J. Phys. Chem. 1996, 100, 1643-1656
1643
Kinetics and Mechanism of the Complex Bromate-Iodine Reaction1 Cordelia R. Chinake and Reuben H. Simoyi* Center for Nonlinear Science and the Department of Chemistry, West Virginia UniVersity, Box 6045, Morgantown, West Virginia 26506-6045 ReceiVed: July 11, 1995; In Final Form: October 12, 1995X
The mechanism of the reaction between bromate and iodine in an acidic medium (HClO4), in a closed system, has been investigated by both experimental and computer simulation techniques. The stoichiometry of the reaction is 2BrO3- + I2 f 2IO3- + Br2. The reaction is preceded by an induction period whose length is inversely proportional to the concentration of bromate and the square of the acid concentration. The induction period increases upon the addition of iodide and bromide ions, with the effect of bromide ions being less marked. These ions consume HOI and HOBr molecules, which are precursors to the oxidation of iodine. At the end of the induction period iodine is suddenly depleted while simultaneously a transient interhalogen, iodine bromide, IBr, is formed and consumed rapidly. As soon as the IBr concentration reaches its maximum value, i.e., [IBr]max ) 2[I2]0, it is rapidly consumed at an exponential rate given by -d[IBr]/dt ) k1[IBr]. When all the IBr has been depleted, molecular bromine is formed at the rate d[Br2]/dt ) k2[H+][BrO3-][I2]. Values of k1 and k2 were evaluated as 0.47 ( 0.10 s-1 and 0.26 ( 0.02 M-2 s-1, respectively. A 17-step mechanism which encompasses the mechanisms of the bromate-iodine and bromate-iodide reactions gives good agreement between experimental data and computer simulation. An extensive set of experimental data is presented that supports a molecular mechanism over a radical-dominated one.
Introduction Upon mixing a 1.2:1 mole ratio of bromate to iodide ions in acidic solution, one initially observes a slow darkening of the reaction solution to a brownish color. The intensity of the reddish-brown color finally reaches a peak where it is maintained for some time before the coloration suddenly and rapidly disappears. Hence the bromate-iodide reaction is known as a “clock reaction”.2 Bromate ions are known to oxidize iodide ions to molecular iodine in acidic solution.3-7 In the presence of excess bromate the iodine is further oxidized to iodate.8 The two reactions occur in tandem, the bromate-iodide reaction going to completion before the bromate-iodine reaction commences (Figure 1).9 This has been observed both experimentally and in computer simulations.10 It is this stepwise oxidation of iodide to iodate which makes the reaction interesting. The bromate-iodide reaction shows sustained oscillations and bistability in a continuously stirred tank reactor (CSTR).11 In a CSTR, at high input concentrations of iodide and bromate, the system displays oscillations in the redox potential and in the concentrations of bromine, iodine, bromide, and iodide. Extensive computer simulation studies of the mechanism of the oscillatory bromate-iodide reaction have shown that a complete description of the oscillator is only possible after involving both the bromate-iodide and the bromate-iodine reactions.10 Due to a switching mechanism which allows only one of the reactions to proceed at a time in an environment in which both are thermodynamically viable, it is possible to study the reactions independently. The bromate-iodide reaction has been extensively studied, and its kinetics and mechanism have been adequately established.3-7 Not much, however, has been done in the way of mechanistic studies on the bromate-iodine reaction although it holds the key to a better understanding of the bromate-iodide oscillator.11 It is generally accepted that oscillatory behavior, especially relaxation oscillations, can be produced from the coupling of X
Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-1643$12.00/0
slow molecular processes with rapid radical processes. In the bromate-iodide oscillator, the slow molecular processes would be the reactions which form iodine, and the rapid radical process would be the BrO3--I2 reaction. A radical mechanism would implicate the BrO2‚ radical.12 In excess and constant BrO3the reaction would be initiated by trace amounts of Br- with the following sequence:13
BrO3- + Br- + 2H+ a HBrO2 + HOBr
(R1)
BrO3- + HBrO2 + H+ a 2BrO2• + H2O
(R2)
2BrO2• + I2 a 2IBrO2
(R3)
2IBrO2 + 2H2O f 2HBrO2 + 2HOI
(R4)
HBrO2 is the autocatalytic species in the above sequence, R1R4. A core mechanism that involves R1-R4 can explain the BrO3--I2 reaction features of an induction period and a rapid iodine consumption. Sequence R1-R4 fails in a critical area. It fails to account for the formation of IBr, an important feature of the reaction. It also fails to address the delayed formation of bromine. Either sequence R1-R4 is not the sole operating mechanism or it is not the one responsible for the observed kinetics. In this paper we have undertaken the study of the kinetics and mechanism of the bromate-iodine reaction as a natural follow-up to the study of the bromate-iodide reaction.9 We will make constant reference to the bromate-iodide reaction in this study because we also feel that the bromate-iodine reaction is only one of a number of important reactions which occur in acidic mixtures of bromate, iodide, and iodine. We propose a mechanism for the bromate-iodine reaction and also show how this mechanism fits in with that for the bromateiodide “clock” system. Preliminary experiments had shown a most complex reaction pattern. While the consumption of iodine is rapid in high excess © 1996 American Chemical Society
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Figure 1. Optical density trace at λ ) 460 nm for the production of iodine in the bromate-iodide reaction in excess bromate. Two traces at different initial acid concentrations have been chosen to show the effect of acid. In this paper the focus is on the second stage of the reaction, in which iodine is suddenly depleted. [BrO3-]0 ) 5. × 10-3 M, [I-]0 ) 5 × 10-4 M.
