Reexamination of Gas Production in the BrayâLiebhafsky Reaction

Article pubs.acs.org/JPCA

Reexamination of Gas Production in the Bray−Liebhafsky Reaction: What Happened to O2 Pulses? Erik Szabo* and Peter Ševčík

Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Mlynská dolina, 842 15 Bratislava, Slovakia ABSTRACT: Results of high-precision measurements of gas production in the BL reaction are presented, and an efficient kinetic model for their analysis is proposed. Based on this model, the data have been examined pulse by pulse, and for the first time, the entire records of gas production could be successfully reduced to series of just a few key parameters. It has been confirmed that the kinetics of O2(g) production is of the first order with respect to its precursor. Overall, only two steps have been found necessary to fit the observed pulses in gas production. The first step produces the precursor of the recorded O2(g), and its rate has two components. One component provides the peaks, and its approximation in the form of Gaussian functions has been found as satisfactory. The other component provides the constant baseline of gas production between the pulses. Finally, the precursor gives rise to O2(g) in the second step, and the simple first-order kinetics suggests that the precursor is otherwise relatively unreactive, making O2(aq) a logical candidate. However, the rate constant of this process showed almost perfect linearity with the actual concentrations of H2O2, and it was affected only little by variations in the rate of stirring. It thus seems possible that this final step in gas production, responsible for the majority of O2 produced in pulses, might not be the interphase transport O2(aq) → O2(g), as expected. Instead, it might be a truly chemical process, giving rise to O2(g) in a reaction of H2O2 with another precursor, which is not involved significantly in any other process, but it is not O2(aq). If this is true, the second-order rate constant of this process in the system with initial composition of 0.360 M KIO3, 0.345 M H2O2, and 0.055 M HClO4 at 60 °C would be 0.25−0.30 M−1·s−1, depending on the rate of stirring.

1. INTRODUCTION The Bray−Liebhafsky (BL) reaction is the oldest of the oscillating reactions, where the core of oscillations is now understood to be purely chemical. It might also seem as one of the simplest, since it starts from only three purely inorganic reactantsan alkali metal iodate, hydrogen peroxide, and an acid, usually sulfuric of perchloric. Yet, this seemingly simple mixture gives rise to very complex behavior, and even today it is often considered as one of the lesser explained oscillating reactions. Since the first report of oscillations in this system by Bray,1 there has been a long history of efforts to explain the intricate details of this interesting reaction, and in principle, two main lines of approaches to this problem can be identified. Thorough overviews of the early progress can be found in papers by authors grouped around Noyes,2−5 and these works also represent the foundations of the interpretation of the BL reaction that is somewhat analogous to the generally accepted explanation of bromate oscillators. The mechanism contains both radical and nonradical processes, and interestingly, in the radical part of the mechanism, O2 is considered a reactive intermediate, unfortunately making the mechanism quite vulnerably dependent on the rate of its interphase transport. Additionally, examinations of this mechanism proceeded exclusively through mathematical rearrangements, and thus its © 2013 American Chemical Society

applicability in direct numerical modeling of the BL reaction seems as limited. The second line of interpretation of the reaction can be, in fact, traced back as far as the works of Liebhafsky and his coworkers,6 who pursued explanation of the reaction in terms of purely nonradical processes. Over the years, much of the relevant chemistry was subject to thorough reexaminations, the work of Furrow7 being one of the most notable examples. The proposed mechanisms of the BL reaction evolved accordingly. The most recent and generally the most accepted in this line of work is the mechanism proposed by Schmitz and KolarAnić,8−10 shown to be capable of reproducing some of the key features of the reaction by direct numerical integration and without any further assumptions. It has also been employed in a number of studies of processes related to the reaction potentially influencing its observation, and hence importance of added reaction steps, most notably the interphase transport of I2 or O2, was also suggested.11,12 With the first of the named effects included, the reaction is represented by mechanism consisting of reactions 1.1−1.9. Received: July 29, 2013 Revised: September 13, 2013 Published: October 3, 2013 10604

dx.doi.org/10.1021/jp407540s | J. Phys. Chem. A 2013, 117, 10604−10614

The Journal of Physical Chemistry A

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relationship of the extracted parameters to the actual concentrations of H2O2 in the system. However, to distinguish these chemical effects from changes in gas production due to purely physical effects, for example, the variations in the amounts of gas bubbles dispersed in the reaction medium, the measurements of gas production had to be repeated for various rates of stirring. Although we were not primarily concerned with the stirring effects, the contrast between the changes in gas pulses due to varied rates of stirring and their changes due to decrease of H2O2 during the reaction was found to be a very useful indicator of the most likely origins of our observations, and in the end, the results obtained were found to imply a rather unexpected conclusion.

