2592
J. Phys. Chem. 1994,98, 2592-2594
Oscillatory Reaction in the Hydrogen Peroxide-Sulfite Ion-Hydrogen Ion-Hexacyanoferrate( 11) Ion System in a Semibatch Reactor Gyula RBbail and Ichiro Hanazaki' Institute for Molecular Science, Myodaiji, Okazaki 444, Japan Received: October 25, 1993; In Final Form: December 17, 1993'
Damped pH oscillations have been measured in the unbuffered reaction mixture of H~0&03~--H+-Fe(CN)& in a semibatch reactor when all the reagents were simultaneously flowed, at a constant controlled rate, into the reactor containing pure water in the beginning. Oscillations occurred within a limited range of the ratio of incoming reagent concentrations: 1.1 < [ H ~ O ~ ] O / [ S O ~ 1.0; [S032-]~/ [H+]o > 2. The known simple model, consisting of the empirical rate laws of the component reactions, has successfully been used to simulate the dynamical behavior.
Introduction In addition to the study of chemical reactions in a closed and continuous-flowstirred tank reactor (CSTR), experiments in the intermediate configuration, dubbed semibatch reactor,2can also be of practical and theoretical importance. A typical experiment in a semibatch reactor is performed by the controlled continuous admission of one or more reactants to a reaction vessel in which the other reactants are already present. It is also possible to introduce all the reactants into a reactor containing none of them at the start. In this latter case, only pure solvent was previously placed in the semibatch reactor. The most important difference between a CSTR and a semibatch reactor is that there is no outflow of the reaction products in the latter, and when the vessel is full, the input flow is stopped. Hence any phenomenon observed in a semibatch reactor can only be transient. Since many natural and industrial processes are realized in this intermediate configuration, the experiments with a semibatch reactor can serve as models for them. Furthermore, it can provide additional information for understanding of the mechanism of complex reactions, for example, chemical oscillators. Both closed reactor and CSTR problems with homogeneous oscillatory reactions have received very extensive treatment in the literature, and both of them have been proved to be powerful tools for experimental study of these phenomena. There are, however, many questions which cannot be answered on the basis of closed reactor or CSTR experiments. For instance, how does the gradual accumulation of certain products affect the dynamical behavior of the reaction? What does the lack of outflow cause in an otherwise open system? The answerscan provide additional mechanistic insights for the known oscillatory reactions so the application of the semibatch reactor in the study of nonlinear dynamical phenomena is justified. Although there has been no systematic application of semibatch reactor in this field, several important discoveriesare strongly connected to it. For example, the oscillatoryoxidationof benzaldehydes or NADH4with oxygen and the oscillatory reduction of bromate by Hz5 should be mentioned. In these cases, a continuous gas transfer from the gas phase to the liquid reaction mixture was maintained. A semibatchreactor has recently been suggested for the experimental study of several chemical reactions showing pH-regulated oscillations in a CSTR, and they have been found to show oscillations in the semibatch configuration as we11.6 The H20rS032--H+-Fe(CN)6C reaction system is known to oscillate and to show bistability in a CSTR.7 Large-amplitude oscillations were measured in the pH and simultaneously smallamplitude oscillations were observed in the concentration of the Abstract published in Advance ACS Absrracts, February 15, 1994.
0022-3654f 94f 2098-2592SO4.50f 0
hexacyanoferrate(II1) ion at certain values of the experimental constraints. An empirical rate law model was suggested to describe the dynamical behavior of the reaction system. The aim of the present study is to apply the semibatch reactor configuration to this system and to confirm if the suggested empirical rate law model could describe the dynamical behavior under semibatch conditions. On the other hand, the present system is closely related to the H202-Fe(CN)& reaction which has recently attracted considerable interest because of its light sensitivity.&ll Any new reliable information about H20&30p2--H+-Fe(CN)6k system is expected to be useful for refining the mechanism of the light induction and inhibition of the oscillation in the H 2 0 ~ F e ( c N ) ~ ~ reaction.
