Kinetics and Mechanism of the Oxidation of Pentathionate Ion by

Article pubs.acs.org/JPCA

Kinetics and Mechanism of the Oxidation of Pentathionate Ion by Chlorine Dioxide in a Slightly Acidic Medium Li Xu, György Csekő, Andrea Petz, and Attila K. Horváth* Department of Inorganic Chemistry, University of Pécs, Ifjúság útja 6, H-7624 Hungary János Szentágothai Research Center, Pécs, Ifjúság útja 20, H-7624 Hungary ABSTRACT: The chlorine dioxide−pentathionate reaction has been studied at a slightly acidic medium by conventional UV−vis spectroscopy monitoring the absorbance at 430 nm. We have shown that pentathionate was oxidized to sulfate, but chlorate is also a marginal product of the reaction besides the chloride ion. The stoichiometry of the reaction can be established as a linear combination of two limiting stoichiometries under our experimental conditions. Kinetics of the reaction was found to be also complex because initial rate studies revealed that formal kinetic orders of both the hydrogen ion and chlorine dioxide is far from unity. Moreover, log−log plot of the initial rate against pentathionate concentration indicated a nonconstant formal kinetic order. We also observed a significant catalytic effect of chloride ion. Based on our observations and simultaneous evaluation of the kinetic curves, an 11-step kinetic model is obtained with 6 fitted rate coefficients. A relatively simple rate equation has also been derived and discussed.

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INTRODUCTION

EXPERIMENTAL SECTION Materials and Buffers. Potassium pentathionate was first prepared as described previously, and its purity was found to be better than 97%.22 The chlorine dioxide stock solution was prepared by acidification of the sodium chlorite solution with 50% (v/v) sulfuric acid. Chlorine dioxide evolved was removed with an air stream and dissolved in cold water. The stock solution was kept refrigerated and was protected from light to avoid its photochemical decomposition. Purity of the chlorine dioxide stock 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. Concentration of stock chlorine dioxide solution was determined by standard iodometric method and/or spectrophotometrically before each experiment. All the other chemicals were of the highest purity commercially available (acetic acid, sodium acetate, and sodium chloride) and were used without further purification. Stock solutions were freshly prepared each day from double-distilled and twice ion-exchanged water. The ionic strength was adjusted to 0.5 M in all measurements with sodium acetate as a buffer component. The pH of solutions was regulated between 4.25 and 5.45 by adding the appropriate amount of acetic acid taking the pKa of acetic acid as 4.55.23 The temperature of the reaction vessel was maintained at 25.0 ± 0.1 °C. Initial concentrations of the chlorine dioxide and pentathionate ion were varied in the ranges 0.238−5.87 and 0.054−1.080 mM, respectively. The effect of initially added chloride ion on the reaction was also

It is generally well-known that oxidation of thiosulfate ion by different oxidizing agents leads finally to sulfate ion via formation of different polythionates as long-lived intermediates. These reactions of thiosulfate, for example, with chlorite, bromate, and periodate, exhibit several exotic nonlinear dynamical phenomena such as autocatalysis under batch condition,1−3 bistability and complex periodic and aperiodic behavior4−6 in a continuously stirred tank reactor (CSTR), and an appearance of varieties of different reaction−diffusion patterns (chemical waves and chemical reaction fronts) in unstirred system.7−10 It seems to be well-established that formation of polythionates and their further reactions with the corresponding oxidants sometimes displaying fascinating kinetics11 play a substantial role in the appearance of these exotic behaviors. Recently, a series of investigations confirmed that besides the sulfate ion, polythionates12−16 (such as tri-, tetra-, and pentathionate) and chlorine dioxide17 are also produced during the oxidation of thiosulfate by chlorite ion. The stability of polythionates especially of higher polythionates greatly increases with decreasing pH,18,19 which may provide a significant contribution of polythionate−chlorine dioxide reactions to the overall kinetic behavior of the parent system. As a result of systematic investigations, the kinetics and mechanism of the tetrathionate−chlorine dioxide20 and trithionate−chlorine dioxide21 reactions have already been reported. As a part of our systematic kinetic studies, here we report the detailed investigations of the pentathionate−chlorine dioxide reaction. © 2014 American Chemical Society

