem. (Engl. Transl.) 1978, 14, 142. (11) Knight, G . C.; Thompson, R. C. Inorg. Chem. 1973, J2,63. (12) (a) Forsterling, H. D.; Lamberg, H.; Schreiber, H. 2.Naturforsch., A 1980, 3 5 4 329. (b) Forsterling, H. D.; Lamberg, H. J.; Schreiber, H. Ibid. 1980, 35A, 1354. (c) Forsterling, H. D.; Lamberg, H. J.; Schreiber, H. Ibid, in press. (d) Forsterling, H. D.; Lamberg, H. J.; Schreiber, H.; Zittlau, W. Acta Chim. Acad. Sci. Hung. 1982, 110, 251. (13) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J. Phys. Chem. 1983, 87, 510. (14) Sullivan, J. C.; Thompson, R. C. Inorg. Chem. 1979, 18, 2375.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 13, 1984 2845
Bromate-Cerous System TABLE I: Rate Constants of NFT Mechanism“ “0” setb reaction forward backward 1 2.1 1 x 104 2 2 x 109 5 x 10-5 3 8 x 109 1.1 x 102 4 1 x 104 2 x 107 5 6.5 x 105 2.4 x 107 6 9.6 1.3 x 10-4 I 4 x 107 2.1 x 10-10
forward 2 2 x 106 8 x 109 10 6 X lo5 10 2 x 103
“LO”setC backward 10 5 x 10-5 1 x 102 2 x 107 2 x 106 1.5 X 10” 10-8
forward 2 2 x 109 8 x 109 7 x 103 6 X lo5 10 2 x 109
“Hi” setC backward 104 5 x 10-5 110 2 x 107 5 x 107 4.20 x 10-5 1 x 10-8
@Waterconcentration is assumed to be constant with unit activity. Slightly different values of some of the rates of the “Hi” set appear in the final version of ref 7 . These variations would not affect significantly the conclusions of the present work. bThe set previously used in ref 2 and 3. CTheset suggested by Tyson’ (see text). since reactions 4, 5, and 6 and 1, -2, and 7 sum to null reactions. In view of the new experimental data and the widely different estimates of the various rate constants, we have decided to repeat the previous computations and compare the results obtained from all three sets of constants with the experimental data.
L 0 9 [B r‘],
-3
Calculations The N F T mechanism is given in the following set of chemical equations, and the appropriate sets of rate constants are shown in Table I.
+ Br- + 2H+ e HBr0, + HOBr HBr0, + Br- + H+ 2HOBr HOBr + Br- + H + + Br, + HzO Br03- + H B r 0 2 + H+ + 2BR0,. + HzO Ce3+ + BRO,. + H + * Ce4+ + HBr0, Ce4+ + BrO,. + H,O F? Ce3+ + Br03- + 2H+ 2HBr0, e Br03- + HOBr + H+ Br03-
F?
-4
-5
(1)
(2) (3)
E
(4)
(5)
-7
(6)
(7) -8
To the rate equations formed from reactions 1-7, taking the water to be always at unit activity, the terms ko(Co,- Ci) are added, where C, is the concentration of species i, Coiis the concentration of this species in the feed flow, and ko is the ratio between the flow rate, V, and the volume of the reaction vessel. The location of the Ss was found by solving the equations ti = 0 by Newton’s method. At certain values of the constants only one SS is obtained, while at other values three SS can coexist. Of these three SS two are stable; Le., all the eigenvalues of the Jacobian matrix are negative or have a negative real part, and one is unstable and has one eigenvalue with a positive real part. Physically, this SS is unattainable. In agreement with previous p~blications,2.~~~ SSI marks the SS in which there is comparatively high [Br-Iss and low [Ce4+Iss, SSII marks the SS in which there is low [Br-1, and high [Ce4+],,, and SSIII is the unstable SS between the two. The points where one eigenvalue changes sign are the hysteresis limits, i.e., the points where a SS ceases to exist and there is sharp jump to the other SS. When only one SS exists, one looks for the points where the real parts of a complex conjugate eigenvalues change sign. These points are called Hopf bifurcation and mark the change from a stable to an unstable SS where oscillations occur. The various points were calculated as functions of the constraints. There are five of them, namely [BrO3-Io,.[Br-],, [,Ce3+],, [H’],, and k,. The results are given in two-dimensional projections of the five-dimensional figure. In principle, the temperature is also a constraint, through its influence on the rate constants. The system as a whole is very sensitive to temperature. This can be judged from the results of Geiseler and B a ~ E l iin~ which , ~ a change as small as 5 OC can take the system from one side of the oscillation region to the other. No data is known on the temperature dependence of the rate constants. We have used the three sets of rate constants and
-9
-IC
W[Br
oil0
Figure 1. [BrO