Experimental Section Materials. Analytical-grade reagents were used for all experiments. Potassium hexacyanoferrate(I1) was recrystallized from deoxygenated hot water in darkness. The other chemicals were used without further purification. All water was deionized and distilled from alkaline potassium permanganate in an allglass still. In order to avoid autooxidation and light-induced decomposition, stock solutionsof potassium hexacyanoferrate(I1) and sodium sulfite were prepared and kept from light under argon during storage. In spite of all these precautions, sodium sulfite solutions had to be prepared daily, because the decrease in its concentration was significant. Stock solutions of hydrogen peroxide were stored in plastic bottle to retard decomposition. Diluted sulfuric acid was used as source of hydrogen ion. The concentrations were determined by iodometric (in the case of Na2SOs), permanganometric (H202), and acid-base (H2SO4) titrations. Semibatch Reactor. A cylindrical-shaped glass vessel with a volume of ea. 500 mL (8 cm i.d. X 10 cm height) was used as a semibatch reactor. The temperature could be kept constant by circulating water regulated with a thermostat4 water bath in a double jacket surrounding the reactor. In order to measure the pH, the reactor was quipped with a combined SCEglass electrode. The reaction mixture was stirred at about 500 rpm with a magnetic stirring bar of 6 cm long. The reagent solutions were flowed in by a peristaltic pump (EYELA MP-3 type) at measured rates through two inlet tubes (i.d. 1.0 mm). The input points of the reactants were close to each other and close to the bottom of the reactor. The reactor was kept from light. Procedure. The desired volume of water was previously poured into the reactor. Stock solutions of Na2SO3 and H2SO4 were premixed with &Fe(CN)6 solution in a dark flask under argon, and this mixture was introduced into the stirred reaction mixture 63 1994 American Chemical Society
Oscillatory Reaction in H201S032--H+-Fe(CN)6’ PH
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Figure 1. Measured oscillatory pH-time curve in a semibatch reactor. Initial volume of the reaction mixture is 250 mL, and the flow rate is 5.55 X mL s-l. [H202]0 = 0.067 M, [S032-]~= 0.05 M, [ F c ( C N ) ~ ~ ] O = 0.02 M, [H+]o 0.014 M, T = 25 OC.
through one of the inlet tubes. Our control experiments showed that maintaining the reactor under the argon atmosphere was not necessary. Hydrogen peroxide solution was introduced through the other inlet tube. The flow rates of the two input solutions were the same so that the reactant solutions weremixed in a ratio of 1:l by volume. All measurements were conducted at 25.0 f 0.1 OC. The pH of the reacting mixture was monitored continuously. The efficiency of mixing is a key factor in a reacting system with a continuous inflow of reactants. It is especially true in case of an oscillating reaction. The present reaction is slow compared to the time required by mixing, and in the control experiments with different initial reactor volumes (250mL with 5.55 X 10-3 mL s-1 inflow rate, and 1000 mL with 2.22 X 10-2 mL s-1 inflow rate) the same dynamical behavior could be measured. Increasing the stirring rate from 500 to 1000 rpm has caused no noticeable effect on the observed kinetics.
Results Experimental Results. Our first task was to decide whether the system of H2O2SOp2--H+-Fe(CN)6’ was able to show oscillations under semibatch conditions. In an earlier work, several semibatch oscillators were created by introducing one of the reagents into the reaction mixture containing all the other components.6 The results of preliminary experiments led us to the conclusion that, in the present case, neither of the reagents can be applied in high excess if one wants to see oscillations. For this reason, none of the reagents could be placed in the reactor, but all of them had to be flowed simultaneously into pure water placed in the reactor previously so that the high excess of any reagent could be avoided. With this experimental setup, oscillatory pH-timecurves were measured. A typical oscillatorycurve, which is shown in Figure 1, is obtained when the initial volume of water in the reactor is 250 mL, the sum of the two incoming flow rates is 5.55 X 10-3 mL s-I, and the input concentrations of H202, SOa2-, Fe(CN)6’, and H+ calculated in the combined feed are 0.067, 0.05,0.02,0.014 M,respectively.