Received: December 17, 2013 Revised: February 1, 2014 Published: February 3, 2014 1293

dx.doi.org/10.1021/jp412333e | J. Phys. Chem. A 2014, 118, 1293−1299

The Journal of Physical Chemistry A

Article

studied in the concentration range 0−24.2 mM in a series of experiments. By this experimental setup altogether the title reaction was investigated at 132 different experimental conditions. Some experiments were also repeated that convinced us about a good reproducibility of the kinetic curves. Methods and Instrumentation. The reaction was followed by a Zeiss S600 diode array spectrophotometer in the wavelength range 400−650 nm. Within this wavelength range only chlorine dioxide was proven to have absorption. The reaction was carried out in a standard quartz cuvette equipped with magnetic stirrer and a Teflon cap having 1 cm optical path. The buffer components followed by the chlorine dioxide solution and if necessary the sodium chloride solution were delivered from a pipet. The spectrum of these solutions was always recorded just before initiation of the reaction to determine the initial chlorine dioxide concentration precisely. The reaction was started with an addition of the necessary amount of pentathionate solution from a fast delivery pipet. It should be noted that during the whole course of experiments, the deuterium lamp of the spectrophotometer was always switched off to eliminate the undesired photochemical decomposition of chlorine dioxide.24,25 To confirm the purity of potassium pentathionate and to check the sulfur- and chlorine-containing end products of the reaction, Raman spectroscopy was also carried out by an NXR FT-Raman spectrometer.

Table 1. Measured (SRm) and Calculated (SRc) Defined as ([ClO2]0 − [ClO2]∞)/[S5O62−]0 in an Excess of Chlorine Dioxide [ClO2]0/mM

[S5O62−]0/mM

pH

A∞ at 430 nm

SRm

SRc

1.403 1.428 1.410 1.404 1.345 1.865 1.850 1.865 1.850 1.779 5.888 5.496 3.876 3.118 2.056

0.22 0.14 0.1049 0.07944 0.05396 0.3 0.3 0.3 0.3 0.3 0.36 0.36 0.36 0.36 0.36

4.85 4.85 4.85 4.85 4.85 4.25 4.55 4.85 5.15 5.45 4.55 4.55 4.55 4.55 4.55

0.0136 0.063 0.091 0.1124 0.1305 0.005 0.009 0.017 0.027 0.0281 0.513 0.457 0.2155 0.11 0.015

5.98 7.30 7.85 8.55 9.32 6.11 5.97 5.85 5.59 5.33 7.16 7.08 6.91 6.69 5.44

6.19 7.64 8.10 8.50 8.84 6.16 6.03 5.96 5.72 5.49 6.71 6.68 6.54 6.47 5.61

excess, the stoichiometric ratio exceeds 4 and reaches almost 10. These measurements clearly hint that chloride is probably not the only chlorine-containing end product. As known from previous studies,20,21 such a shift in a stoichiometric ratio indicates that a significant amount of chlorate can also be detected among the end products. Figure 1 displays the Raman spectrum of the end products of a reacting solution after purging out the chlorine dioxide excess by N2 gas.