of bromate, the rest of the other processes involved in the reaction system were very slow and could be studied by conventional techniques, e.g. UV/vis spectrophotometry. Experimental Section Materials. The following reagents were used without further purification: potassium bromate, potassium iodide (free-flowing granular), sodium bromide, sodium thiosulfate, soluble starch (Fisher); bromine, isonicotinic hydrazide, 2,3,5-triphenyltetrazolium chloride (Aldrich); and iodine bromide (Fluka). Ionic strength was maintained by using sodium perchlorate (1.0 M). Stock solutions of 5 M sodium perchlorate (Fisher) were filtered before use. Iodine crystals (Fisher) were washed twice with doubly distilled water before use. Saturated iodine solutions were prepared by vigorously mixing iodine crystals in doubly distilled water. These solutions were allowed to stand overnight before filtration.14 The flasks containing the solutions were wrapped in aluminum foil and stored in the dark to minimize exposure to light. Solutions prepared in this manner gave an aqueous iodine solution of approximately 9.5 × 10-4 M. In cases were high iodine concentrations were desirable this was achieved by dissolving iodine crystals in a known amount of potassium iodide. In other experiments the iodine was prepared in situ by reacting excess acidic bromate with iodide. Methods. The experiments were carried out by mixing aqueous iodine solutions with potassium bromate and perchloric acid in a 100 mL thermostatable reactor (25.0 ( 0.1 oC). When necessary, ionic strength was maintained at 1.0 M (NaClO4). Potentiometric measurements were carried out using a platinum electrode with a double-junction calomel reference. The bromide and iodide concentrations were monitored using appropriate Orion ion-specific electrodes and a reference electrode for halides. For long reaction times, in the BrO3--I2 reaction, spectrophotometric studies were carried out on a Perkin Elmer Lambda 2S UV/vis spectrophotometer. Faster reactions were monitored
using a Hi-Tech Scientific SF-61AF stopped-flow spectrophotometer. This instrument is equipped with an M300 monochromator and a spectrascan control unit. The signal from the SF-61AF was amplified and digitized via an Omega Engineering DAS-50/1 16-bit board interfaced to a computer. Iodine absorbance was monitored at the I2/I3- isosbestic point of 460 nm. The molar absorptivity15 at this wavelength was taken as 770 M-1 cm-1. The concentrations of bromine and iodine bromide were both monitored at the same wavelength of 390 nm. Molar absorptivity coefficients for bromine and iodine bromide at 390 nm were taken as 161 and 346 M-1 cm-1, respectively.16 Stoichiometric studies and product analyses were carried out by using spectrophotometric, volummetric, and argentometric techniques. In excess I2 conditions, standard sodium thiosulfate titrimetric techniques for the determination of iodine were ineffective, as the solution does not lose any of its oxidizing power in going from I2 to Br2. By adding excess I- to the reaction solution, however, the Br2 formed would react to liberate I2. A comparison of the absorbance at 460 nm before and after addition of the I- established the stoichiometry. The colorimetric procedure of forming a pink complex (λmax ) 480 nm)17 from the reaction between isonicotinic acid hydrazide and 2,3,5-triphenyltetrazolium chloride in the presence of iodate and/or bromate confirmed that 1 mol of bromate liberates 1 mol of iodate on reacting with iodine. Reacting 1:1 mixtures of isonicotinic acid hydroxide with 2,3,5-triphenyltetrazolium chloride in dilute HCl gives a pink color in the presence of IO3- at room temperature. BrO3- gives the pink color only upon heating. The complex formation is very sensitive to pH, and so a standardization with known amounts of IO3- and BrO3- was necessary before any analytical determinations could be made. The method has a detection limit of 2 µg/mL iodate and 3 µg/mL bromate. Spectrophotometric Studies. Several species dominate in the bromate-iodine reaction. Most of these species are active in the UV/visible spectral range. The important species for
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J. Phys. Chem., Vol. 100, No. 5, 1996 1645
Figure 2. Composite spectrum showing the spectra of four important species in solution: I2, Br2, I3-, and IBr. Both IBr and Br2 have the same absorption peak at 390 nm, although the absorptivity coefficient of Br2 is higher. [Br2] ) 1.80 × 10-3 M, [I2] ) 2.25 × 10-4 M, [I3-] ) 4.50 × 10-4 M, [IBr] ) 4.50 × 10-4 M.
stoichiometric analyses are I2(aq), Br2(aq), I3-(aq), and IBr(aq). Figure 2 shows a composite spectrum for these four species between 250 and 600 nm. Iodine shows a peak at 474 nm while I3- has two peaks at 286 and 353 nm. Both Br2(aq) and IBr(aq) have the same peak at 390 nm. The isosbestic point for I2/I3- was 460 nm.15 All the spectrophotometric studies were thus carried out at either 460 or 390 nm. No attempt was made to accommodate contributions from Br3-, which has an absorptivity coefficient six times higher than that for Br2(aq) at 390 nm.18 In excess BrO3- an accumulation of Br3- is not expected. Upon repetitive scanning of the spectrum the active peaks could be easily identified. Figure 3A shows the type of spectral activity observed between t ) 7 and 19 min in the range λ ) 250-700 nm for the BrO3--I- reaction. The peaks at 286 and 353 nm decrease as the peak at 460 nm increases (I3going to I2). The oxidation of I- by BrO3- depletes the I3species in favor of I2. This is the first stage of the reaction in which I2 is formed (Figure 1). Figure 3B shows the BrO3--I2 reaction. The BrO3--I2 reaction is characterized by a sudden collapse of the absorbance peaks at 460 nm. The rapid consumption of I2 makes it difficult to produce several spectral scans. At time t ) 0 there exists a single peak at 460 nm. I2 consumption (at the conditions indicated) commences at t ) 60 s as the absorbance at 460 nm goes down and a new peak starts forming at 390 nm. Results Figure 1 shows both the bromate-iodide and the bromateiodine reactions. On the time scale of Figure 1, it is not possible to characterize the bromate-iodine reaction. The consumption of iodine has only been reported as “rapid and sudden”. The stoichiometry of the bromate-iodide reaction in excess bromate had been established as9
BrO3- + 6I- + 6H+ f Br- + 3I2(aq) + 3H2O (R5) In excess iodide the product of the reaction becomes I3-(aq). Our study confirms an earlier study on the stoichiometry of the bromate-iodine reaction:8
2BrO3- + I2(aq) f 2IO3- + Br2(aq) Both I2 and Br2 were determined spectrophotometrically.
(R6)
Figure 3. (A) Spectrum of the bromate-iodide reaction from 7 to 19 min. [BrO3-]0 ) 5 × 10-4 M, [I-]0 ) 2.5 × 10-4 M, [H+]0 ) 0.05 M, [NaClO4] ) 0.5 M. The peaks at 286 and 353 nm grow smaller as I(and subsequently I3-) is consumed, and the peak at 460 nm continues to grow as I2 is produced. (B) Spectrum of the bromate-iodine reaction at the point of “clocking”, i.e. when the I2 is suddenly and rapidly decolorized. The spectra are labeled to show how rapidly the 460 nm peak falls while the 390 nm peak rises slowly. [BrO3-]0 ) 0.01 M, [I2]0 ) 3.43 × 10-4 M, [H+]0 ) 0.3 M.
Reaction Dynamics. The reaction is characterized by a long induction period during which no consumption of iodine is observed (Figure 1). At the end of the induction period the iodine is consumed in a rapid and autocatalytic manner. At 460 nm the reaction only shows the disappearance of I2 at the point of “clocking”. The absorbance data information at 390 nm show more activity. There is an initial absorbance decrease followed by an increase in absorbance. The absorbance increase at 390 nm coincides with the decrease in I2 absorbance at 460 nm. The maximum absorbance at 390 nm is attained when the I2 absorbance has decayed to the background value. There is another rapid decrease in absorbance followed by a slower increase. Figure 4 shows a superimposition of the two traces, one at 460 nm and the other at 390 nm, to show their relationship. The initial decrease in absorbance at 390 nm is due to the consumption of I- and Br-. The first increase in absorbance is due to the formation of IBr. IBr is a transient
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Figure 4. Superimposition of absorbance traces at 390 and 460 nm to show their relationship. IBr (390 nm) attains its maximum value as the I2 absorbance decays to zero. [BrO3-]0 ) 0.01 M, [H+]0 ) 0.10 M, [I2]0 ) 0.00034 M.
