Kinetics and Mechanism of the Chlorine Dioxide–Trithionate Reaction

Article pubs.acs.org/JPCA

Kinetics and Mechanism of the Chlorine Dioxide−Trithionate Reaction György Csekő and Attila K. Horváth* Department of Inorganic Chemistry, University of Pécs, Ifjúság útja 6., H-7624 Pécs, Hungary ABSTRACT: The trithionate−chlorine dioxide reaction has been studied spectrophotometrically in a slightly acidic medium at 25.0 ± 0.1 °C in acetate/acetic acid buffer monitoring the decay of chlorine dioxide at constant ionic strength (I = 0.5 M) adjusted by sodium perchlorate. We found that under our experimental conditions two limiting stoichiometries exist and the pH, the concentration of the reactants, and even the concentration of chloride ion affects the actual stoichiometry of the reaction that can be augmented by an appropriate linear combination of these limiting processes. It is also shown that although the formal kinetic order of trithionate is strictly one that of chlorine dioxide varies between 1 and 2, depending on the actual chlorine dioxide excess and the pH. Moreover, the otherwise sluggish chloride ion, which is also a product of the reaction, slightly accelerates the initial rate of chlorine dioxide consumption and may therefore act as an autocatalyst. In addition to that, overshoot−undershoot behavior is also observed in the [·ClO2]−time curves in the presence of chloride ion at chlorine dioxide excess. On the basis of the experiments, a 13-step kinetic model with 6 fitted kinetic parameter is proposed by nonlinear parameter estimation.

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INTRODUCTION The chlorite−tetrathionate reaction (CT) has been brought into the focus of interest during the last decades by investigating several different spatiotemporal behaviors in connection with front propagation.1−4 A simplified model suggested by Tóth et al. for evaluation of the experiments worked consistently well in a narrow concentration range of the reactants but significant deviation was encountered between the measured data and the model prediction in the concentration dependence of the front velocity.1 Very recently a more accurate kinetic model has been proposed to give a better prediction of the unusual concentration dependence of 1D-front velocity.5 This study has also revealed that in some cases measurements may be seriously affected by side reactions caused by alkaline decomposition of tetrathionate.6 Because alkaline decomposition of tetrathionate leads to the formation of thiosulfate, sulfite, and trithionate, their reactions with chlorite may significantly contribute to the overall behavior of the parent system. Although reactions of chlorite with thiosulfate7 and with sulfite8 are well-known in the literature, no information is yet available on the chlorite− trithionate reaction. A precise knowledge on the kinetics of the chlorite−trithionate reaction is, however, eagerly expected because it is well-known that trithionate is considerably more stable toward alkaline degradation than tetrathionate.9 It straightforwardly means that a mixture of chlorite and trithionate can be conveniently stored in alkaline solution for a long time without any decomposition or side reaction. This feature may make the chlorite−trithionate reaction more attractive to be used in studying the dynamics of spatiotemporal structures. Our primary aim was therefore to study the chlorite− trithionate reaction, but preliminary experiments revealed that chlorine dioxide is formed in considerable amount during this © 2012 American Chemical Society

reaction although in trithionate excess it disappears in a slow reaction. It means that trithionate reacts with a moderate rate in presence of chlorine dioxide as well; therefore, we decided to study first the trithionate−chlorine dioxide reaction.

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EXPERIMENTAL SECTION Materials and Buffers. Sodium trithionate was prepared as described previously, and its purity was found to be better than 99.5%.10 Chlorine dioxide stock solution was also prepared by a standard method published elsewhere.11 The concentration of stock chlorine dioxide solution was checked each day prior to use for chloride, chlorite, and chlorate impurities after purging out its ·ClO2 content. None of these impurities could be detected up to a month. All the other chemicals were of the highest purity commercially available (acetic acid, sodium acetate, sodium chloride) and were used without further purification. Stock solutions were freshly prepared each day from double-distilled and twice ion-exchanged water. The pH of solutions was regulated between 4.35 and 5.70 by acetic acid/acetate buffer taking the pKa of acetic acid as 4.55. The acetate concentration was always kept constant at 0.167 M and the ionic strength was adjusted by sodium perchlorate to 0.5 M. The desired pH was adjusted by the necessary amount of acetic acid. Temperature of the reaction vessel was maintained at 25.0 ± 0.1 °C. The concentrations of trithionate and chlorine dioxide ranged between 0.1 and 1.4 mM and 0.24 and 5.4 mM, respectively. Because it turned out that initially added chloride ion also affects Received: December 5, 2011 Revised: February 13, 2012 Published: March 9, 2012 2911