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DATA TREATMENT Because the only absorbing species is chlorine dioxide within the wavelength range studied, λ = 430 nm was chosen for data evaluation. Molar absorbance of chlorine dioxide was determined to be 155 ± 4 M−1 cm−1 at this wavelength. Absorbance−time curves contained initially 200−1600 experimental points; therefore, it was necessary to reduce the number of points to 50 data pairs in each kinetic curve to avoid unnecessary and time-consuming calculation process. The essence of this method, based upon the principle of equivalent archlength, was already published elsewhere.26 To obtain the kinetic model and the rate coefficients, an absolute fitting procedure has been chosen to minimize the average deviation between the measured and calculated absorbances by the program package ZiTa27 developed for simultaneous evaluation of basically unlimited number of kinetic curves. Altogether more than 6600 experimental points from 132 kinetic runs were used for data evaluation. Our quantitative criterion for an acceptable fit was that the average deviation for the absolute fit approached 0.006 absorbance unit, which was close to the experimentally available limit of error of the spectrophotometer in the visible range.

Figure 1. Raman spectrum of the end product of the pentathionate− chlorine dioxide reaction compared with spectrum of the sodium chlorate solution. Conditions are as follows: [S5O62−]0 = 6.0 mM and [ClO2]0 = 12.6 mM.

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RESULT Stoichiometry. A series of qualitative tests revealed that in excess chlorine dioxide the only sulfur-containing end product is sulfate. A significant amount of chlorine dioxide is reduced to chloride ion; therefore, the thermodynamically most favorable stoichiometry is

The appearance of characteristics peaks of chlorate at 947, 623, and 484 cm−1 clearly supports the fact that chlorate forms in a significant amount during the course of reaction. It also means that formally 6ClO2 + 3H 2O → 5ClO3− + Cl− + 6H+

(2)

also plays a significant role in determining the stoichiometry of the reaction. At any initial concentration ratio of the reactants an appropriate linear combination of eqs 1 and 2 properly describes the stoichiometry of the reaction. One may see that the highest SR ratio near 10 can easily be obtained by an algebraic sum of eqs 1 and 2.

S5O6 2 − + 4ClO2 + 6H 2O → 5SO4 2 − + 4Cl− + 12H+ (1)

Table 1 contains the stoichiometric ratio (SR) in excess of chlorine dioxide defined as SRm = ([ClO2]0 − [ClO2]∞)/ [S5O62−]0. As can be seen especially at higher chlorine dioxide 1294



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S5O6 2 − + 10ClO2 + 9H 2O → 5SO4 2 − + 5ClO3− + 5Cl− + 18H+

(3)

Initial Rate Studies. Figure 2 indicates the results of the initial rate studies at a constant initial pentathionate

Figure 4. Initial rate studies to determine the formal kinetic order of pentathionate ion. Conditions are as follows: [ClO2]0 ≈ 1.45 mM and pH = 5.45 (black); [ClO2]0 ≈ 1.45 mM and pH = 5.15 (blue); [ClO2]0 ≈ 1.41 mM and pH = 4.85 (green); [ClO2]0 ≈ 1.2 mM and pH = 4.55 (cyan); [ClO2]0 ≈ 1.41 mM and pH = 4.25 (red). Figure 2. Initial rate studies to determine the formal kinetic order of chlorine dioxide. Conditions are as follows: [S5O62−]0 = 0.36 mM, pH = 5.45 (black), 5.15 (blue), 4.85 (green), 4.55 (cyan), 4.25 (red).

concentration. As can be seen, independently of the pH, the formal kinetic order of chlorine dioxide is markedly higher than unity. Furthermore, Figure 3 inevitably shows that that of

Figure 5. Initial rate studies to determine the formal kinetic order of initially added chloride ion. In all these experiments [S5O62−]0 = 0.36 mM was kept constant. Conditions are as follows: [ClO2]0 ≈ 1.43 mM and pH = 5.45 (black); [ClO2]0 ≈ 1.41 mM and pH = 5.15 (blue); [ClO2]0 ≈ 1.44 mM and pH = 4.85 (green); [ClO2]0 ≈ 1.4 mM and pH = 4.55 (cyan); [ClO2]0 ≈ 1.42 mM and pH = 4.25 (red).