2. EXPERIMENTAL SECTION Chemicals. The following substances were employed to prepare the BL oscillator: KIO3 (ACS reagent, Sigma-Aldrich, product number 215929, lot MKBF5678V), certified as 99.5%, was employed as supplied; HClO4 (ACS reagent, SigmaAldrich, product number 244252, lot STBC3344V), supplied at 70.0%, was diluted to 0.46 M stock solutions, stored for no longer than a week; stabilizer-free H2O2 (puriss. p.a., ACS reagent, Sigma-Aldrich, product number 95313, lot BCBG6364V) was also used as supplied, at 30.8% concentration, which was regularly checked by a standard manganometric procedure. All chemicals were stored and used taking all precautions against any modification of their guaranteed composition. The certificates of analysis with detailed specifications of their quality are available online at the supplier’s Web site or can be provided upon request. All glassware for manipulation with the chemicals, flasks as well as pipettes, were brand new and had never been in contact with any other chemicals. Employed throughout was only water from a Demiwa ROI water purification unit, decontaminated of organic matter and deionized to specific conductivity ≤1 μS·cm−1. The saturated mercurosulfate reference electrode was prepared from polarographic mercury (puriss. p.a., Fluka), Hg2SO4 (≥98%, Aldrich) mildly acidified with H2SO4 (p.a., Merck), and K2SO4 (puriss. p.a., Sigma-Aldrich). As the hydraulic fluid in the detection compartment of the apparatus, 5.0−5.5% solutions of nonionic neutral pH detergent AQUET (Bel-Art Products) were employed. After each measurement, the whole apparatus was cleaned with laboratory glassware cleaner Mucasol (Merz Hygiene GmbH). It was shown not to affect the reaction even after adding 0.5 cm3 of concentrate into 30 cm3 of the BL reaction mixture. On the other hand, without cleaning the apparatus, reproducibility of the results gradually deteriorated significantly. Apparatus. Measurements were conducted in the same apparatus as our earlier measurements of gas evolution from UBOs.41 Reactions took place in a cylindrical round-bottom vessel charged with 30 mL of the reaction mixture, the vessel being jacketed and connected to thermostat LAUDA E100. Stirring was maintained by a digital magnetic stirrer IKAMAG RCT and a 10 × 10 × 5 mm cross-shaped PTFE-coated magnetic stir-bar. The reaction was monitored potentiometrically by two electrodes. The mercurosulfate reference electrode was prepared from mercury covered with a paste of Hg2SO4 in 0.01 M H2SO4 saturated with K2SO4, and surrounded with crystals of K2SO4 in its saturated solution. The indicator electrode was made of Pt wire, 0.5 mm in diameter and 5 mm

Still, this is most likely not the final mechanism of the BL reaction, as the field remains quite active. Important information continues to be published, regarding the kinetics of the relevant chemistry of iodine,13−21 as well as the role of radicals in the reaction,22−25 the overall dynamics of oscillations,26,27 or new methods applicable to their monitoring.28 Unfortunately, very little effort has been dedicated to studying the gaseous products in the BL reaction, despite the fact that H2O2 is one of its core reactants and O2 is the main product of its decomposition. Measurements of its production were reported mainly in the earlier works concerning the reaction,1,29−35 and even though several slightly more recent papers are related to the dynamics or composition of the gaseous products of the BL reaction,36−39 only one work was concerned with measurement of the gas phase explicitly.40 This is most probably due to the fact that precise experimental work with gases is inevitably accompanied with many practical complications, and so, such measurements are not very popular. However, we have recently reported a fully automatic method of high-precision measurement of gas production, based on monitoring displacement of liquid by the gas on a digital balance, and it was successfully applied even to the uneasy task of time-resolved quantification of very small amounts of gas produced in uncatalyzed bromate oscillators (UBOs), conventionally coined as bubble-free.41 Herein we would like to present the results of our method applied to production of O2 in the BL reaction and their analysis. At the beginning of our work, our main objective was to verify if the production of O2(g) really follows kinetics of the first order, as previously assumed in numerical modeling,12 and if it does, what is the rate constant of this process. Therefore, the primary task was to develop a working numerical model, which could be used to analyze the records of gas production pulse by pulse, and determine the corresponding rate constants and their evolution during the reactionsince such analysis of gas pulses in any oscillating reaction had never been attempted before. After the model had been developed and successfully applied, our assumptions were confirmed, and for the first time, the entire records of gas pulses in the BL reaction were successfully reduced into series of just a few key parameters. Analysis of the results showed that it could be interesting to investigate the 10605



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Figure 1. Typical results of the measurements of the BL reaction (for details of composition and reaction conditions, please, refer to the text) at two different rates of stirring; 250 rpm (a) and 1000 rpm (b): greenthe potentiometric signal of a Pt electrode, bluethe volume of O2 produced, yellowthe corresponding rate of gas production. Scales relevant for each signal are in the same color. (Please, note that ratios of the maxima of blue and yellow scales are different for the full graphs and for their details).

rates of their stirring were varied among values of 250, 500, or 1000 rpm. Each measurement started with charging the reaction vessel with approximately 2.33 g of powdered KIO3, 3.5 cm3 of approximately 0.46 M stock solution of HClO4, and 25.5 cm3 of water. All of the substances and glassware were weighed with each step of preparation of the reaction mixture, to determine its composition as exactly as possible. The apparatus was then assembled, and the reaction vessel was veiled with aluminum metal foil. Several readings of the digital balance were recorded for various heights of the hydraulic liquid level in the detection cylinder to determine the parameters needed for subsequent evaluation. The glovebox containing the whole setup was then closed, and stirring of the reaction mixture, as well as heating the jacket of the reaction vessel with thermostat set to 60 °C, was initiated. After the target temperature had been reached, the setup was left to thermally equilibrate for further 1800 s. Finally, the stopcock on the pipettor-like construction element above the reaction mixture, charged with 1.0 cm3 of H2O2, was opened, letting this last reactant initiate the reaction. The reaction was then monitored undisturbed for total of 12 000 s. When the measurement had been finished, the apparatus was dismounted and thoroughly cleaned. Evaluation. The readings of mass indicated on the balance for various heights of the detection liquid level, recorded before the measurement, were used to calculate the parameters of the relationship between these two quantities, specific for the actual setup. The relationship was then employed to convert the data from the balance, recorded during the reaction, into the corresponding heights of the level of liquid in the detection compartment and the volumes of gas enclosed inside the apparatus. The pressure inside the apparatus was calculated based on the pressure data from the thermohygrobarometer and the hydrostatic pressure of the liquid in the detection column. Using the state equation of gas inside the apparatus determined during its calibration, the volumes of gas inside the apparatus were converted to the corresponding volumes at 25 °C and 101 325 Pa. The amount of gas present in the