species which is rapidly consumed to make way for the second increase in absorbance, which is due to the formation of the final product, Br2(aq):
6BrO3- + 5I- + 6H+ f 5IO3- + 3Br2 + 3H2O (R7) Bromate-Iodide Reaction. In this section of the paper we first present experimental results which, although they involve the BrO3--I- reaction, are essential in elucidating the mechanism for the BrO3--I2 reaction. In an acidic reaction mixture in which the ratio R ) [BrO3-]/[I-]0 > 1.2, both reactions can be studied.9 When R < 1.2, there is insufficient BrO3- to oxidize I- all the way to IO3- and the reaction will not display clock reaction characteristics. Combining 5R5 + 15R6 + R8
BrO3- + 5Br- + 6H+ f 3Br2 + 3H2O
(R8)
gives the overall stoichiometry of R7. (i) BrO3 Dependence. At 390 nm the traces obtained with varying [BrO3-]0 are shown in Figure 5A. Corresponding traces at 460 nm can be seen in Figure 5B. A measurable parameter is the induction period of the reaction (time needed for the reaction to “clock”). There is an inverse relationship between the initial bromate concentrations and the induction period (Figure 5C). The intercept on the x-axis confirms the stoichiometry of the reaction: the induction period goes to infinity, i.e. 1/induction period f 0, when the ratio R falls below 1.2. The inverse relationship suggests that the precursor reaction before the consumption of I2 has a positive dependence on BrO3- concentration to the first power. (ii) Acid Dependence. Varying acid in the BrO3--I- reaction gives a linear relationship between the induction period and 1/[H+]2 (Figure 6). Oxybromine reactions have been known to give exclusively the second-order dependence on acid concentration.19 Apart from the catalytic effect of acid, other important relationships can be observed from the aciddependence plots. It is important to quantify the rates of formation and decay of the IBr intermediate as well as the maximum IBr concentration obtained with respect to the initial acid concentrations. We shall refer to this data later in this paper. (iii) Iodide Dependence. Since these reactions were run in excess bromate, only very minimal changes are expected with respect to [I-]0 as long as bromate is maintained in excess. A number of important reaction indicators, however, changed with
Figure 5. (A) Absorbance traces at 390 nm for the BrO3--I- reaction showing the effect of initial BrO3- concentration. [H+]0 ) 1.5 M, [I-]0 ) 0.001 M. [BrO3-]0: (a) 0.003 M, (b) 0.004 M, (c) 0.005 M, (d) 0.006 M, (e) 0.007 M. (B) Absorbance traces at 460 nm under the same conditions as in part A. The shortening of the induction period can be clearly seen. [BrO3-]0: (a) 0.002 M, (b) 0.003 M, (c) 0.004 M, (d) 0.005 M, (e) 0.006 M, (f) 0.007 M. (C) Inverse relationship of the induction period and initial BrO3- concentration derived from the data in Figure 5B.
[I-]0. It is apparent that the complete consumption of iodide is the precursor reaction to the “clocking”, and thus added iodide will lengthen the induction period (Figure 7A and B). There is
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Figure 6. Effect of acid on the reciprocal of the induction period at 460 nm. [BrO3-]0 ) 0.002 M, [I-]0 ) 0.001 M.
no dramatic change in induction period, but the amount of transient IBr increased linearly with [I-]0 (Figure 7C). Figure 7B (λ ) 460 nm) shows that higher [I-]0 will give higher [I2]0 for the subsequent BrO3--I2 reaction. All the I- ions will proceed through I2 before oxidation to IO3-. Bromate-Iodine Reaction. Similar experiments were carried out for the BrO3--I2 reaction. While the BrO3--Ireaction involves both the formation and the consumption of iodine, the BrO3--I2 system only involves the consumption of iodine. The traces at 460 nm show only the induction period and the consumption of iodine (Figure 8) while those in Figure 5B also show an initial step involving iodine formation from iodide ions. The dependence of the induction period on acid and bromate was the same as in the BrO3--I- reaction. The plot of induction time vs 1/[H+]2 gave a straight line passing through the origin, while the plot of induction time vs 1/[BrO3-] had a positive intercept on the 1/[BrO3-] axis. The fact that these dependencies are the same in both the BrO3--I- and the BrO3--I2 reactions indicates that both parts of the reaction (formation and consumption of I2) obey the same kinetics rate law. The traces at 390 nm give a better insight into the reaction mechanism. The curve for the formation of IBr has a long linear section whose slope is sensitive to initial reagent concentrations. A comparison of the type of trace obtained can be made by varying one reactant while keeping the others constant. The acid- and bromate-dependence plots were quite similar to Figures 6 and 5A, respectively, with the same dependencies. The effect of iodine, however, was much more dramatic (see Figure 9). Higher [I2]0 gave elevated concentrations for all the reactive intermediates especially if bromate was in overwhelming excess over iodine. Higher [I2]0 also lengthened the induction period. (i) Maximum IBr Formation. Acid does not seem to have any effect on the amount of transient IBr formed at low acid concentration ([H+]0 e 0.6 M). BrO3- gives an inverse relationship (Figure 10A). With iodine, there is a direct linear relationship between its initial concentration and the amount of transient IBr formed (Figure 10B). (ii) Rate of Formation of IBr. The rate of formation of IBr is very important in determining the overall mechanism of the reaction. Reaction conditions were such that [BrO3-]0, [H+]0 . [I2]0, [I-]0. Thus, although IBr is formed halfway into the reaction, the concentrations of BrO3- and H+ will still be very close to the initial values. The variations of rate of formation of IBr with respect to H+, BrO3-, and I2 were all linear. All graphs showed a positive dependence.
Figure 7. (A) Effect of [I-]0 on the absorbance traces at 390 nm for the BrO3--I- reaction. There is a slight but systematic increase in induction period with increase in [I-]0. [BrO3-]0 ) 0.002 M, [H+]0 ) 1.5 M. [I-]0: (a) 8.0 × 10-4 M, (b) 1.0 × 10-3 M, (c) 1.2 × 10-3 M, (d) 1.4 × 10-3 M, (e) 1.6 × 10-3 M, (f) 1.8 × 10-3 M. (B) Effect of [I-]0 on the bromate-iodide reaction at 460 nm. Higher [I-]0 values give higher [I2] absorbance values. Initial conditions are as in Figure 7A. [I-]0: (a) 1.8 × 10-4 M, (b) 1.0 × 10-3 M, (c) 1.2 × 10-3 M, (d) 1.4 × 10-3 M, (e) 1.6 × 10-3 M, (f) 1.8 × 10-3 M. (C) BrO3--I-: the effect of [I-]0 on the maximum amount of transient IBr formed at 390 nm. The linear relationship and the amount of IBr obtained suggest that all the iodine-containing species pass through the intermediate, IBr. [BrO3-]0 ) 0.002 M, [H+]0 ) 1.5 M.
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(A)
Figure 8. Absorbance traces for the BrO3--I2 reaction at 460 nm showing the catalytic effect of [H+]0. [BrO3-]0 ) 0.01 M, [I2]0 ) 0.0034 M. [H+]0: (a) 0.4 M, (b) 0.5 M, (c) 0.6 M, (d) 0.7 M.
Figure 9. BrO3--I2 reaction: absorbance traces at 390 nm and their response to [I2]0. Both the induction period and the [IBr]max are increased. [BrO3-]0 ) 0.01 M, [H+]0 ) 1.0 M. [I2]0: (a) 3.44 × 10-5 M, (b) 6.8 × 10-5 M, (c) 1.03 × 10-4, (d) 1.37 × 10-4 M, (e) 1.71 × 10-4 M, (f) 2.05 × 10-4 M.