lower the formal kinetic order of the chloride ion is. Later we shall see that this important observation can also be explained by our proposed kinetic model. Proposed Kinetic Model. To setup the kinetic model, the following species should be taken into account according to our measurements: the reactants (pentathionate, chlorine dioxide), the products (sulfate, chlorate, chloride), and some intermediates like short-lived radicals (S5O6ClO22−, ClO, S5O6−) and nonradical species (S5O72−, Cl2O3, Cl2O2, S5O82−, S5O92−, S5O102−, and chlorite ion). The chlorine-containing species are well-accepted species from the oxidation chemistry of chlorine species. The sulfur-containing radicals are proposed on the basis of our previous studies of polythionate−chlorine dioxide reactions.20,21 The essence of the method with which we arrived at the best-fitted kinetic model has already been published elsewhere26 and applied successfully in several different cases. As a start, we should consider all the conceivable species to be possibly involved in the kinetic model. Then all the reactions between these species are initially added to the model including their H+- and Cl−-catalyzed pathways. Properly setting the initial values of the rate parameters the fitting

Figure 3. Initial rate studies to determine the formal kinetic order of hydrogen ion. Conditions are as follows: [S5O62−]0 = 1.08 mM and [ClO2]0 = 1.1 mM (black); [S5O62−]0 = 0.3 mM and [ClO2]0 = 1.86 mM (blue); [S5O62−]0 = 0.3 mM and [ClO2]0 = 3.23 mM (green); [S5O62−]0 = 0.3 mM and [ClO2]0 = 3.87 mM (cyan); [S5O62−]0 = 0.36 mM and [ClO2]0 = 1.42 mM (red).

hydrogen ion is around 0.5. Although the formal kinetic orders of both reactants seem to be constant within the concentration range studied, the numbers obtained clearly suggest an appearance of complex kinetics. On the basis of Figure 4 this fact can further be supported because the log−log plot of the initial rate−concentration diagram displays a nonlinear relationship, indicating a changing kinetic order of pentathionate. We emphasize that this behavior seems to be similar to what we found in the tetrathionate−chlorine dioxide reaction.20 Figure 5 also indicates that initially added chloride ion has a significant catalytic effect on the initial rate of the reaction. Moreover, as can be seen, the formal kinetic order of the chloride ion varies with respect to pH. The lower the pH is, the 1295



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procedure was started. The reactions considered to be unnecessary (vanishingly low rate parameters were obtained by the fitting procedure) have been removed stepwisely. After lengthy but straightforward elimination of these reactions, finally we arrived at the following kinetic model: S5O6 2 − + ClO2 ⇌ S5O6 ClO2 2 −

(R1)

S5O6 ClO2 2 − → S5O6− + ClO2−

(R2)

S5O6 ClO2 2 − → S5O7 2 − + ClO

(R3)

S5O6 ClO2 2 − + ClO2 → S5O7 2 − + Cl 2O3

(R4)

S5O7 2 − + Cl 2O3 → S5O82 − + Cl 2O2

(R5)

S5O6− + ClO2 + H 2O → S5O9 2 − + Cl− + 2H+

(R6)

S5O9 2 − + 2ClO2 → S5O10 2 − + 2ClO2−

(R7)

ClO2 + ClO → Cl 2O3

(R8)

Figure 6. Measured (filled circles) and calculated (solid lines) absorbance−time curves in the absence of initially added chloride ion at a constant pentathionate concentration and pH. Conditions are as follows: pH = 4.25, [S5O62−]0 = 0.3 mM, [ClO2]0/mM = 5.08 (black), 4.52 (blue), 3.95 (green), 3.03 (cyan), 2.28 (red), 1.29 (magenta), 0.46 (brown).