long. The potential difference was measured on a digital multimeter METEX M-4660A, transmitting the signal to a desktop PC. The gas produced in the reaction vessel was conducted into the detection compartment, consisting of a bottomless graduated cylinder immersed in a beaker with detection hydraulic liquid. Gas entered the cylinder through the opening at its top, and the open bottom of the cylinder remained the only point where the system was in mechanical contact with the surroundings. Therefore every change in the amount of gas inside the apparatus was reflected in movement of the detection liquid, measured very precisely on a digital balance Axis AD200 placed under the beaker. The readings of the balance were, too, transmitted to the PC, as well as the readings of a digital thermohygrobarometer COMET D4130, monitoring atmospheric pressure and the temperature in the insulating glovebox, where the whole apparatus was enclosed. Calibration of the apparatus was based on injecting known amounts of air at room temperature and on measurements of the quantitative decomposition of known amounts of H2O2 with MnO2 at the elevated temperature of the BL oscillator. As demonstrated by the calibration results, the relationship between the volume of gas enclosed within the apparatus and the readings of the balance was linear. Its relationship to the data of pressure and temperature from the thermohygrobarometer corresponded very well to the ideal state equation of a gas consisting of one fraction that is at the temperature of the reaction vessel and the remainder at the indicated temperature of the surroundings. Further details of the construction of the apparatus, as well as its calibration, can be found in our paper on measuring gas production in UBOs,41 where the apparatus is depicted in Figure 1. Procedure. Measurements were performed for BL oscillators with compositions as close to 0.360 M KIO3, 0.345 M H2O2, and 0.055 M HClO4 as possible. The total amount of the reaction mixture was 30 cm3, the reaction temperature was 60 °C, and all measurements were performed in dark. Reactions were initiated with H2O2 added as the last reactant, and the 10606



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dependence of tpk,N on their number in the record N was expressed by a single cubic equation, and thus all the original information of the distribution of oscillation in the reaction was compressed into just four parameters, efficiently avoiding any possibility of deformation of the results by random fluctuation. Based on the acquired equations of the polynomials tpk(N), the induction period of the reaction (as a result of the polynomial fitting free from any fluctuations in the proximity of peak 1) was calculated as the value of tpk(N) for N = 1. The initial period of oscillations (as a result of the polynomial fitting free of any fluctuations in the proximity of peaks 1 or 2, and free from the effect of period growth between peaks 1 and 2) ′ (1), the first derivative of tpk(N) at N = 1. was calculated as tpk Finally, the number of oscillations (with the help of the polynomial fitting not limited to an integer) at time 6000 s, when all reactions neared completion, was calculated as the value of N yielding tpk(N) = 6000. We believe, that these parameters, obtained as described, should carry enough information with enough precision to relate our experimental conditions and our results with those of future works, and the values of these parameters measured at various stirring rates are summarized in Table 1.

apparatus at the beginning of the reaction and the amount representing water vapor were subtracted, and the corresponding rates of production were calculated by simple centered numerical derivation. Finally, the results acquired were examined, searching for kinetic models that could fit the measured O2 production, in order to help reduce the data to only a few key parameters and relationships. At the same time, one of the main objectives of this work was to verify the hypothesis that the release of O2 can be broken down into two subsequent processes, the first encompassing all the nonlinear behavior and the second following simple kinetics of the first order. Ultimately, the key parameters of the resulting kinetic models of the best fit were expected to be analyzed from two contrasting points of view, showing how the results were affected, on one hand, by the varied rates of stirring and, on the other hand, by purely chemical influence of the concentrations of H2O2 changing in the course of the reaction, as calculated from the recorded volumes of O2.

3. RESULTS AND DISCUSSION Altogether, 34 well-reproducible measurements of the BL reaction were performed, 11−12 for each rate of stirring, the actual compositions ranging in the intervals 0.3639−0.3693 mol·kg−1 KIO3, 0.3405−0.3531 mol·kg−1 H2O2, and 0.0547− 0.0560 mol·kg−1 HClO4, in total of 32.440−32.528 g of reaction mixtures (if zero change of volume due to mixing is assumed, this corresponded to 30.108−30.201 mL of solution). The preceding set of 13 measurements was affected by deteriorating reproducibility due to the necessity of cleaning the apparatus with detergent after each reaction, and so, these results were not considered in further evaluation. The potentiometric monitoring of the reactions afforded typical BL traces, and in all cases the data of O2 production clearly showed well-pronounced pulses, as reported previously.1,32,33,40 Typical results obtained are depicted in Figure 1, which also demonstrates the obvious effect of the varied rates of stirring on the courses of all of the signals measured. 3.1. General Characterization of Observed Reactions. As already mentioned, investigation of the effects of stirring on the reactions was not the primary objective of this work, and stirring was used only as an indicator of the extent to which the observed dynamics of gas pulses might be affected by physical, rather than chemical factors. Nevertheless, general characterization of the observed reaction and their changes at various stirring might provide important reference information for relating our experimental conditions with those of future studies. Therefore, analysis of changes in distribution of oscillations, as well as the total gas production at various stirring, could not be left unaddressed. Distribution of Oscillations. Before evaluation of the measured gas production, we first examined the potentiometric signals. To minimize the possibility of the results being affected by imperfections in the course of the reaction natural for any record of an oscillation reaction, the parameters of interest were extracted by numerical analysis of the data according to the following algorithm. The discrete series {tpk,1, tpk,2, ... tpk,N, ...} of the times tpk, when peaks number 1, 2, ... N, ... appeared in the potentiometric signal, was first converted into a continuous function tpk(N), expressed in the most general form of a polynomial. More specifically, third order polynomials were sufficient to reach correlation coefficients between tpk and N that were practically 1 for all records. In other words, the