(iii) Consumption of IBr. Standard data fitting techniques showed that the traces for the consumption of IBr are exponential. Thus one can evaluate an apparent rate constant, kapp, for the first-order disappearance of IBr. The rate of depletion of IBr was inversely proportional to the acid concentration. However, there appeared to be no relationship between the rate of consumption of IBr and the initial BrO3-, I-, and I2 concentrations. Since Br2 and IBr absorb maximally at the same wavelength, 390 nm, it is difficult to separate depletion of IBr from formation of Br2. The encroachment of Br2 formation on IBr consumption was much more pronounced at high acid concentration. The following rate law was derived:
-d[IBr]/dt ) k1[IBr]
(1)
The value of k1 was determined as -1
k1 ) 0.47 ( 0.10 s
(B)
Figure 10. (A) BrO3--I2 reaction: effect of [BrO3-]0 on the maximum transient IBr formed. The decrease in absorbance with [BrO3-]0 means BrO3- either catalyzes consumption of IBr or retards its formation. The BrO3- effect is not that strong. [I2]0 ) 0.0034 M, [H+] ) 1.0 M. (B) Strong dependence of [IBr]max on [I2]0. The graph has an intercept of zero, which means most (if not all) of the I2 goes through IBr.
very slow, and it can take up to 6 h for the full stoichiometric amounts of bromine to form at low acid concentrations (see Figure 11A). Low acid conditions were necessary in order to separate the IBr consumption from Br2 formation. The most interesting feature of Br2 formation is the first-order dependence on acid concentrations (Figure 11B). This is unexpected in oxyhalogen chemistry, where reaction rates generally show a second-order dependence on acid concentration.19 The rate also had a first-order dependence on [BrO3-]0. The formation of bromine is exponential, and analysis of the traces gave
d[Br2]/dt ) k2[BrO3-][H+][Int]
(3a)
where Int is the intermediate species, HOI, which is formed after hydrolysis of IBr. HOI can be substituted by I2, and hence eq 3a can be written as
d[Br2]/dt ) k2[BrO3-][H+][I2]
(3b)
(2)
(iV) Formation of Bromine. The formation of Br2 is the last step in this complex reaction scheme. The formation rate is
Equation 3b is again based on the assumption that BrO3- and H+ are in high and constant supply. The pseudo-first-order rate constant derived was equated to k2[BrO3-]0[H+]0, and the
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Figure 11. (A) BrO3--I2 reaction: absorbance traces at 390 nm showing the formation of Br2(aq) at different [H+]0. At high acid concentrations the formation of Br2 starts before the complete consumption of IBr so that it is not possible to separate the two processes. [BrO3-]0 ) 0.01 M, [I2]0 ) 0.00035 M. [H+]0: (a) 0.05 M, (b) 0.10 M, (c) 0.15 M, (d) 0.20 M, (e) 0.25 M. (B) Dependence of the apparent rate constant, kapp, for the formation of Br2 on [H+]0. Data show a clear first-order dependence. [BrO3-]0 ) 0.01 M, [I2]0 ) 0.00035 M.
following value for k2 was deduced:
k2 ) 0.26 ( 0.02 M-3 s-1
(4)
Further Experiments. In a clock reaction such as this one, the most important parameter is the induction period. For this reaction system the induction period is monitored at 460 nm and is marked by the sudden disappearance of the brown iodine color. At 390 nm some activity is observed during the induction period. The further experiments reported here focus on the induction period and formation of IBr. (i) Effect of Iodine. Experiments were run with BrO3- in at least 40-fold excess. One would expect no major effect on the reaction upon varying I2. On the contrary I2 concentrations play an important role in the reaction characteristics. At 460 nm, iodine, as expected, affects the initial absorbance values linearly (Figure 12A). Surprisingly, I2 has quite a noticeable effect on the induction period (Figure 12B). (ii) Effect of Iodide. A series of experiments were performed in which I- was deliberately added to the reaction mixture. With small amounts of I-, such that [I2]0 . [I-]0, the effect of Iwas to strongly increase the induction period. When I- was
Figure 12. (A) BrO3--I2 reaction: effect of [I2]0 on the absorbance traces at 460 nm. Despite very low quantities of iodine (BrO3- in at least 100-fold excess), [I2]0 effectively alters the induction period. [BrO3-]0 ) 0.01 M, [H+]0 ) 1.0 M. [I2]0: (a) 3.44 × 10-5 M, (b) 6.8 × 10-5 M, (c) 1.03 × 10-4 M, (d) 1.37 × 10-4 M, (e) 1.71 × 10-4 M, (f) 2.05 × 10-4 M. (B) Induction period for data in Figure 14A vs [I2]0.
high enough such that [I-]0 > [I2]0, the spectrum changed significantly, to resemble that of the BrO3--I- reaction. First there is an increase in the I2(aq) absorbance as the added Iions are first converted to I2(aq), followed by the standard induction period (as in Figure 5B). A log-log plot of induction period vs [I-]0 gives a straight line (Figure 13A). From extrapolation and assuming an induction period of 10-2 s as being kinetically equivalent to zero, one can deduce that the induction period can be eliminated when [I-]0 falls below 1.8 × 10-6 M. A standard saturated solution of I2(aq) contains 6.4 × 10-6 M iodide ions.20 Thus most I2(aq) solutions will contain enough I- to give the reaction a finite induction period. An increase in [I-]0 also increases the amount of transient IBr formed (Figure 13B). There is a linear relationship between the maximum IBr formed and the amount of I- added. (iii) Effect of Bromide. The Bromide effect is more difficult to evaluate. Addition of Br- ions also increased the induction period but not as vigorously as I-. Figure 14 shows a superimposition of both the traces at 460 and 390 nm. Except for the induction period, Br- does not seem to affect anything else. The reaction was also followed by means of an ion-selective electrode (ISE) specific for bromide whose potential reading
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Chinake and Simoyi reaction medium. The concentration of I- never rises again during the course of the reaction. Figure 15 shows the bromide ISE trace in the BrO3--I- reaction. The observed initial increase in ISE response is due to the consumption of I- by BrO3-. The rapid decrease in electrode potential (corresponding to an increase in [Br-]) coincides with the consumption of IBr. The lowest ISE potential reading, and hence the highest Brconcentration, coincides with the total consumption of IBr. The Br- concentration then slowly decreases in the last stage of the reaction as Br2 is formed. (iV) Reaction of IBr. A set of kinetics experiments were set up to investigate the rate of oxidation of IBr with BrO3-. With at least 50-fold excess of BrO3- over IBr, the reaction is quite slow and requires up to 30 min for completion depending on acid concentration. The reaction is catalyzed by acid and has a positive dependence on BrO3- concentration. The absorbance trace at 390 nm shows the sigmoidal decay curve indicative of autocatalysis (Figure 16). (V) Formation of Iodate. Using a 1:1 mixture of isonicotinic acid and 2,3,5-triphenyltetrazolium chloride, the formation of the pink complex formed with IO3- could be followed at 480 nm.17 On prolonged standing, the reagents also show a pink color in the presence of Br2 and I2. However, within the time frame of our experiment, the interference from halogens was small. Absorbance traces at 480 nm show that most of the IO3is formed in the last stage of the reaction and that the rate of formation of IO3- is the same as the rate of formation of Br2 (λ ) 480 nm traces very similar to the data in Figure 11A). (Vi) Effect of HOBr. Aqueous bromine was titrated against AgNO3. The end point was taken as the point when addition of more AgNO3 did not produce any further precipitation. Ag+ ions precipitate Br- ions and push the hydrolysis equilibrium of Br2 to the right.
Br2(aq) + Ag+(aq) + H2O f HOBr + AgBr(s) + H+ (R9) Figure 13. (A) Log-log plot of the induction period vs [I-] at 460 nm. (B) Effect of addition of iodide ions on the peak at 390 nm. [BrO3-]0 ) 0.01 M, [H+]0 ) 1.0 M, [I2]0 ) 1.8 × 10-4 M. [I-]0: (a) no added iodide (b) 1 × 10-6 M, (c) 1 × 10-5 M, (d) 1 × 10-4 M, (e) 1 × 10-3 M. The same initial conditions were used in Figure 13A.