dx.doi.org/10.1021/jp211704h | J. Phys. Chem. A 2012, 116, 2911−2919

The Journal of Physical Chemistry A

Article

the rate (see later), [Cl−]0 was also varied in several experiments between 0 and 20.0 mM. In this experimental setup we investigated the reaction at 118 different experimental conditions and we also repeated our experiments in several different cases that convinced us about good reproducibility of the kinetic curves. Methods and Instrumentation. The reaction was followed by a Zeiss S10 and S600 diode array spectrophotometer. The reaction has been carried out in a standard quartz cuvette equipped with magnetic stirrer and Teflon cap having 1 cm optical path. The buffer components and sodium perchlorate followed by the chlorine dioxide solution were delivered from a pipet. The spectrum of these solutions was always recorded just before starting the reaction to determine the exact chlorine dioxide concentration. The reaction was started with addition of the necessary amount of trithionate solution from a fast delivery pipet. The spectrum of the reacting solutions at the wavelength range of 400−600 nm was acquired up to approximately 15000−50000 s in every 20 s. Within this wavelength range only chlorine dioxide was proven to absorb the light. Note as well that the deuterium lamp of the photometer was always switched off during the whole course of experiments to eliminate the undesired photochemical decomposition of chlorine dioxide.12,13 Data Treatment. The measured absorbance−time series were transformed into concentration−time series by the determined molar absorbance of chlorine dioxide at the wavelength range studied. Only values of absorbance (at different wavelengths) between 0.1 and 1.0 were used to obtain chlorine dioxide concentrations at each time point of each series because outside this absorbance region the error of absorbance measurement starts to increase not to provide linear relationship between the concentration and the absorbance. Originally, each kinetic run contained more than 500 concentration−time data pairs; therefore, it was necessary to reduce the number of time points (60−70) to avoid unnecessary time-consuming calculations. The essence of this method has already been described elsewhere.14 To obtain the kinetic model and the rate coefficients, a relative fitting procedure has been chosen to minimize the average deviation between the measured and calculated concentrations by the program package ZiTa15 developed to fit basically unlimited experimental series. Altogether almost 7000 experimental points from the 118 kinetic series were used for the simultaneous evaluation. Our quantitative criterion for an acceptable fit was that the average deviation for the relative fit approach 4%, which is close to the experimentally achievable limit of error under present experimental conditions, if one takes into account the unavoidable loss of chlorine dioxide due to its distribution between the aqueous liquid phase and the minimum volume of air in a closely tighted quartz cuvette.

chlorine containing end product. The appearance of chlorate was confirmed by the evaporated Raman spectrum of the end products shown in Figure 1 by its characteristic Raman peaks at

Figure 1. Raman spectrum of the vacuum-evaporated reacting solution at [S3O62−]0 = 1.75 mM and [·ClO2]0 = 17.5 mM in unbuffered medium (black curve). The pH of the solution was adjusted to slightly alkaline by sodium hydroxide to avoid the formation of hydrogen sulfate peak. The blue curve is the Raman spectrum of solid potassium chlorate shifted by +25 Raman intensity unit along the left Y-axis. The red curve is the Raman spectrum of the evaporated solution containing potassium chlorate, sodium sulfate and sodium chloride in alkaline pH. (red curve) Note the right Y-axis belongs uniquely to the black curve and it was shifted by +15 Raman intensity unit for better visibility.

947, 623, and 484 cm−1. Table 1 shows the SR calculated from the initial concentrations of the reactants and that of the Table 1. Measured SR (Defined as ([·ClO2]0−[·ClO2]∞)/ [S3O62−]0) in an Excess of Chlorine Dioxide [·ClO2]0/mM [S3O62−]0/mM 3.46 2.76 0.863 0.835 0.810 0.882 0.882 5.43 4.90 3.12 2.05 1.49 1.46 1.44 1.44 1.45 1.47 1.48 1.31 1.31 1.30 1.31 1.30 1.30

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RESULTS Stoichiometry. Among sulfur-containing anions only sulfate could be detected under our experimental conditions as end product; therefore, the thermodynamically most favorable stoichiometry of the reaction is 5S3O62 − + 8·ClO2 + 14H2O → 15SO4 2 − + 8Cl− + 28H+

(1) ·

[ ClO2]/[S3O62−]

which would suggest a consumed stoichiometric ratio (SR) to be 1.6. However, in an excess of chlorine dioxide, besides the chloride ion ClO3− appears as an additional

0.665 0.665 0.1 0.167 0.25 0.375 0.469 0.665 0.665 0.665 0.669 0.669 0.351 0.351 0.351 0.351 0.351 0.351 0.353 0.353 0.353 0.353 0.353 0.353

pH 5.45 5.45 4.55 4.55 4.55 4.55 4.55 4.55 4.55 4.55 4.55 4.55 3.68 4.14 4.35 4.55 5.15 5.45 4.55 4.55 4.55 4.55 4.55 4.55

[Cl−]0/mM [·ClO2]∞/mM 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.0 2.0 5.0 7.0 14.0

0.931 0.485 0.567 0.39 0.207 0.114 0.045 3.57 2.96 1.46 0.699 0.200 0.657 0.627 0.612 0.580 0.552 0.502 0.464 0.494 0.503 0.535 0.546 0.570

SR 3.81 3.41 2.96 2.67 2.41 2.05 1.79 2.79 2.92 2.50 2.02 1.93 2.28 2.31 2.37 2.48 2.63 2.79 2.39 2.32 2.27 2.19 2.13 2.06

measured final concentration of ·ClO2 in an excess of chlorine dioxide at some representative experiments. It clearly indicates 2912