Table 1. Variation in the Distribution of Oscillation in the BL Reaction with Varied Stirring stirring rate

induction period (s)

period of oscillations at their onset (s)

number of oscillations at 6000 s

250 rpm 500 rpm 1000 rpm

636.0 ± 37.2 788.1 ± 38.8 830.0 ± 38.7

232.6 ± 8.4 234.7 ± 7.9 262.7 ± 9.6

23.4 ± 0.4 18.8 ± 0.4 17.6 ± 0.5

Total Production of Gas. As another important parameter of general characterization of our experimental conditions and results, the recorded volumes of gas were compared with the amounts of H2O2 charged into the reaction mixture. In all cases more O2 was produced than what would correspond to stoichiometric decomposition of H2O2, and this excess varied with the rate of stirring. While the excess O2 production at 250 rpm was only 2.44 ± 0.21% (0.512 ± 0.001 equiv of H2O2), at 500 rpm it was increased to 4.66 ± 0.23% (0.523 ± 0.001 equiv of H2O2) and at 1000 rpm to 6.13 ± 0.37% (0.531 ± 0.002 equiv of H2O2). These figures, too, confirm that stirring does influence the BL oscillator on a chemical level, and this aspect needs to be taken into account when oscillations in the BL reaction are studied, and in particular, when results from different apparatuses have to be compared. However, the work presented was intended to focus on the analysis of the dynamics of gas production, and the varied rates of stirring were supposed to serve only as a factor in contrast to purely chemical influences on the reactions. Therefore, the data collected do not provide enough detail to make any further comments on the origins of these stirring effects, and closer examination of these observations must be pursued in the future. 3.2. Dynamics of Gas Production in Induction Period. In all measurements, gas was produced right from the initiation of the reaction, and the rate of this production was increasing consistently. However, the increase gradually slowed down, and soon, the rate of gas production was almost constant. When examined more closely, the course of these changes in the rates of gas production seemed to be exponential in essence. 10607



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Extracted Values of Rate Constants. When all results were compared, the acquired optimal values of k1 and kg, as well as the values of volumes of gas Vg at the onset oscillations, were generally very consistent. They showed clear dependence on the rate of stirring, and it is interesting to note that on one hand, the measured values of the rate of gas production v2 just before the onset of oscillations varied with stirring relatively little. On the other hand, the results of the model suggest that the shape of this rate of production (as opposed to the final values) was affected to a much greater extent, as indicated by the pronounced influence of stirring on the rate constants k1 and kg. The individual values are summarized in Table 2. Hypothetical Gas Phase and No Loss of Generality. Regarding the generality of the given values, the first-order rate constant kg is independent from the total amount of reaction mixture, as well from the choice of the reference conditions. It applies as long as both variables in models 2.1−2.2 (the gas produced and its precursor) are expressed in the same way, whether gas phase volumes (Vg and Vhyp) or concentrations in the reaction solution ([O2(g)] and [O2(hyp)], or [O2(aq)], for example). On the contrary, the given values of the rate constant k1 only apply if the precursor variable is expressed as volume of gas Vhyp. However, should the precursor be needed expressed in terms of concentration in the reaction solution, the rate constants k1 from Table 2 only need to be converted according to the ideal gas law and the approximation of the volume of reaction solution 30.155 ± 0.024 cm3; that is, the values need to be divided by the factor of 737.8 ± 0.6 mL·M−1. Analogously, if this factor is used to multiply the rate constant kg, it is also applicable to a modified model with the precursor variable expressed in terms of concentration and O2(g) expressed in terms of gas phase volume. In other words, after these conversions, with rate constants as k′1 = k1/(737.8 ± 0.6 mL· M−1) and kg′ = kg(737.8 ± 0.6 mL·M−1) the model of gas production 2.1−2.2 can also be transformed as follows:

Searching for the most parsimonious model to approximate the observed behavior, a sequence of two processes, the first step with a constant rate and the second step following kinetics of the first order, appeared as a sensible choice. Introduction of Hypothetical Gas Phase. Even though such a model requires another variablea precursor to O2(g)and in our measurements only O2(g) was followed, we managed to bypass this obstacle without any loss on generality of the model. A hypothetical gas phase O2(hyp) was assumed, representing what O2(g) would be like, if the second process were infinitely fast. This hypothetical phase can be either identified directly with O2(aq), should the second process be the interphase transport, as suggested in previous works,12 but as will be shown later, it can also serve equally well to extract relevant information for any other precursor to O2(g). Two-Step Gas Production in Induction Period. The measured production of O2(g), expressed as its volume Vg, was, therefore, compared to a two-step model, where we had to determine the course of one extra variablethe volume Vhyp of the hypothetical gas phase O2(hyp), and the values of two unknown parametersthe rate constants k1 and kg:

As Figure 2 demonstrates, this model met the experimental data very well. In all cases, the trace of O2(g) volume Vg, obtained from the model after identifying optimal values of k1 and kg, was practically identical with the results of measurements.