The solution obtained was quickly filtered and used in the BrO3--I2 reaction. A few drops of the dilute HOBr solution almost instantaneously decolorized the I2 with no induction period. A pure reaction of the HOBr solution with I2 was too fast to follow on our stopped flow spectrophotometer. A kinetics study of the HOBr-I2 reaction is also difficult to undertake due to the instability of the HOBr. Mechanism We have presented in this study an exhaustive amount of reaction kinetics data which is necessary to evaluate the mechanism of this very complex reaction. The radical and molecular mechanisms both have their strong points, and it is only through such extensive data collection that they can be separated. Induction Period. This study has confirmed the reports in previous studies that iodide is indeed responsible for the induction period.8,9 As long as iodide is present above a certain threshold value, no consumption of iodine can commence. Any oxidation of iodine will have to pass through HOI. If there are any iodide ions in the reaction mixture, they will immediately scavenge the HOI molecules to give back iodine:
Figure 14. Superimposition of traces at 460 and 390 nm showing the inhibitory effect of adding Br‚-. [BrO3-]0 ) 0.01 M, [H+]0 ) 1.0 M, [I2]0 ) 0.0035 M. [Br-]0: (a) no added Br-, (b) 1.0 × 10-5 M, (c) 3.0 × 10-5 M, (d) 5.0 × 10-5 M, (e) 7.0 × 10-5 M.
Br-
has a negative log relationship with the concentration. The interference from I- ions was minimal after the initial induction period. In the beginning, the reaction mops up all the I- in the
HOI + I- + H+ h I2(aq) + H2O
(R10)
In BrO3--I- mixtures, the initial reactions should be
BrO3- + 2H+ + I- h HBrO2 + HOI
(R11)
In the presence of excess I- ions, HOI will immediately be converted to I2 as in reaction R10. Reaction R10 has been
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J. Phys. Chem., Vol. 100, No. 5, 1996 1651
Figure 15. Bromide-specific electrode trace (pBr-) for the BrO3--I- reaction. Initial increase in potential is interference from the initial iodide concentration. More accurate pBr- readings are obtained when IBr consumption commences with a corresponding increase in Br- concentration. Note that the highest Br- value occurs when all the IBr has been consumed and Br2 production has not yet commenced. Region A: consumption of I-, I3-. This region covers the induction period if the reaction is monitored at 460 nm. Region B: consumption of I2 combined with formation and consumption of IBr. Region C: the last stage of the reactionsformation of Br2. [BrO3-]0 ) 0.005 M, [H+]0 ) 0.05 M, [I2(aq)]0 ) 1.0 × 10-3 M (I2 crystals dissolved in KI).
Figure 17. Schematic diagram showing how I- controls the induction period. Reduction processes for HOI, HIO2, and IO3- are arranged going upward from left to right. Figure 16. Direct reaction of BrO3- with IBr. This figure shows that this is a very slow reaction compared to the observed rate from the BrO3--I2 reaction, which is over in about 5 s. [BrO3-]0 ) 0.016 M, [IBr]0 ) 0.002 M, [H+]0 ) 0.01 M.
excess oxidant:22
IBr + H2O a HOI + Br- + H+
(R14)
Kustin21
studied by Eigen and and was found to have an equilibrium constant which lies overwhelmingly to the right. Bromous acid will also oxidize I- ions in the following sequence:
HBrO2 + I- + H+ a HOBr + HOI
(R12)
HOBr + I- + H+ a IBr + H2O
(R13)
Iodine monobromide, IBr, can hydrolyze in the presence of
Adding 3R10 + R11 + R12 + R13 + R14 gives the stoichiometry of the first part of the reaction (formation of I2, reaction R5). Br-, formed in stoichiometry R5, is unstable with respect to Br2 in the presence of an acidic BrO3- solution:
BrO3- + 5Br- + 6H+ f 3Br2 + 3H2O Combining 5R5 + R8 gives R15:
(R8)
1652 J. Phys. Chem., Vol. 100, No. 5, 1996
Chinake and Simoyi
TABLE 1: Mechanism of the Bromate-Iodine-Iodide System reaction no.
reaction
rate constant
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17
BrO3- + I- + 2H+ f HBrO2 + HOI BrO3- + HOI + H+ f HBrO2 + HIO2 BrO3- + HIO2 f IO3- + HBrO2 BrO3- + Br- + 2H+ h HBrO2 + HOBr BrO3- + IBr + H2O f IO3- + Br- + HOBr + H+ HBrO2 + HOI f HIO2 + HOBr HBrO2 + Br- + H+ f 2HOBr 2HBrO2 f HOBr + BrO3- + H+ HOBr + I2 h HOI + IBr HOBr + Br- + H+ h Br2 + H2O HOBr + HIO2 f IO3- + Br- + 2H+ HOBr + HOI f Br- + HIO2 + H+ HIO2 + HOI f IO3- + I- + 2H+ I- + HOI + H+ h I2 + H2O IBr + H2O h HOI + Br- + H+ IBr + I- h I2 + BrBr2 + I2 h 2IBr
44.3 M-3 s-1 2.6 × 10-1 M-2 s-1 9 M-1 s-1 2.1 M-3 s-1, 1 × 104 M-1 s-1 8 × 10-4 M-1 s-1 2.5 × 108 M-1 s-1 2 × 106 M-2 s-1 2.2 × 102 M-1 s-1 8 × 108 M-1 s-1, 1 × 102 M-1 s-1 4.1 × 109 M-2 s-1, 1.1 × 102 s-1 1 × 106 M-1 s-1 1 × 106 M-1 s-1 6 × 102 M-1 s-1 3.1 × 1012 M-2 s-1, 2.2 s-1 8. × 10-1 s-1, 1 × 108 M-2 s-1 2 × 1010 M-1 s-1, 4.74 102 M-1 s-1 1.3 × 105 M-1 s-1, 1.0 M-1 s-1
2BrO3- + 10I- + 12H+ f Br2(aq) + 5I2(aq) + 6H2O (R15) Stoichiometry R15 is not observed because Br2(aq) will oxidize I2(aq) further, via the interhalogen, IBr:23
Br2(aq) + I2(aq) a 2IBr(aq)
(R16)
The induction period can thus be easily explained through a combination of kinetics and thermodynamics control. Any iodine oxidation state greater than zero will be unstable with respect to I(0) (in the presence of I- ions) in acidic solutions. The following reactions are thermodynamically feasible:
HIO2 + I- + H+ a 2HOI
(R17)
IO3- + I- + 2H+ a HIO2 + HOI
(R18)
Reaction R17 is a disproportionation24 which gives the observed stoichiometric consistency in iodine oxidations, especially when the reductant is in stoichiometric excess. Reaction R18 is the iodate analogue of reaction R1125 and is the rate-determining step in the Dushman reaction.26 The effectiveness of I- in controlling the induction period can be seen in the schematic reaction scheme drawn in Figure 17. The reaction commences by the formation of I2 (to the left of the diagram). For the BrO3--I2 reaction the reaction scheme will commence with I2 (without the initial formation of I2). Oxidation of iodine (represented by [O]) will give HOI. In the presence of I-, the HOI will be converted to I2. If HOI is further oxidized, it will proceed to HIO2. HIO2 can also either be reduced (reaction R17) or oxidized to IO3- (e.g. reverse of reaction R18). The sketch is organized such that all reduction processes proceed going up from left to right, while all oxidation processes proceed downward from left to right. In excess acidic BrO3- conditions the species are arranged such that the most stable (IO3-) are at the bottom and the least stable (I-, I2) are at the top. Although reaction R10 is very fast (kinetics control), any iodine species that proceeds toward I(III) and I(IV) will still be brought down to I(0) (thermodynamics control) as long as I- is still in the reaction solution, thus giving an induction period. A description of the induction period, It, was formulated as follows:
It ) A/[BrO3-][H+]2
(5)
where A is a constant which was evaluated as (2.80 ( 0.1) × 10-1 M3 s. The form of eq 6 also confirms the role of iodide in the induction period: the consumption of iodide by bromate
is governed by the rate law9
-1/6 d[I-]/dt ) k0[BrO3-][H+]2[I-]
(6)