The oscillations are preceded by a long nonoscillatory stage. The initial pH of water in the reactor is about 6due to thedissolved air-CO2. The incoming reagent solutions are slightly alkaline, because the sulfite ion is in an excess over the hydrogen ion, and the pH quickly goes up to 7 as the reagents start to flow in. Then it drops suddenly, due to the oxidation of sulfite, and goes through a shallow minimum at pH 3.5-4.After the preoscillatory period, the pH starts to oscillatewith decreasingamplitude. Thenumber of oscillatory periods strongly depends on the experimental constraints and it can be as many as 30under favorableconditions. The periodic time of the oscillations ranges from 4 to 40 min depending mostly on the flow rate. The ratios of input concentrations are critical for the oscillation to occur. Since there are four reagents (H202, H+, Fe(CN)6’) in this reaction system, the optimum values of any ratio of two are affected by the values of other two component concentrations. Oscillation takes place only if the input concentration of hydrogen peroxide exceeds that of sulfite ion. The optimum appears to be 1.1 < [H202]0/ [SOa2-]o < 1.4 at [H+]0 = 0.0 14 M and at [Fe(CN)6’]o = 0.020M.Thelower limit of [Fe(CN)6C]o/[H+]~isalsocritical. At any value of the concentrations of other two components, no oscillations can be obtained if the concentration of hydrogen ion is not exceeded by that of hexacyanoferrate(I1). The upper limit of [Fe(CN)64]~/[H+]~ is, however, not so strict, and the oscillations gradually disappear as the ratio approaches 5. The ratio [S032-]~/[H+]~ is also important and it should exceed 2; otherwise the system remains in low pH state during the course of the reaction. The effect of absolutevaluesof the concentrations on the dynamical behavior is far less important than that of the ratios. Calculations. After showing experimentally that this system is capable of oscillating under semibatch conditions, our next task is to try to simulate this dynamical behavior. An empirical rate law model pertinent to this system has been proposed7 as summarized in Table 1. The model consists of eight-component reactions. It is emphasized that they are not elementary steps but complex component reactions, and many of them were studied separately. Their rate laws and the numerical values of the rate constants have recently been discussed and summarized,’ and they are shown in Table 2. The semibatch reactor experiments can be simulated by augmenting the empirical rate law model with inflow terms. The inflow terms are obtained by multiplying the input concentrations with the inflow rate constant which is defined by k, = r/V, where Vis the volume of reaction mixture in mL and r is the incoming flow rate in units of mL s-1. Although Vvaries with time as
Rdbai and Hanazaki
2594 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994
V = Vo+rt
PH
where VOis the volume of pure water at t = 0, it is satisfactory in our case to use an average value for the inflow constant: 7
The numerical integrations were carried out by a semiimplicit Runge-Kutta method.12 We found that no modification of the earlier proposed model is necessary in order to calculatethe main featuresof the dynamical behavior in semibatch reactor. However, a higher rate constant value (k5= 4 X 105 M-2 s-1 instead of 1 X 10s M-2 s-l) for reaction 5 gives better agreement between the calculated and measured curves. Reaction 5 affects the dynamics in a CSTR only slightly, because Fe(CN)&does not accumulatein CSTR mode. A typical calculated oscillatory curve is shown in Figure 2. It agrees well with the measured curve in Figure 1. The experimental and calculated periods are similar, and the calculated amplitudes are also similar to the measured ones. The number of oscillatory periods on the calculated curves depends strongly on the input concentrationof the sulfite ion: with the other three components and the flow rate being fixed ([HzOzlo = 0.06; [H+]o= 0.014; [Fe(CN)sC]o 3 0.02 M; ko 3 2 X It5S-’) at [s03’-]0 = 0.041 M two periods, at [S032-]~= 0.045 M 30 peaks, at [SOJ~-]O = 0.05 M two peaks appeared. No oscillations could be calculated beyond these concentration limits which agrees with the experiments. Similarlyto the experimentalfindings, the concentration of hexacyanoferrate(I1) can be varied on a larger scale than that of the sulfite ion, but oscillations can be calculated only if [Fe(CN)6’] is higher than [H+]. Discussion The experimental investigationsand modeling