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Proposed Kinetic Model. We propose here the following kinetic model that describes adequately all the observations of our experiments under the present experimental conditions. The essence of the method with which we obtained the best fitting model has already been published elsewhere.14,16 Later we shall point out that all the steps proposed here are essential parts of the kinetic model that either help to account for the change of the stoichiometry during the course of the reaction or have meaningful kinetic relevance.

that the SR significantly increases from 1.79 to 3.81 in chlorine dioxide excess, suggesting the following limiting stoichiometry as well: S3O62 − + 4·ClO2 + 4H2O → 3SO4 2 − + 2Cl− + 2ClO3− + 8H+

(2)

In addition to that, one may easily realize that an increase of initial trithionate and chloride concentrations shifts the overall stoichiometry toward eq 1, whereas an increase of initial chlorine dioxide concentration and that of pH shifts it toward eq 2. We shall see later that this observation can readily be explained by the proposed model. We therefore concluded that the overall stoichiometry of the reaction at an actual initial concentration of the reactants can be established as an appropriate linear combination of eqs 1 and 2. Initial Rate Studies. Figure 2 shows the results of the initial rate studies. As seen, it is clear that the formal kinetic order of

CH3COOH ⇌ H+ + CH3COO−

(E1)

S3O62 − + ·ClO2 ⇌ ·S3O6ClO2 2 −

(R1)

·S O ClO 2 − + H+ → ·S O − + HOCl 3 6 2 3 7

(R2)

·S O ClO 2 − + ·ClO → S O 2 − + Cl O 3 6 2 2 3 7 2 3

(R3)

S3O7 2 − + 2H2O → 3HSO3− + H+

(R4)

Cl2O3 + H2O → HOCl + ClO3− + H+

(R5)

Cl2O3 + S3O62 − + 3H2O → 2Cl− + 3SO4 2 − + 6H+ (R6)

HSO3− + ·ClO2 → SO4 2 − + ·ClO + H+

(R7)

·ClO + ·ClO → Cl O 2 2 3

(R8)

·

+ S3O7− + 2H2O → ·SO3− + 2HSO− 3 + 2H

(R9)

·ClO + ·S O − + 3H O → 3HSO − + ClO − + 3H+ 2 3 7 2 3 3 (R10)

·

SO3− + ·ClO2 + H2O → SO4 2 − + ClO2− + 2H+

Figure 2. Initial rate studies at different conditions. In the case of the black curves, the X-axis title c0 corresponds to [S3O62−]0 at pH= 4.55 and [ClO2]0 = 0.99 mM (●); and pH = 4.14 and [ClO2]0 = 0.88 mM (○). In the case of the blue curves, the X-axis title c0 corresponds to ClO2 at pH = 4.55 and [S3O62−]0 = 0.666 mM; and pH = 5.45 [S3O62−]0 = 0.666 mM (○). In teh case of the red curves, the X-axis title c0 corresponds to [H+] at [S3O62−]0 = 0.35 mM and [ClO2]0 = 1.44 mM (●); and [S3O62−]0 = 0.70 mM and [ClO2]0 = 1.4 mM (○). In the case of the green curve, the X-axis title corresponds to [Cl−]0 at pH = 4.55, [S3O62−]0 = 0.353 mM and [·ClO2]0 = 1.30 mM.

(R11)

HSO3− + HOCl → SO4 2 − + Cl− + 2H+

(R12)

HSO3− + ClO2− → SO4 2 − + HOCl

(R13)

The average deviation between the measured and calculated concentrations of all the kinetic curves was found to be 4.2% with 6 fitted and 9 fixed parameters. The final result of the calculation is summarized in Table 2. Representative results of the fitting procedure are illustrated in Figures 3−7 supporting the validity of the kinetic model. Discussion. Step R1 is the initiating, rapid equilibrium between the reactants to form an unstable adduct. Formation of such an unstable adduct was already proposed in the tetrathionate−chlorine dioxide reaction.17 We shall see later that the equilibrium constant (K1 = k1/k−1) cannot be determined from our experiments. Any arbitrary small value, resulting from the ratio of k1 and k−1, providing that the equilibrium is established basically instantaneously, will lead to the same final result. In other words, it means that only the product of K1 with k2 and k3 can be determined unambiguously from our experiments. Step R2 is one of the possible fate of the adduct radical · S3O6ClO22− to form ·S3O7− and hypochlorous acid. We found this step to be one of the rate limiting processes. Because it is experimentally found that the rate of the disappearance of chlorine dioxide increases with [H+] and [Cl−]0, we tried to fit our data by supposing several different rate equations for v2.