The value for k0 obtained in this study also confirmed a previously deduced value of 44.3 ( 1.1 M-2 s-1. The ratedetermining step is reaction R11. Thus the time taken to consume iodide would be proportional to 1/[BrO3-][H+]2, which is the form of eq 6. The less marked effect of bromide on the induction period is to be expected because the product of the bromate-bromide reaction, bromine, is powerful enough to oxidize iodine. Bromate-Iodine-Iodide System. The importance of iodide ions to the commencement of the oxidation of iodine has been established.8,9 A mechanism that encompasses both the bromate-iodide and the bromate-iodine reactions can now be postulated. Although the bromate-iodine reaction occurs in three stages, for the sake of mechanistic studies, the reaction can be divided into two major events: The first stage is from the initial depletion of iodine to the point where IBr attains its maximum value. The second stage is from the initial depletion of the IBr to the formation of molecular bromine. Table 1 shows a 17-step reaction scheme for the bromate-iodine-iodide reaction system. Addition of reactions M1, M6, M9, and M13 generates the stoichiometry of the first stage of the reaction:
BrO3- + I2 f IO3- + IBr
(R19)
This stoichiometry has been confirmed in two other studies.8,9 The sum of M2, M7, M10, M11, and M15 gives the stoichiometry of the second stage of the reaction:
BrO3- + IBr f IO3- + Br2
(R20)
Addition of reactions R19 and R20 gives the stoichiometry of the reaction under study, reaction R6. (Reactions numbered with the prefix M are taken from the numbering sequence in Table 1). (i) Formation of IBr. From an examination of the maximum absorbance of IBr observed, it appears all the iodine passes through IBr before proceeding to IO3-. Data to support this includes the observation that the maximum IBr observed increases with [I2]0 and [I-]0 while it is unaffected by changes in added [Br-]0. The initiator for the formation of IBr can be either R11 or R21 or both:
BrO3- + Br- + 2H+ f HBrO2 + HOBr
(R21)
Complex Bromate-Iodine Reaction
J. Phys. Chem., Vol. 100, No. 5, 1996 1653
Formation of IBr requires only catalytic amounts of Br- to initiate the reaction and the Br- that is normally found in BrO3solutions (∼10-6 to 10-7 M) is sufficient.27 Thermodynamically and kinetically, there will be no difference whether reaction R11 or R21 is the reaction initiator. The reaction of I2(aq) with HOBr to form IBr is very rapid:
I2(aq) + HOBr h IBr(aq) + HOI
(R22)
The remaining oxyhalogen species then react to form IO3-:
HOI + HBrO2 f HIO2 + HOBr
(R23)
HIO2 + HOBr f IO3- + 2H+ + Br-
(R24)
Addition of R21 + R22 + R23 + R24 gives the stoichiometry of the reaction at the maximum IBr concentration, reaction R19. The Br- used in reaction R21 is formed in reaction R24. With reaction R11 as the initiator reaction, a further reaction, reaction R23, is needed to produce the required HOBr. After reaction R22 the oxyiodine and oxybromine species rearrange:
HBrO2 + HOI f IO3- + Br- + 2H+
(R25)
which gives the same stoichiometry as reaction R19 (from R19 + R21 + R25). (ii) Oxidation of Iodine. It can be suggested that reaction R22 is not an elementary process and that it is a composite of the sequence R13 + (-R10). Our experiments show that reaction R22 is very rapid while the equilibrium of reaction R10 lies overwhelmingly to the right. Though equilibrium attainment for reaction R10 may be rapid, the equilibrium constant of 2.5 × 10-13 is too unfavorable.21 We postulate here on the reaction proceeding through an iodine complex with water, H2OI2(aq), in which the I2 molecule is aligned along the water C2V axis:28
H2OI2 + HOBr a IBr + HOI + H2O
(R26)
(iii) Consumption of IBr. IBr is consumed just as rapidly as it is formed. The rate of consumption of IBr is unaffected by all the other reactants except acid. The pseudo-first-order kinetics as well seem to suggest that the hydrolysis reaction of IBr, reaction R14, is the rate-determining step:
-d[IBr]/dt ) k14[IBr] - k-14[HOI][Br-][H+]
(7)
Since the solvent, water, is at constant concentration, the observed first-order decay is justifiable. The derivation for the rate law for consumption of IBr is given in the appendix. (iV) Maximum IBr Formed. The work by Margerrum et al.22 confirms that reaction R14 is a fast hydrolysis. How, then, can the maximum IBr be attained such that [IBr]max ) 2[I2]0 when formation of IBr is competing with reaction R14? This process is also controlled by I-. Consider the following cycle: after oxidation of I2 to HOI and IBr in reaction R22, IBr hydrolyzes (reaction R14) to give HOI and Br-. In the presence of I-, HOI is quickly reduced back to I2 (reaction R10). When I2(aq) is still present in solution, the following reactions will occur:
I2(aq) + Br- a I2Br-(aq)
(R27)
I2Br- a IBr + I-
(R28)
Iodide ions will then react with HOI, resulting in the reaccumulation of I2. The cycle continues until all the I2 and I- ions are consumed.
(V) Formation of Bromine. The bromide-specific electrode traces show that Br- ion concentration is at its maximum value just before the formation of Br2. The reaction responsible for Br2 formation is21
HOBr + Br- + H+ a Br2(aq) + H2O
(R29)
Since reaction R29 is very fast,21 Br2 formation, then, must be controlled by the rate of formation of HOBr. Experiments with isonicotinic acid/2,3,5-triphenyltetrazolium chloride show that IO3- is formed at the same rate as Br2. All reactions after formation of HOBr must be rapid enough so as not to be ratedetermining. After hydrolysis of IBr (reaction R14), further oxidation of the iodine species is by BrO3-:
BrO3- + HOI + H+ f HBrO2 + HIO2
(R30)
HBrO2 + HIO2 f IO3- + HOBr + H+
(R31)
HOBr formed in reaction R31 can then combine with the Brfrom IBr hydrolysis (reaction R14) to form Br2, as in reaction R29. The rate-determining step is reaction R30, since reaction R31 is generally assumed to be fast.
d[Br2]/dt ) d[IO3-]/dt ) k[BrO3-][HOI][H+]
(8)
At t ) 0, [HOI] ) [IBr]max. In this case, t ) 0 indicates the position where Br2 starts being formed. Since [BrO3-]0, [H+]0 . [HOI], then eq 8 becomes
rate ) k′[HOI] ) k′[I2]
(9)
where k′ ) k[BrO3-][H+] From the experimental data, k was evaluated as 0.26 ( 0.02 M-2 s-1. Computer Simulations The BrO3--I2-I- reaction system was simulated using the 17-step reaction scheme shown in Table 1. The kinetics parameters and the rate laws used are shown in Table 1. A number of reactions used to describe the detailed mechanism in the text were not utilized in the simulations, hence the new numbering system, Mi, i ) 1, ..., 17, used in the table. The basic criterion used in leaving out some reactions was the effective concentrations of the reactive species. Reaction R17, for example, was not included because, at the point where HIO2 is formed, I- will have decayed to negligible levels. Other reactions in the text were omitted because they are not elementary reactions. The reaction scheme was simulated using semiimplicit Runge-Kutta methods implemented for stiff systems of ordinary differential equations by Kaps and Rentrop.29 Analysis of Reactions. There are essentially three groups of reactions in this mechanism. First there are the standard oxybromine reactions, second the oxyiodine reactions, and third the oxybromine-oxyiodine reactions. The kinetics parameters and rate laws for the oxybromine reactions have been studied and are generally well-known. The other two groups of reactions are not as well understood. Since the reactions are run in excess BrO3-, oxyiodine reactions by themselves are not as significant and only two such reactions were used (M13 and M14). Oxybromine-oxyiodine reactions were simplified by assuming a net driving force toward oxidation of the iodine center and reduction of the bromine center. In this direction, these reactions were considered essentially irreversible.