S5O82 − + 8ClO2 + 4H 2O → 5SO4 2 − + 4Cl 2O2 + 8H+ (R9)

S5O10 2 − + 3ClO2− + 4H 2O → 5SO4 2 − + 3Cl− + 8H+ (R10)

Cl 2O2 + H 2O →

ClO3−

−

+ Cl + 2H

+

(R11)

Rate coefficients determined by nonlinear simultaneous parameter estimation are indicated in Table 2. Table 2. Fitted and Fixed Rate Coefficients of the Proposed Kinetic Modela step

rate equation

parameter value

R1

k1[S5O62−][ClO2] k−1[S5O6ClO22−] k2[S5O6ClO22−][Cl−] k2′ [S5O6ClO22−][H+][Cl−] k″2 [S5O6ClO22−][H+][S5O62−] k3[S5O6ClO22−] k3′ [S5O6ClO22−][H+] k4[S5O6ClO22−][ClO2] k5[S5O72−][Cl2O3] k6[S5O6ClO2] k7[S5O92−][ClO2] k8[ClO2][ClO] k9[S5O82−][ClO2] k10[S5O102−][ClO2 k11[Cl2O2]

1000 M−1 s−1 104 s−1 389 ± 6 M−1 s−1 (4.53 ± 0.07) × 107 M−2 s−1 (1.29 ± 0.02) × 108 M−2 s−1 (2.23 ± 0.04) × 10−1 s−1 (3.35 ± 0.02) × 104 M−1 s−1 90.3 ± 1.4 M−1 s−1 ≥105 M−1 s−1 ≥103 M−1 s−1 ≥103 M−1 s−1 ≥106 M−1 s−1 ≥102 M−1 s−1 ≥102 M−1 s−1 ≥10 s−1

R2

R3 R4 R5 R6 R7 R8 R9 R10 R11

Figure 7. Measured (filled circles) and calculated (solid lines) absorbance−time curves in the absence of initially added chloride ion at a constant chlorine dioxide concentration and pH. Conditions are as follows: pH = 4.85, [ClO2]0 ≈ 1.42 mM, [S5O62−]0/mM = 1.08 (black), 0.84 (blue), 0.60 (green), 0.42 (cyan), 0.36 (red), 0.22 (magenta), 0.14 (brown), 0.105 (gray), 0.079 (yellow), 0.054 (purple).

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DISCUSSION Step R1 is the equilibrium formation of the adduct S5O6ClO22−. This process is a complete analogy of both the tetrathionate− chlorine dioxide20 and trithionate−chlorine dioxide21 reactions. As we shall see later, the equilibrium constant K1 = k1/k−1 cannot be determined from our experiments (see Formal Kinetics); therefore, an arbitrarily small value (K1 = 0.1 M−1) was chosen to keep the concentration of S5O6ClO22− low enough. In other words, it means that only the product of K1 with k2, k2′ , k2″, k3, and k3′ can be calculated from our experiments. This is also reflected in the overall rate equation derived (see later). Step R2 produces pentathionate radical and chlorite ion as a result of a formal electron transfer reaction between the reactants. As one can see, this process was found to be catalyzed by chloride ion, hydrogen ion, and the reactant pentathionate as well. We can provide indirect evidence to support that all these possibilities are necessary to describe our kinetic data simultaneously. Stepwise elimination of k2, k2′ , and k2″ leads to

a No error indicates that the given parameter is fixed during the calculation process.

The average deviation was found to be 0.0063 absorbance unit by an absolute fitting procedure. Altogether only six fitted parameters were used, and the rest of the parameters were either fixed or directly taken from previous reports to fit 6565 points of 132 absorbance−time curves. Figures 6−9 demonstrate the quality of the fit for representative examples and also support the fact that the proposed kinetic model is working properly under our experimental conditions. 1296