trithionate ion is unity regardless of the pH. Although at lower pH the formal kinetic order of chlorine dioxide is 1, at higher pH it starts to increase. At pH = 5.55, we determined 1.23 ± 0.01, indicating that the reaction is no longer first order with respect to chlorine dioxide. Later we shall see as well that this phenomenon can easily be explained by the proposed kinetic model. It is also interesting to note that the log−log plot of the initial rate vs [H+] does not provide a linear dependence, indicating no exact formal kinetic order of the hydrogen ion. Second-order polynomial (y = a·x2 + b·x + c) least-squares fit of the measured data is also illustrated in Figure 2, suggesting a complex pH dependence. Later this result will also be analyzed by the proposed kinetic model. It should also be worthwhile to mention that initially added chloride ion (as seen in Figure 2) increases the initial rate of the reaction, so the otherwise sluggish chloride ion has a dual role: on the one hand, it catalyzes the reaction, and on the other hand, it alters the overall stoichiometry. 2913



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Table 2. Fitted and Fixed Rate Coefficients of the Proposed Kinetic Modela no.

rate equation

parameter

R1 R−1

k1[S3O62−][·ClO2] k−1[·S3O6ClO22−] k2[H+][·S3O6ClO22−] k2′ [H+][Cl−][·S3O6ClO22−] k2″[H+]2[·S3O6ClO22−] k3[H+]−1[·S3O6ClO22−][·ClO2] k4[S3O72−] k5[Cl2O3] k6[Cl2O3][S3O62−] k7[H+]−1[HSO3−][·ClO2] k8[·ClO2][·ClO] k9[·S3O7−] k10[·S3O7−][·ClO2] k11[·ClO2][·SO3−] k12[HSO3−][HOCl] k13[HSO3−][ClO2−][H+]

100 M−1 s−1 106 s−1 (5.67 ± 0.08) × 107 M−1 s−1 (7.64 ± 0.35) × 109 M−2 s−1 (5.99 ± 0.17) × 1011 M−2 s−1 1.42 ± 0.04 s−1 104 s−1 104 s−1 (2.07 ± 0.11) × 107 M−1 s−1 1.042 s−1 7 × 109 M−1 s−1 106 s−1 (8.35 ± 0.40) × 108 M−1 s−1 5 × 109 M−1 s−1 7.6 × 108 M−1 s−1 8.2 × 109 M−2 s−1

R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13

Figure 4. Measured (filled circles) and calculated (solid lines) [·ClO2]−time curves at [S3O62−]0 = 0.665 mM and pH = 4.54 with different initial chlorine dioxide concentrations. [·ClO2]0/mM = 5.43 (black), 4.90 (blue), 4.64 (green), 3.38 (cyan), 3.12 (red), 2.05 (magenta), 1.49 (brown), 1.108 (light gray), 0.607 (purple), 0.356 (orange).

a

No error indicates that the value in question was fixed during the fitting procedure.

Figure 5. Measured (filled circles) and calculated (solid lines) [·ClO2]−time curves at [S3O62−]0 = 0.702 mM and [·ClO2] ≈ 1.40 mM at different pHs. pH = 3.68 (black), 3.90 (blue), 4.14 (green), 4.35 (cyan), 4.55 (red), 4.85 (magenta), 5.15 (brown), 5.45 (yellow).

Figure 3. Measured (filled circles) and calculated (solid lines) [·ClO2]−time curves at [·ClO2]0 ≈ 0.96 mM and pH = 4.14 with different initial trithionate concentrations. [S3O62−]0/mM = 0.1 (black), 0.125 (blue), 0.167 (green), 0.25 (cyan), 0.31 (red), 0.375 (magenta), 0.469 (brown), 0.625 (light gray), 0.848 (dark gray), 1.06 (purple), 1.41 (orange).

concentration (k2″ = 0) yields the average deviation of 7.6% and 5.6%, respectively. A significant increase in the average deviation along with the fact that the quality of fit decreased at lower pHs confirmed our keeping both terms in the rate equation. Step R3 is the alternative route for ·S3O6ClO22− to be consumed. This reaction is first order with respect to chlorine dioxide that will lead to an overall kinetic order for chlorine dioxide higher than one. As one may see, the rate of this reaction is inversely proportional to [H+], meaning that this route becomes more important at higher pHs. The deviation of the formal kinetic order of chlorine dioxide from unity is observed at higher pHs (see before); therefore, the role of this step is also well-established in the kinetic model. It also means that this step along with steps R1 and R2 has a kinetic relevance. The increasing formal kinetic order of chlorine dioxide with increasing pH will further be highlighted. (see Formal Kinetics). Step R4 is a rapid hydrolysis of S3O72−, leading to hydrogen sulfite. According to our measurements this reaction has to be fast; any value for k4 higher than 0.1 s−1 will lead to the same

Among them the following v2 = (k2[H+] + k2′ [H+][Cl−] + k2″[H+]2)·[S3O6ClO22−] empirical rate equation was found to provide the best fit of the experimental data. It shows a complex pH and chloride ion dependence of the overall reaction that is already manifested in the individual formal kinetic order of H+ as well as that of Cl−. The question about the necessity of all the terms in the rate equation seems to be straightforward; therefore, we carried out additional fitting with step by step elimination of these terms. Certainly the role of k2′ is firmly established because this is the only reaction whose rate depends on [Cl−], so the experimentally found accelerating effect of the initial rate with respect to chloride ion can be explained by this part of the rate equation. Moreover, the hydrogen dependence in the corresponding rate term (k2′ [H+][Cl−]) is also in complete agreement with that found in the tetrathionate−chlorine dioxide reaction.17 Elimination of the rate term that depends on the hydrogen ion concentration (k2 = 0) or the square of the hydrogen ion 2914