1654 J. Phys. Chem., Vol. 100, No. 5, 1996 The following analysis describes each of the 17 reactions in detail and how each kinetics parameter was derived. Reaction M1. This reaction has been well studied, and the rate constant used was taken from Simoyi et al.9 Reaction M2. Although this reaction is just an oxygen transfer reaction, it is not expected to be very fast. We considered this to be the rate-determining step in the formation of Br2. The value of kf used was estimated in this study from the rate of formation of Br2 (aq) at the end of the reaction. Unlike previous studies10 this reaction has been made irreversible. Reaction M3. This value was taken from Faria et al 30 as the value given by Citri and Epstein10 was found to be too fast. Reaction M4. The rate constants used here were those given by Field et al.31 and by Citri and Epstein.10 Reaction M5. Experimental measurements of this rate constant showed it to be much slower than the value given by Citri and Epstein10 (see Figure 16). Reaction M6. A slight deviation from the value given by Faria et al.30 was found to give good agreement with the experiments. Reaction M7. We used the value given by Gao and Fo¨rsterling.32 To simplify our simulations, we also ignored the negligible reverse rate constant. Reaction M8. The rate constant was taken from the work of Fo¨rsterling and Varga.33 We, however, ignored the protonation of one of the HBrO2 molecules as a prerequisite for this reaction to occur, as they assert. Reaction M9. The forward rate constant is an order of magnitude higher than that used in previous studies. The reverse rate constant is taken from Citri and Epstein.10 Reaction M10. The initial guess values used were from the work of Eigen and Kustin.21 Reaction M11. The value used for the rate constant was taken from Faria et al.30 The value used by Citri and Epstein10 was found to be too high and was not used. Reaction M12. This reaction was included because it helps explain why Br- has a smaller effect on the induction period than I-. The value of the rate constant is taken from Faria et al.30 Reaction M13. This reaction is more important written in the reverse. It is the oxyiodine analogue of M4.25,26 The kinetics parameters are taken from Treindl and Noyes and other references quoted therein.34 Production of iodide by this reaction will inhibit the consumption of iodine as long as the iodide is above the threshold value. The iodide produces more HOI through reaction M1, which is a precursor to the formation of IBr. Reaction M14. These values are from Eigen and Kustin.21 This is the most important reaction in the explanation of the induction period and in the formation of [IBr]max. Reaction M15. Interhalogen hydrolysis has been recently studied by Margerrum et al.22 The dissymmetric interhalogens can more easily hydrolyze compared with the halogens themselves. Reaction M16. This reaction is important because it stops hydrolysis of IBr in the presence of I-. Reaction M17. This reaction is heavily favored to the right.23 It stops formation of Br2 and its accumulation in the presence of I2. The hydrolysis of IBr (reaction M15) returns the Br2(aq) back to Br-. From the above analysis, it is clear that reactions M1, M4, M7, M10, M14, and M17 have been studied to the extent that their kinetics parameters have been accurately measured. Our present work allows us to give reasonably accurate kinetics parameters for M2 and M5. The majority of reactions whose kinetics parameters had to be guessed are essentially irreversible
Chinake and Simoyi
Figure 18. (A) Comparison between the experimental formation of IBr and computer simulations. [BrO3-]0 ) 1 × 10-2 M, [I-]0 ) 1 × 10-3 M, [I2]0 ) 2.05 × 10-4 M, [H+]0 ) 1.0 M. (B) Simulations of the concentration of bromine and bromide in the same solution as in Figure 21a.
and in most cases are not rate-determining. The induction time, depletion of I2, and formation of IBr were strongly influenced by the rate constants for M2, M7, M15, and M17. Figure 18 shows the comparisons between experimental and simulated traces. The simulations correctly predicted the induction period and the sudden, rapid formation and consumption of IBr. The simulations also confirm that IBr reaches a peak value before being rapidly consumed (Figure 18A). It was difficult to compare the bromine formation with the experimental values because in high acid, at the commencement of bromine production, iodine bromide would still be absorbing at the same wavelength, 390 nm. Figure 18B shows the calculated traces for Br2 and Br-. The simulations correctly predict the position where Br2 formation commences. Discussion The large amounts of data presented here are needed to separate the radical pathway, which fails to account for the observed complex kinetics, from the molecular pathway, which can adequately explain the complexity of the reactions. Detection of Free Radicals. Several experiments were carried out to detect the formation of radicals, if any, during the course of the reaction. The first method involved the addition of styrene to the reaction mixture. The presence of styrene did not affect any of the reaction indicators. The styrene
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J. Phys. Chem., Vol. 100, No. 5, 1996 1655
did not polymerize. Polymerization of the styrene as the reaction proceeded would have indicated the presence of free radicals in the reaction mixture. In another set of experiments a 5,5-dimethylpyrroline N-oxide (DMPO) trap was employed.35,36 Any radicals formed would be trapped by the DMPO, giving stable radicals which can de detected by EPR (Bruker ER-200 spectrophotometer). This experiment failed to show the formation of radicals in the reaction mixture. The last method involved continuous flow of reactants through an EPR cavity. This method can detect radical concentrations as low as 10-8 M by integrating the EPR signal.37 No radicals were detected by this method. Our suspected radical species BrO2‚ is heavy and so may be difficult to trap or to catch under continuous flow, but it is expected that it should be able to initiate polymerization of styrene. Reaction Initiation. In this mechanism we postulate reaction initiation through trace amounts of Br- or I-. The route works very well in our simulations. The other possibility would have been direct reaction between aqueous I2 and bromate: -
+
BrO3 + /2I2 + H f HBrO2 + HOI 1
-d[IBr]/dt ) k14[IBr] - k-14[HOI][Br-][H+] Since [H+]0 . [IBr]0, [I2]0, then
-d[IBr]/dt ) k14[IBr] - k-14′[HOI][Br-]
HOBr + H+ + 2e- f Br- + H2O
(R33)
HBrO2 + Br- + H+ f 2HOBr
(R34)
χ ) [IBr]0 - [IBr]
Acknowledgment. The authors would like to acknowledge the assistance of numerous undergraduate students at the University of Zimbabwe (Harare, Zimbabwe) who have worked on this fascinating project since 1983. We also thank Professor Naresh S. Dalal for assistance with the EPR measurements. This project was initially supported by the University of Zimbabwe Research Board (Grant Number 2.9999.10:2789) and later by the West Virginia EPSCoR program. Appendix Rate Law for Consumption of IBr. IBr consumption is mainly through its hydrolysis, since the direct BrO3--IBr reaction is so slow (see Figure 16):
IBr + H2O a HOI + Br- + H+ The rate of reaction is given by
(R14)
(A3)
Equation A1 now changes to
dχ/dt ) k14([IBr]0 - χ) - k-14′([HOI]0 + χ)([Br-]0 + χ) ) k14[IBr]0 - k-14′[IBr]0[Br-]0 - (k14 + k-14′[Br-]0 + k-14[HOI]0)χ - k-14′χ2 (A4) We can define the following constants
R ) k14[IBr]0 - k-14′[Br-]0[HOI]0
(A5a)
β ) -(k14 + k-14[Br-]0 + k-14[HOI]0
(A5b)
γ ) -k-14
(A5c)
dχ/dt ) R + βχ + γχ2
(A6)
and eq A4 becomes
Expression A6 can then be integrated with the boundary conditions t ) 0, χ(0) ) 0 to obtain
ln{[χ + (β - z1/2)/2γ]/[χ + (β + z1/2)/2γ]} ) z1/2 t + 2ζ (A7) where
Conclusion We feel the mechanism presented here is the most concise to best explain the reaction’s complex behavior. The mechanism has been tested against large amounts of experimental data and still holds up. In particular, the transient formation of IBr as well as the first-order dependence of Br2 formation would have been difficult to explain by any other mechanism. Our proposed mechanism for the BrO3--I2 reaction is also able to simulate the BrO3-I- reaction just by elevating the initial I- concentration.