Induction Period and the Precursor to O2(g). Regarding the volumes of gas that had already been produced at the onset of oscillations, as stated in Table 2, these values apply to the total amount of the reaction mixture 32.484 ± 0.025 g. The corresponding volumes of the hypothetical precursor gas phase O2(hyp) were around 20 mL at stirring of 1000 rpm and around 50 mL at stirring of 250 rpm, or around 0.03 and 0.065 M, respectively, if expressed as concentrations. It is not completely impossible that these concentrations represent O2(aq) dissolved in the reaction mixture due to supersaturation. It has been mentioned in a previous paper12 concerning the dynamics of gas production in the BL reaction

Figure 2. Gas production during the induction period of BL reaction, obtained from model 2.1−2.2 with optimized parameters k1 and kg, compared to experimental data; the total volume of gas produced (a), and the rate of its production (b): blueexperiment, redmodel rate of production of gas, greenmodel rate of production of the hypothetical precursor gas phase.

Table 2. Parameters of Gas Production during the Induction Period of BL Reaction gas production at onset of oscillationsa

a

rate constantsb

stirring

volume Vg (mL)

rate v2 (10−2 mL·s−1)

k1 (10−2 mL·s−1)

kg (10−3 s−1)

250 rpm 500 rpm 1000 rpm

12.9 ± 1.4 17.1 ± 1.1 21.7 ± 1.2

3.24 ± 0.09 3.72 ± 0.09 3.87 ± 0.09

9.62 ± 0.49 4.99 ± 0.49 4.68 ± 0.51

0.71 ± 0.14 1.74 ± 0.33 2.29 ± 0.50

Measured experimentally. bEvaluated from experiment by fitting to models 2.1−2.2. 10608



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reasons a Gaussian function seemed to be the best choice, as it is perfectly continuous, expressed by a single equation and at the same time offers quite a lot of flexibility within just a few key parameters. Finally, out of the several possibilities to specify a Gaussian, the following parameters were chosen for the most graphical representation of the rate vpk responsible for the peaks in production of the precursor to O2(g): the time of the peak center tpc, total volume of the gas pulse under the peak Vpls, and the maximum of gas production rate vmax. Modeling the Baseline Gas Production Rate. To represent the baseline rate of gas production vbas and its transition from the level vbbf before the peak to the level vbaf after the peak, it seemed the most sensible to synchronize this function with the Gaussian, and so the formulation of vbas was based on the integral of vpk. However, it showed impractical to superimpose vbas into the first step of the model together with vpk. Even though theoretically it should be a part of this step, contributing to production of the precursor variable, this would have an unpleasant effect on the results of numerical integration of the model. In the beginning of the integration, until such amount of precursor is accumulated that it sustains the required steady state baseline rate of gas production, the production of gas would be exponentially curved. Therefore, vbas had to be included as a part of the second step, so that the model is able to fit the experimental data, reproducing a constant rate of gas production right from the start of its integration. Complete Model of Gas Pulses. Altogether, the model for representing and examining the experimental data for a single O2 pulse was designed as follows:

that, on the basis of the reported temperature dependence of critical supersaturation of O2 in water,42 a concentration of 0.065 M can be estimated for its value at 60 °C. If supersaturated O2 is the key precursor to the recorded phase, the agreement of this value with the concentration obtained by analysis of our experimental records according to the proposed model is rather astonishing. Otherwise, should the precursor variable stand for any other intermediate species in the mechanism of the BL reaction, the observed difference in its concentrations would be quite a remarkable effect of stirring. It seems quite likely that this might be the case, if we consider that induction periods are followed by a relatively intensive pulse of O2 production, and this would most probably induce a release of a significant part of such supersaturation. Under these conditions, with supersaturation being the cause of the differences in gas production during the induction period, the volume of O2 produced in the first pulse should be somewhat larger at low rates of stirring, since the supersaturation is much larger, too. But as will be described next, exactly the opposite was observed. 3.3. Model for the Dynamics of Gas Pulses. As the pulses of gas production following the induction period were examined more closely, it was found that they all exhibited the same structure. Right before the pulse, the gas was produced at a practically constant rate. The pulse in gas production then consisted of a sharp peak in the rate of gas production, followed by a relatively gradual decrease, which again seemed to be exponential. Eventually the gas production settled again to a constant rate, each time a bit lower than the previous. Two-Step Gas Production in Pulses. As in the case of the production of gas in the induction period, it seemed sensible to represent the observed signal as a result of a sequence of two steps, the first producing a precursor to O2 gas phase and the second following the kinetics of the first order. However, this time the first step required more attention, as it had to incorporate a component giving rise to the sharp peaks in gas production, as well as two different levels of baseline gas production, before and after the peak. Modeling the Peaks in Gas Production Rate. To choose an adequate representation of the peaks in the rate of production of the gas phase precursor, it was necessary to consider what kind of information these peaks can provide. Of course, in theory the peaks are a complex reflection of the kinetics of entire system, and details of their shape depend on details of all preceding reaction steps. In reality, the possibilities of analysis of the peaks are not without limitations. The peaks in the rate of O2(g) production are already rather sharp. Luckily, our highprecision data were able to capture the first-order decay on their trailing edges. However, after this is isolated, the peaks in the rate of production of the precursor to O2(g) are even sharper, and this remains as the most prominent feature in their shape. Adding that the precision, and particularly, time resolution of our data is finite, there is not much more kinetic information left to be extracted. Fortunately, our ambitions were much more realisticour objective was to study the dynamics of gas production, not the core of oscillations. For this purpose, the peaks in the rate of production of the precursor to O2(g) do not need to be represented to the very details of their kinetic structure. The sharpness of the peak was, in fact, such a prominent feature of its shape, that any mathematical function providing a peak could probably be useda triangular peak would very likely do as well as a sawtooth peak, for example. However, for practical