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Step R7 is the initial step of the well-known fast sulfite− chlorine dioxide reaction that probably proceeds via a formal O-atom transfer.19 Because, under our experimental conditions, the major S(IV) species is HSO3−, the rate equation is given as v7 = k7[H+]−1[HSO3−][·ClO2]. It completely coincides with earlier observations that among S(IV) species the most reactive one is sulfite toward chlorine dioxide.19,20 Taking into account that according to ref 19 the individual rate coefficient between sulfite and chlorine dioxide is 2.08 × 106 M−1 s−1 one can easily obtain k7 = 2.08 × 106 × KS(IV) = 1.042 s−1, where KS(IV) = 5 × 10−7 M is the acid dissociation constant of hydrogen sulfite.21 Step R8 is also a fast diffusion-controlled radical−radical reaction to produce Cl2O3. The individual rate coefficient (k8) was determined by Wang and Margerum22 to be k8 = 7 × 109 M−1s −1; therefore, we fixed this value during the calculation process. Step R9 is one of the possible route for ·S3O7− to generate the final products via series of steps. The first-order decomposition of this radical may take place via scission of the sulfur chain to produce hydrogen sulfite and sulfite radical. Because it is a shortlived radical, the halftime of the reaction should be very short, but it cannot be determined unambiguously from our experiments. We found that k9 is in total correlation with k10, meaning that only their ratio can be calculated; therefore, we fixed k9 for a sufficiently high value (106 s−1) to ensure low steady-state concentration for this radical and to calculate k10. Step R10 is also a rapid radical−radical reaction between chlorine dioxide and ·S3O7− to produce chlorate and hydrogen sulfite. The most important consequence of this step is that chlorate forms, meaning that this pathway is responsible for higher SR in an excess of chlorine dioxide. As pointed out previously, we could only calculate k10/k9 = 835 ± 40 M−1, so k10 was found to be 8.35 × 108 M−1 s−1 at a given k9. Steps R11 is a fast radical−radical reaction as well between the sulfite radical and chlorine dioxide to produce sulfate and chlorite ions. As one can easily see, this pathway dominates at lower chlorine dioxide concentrations because the rate determining pathway is the formation of ·S3O7− via step R2. As we pointed out previously, at lower chlorine dioxide concentrations, the SR decreases, meaning that less chlorate forms. Chlorite generated from this step will react further with sulfite to produce sulfate and chloride exclusively preventing the formation of chlorate to maintain the SR in the appropriate region. Any value higher than 105 M−1 s−1 for k11 will lead to the same final result; therefore, we fixed this rate coefficient as 5 × 109 M−1 s−1, which is close to the diffusion controlled limit and usual for a rapid radical−radical reaction. Step R12 is the well-known rapid oxidation of hydrogen sulfite by hypochlorous acid. This rate coefficient was fixed during the whole calculation process to 7.6 × 108 M−1 s−1, which was determined independently by Fogelman et al.23 One can easily argue that additional reactions of hypochlorous acid should also be considered such as the following one:

Figure 6. Measured (filled circles) and calculated (solid lines) [·ClO2]−time curves in stoichiometric excess of chlorine dioxide at [S3O62−]0 = 0.35 mM, [·ClO2] ≈ 1.40 mM, at different pHs. pH = 3.68 (black), 3.90 (blue), 4.14 (green), 4.35 (cyan), 4.55 (red), 4.85 (magenta), 5.15 (brown), 5.45 (yellow).

Figure 7. Measured (filled circles) and calculated (solid lines) [·ClO2]−time curves in at [S3O62−]0 = 0.700 mM, [·ClO2] ≈ 0.68 mM and pH = 4.55 at different initial chloride concentrations. [Cl−]0/ mM = 0 (black), 1.0 (blue), 2.0 (green), 5.0 (cyan), 7.0 (red), 10.0 (magenta), 14.0 (brown), 20.0 (yellow).

average deviation. We fixed k4 = 104 s−1 to provide that S3O72− is a short-lived intermediate. Step R5 is the well-known rapid hydrolysis of Cl2O3 that leads to hypochlorous acid and chlorate ion.13,18 The individual rate coefficient of the hydrolysis cannot be calculated from our experiments and we found that only the ratio k6/k5 can be determined. We therefore set k5 = 104 s−1, providing Cl2O3 to be a short-lived intermediate throughout the whole calculation process, and calculated k6. Step R6 is also a rapid reaction that directly leads to the formation of sulfate and chloride ions. Evidently, this reaction is an overall process and our experiments do not provide a solid basis to divide it into elementary ones. This pathway is responsible for the shift in the SR at higher trithionate concentrations. As one can easily see, this pathway decreases the SR because it prevents the formation of chlorate. The opposite pathway (the disproportionation of Cl2O3, see step R5), however, produces chlorate and hence increases the SR. We have calculated the k6/k5 ratio to be 2072 ± 80 M−1, so k6 was found to be 2.07 × 107 M−1 s−1 if k5 was set to 104 s−1.