(A2)
where k-14′ ) k-14[H+]0. We can introduce a progress variable such that
(R32)
Further reaction will successively give HOBr and Br-. Reaction R32 was not used because (a) it is actually a five-molecule encounter (2BrO3- + I2 + 2H+) and may not be an elementary process but a composite of initial iodine hydrolysis followed by reaction R11 and because (b) it fails to account for the quantitative formation of IBr. Autocatalysis by HOBr. Experimental data suggest HOBr as the autocatalytic species. Formation of IBr and consumption of I2 appear autocatalytic. By material balance, these two processes are kinetically the same process. Quadratic autocatalysis by HOBr can be effected from addition of R33 + R34.
(A1)
z ) β2 - 4Rγ
(A8)
ζ ) ln[((β - z1/2)/(β + z1/2))]
(A9)
Expression A7 can be simplified further by applying the following boundary conditions:
t ) 0, [HOI]0 ) [Br-]0 ) 0, χ ) 0
(A10)
Using expression A7, one can evaluate an upper limit first-order rate constant for the consumption of IBr (evaluated around t ) 0 before the reverse rate constants come into play). Our reported value for k1 was evaluated in this limit. References and Notes (1) Nonlinear Dynamics in Chemistry Derived from Sulfur Chemistry. 17. Part 16: Martincigh, B. S.; Hauser, M. J. B.; Simoyi, R. H. Volcanic Eruptions and Thermal Plumes in Autocatalytic Exothermic Chemical Reactions. Phys. ReV. E, in press. (2) Simoyi, R. H. J. Phys. Chem. 1985, 89, 3570. (3) Randall, D. L. J. Am. Chem. Soc. 1910, 32, 644-648. (4) Britton, H. T. S.; Britton, H. G. J. Chem. Soc. 1952, 3887-3891. (5) Clark, R. H. J. Phys. Chem. 1909, 10, 679-683. (6) Barton, A. F.; Wright, F. A. J. Chem. Soc. A 1968, 1747-1753. (7) Barton, A. F. M.; Loo, B.-H. J. Chem. Soc. A 1971, 3032-3035. (8) King, D. E. C.; Lister, W. M. Can. J. Chem. 1968, 46, 279-286. (9) Simoyi, R. H.; Masvikeni, P.; Sikosana, A. J. Phys. Chem. 1986, 90, 4126-4131. (10) Citri, O.; Epstein, I. R. J. Am. Chem. Soc. 1986, 108, 357-363. (11) Alamgir, M.; De Kepper, P.; Orban, M.; Epstein, I. R. J. Am. Chem. Soc. 1983, 105, 2641-2643. (12) Field, R. J.; Fo¨rsterling, H. D. J. Phys. Chem. 1986, 90, 5400.
1656 J. Phys. Chem., Vol. 100, No. 5, 1996 (13) Field, R. J.; Koros, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94, 8649. (14) Freshly stirred iodine solutions contain small, nearly colloidal particles of solid iodine. These particles make it difficult to accurately determine the true concentration of dissolved iodine. By allowing the solution to stand overnight, followed by filtration, this problem was eliminated. (15) The value of the absorptivity coefficient was derived from standardization of iodine against sodium thiosulfate with starch as indicator and then calculating the coefficient from the absorbance of iodine at 460 nm. (16) The value of 180 M-1 cm-1 was derived from a local standardization method as in ref 7, and the value of 346 M-1 cm-1 was taken from ref 2. (17) Hashmi, M. H.; Ahmad, H.; Rashid, A.; Azam, F. Anal. Chem. 1964, 36, 2471. (18) Simoyi, R. H.; Epstein, I. R. J. Phys. Chem. 1987, 91, 5124. (19) Noyes, R. M. Ber. Bunsen-Ges. Phys. Chem. 1980, 84, 295. (20) Cotton, F. A.; Wilkinson, G. AdVanced Inorganic Chemistry, 5th ed.; Wiley Interscience: New York, 1988; p 565. (21) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84, 1355-1361. (22) Wang, Y. L.; Nagy, J. C.; Margerrum, D. W. J. Am. Chem. Soc. 1989, 111, 7838.
Chinake and Simoyi (23) Willis, R. E.; Clark, W. W., III. J. Chem. Phys. 1980, 72, 4946. (24) Noyes, R. M.; Kalachev, L. V.; Field, R. J. J. Phys. Chem. 1995, 99, 3514. (25) Liebhafsky, H. A.; Roe, G. M. Int. J. Chem. Kinet. 1979, 11, 693. (26) Dushman, S. J. Phys. Chem. 1904, 8, 453. (27) Fisher analytical grade reagent NaBrO3 contains 0.05% NaBr, which is difficult to remove despite several recrystallizations. (28) Fonslick, J.; Khan, A.; Weiner, B. J. Phys. Chem. 1989, 93, 3836. (29) Kaps, P.; Rentrop, P. Numer. Math. 1979, 23, 55. (30) Faria, R. B.; Lengyel, I.; Epstein, I. R.; Kustin, K. J. Phys. Chem. 1993, 97, 1164. (31) Field, R. J.; Fo¨rsterling, H. D. J. Phys. Chem. 1986, 90, 5400. (32) Gao, Y.; Fo¨rsterling, H. D. J. Phys. Chem. 1995, 99, 8638. (33) Fo¨rsterling, H. D.; Varga, M. J. Phys. Chem, 1993, 97, 7932. (34) Treindl, L.; Noyes, R. M. J. Phys. Chem. 1993, 97, 11354. (35) Janzen, E. G.; Liu, J. I. P. J. Magn. Reson. 1973, 9, 510. (36) Janzen, E. G.; Evans, C. A.; Liu, I. J. P. J. Magn. Reson. 1973, 9, 513. (37) Bolton, J. R.; Borg, D. C.; Swartz, H. M. In Biological Applications of Electron Spin Resonance; Swartz, H. M., Ed.; Wiley Interscience: New York, 1972.
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