The experimental data of gas production were examined according to this model pulse by pulse, and the parameters of the model 4.1−4.4 were optimized for the best fit with the observed data. The individual components of model, as well as the typical results of its performance at representing the experimental data, are illustrated in Figure 3. Adequacy of the Proposed Gas Pulse Model. As clearly seen from Figure 3, the formulated model 4.1−4.4 was very successful in representing the experimental results. This procedure worked very well for almost all examined gas pulses within our measurements, except for a number of pulses at the very end of a couple of records, when the production of gas was very weak and the signal was deformed by noise or small mechanical disturbances of the setup. Based on these results, it can be concluded that the production of the precursor to O2(g) really can be quite safely broken down into two components, one providing the peak and the other the baseline levels in its rate. More importantly, it also seems justified to formulate the final conversion of the precursor into O2(g) as a process with first-order kinetics. This proved to work very well throughout the reactions and for all rates of stirring, and thus this idea seems well-grounded, even in spite of the small systematic deviation from the perfect firstorder behavior, as visible in the overview of a gas pulse in 10609



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stirring rates, but even more so due to the course of the reaction. To quantify this observations exactly, we took notice of two important facts. First, unlike the influence of stirring, the extent of reaction affects the production of gas in a way that is predominantly chemical in its nature. So it makes sense, when looking for the origins of this effect of the extent of reaction, to search for the responsible reactants, or intermediates. From this point of view it was very important that during the reactions all of the observed parameters gradually decreased to zero, and the overall shape of their dependence on time was very similar to that of the total amount of gas produced, only inversed. Therefore it seemed sensible that the data should be confronted against the corresponding [H2O2]. Luckily, these could be easily approximated from the recorded amounts of O2 based on the assumptions that the total volume of gas produced corresponds to all H2O2 having decomposed and that the same proportionality between these two applies during the whole reaction. The typical results of the obtained dependences of the parameters of interest on [H2O2], as well as the varied rates of stirring, are depicted in Figure 4. Figure 3. A pulse in gas production during a BL reaction, as obtained from model 4.1−4.4 with optimized parameters vbbf, vbaf, vmax, tpc, Vpls, and kg, and from experimental data compared; the total volume of gas produced (a), the rate of its production, detail of the bottom of the peak (b), and the overview of the whole peak (c): blueexperiment, redmodel rate of production of gas, greenbaseline rate of gas production, violetGaussian peak representation of the gas pulse.

Figure 3c. Difficulties were also observed in the optimized values of the maximum rates of gas production vmax, which were much less regular than the measured peak maxima, as illustrated, for example, in Figure 1. But at this point, it is important to realize that the formulated model and the procedure of fitting were incredibly simple, and thus there are several possible sources of error. First, in reality, the pulse in the rate of production of the precursor to O2(g) phase is most probably not Gaussian but has a more intricate structure. Likewise, the mechanism of the final step in the production of O2(g) might, in fact, encompass more channels producing O2(g) simultaneously, as also suggested by the reaction mechanism 1.1−1.9, where both reactions 1.5 and 1.8 yield O2. Not mentioning, that as explained earlier, for practical reasons our model 4.1−4.4 incorporates the baseline level of production of the precursor variable in the second step of the model instead of the first. At the same time, it is important to bear in mind that optimization of the model to fit the experimental data is a rather nonlinear optimization problem, and it can get trapped in local optima, especially if we remember that our data is, in fact, discrete, and the peaks in gas production are rather sharp. Actually, considering all of these possible obstacles of the model, it should be concluded that it proved as working surprisingly well and deserves to be considered as very useful for further examinations of the O2 pulses in the BL reaction. 3.4. Extracted Parameters of Gas Production. With the help of the developed model 4.1−4.4, all of the measured traces of gas production in the BL oscillators were successfully reduced, pulse by pulse, to sequences of just a few parameters, as the pulse in Figure 3, and further analysis focused only on these obtained values. Chemical Effects behind Gas Pulses. It was observed that all of the parameters of the model 4.1−4.4 varied due to different

Figure 4. Typical results of dependences of the parameters describing production of gas during the BL reaction according to model 4.1−4.4 on changes of [H2O2] in the course of the reaction, as well as on varied rates of stirring (for clarity, only a few selected experiments with the greatest dispersion of the results are presented); the volume Vpls of gas produced in individual pulses (a), the baseline rate vbbf of gas production outside pulses (b), and the rate constant kg of the final step of gas production (c): purple ■, 250 rpm stirring; blue ●, 500 rpm stirring; green ▲, 1000 rpm stirring. 10610



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Table 3. Dependence of the Parameters of Gas Pulses on [H2O2]