S3O62 − + HOCl → S3O7 2 − + Cl− + H+

(3)

Therefore, we have done additional fitting to include this reaction into the final model, but all of our efforts failed. Probably it means that the concentration of HOCl is quite low under our experimental condition and no other reaction can compete efficiently with the very rapid Step R12. Step R13 is the initiating step of the hydrogen sulfite− chlorite reaction. Under our experimental condition it is a fast 2915



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is attained by chloride ion. Unfortunately, this behavior cannot be explained by our proposed model, and certainly more experiments are required to explain the origin of this effect, but it appears to establish a new feature of the otherwise sluggish chloride ion. Further work is still under way in our laboratory to exploit this effect more thoroughly. Formal Kinetics. As one may easily notice, no long-lived intermediate accumulates in detectable amount during the course of the reaction; therefore, steady-state approximation may be applied to derive a rate equation under specific conditions to account for most of the experimental observations (complex [H+] dependence, higher formal kinetic order of chlorine dioxide, etc.). To follow the derivation more easily, the proposed kinetic model is simplified by elimination of S3O72−, ·ClO, ·SO3−, hypochlorous acid and chlorite species with proper change of the stoichiometry of the given step. In this way the following simplified kinetic model is obtained, where A, B, C, D, E, F, and P stands for S3O62−, ·ClO2, ·S3O6ClO22−, HSO3−, ·S3O7−, Cl2O3, and the products, respectively:

reaction and its rate coefficient is known from independent studies.8,14,24 The pH-dependent rate coefficient is ranged between 2 × 108 and 8.2 × 109 M−2 s−1 and we fixed k13 to be the latter one in a view of the mostly corresponding experimental condition. Finally, it should also be emphasized that both hydrogen ion and chloride ion may act as autocatalysts of the reaction because they are products and also accelerate the rate of the reaction. Under our experimental condition, however, the S-shaped type of kinetic curve is not manifested. The autocatalytic feature of the hydrogen ion is completely suppressed in buffered medium; therefore, it cannot be anticipated. However, the autocatalytic feature of chloride ion may be enlarged at an appropriate initial condition; therefore, we started to extend the concentration range of the reactants where the S-shaped type kinetic curve becomes visible. So far, all of our efforts to find an appropriate initial condition have failed, possibly emerging from the low formal kinetic order of chloride ion. Meanwhile, doing this series of experiments, we discovered a new feature of the chloride ion shown in Figure 8.

k1,k−1

A + B HooooooI C k2 ,k2′ ,k2″

C + (D) ⎯⎯⎯⎯⎯⎯⎯⎯→ E k3

C + B → 3D + F k5

F + (D) → P k6

k7

D + 2B → F k9

E + (B) → P k10

E + B ⎯⎯→ 3D

(M3) (M4)

(M6) (M7) (M8)

where bracketed terms mean that the corresponding species participates only in the stoichiometry of the reaction but does not have influence on the rate equation of the given step. One may note as well that we preserved the rate equation of the original model along with the rate coefficients; that is why the numbering of the rate coefficients and that of the equations does not match each other. The consumption of B (chlorine dioxide) may be written as if one also takes into account the hydrogen dependence of the given steps:

As seen at high chloride concentration, the chlorine dioxide concentration−time curve goes through a minimum before reaching its final value in chlorine dioxide excess, meaning that a chlorine dioxide recovery process should be included in the final model to explain this feature. This overshoot−undershoot behavior is a well-known phenomenon in the reactions of oxyhalogens and oxysulfur species,11,25 but to our knowledge it has not been yet reported that the overshoot−undershoot behavior −

(M2)

(M5)

A+F→P

Figure 8. Measured [·ClO2]−time curves at different [Cl−]0/mM = 0 (●) and 20.0 (○). Other concentrations: [S3O62−]0 = 0.353 mM, [·ClO2]0 = 1.21 mM, pH = 3.90.

(M1)

d[B] = k1[A][B] − k−1[C] + k3[H]−1 [B][C] + 2k 7[H]−1 [B][D] + k 9[E] + k10[E][B] dt

(4)

where [H] stands for the hydrogen concentration. Applying steady-state approximation for the species E (·S3O7−), we obtain

[E]ss =

(k2[H] + k2′ [H][Cl] + k2″[H]2 )[C] k 9 + k10[B]

(5)

where [Cl] stands for chloride ion concentration. 2916



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Considering that species F (Cl2O3) and D (HSO3−) are also short-lived intermediates steady-state approximation gives us k [C][B][H]−1 + k 7[D][B][H]−1 [F]ss = 3 k5 + k6[A]