of thedynamical behavior of the reaction system of H202-S032--H+-Fe(CN).?in a semibatch reactor have been presented. The system shows sustained oscillations in a CSTR, but the oscillations are damped in a semibatch reactor showing only few peaks. One can wonder why the oscillations cease so quickly. The possible answer lies in the gradual accumulation of the hexacyanoferrate(111) ion during the course of the reaction. According to reaction 8, Fe(CN)& can remove the sulfite ion from the key autocatalytic reaction (reaction 1). The more hexacyanoferrate(II1) accumulates, the more sulfite ion is consumed in reaction 8, which leads finally to the cease of oscillations. This hypothesis can be supported by model calculations. Our simulationsshow that, for the oscillations to be long-lived,it is necessary to reduce the rate of reaction 8, or simply remove it from the model. Experimentally, an increase in the input concentration of the sulfite ion would have the same effect as decreasing [Fe(CN)&]. However, any significant increase in [SOQ] might violate the very delicate balance of the input concentrationratios required by theoscillation and might eliminate or decrease rather than increase the length of the oscillatory stage. Note that there are many other possible versions for realizing the semibatch configuration. For example, one may well ask what would happen if one prepares the solution with all reagents but S032-and feeds only SO3” externally. In this case, oscillations are not expected, because H+ is used up in the reaction between H202 and Fe(CN)64 (reaction 2) by the time S032-reaches the concentrationlevel necessary for the oscillation to occur. In order to avoid the early consumption of the hydrogen ion, another configuration should be applied: the reactor contains H202 and Fe(CN)6Gand the appropriate amount of acid and sulfite ion are fed. Despite searching a wide range of initial concentrations, we were not able to measure or calculate oscillations in this configuration. Other configurations have also been examined without positive outcome. It is, therefore, concluded that all the reagents should be introduced simultaneously into pure water,
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Figure 2. Calculated oecillatory pH-time curve in a semibatch reactor. k l p = 1.85 X 10-5 s-l. Concentrations as in Figure 1.
which seems to be the only configurationthat results in oscillatory kinetics in this system. We have not attempted at this stage to develop a detailed mechanism of this reaction system. Our aim here has been to confirm the empirical rate law model proposed earlier toward the ultimate development of a full mechanism. An empirical rate law model consistsof the rate equations of the complex component processes rather than elementary steps. This approach can be successfully applied for describing the dynamical behavior of a complex reaction system only if there is no significant interference between thecomponent reactions.13 Consequentlyif anempirical rate law model of a complex system can describe all the details of the kinetics, as is in the present case, one can develop a detailed mechanism for the system by summarizing the individual mechanisms of the component reactions. In our case, the mechanisms of all the component reactions but reaction 2 are well-known. The reaction between hydrogen peroxide and hexacyanoferrate(I1) (reaction 2) seems to be the key and the most complex component process. Despite the significant effort that has been made to decipher its mechanism, further work is needed in order to get a complete picture about it. This work is now under way in our laboratory. References and Notes (1) Permanent address: Institute of Physical Chemistry,Kossuth Lajos University, H-4010Debrecen, Hungary. (2) Coppersthwaite, D.P.; Griffiths, J. F.; Gray, B. F. J. Phys. Chem. )5, 6961. Jenacn, J. H. J . Am. Chem. Soc. 1983,105,2639. Lazar, J.; Ross, J. J. Chem. Phys. 1990,92, 3579. OrMn, M.; Eptein, I. R. J. Am. Chrm. Soc. 1981, 103, 3723. Rdbai, Gy.; Eptein, I. R. J. Am. Chrm. Soc. 1992,111, 1529. Rdbai, Gy.; Kustin, K.; Eptein, I. R. J . Am. Chem. Soc. 1989, I l l , Rdbai, Gy.; Kustin, K.; Epstein, I. R. J. Am. Chem. Soc. 1989, I I I , Mori, Y.; Srivastava, P. K.; Hanazaki, I. Chem. Lctf. 1991,669. Mori, Y.;Hanazaki, I. J. Phys. Chem. 1992,96,9083. Mori, Y.;Hanazaki, I. J. Phys. Chrm. 1993,97, 7375. Kap, P.; Pentrop, P. Numer. Marh. 1979, 33, 55. Rdbai, Gy.; Bazsa, Gy.; Beck, M. T. J . Am. Chem. Soc. 1979,101,