Correlation of Parameters with [H2O2]. As indicated in Figure 4, all of the parametersthe total volume Vpls of gas produced in individual pulses, the baseline rate of gas production outside pulses vbbf (and, of course, equally well vbaf), and the rate constant kg of the final step of gas productionthey all show a strong and almost linear dependence on [H2O2]. More precisely, the evolution of the values of Vpls is, in general, well-described by a quadratic dependence. As expected, this is also the most affected by the rate of stirring, since the increased numbers of oscillations at slower stirring yield smaller amounts of gas produced in individual pulses. The values of vbbf exhibit a slightly more complicated evolution, sufficiently described only by a cubic dependence. Finally, the values of the rate constant kg show almost perfect linearity with [H2O2]. In case these should be found useful for the reference of any future works, individual parameters of these dependences, as extracted from our experiments, are summarized in Table 3. It was not very surprising that the relationship between Vpls and [H2O2] is not too simple, in fact the quadratic dependence is still relatively straightforward considering the great number of variables that can influence the shape of a single pulse. To the contrary, the course of vbbf was found as a rather striking contrast. On one hand, the measurements proved that the baseline production of O2 can be quite successfully analyzed as relatively autonomous from the processes giving rise to the pulses. Yet, it was observed to still exhibit a considerable level of nonlinearity, strongly suggesting presence of several competing factors at play. However, the most surprising result came from the dependence of the rate constant kg. What is the Last Step in Recorded Gas Production? Even though a certain extent of the effect of stirring is beyond doubt, the rate constant kg of the very last step of gas production is clearly in almost perfectly linear relationship to [H2O2]. Even though not impossible, this would be rather unlikely if the final step of gas production were a purely physical interphase transport of gas from O2(aq) to O2(g), as in this case it could be expectable that the rate of stirring should have a much greater effect on the process than [H2O2]. Our results seem to suggest exactly the opposite, that by following the gas phase we have measured directly the chemical production of O2 in the reaction. This is of pseudofirst order

only when just one pulse in gas production is considered but is, in fact, second order, when data is observed on a larger scale, where [H2O2] changes appreciably. This does not seem so farfetched if we realize that analogous kinetics of gas production is already present in the currently recognized mechanisms of the BL reaction, namely, in reactions 1.5 and 1.8. However, these cannot be responsible for the observed results as the concentrations of HIO return from their peak values back to the baselines very quickly due to other reactions, and on the other hand, the concentration of iodate is practically constant throughout the reaction. Gas Pulses and the Precursor to O2(g). To account for the observed results in a chemical way, another intermediate reacting with H2O2 to give the majority of gas produced in pulses, but otherwise relatively unreacitve, would have to be identified. That this might, in fact be the case, is to some extent supported by the mechanisms of the BL reaction taking into account the radical processes, where a large contribution to the pulsed production of O2 comes from the second-order decomposition of HOO radicals. Whereas this also would not give satisfactory explanation of our results, it definitely seems worthwhile to continue in considering the alternative that the mechanisms behind our observations might be chemical. Since no other species besides O2 was quantified in our measurements, we realize that the possibilities to discuss the observed results and to interpret the evaluated parameters are, at the moment, rather limited. However, the fact that our data was not sufficient to identify the precursor to O2(g) with definite certainty should not diminish the fact that we have managed to analyze the kinetics of the final step in gas production, determine the respective rate constants, and suggest their relationship to [H2O2]. In fact, it is not at all rare that the kinetics of a reaction can be characterized from measurements of products before all details are known about reactants, and we hope that the data and the methodology presented will stimulate further investigations that could clarify the unknown aspects to a much greater detail. 3.5. Gas Pulses: Experiment and Theory. Having measured and analyzed the experimental records of O2 pulses, it was unavoidable to confront these results with the corresponding predictions of the mechanism, which was shown to work relatively well in so many other regards. 10611



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Therefore, we integrated the mechanism 1.1−1.9, with rate constants in Table 4, taken from a previous work,11 only here expressed with a more convenient unit of time. Table 4. Rate Equations and Rate Constants Used for Integration of Mechanism 1.1−1.9 reaction 1.1

rate equation

v1 =

k1[IO3−][I−][H+]2

− k −1[HIO][HIO2 ]

−3 −1

3

k1 = 3.0 × 10 M ·s ; 1.2

k −1 = 1.318 × 106 M−1·s−1

v2 = k 2[HIO2 ][I−][H+] k 2 = 8.33 × 109 M−2·s−1

1.3

v3 = k 3[I 2O] − k −3[HIO]2 k 3 = 83.3 s−1;

1.4

k −3 = 5.25 × 106 M−1·s−1

v4 = k4[HIO][I−] − k −4[I 2]/[H+] −1 −1

9

k4 = 5.0 × 10 M ·s ; 1.5

k −4 = 7.50 × 10

Figure 5. Results of the BL reaction mechanism 1.1−1.9 for 30 cm3 total volume of reaction mixture and initial composition of 0.360 M KIO3, 0.345 M H2O2, 0.055 M HClO4, and 10−9 M I−: greenthe simulated potentiometric signal of a Pt electrode, bluethe volume of O2 produced, yellowthe corresponding rate of gas production. Scales relevant for each signal are in the same color.

−1

M·s

+

v5 = (k5′ + k5″[H ])[HIO][H 2O2 ] k5′ = 2.0 × 102 M−1·s−1;

1.6

−2

k5″ = 5.0 × 102 M−2·s−1

v6 = k6[I 2O][H 2O2 ] k6 = 3.33 × 103 M−1·s−1

1.7

visible, and the mechanism, in fact, predicts gas to be produced virtually monotonously. Of course, the absence of the exponential decay of the peak rates of gas production back to the baseline levels could be solved by simply supplying the mechanism with an extra process, the interphase transfer of O2 from the solution into an individual gas phase. However, as mentioned above, this still would not account for the observed fact that the rate constant of this process should change in the course of the reaction, and moreover, that it should seem almost perfectly proportional to [H2O2] left in solution. Even so, making the predicted peaks in the rate of gas production as high as to correspond to the experimental values would still inevitably call for some revision in the established parts of the mechanism, as well, perhaps starting with the rate constants employed. However, we have tried many modifications in the rate constants, and we have to conclude that the mechanism seems to be very inflexible in this regard. Our efforts to obtain a better match of its predictions with the measured gas production by only accommodating the rate constants were not met with any success. Therefore the goal of a more fundamental revision of gas production predicted by the mechanism must be set for future work.