(6)

and

[D]ss =

3k3[C][B][H]−1 + 3k10[E][B] − (k2[H] + k2′ [H][Cl] + k2″[H]2 )[C] − k5[F] k 7[H]−1[B]

(7)

Substituting eqs 5 and 6 into eq 7 followed by some algebraic manipulations leads to k [H]−1[B](2k5 + 3k6[A])(k 9 + k10[B]) + (k2[H] + k2′ [H][Cl] + k2″[H]2 )(2k10[B] − k 9)(k5 + k6[A]) [D]ss = C 3 k 7[H]−1[B](2k5 + k6[A])(k 9 + k10[B])

(8)

Because 2k 7[H]−1[B][D] = [C]

2k3[H]−1[B](2k5 + 3k6[A])(k 9 + k10[B]) + 2(k2[H] + k2′ [H][Cl] + k2″[H]2 )(2k10[B] − k 9)(k5 + k6[A]) (2k5 + k6[A])(k 9 + k10[B])

(9)

eq 3 may be written as follows after substitution of eqs 5 and 9: −

d[B] = k1[A][B] − k−1[C] + k3[H]−1 [C][B] + (k2[H] + k2′ [H][Cl] + k2″[H]2 )[C] dt 2k [H]−1[B](2k5 + 3k6[A])(k 9 + k10[B]) + 2(k2[H] + k2′ [H][Cl] + k2″[H]2 )(2k10[B] − k 9)(k5 + k 6[A]) +[C] 3 (2k5 + k6[A])(k 9 + k10[B]) (10)

Taking into consideration that [C]ss =

k1[A][B] k−1 + k2[H] + k2′ [H][Cl] + k2″[H]2 + k3[H]−1[B]

(11)

and with substitution of eq 11 into eq 10 followed by a long but straightforward algebraic manipulation we obtain

−

⎛ 8k [H]−1[B](k + k [A]) + 2(k [H] + k′ [H][Cl] + k″[H]2 )k k1[A][B] d[B] 5 6 2 2 2 5 ⎜⎜ 3 = · dt 2k5 + k6[A] k−1 + k2[H] + k2′ [H][Cl] + k2″[H]2 + k3[H]−1[B] ⎝ 6(k2[H] + k2′ [H][Cl] + k2″[H]2 )k10[B](k5 + k6[A]) ⎞ ⎟⎟ + (k 9 + k10[B])(2k5 + k6[A]) ⎠ (12)

The denominator of the first term can further be simplified because k−1 is much larger than the remaining terms due to the fact that step R1 is established rapidly. Therefore, finally the following expression is obtained: 2917



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⎛ ⎛ ⎞ k ⎜ 8k3[H]−1[B]⎜1 + 6 [A]⎟ + 2(k2[H] + k2″HK + k2″[H]2 ) k5 ⎝ ⎠ d[B] ⎜ + (k2[H] + k2′ [H][Cl] + k2″[H]2 ) − = K1[A][B]⎜ k6 dt 2 + [A] ⎜ k5 ⎝ ⎞ ⎞ k ⎛ k 6[B] 10 ⎜1 + 6 [A]⎟ ⎟ k9 ⎝ k5 ⎠ ⎟ ⎞⎟ ⎛ ⎞⎛ k6 k10 [B]⎟ ⎟ ⎜2 + [A]⎟⎜1 + k5 k9 ⎝ ⎠⎝ ⎠⎠

(13)

Such an interesting dynamical phenomenon caused by the otherwise sluggish chloride ion has not been reported yet. Because the present kinetic model is not yet able to take this phenomenon into account, our future work will focus on elucidating this effect.

It is now easy to see that according to the initial rate study the reaction is first order with respect to trithionate, but the formal kinetic order of chlorine dioxide varies between 1 and 2 depending on the pH range and the actual concentration of the reactant. Moreover, slight chloride dependence of the initial rate is also enlightened via the k2′ term and the complex pH dependence of the initial rate is also well-understandable. In addition to that, eq 13 provides an opportunity to determine the values of k2, k2′ , k2″, and k3 from the initial rates by nonlinear least-squares fit. Unfortunately, the ratios k6/k5 and k10/k9 cannot be determined from the initial rates; therefore, we have fixed k6/k5 and k10/k9 to be 2070 and 835 M−1, respectively, obtained from the simultaneous fit of the kinetic curves. If K1 is considered to be 10−4 M−1, we find that k2 = (7.4 ± 1.0) × 107 M−1 s−1, k2′ = (1.5 ± 0.5) × 1010 M−2 s−1, k2″ = (1.5 ± 0.1) × 1012 M−2 s−1, and k3 = 0.51 ± 0.20 s−1, which are in a very sound agreement with their values determined by nonlinear parameter estimation (Table 2). The difference we may see between the values determined by these two different ways is not surprising because the latter one uses only the initial rates of all the kinetic curves, whereas the simultaneous fit uses the whole course of kinetic curves. We rather suggest that eq 13 may only be used for qualitative purpose such as a smooth understanding that only values of the product of equilibrium constant K1 and k2, k2′ , and k2″ as well as k3 can be calculated from our experiments, but not for determination of the individual rate coefficients. Equation 13 also confirms the fact that the remaining parameters have no kinetic relevance (however, they are essential to keep the stoichiometry of the reaction in the proper range), as well as why only the ratios k6/k5 and k10/k9 can be obtained by simultaneous evaluation of the kinetic curves.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Hungarian Research Fund (OTKA) Grant Nos. K68172 and CK78553. A.K.H is grateful for the financial support of the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. We are thankful to Dr. Andrea Petz for her assistance in the Raman measurements. We are also thankful for an anonymous reviewer for his/her valuable suggestions.