v7 = k 7[HIO2 ][H 2O2 ] k 7 = 10 M−1·s−1

1.8

v8 = (k 8′ + k 8″[H+])[IO−3 ][H 2O2 ] k 8′ = 4.5 × 10−6 M−1·s−1;

1.9

k 8″ = 1.87 × 10−4 M−2·s−1

v9 = [I 2(aq)]

k 9 = 3.33 × 10−4 s−1

Even though it is known that the mechanism does not describe the BL reaction absolutely quantitatively, it has successfully reproduced some of its important qualitative features, for example, the expected shape of oscillations in the signal of a redox electrode. This prediction of the mechanism is depicted together with the predicted rate of gas production and the total volume of gas produced in Figure 5. Regardless the fact that the mechanism predicts an induction period that is too long and thus arrives to a very large volume of gas produced before oscillations begin, the rate of gas production at this point is essentially correct and is in a very good agreement with the experimental results. The mechanism also reproduces the presence of sharp peaks in the rate of gas production, correctly following the peaks in the simulation of the signal of a redox electrode. However, if the prediction of gas production based on the mechanism depicted in Figure 5 is compared to typical experimental results, as shown, for example, in Figure 1, it is obvious that the mechanism fails to reproduce several important observations. First, the prediction of the rates of gas production shows no trace of the exponential decay from the peak rates back to the baseline levels. In fact, the baselines of gas production rates show rise toward the leading edges of the peaks. But much more importantly, the predicted peaks in the rate of gas production are as much as 10 times smaller than the values expected based on the experiment. This dramatic mismatch is particularly obvious in the predicted trace of the total volume of gas produced, where the pulses in gas production are hardly

4. CONCLUSION We have presented data of gas production in the BL reaction recorded in a batch setup, yet with fully automatic highprecision measurement, yielding unprecedented resolution of the data. At the same time we have developed and successfully proved as working an efficient model of description of the gas production, in the induction period, as well as during each of the pulses following it. With the help of the model, the records of the production of gas during reactions have been successfully reduced to sequences of just a few key parameters. It has been found that the gas production during both the induction period and the window of oscillations can be represented by a model of two consecutive processes. The first step produces a precursor, and this gives rise to the measured O2(g) phase in the second step, which proceeds according to 10612



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simple first-order kinetics. For the induction period the results have suggested that the first process produces the precursor at a constant rate. On the other hand, examination of the O2(g) pulses revealed that during oscillations the production of the precursor to O2(g) can be broken down into two relatively autonomous components, running simultaneously side by side. One of the components is responsible for the sharp peaks in production of the precursor, and these were sufficiently approximated by a simple Gaussian function. The other component of the first process is responsible for the constant baseline production of gas outside the pulses, at one level before the pulse, and a somewhat lower level after the pulse. Based on this model we were able to analyze the measured gas production pulse by pulse, and in each oscillation period we determined the total volume of gas production caused by the peak in production of the precursor, the baseline rates of gas production before and after the peak, and the rate constant of the final step of converting the precursor into O2(g) according to first-order kinetics. We have found that all of these parameters show a strong dependence on the actual concentration of H2O2 in the system, as calculated from the recorded extent of its decomposition into O 2 . Most surprisingly, the dependence of the rate constant of the final step in gas production was almost perfectly linear with [H2O2] and was much less dependent on the rate of stirring than expected. This suggests that this final step of gas production might not be merely the interphase transport O2(aq) → O2(g), but a truly chemical process, where the kinetics appears to be of the first order only when a single pulse is analyzed, but is, in fact, of the second order, when the changes in [H2O2] are considered, as well. If this is true, the second-order rate constant of this process, according to Table 3, in the system with initial composition of 0.360 M KIO3, 0.345 M H2O2, and 0.055 M HClO4 at 60 °C would be 0.25−0.30 M−1·s−1, depending on the rate of stirring. Although the measurements of O2(g) did not make it possible to identify its precursor with definite certainty, we hope that the method we have developed for analyzing the gas pulses, our success in determination of the kinetics of the final steps in gas production, including the respective rate constants, as well as the suggestion of their relationship to [H2O2], are of significance on their own accord, and we believe these information could contribute to clarification of the unknown details in the future. Finally, confrontation of these findings with the numerical integration of a mechanism, which has so far proved as the most useful in modeling of the BL reaction, has shown that the mechanism was not able to reproduce the production of O2 to a satisfactory agreement with experiment. Even though the baseline levels of gas production predicted by the mechanism were in the correct levels and peaks in gas production were observed, severe discrepancies have been observed. The gas production between the pulses was curved in the wrong direction, and the peaks showed no (pseudo)first-order decay. But most importantly, the magnitude of the peaks in the rate of gas production was ten times smaller, making the O2 pulses on the trace of the total gas production volume almost invisible. Efforts to obtain a better match of this mechanism with the experiment by only accommodating the rate constants were not met with success.

■

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The work presented has been funded from grant UK/165/2012 under the Young Researchers’ Grant Scheme of Comenius University in Bratislava.

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REFERENCES

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Reexamination of Gas Production in the BrayâLiebhafsky Reaction

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