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REFERENCES

(1) Tóth, A.; Horváth, D.; Siska, A. J. Chem. Soc., Faraday Trans. 1997, 93, 73−76. (2) Gauffre, F.; Labrot, V.; Boissonade, J.; DeKepper, P.; Dulos, E. J. Phys. Chem. A 2003, 107, 4452−4456. (3) Horváth, D.; Tóth, A. J. Chem. Phys. 1998, 108, 1447−1451. (4) Szalai, I.; Gauffre, F.; Labrot, V.; Boissonade, J.; DeKepper, P. J. Phys. Chem. A 2005, 109, 7843−7849. (5) Peintler, G.; Csekö, G.; Petz, A.; Horváth, A. K. Phys. Chem. Chem. Phys. 2010, 12, 2356−2364. (6) (a) Zhang, H.; Dreisinger, D. B. Hydrometallurgy 2002, 66, 59− 65. (b) Varga, D.; Horváth, A. K. Inorg. Chem. 2007, 46, 7654−7661. (c) Zhang, H.; Jeffrey, M. I. Inorg. Chem. 2010, 49, 10273−10282. (7) Nagypál, I.; Epstein, I. R. J. Phys. Chem. 1986, 90, 6285−6292. (8) Hartz, K. E. H.; Nicoson, J. S.; Wang, L.; Margerum, D. Inorg. Chem. 2003, 42, 78−87. (9) Rolia, E.; Chakrabarti, C. L. Environ. Sci. Technol. 1982, 16, 852− 857. (10) Csekö, G.; Horváth, A. K. J. Phys. Chem. A 2010, 114, 6521− 6526. (11) Horváth, A. K.; Nagypál, I. J. Phys. Chem. A 1998, 102, 7267− 7272. (12) Stanbury, D. M.; Figlar, J. N. Coord. Chem. Rev. 1999, 187, 223− 232. (13) Horváth, A. K.; Nagypál, I.; Peintler, G.; Epstein, I. R.; Kustin, K. J. Phys. Chem. A 2003, 107, 6966−6973. (14) Horváth, A. K.; Nagypál, I.; Epstein, I. R. Inorg. Chem. 2006, 45, 9877−9883.

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CONCLUSION The work presented here may be considered as the first comprehensive effort to unravel the kinetics and mechanism of the trithionate−chlorine dioxide reaction, although it is clear that we are only a step further in understanding the underlying chemistry. It is clearly demonstrated that two limiting stoichiometries exist and the initial conditions such as the reactant concentrations and the pH shift the balance between them, resulting in a complex overall stoichiometry. The reaction was proven to be first order with respect to the trithionate ion but the formal kinetic order of the chlorine dioxide changes between 1 and 2 with the varying pH and the actual concentration of chlorine dioxide. It is also shown that addition of chloride ion not only accelerates the reaction but also may result in an overshoot−undershoot type [·ClO2]−time curve. 2918



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(15) Peintler, G. ZiTam, a Comprehesive Program Package for Fitting Parameters of Chemical Reaction Mechanism, version 5.0; Attila József University: Szeged, 1989−1998. (16) Rauscher, E.; Csekö, G.; Horváth, A. K. Inorg. Chem. 2011, 50, 5793−5802. (17) Horváth, A. K.; Nagypál, I.; Epstein, I. R. J. Phys. Chem. A 2003, 107, 10063−10068. (18) Rábai, G.; Kovács, K. J. Phys. Chem. A 2001, 105, 6167−6170. (19) Horváth, A. K.; Nagypál, I. J. Phys. Chem. A 2006, 110, 4753− 4758. (20) Suzuki, K.; Gordon, G. Inorg. Chem. 1978, 17, 3115−3118. (21) IUPAC Stability Constant Database; Royal Society of Chemistry: London, 1992−1997. (22) Wang, L.; Margerum, D. W. Inorg. Chem. 2002, 41, 6099−6105. (23) Fogelman, K. D.; Walker, D. M.; Margerum, D. W. Inorg. Chem. 1989, 28, 986−993. (24) Frerichs, G. A.; Mlnarik, T. M.; Grun, R. J.; Thompson, R. C. J. Phys. Chem. A 2001, 105, 829−837. (25) Rábai, G.; Bazsa, G.; Beck, M. T. J. Am. Chem. Soc. 1979, 101, 6746−6748.

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Kinetics and Mechanism of the Chlorine Dioxide–Trithionate Reaction

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