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of the reaction from eq 1 to eq 3. As can be seen, besides the normal first-order decomposition, this step is also catalyzed by hydrogen ion. We have also tried to eliminate k3 or k3′ from the proposed kinetic model with no success. These calculations have revealed that the average deviation increased to 0.0084 and 0.0208 absorbance unit in the case of elimination of k3 and k3′ , respectively. From this we again concluded that these parameters are also necessary to describe our kinetic data simultaneously. Step R4 is another rate determining step between S5O6ClO22− and chlorine dioxide. Similar reaction was also found to be necessary in the case of the trithionate−chlorine dioxide reaction.21 As we shall see later, this process is responsible for obtaining a higher than unity formal kinetic order with respect to chlorine dioxide. To further confirm the role of this step, we have also tried to eliminate it from the proposed model but a high increase in the average deviation was obtained (0.0082 absorbance unit). Rate coefficients of steps R5−R11 cannot be determined from our experiments; only their lower limits can be calculated. These lower limits are indicated in Table 2, but we should emphasize that any higher values of these parameters lead to the same final results. As an example, we may mention the rate coefficient of step R8. It is known that the rate coefficient of the reaction between ClO and ClO2− is very close to the diffusioncontrolled limit.28 To drive the stoichiometry of the reaction in the proper direction, we need to have step R8 so rapid that the reaction between ClO and ClO2− cannot be competitive. This criterion is fulfilled when k8 ≥ 106 M−1 s−1 stands, as indicated by our calculations; therefore, this value is given in Table 2. As a result, it means that steps R5−R11 are only necessary to complete the stoichiometry of the reaction. As can be seen, the sequence of steps R1, R2, R6, R7, and R10 leads to the stoichiometry represented by eq 1 whereas that of steps R1, R3, R4, R5, R8, R9, and R11 leads to the stoichiometry represented by eq 3. It is also interesting to compare the role of these pathways with the stoichiometric results indicated in Table 1. As can be seen, not only the increase of chlorine dioxide excess shifts the stoichiometry of the reaction toward eq 3 but also the decrease of pH does. This fact can be explained by the fine balance of steps R2, R3, and R4 at the given experimental condition. Furthermore, a crucial test about the comparison of calculated SR values from the proposed model with the measured ones has also been performed. Although the measured and calculated SR values slightly differ from each other, their trends with changing pH and chlorine dioxide excess perfectly agree. Thus we concluded that the efficiency of our proposed kinetic model was well-justified. Another important consequence of the short-lived intermediates and their fast reactions has to be emphasized. The reaction in the present case is driven by the short-lived intermediates indicated above. However, they are only feasible possibilities but not the only ones. Any other short-lived intermediates formed in the rate determining steps and their further reactions would lead to the same final result if they are driven so as to fulfill the necessary requirement of the changing stoichiometry mentioned above. Consequently, we only presented a reasonable but not the only kinetic model to explain our experimental data. Finally, it should be emphasized that hydrogen and chloride ions may both act as autocatalysts because they are products and they also accelerate the rate of reaction. Under our experimental condition, however, the characteristic S-shaped

Figure 8. Measured (filled circles) and calculated (solid lines) absorbance−time curves in the absence of initially added chloride ion at constant chlorine dioxide and pentathionate concentrations. Conditions are as follows: [S5O62−]0 = 0.30 mM, [ClO2]0 ≈ 3.23 mM, pH = 4.25 (black), 4.55 (blue), 4.85 (green), 5.15 (cyan), 5.45 (red).

Figure 9. Measured (filled circles) and calculated (solid lines) absorbance−time curves in the presence of initially added chloride ion at constant chlorine dioxide and pentathionate concentrations and pH. Conditions are as follows: [S5O62−]0 = 0.36 mM, [ClO2]0 ≈ 1.44 mM, pH = 4.85, [Cl0]/mM = 16.0 (black), 12.0 (blue), 8.0 (green), 5.0 (cyan), 2.5 (red), 0.0 (brown).

the average deviation of 0.0087, 0.0105, and 0.0123 absorbance unit, respectively, with the remaining five parameters. Evidently, in all cases the average deviation increased more than 30%, meaning that all these parameters are necessary to describe the kinetic data. Furthermore, the pentathionate-catalyzed decomposition of S5O6ClO22− can easily be explained by the following sequence of reactions: S5O6 2 − + S5O6 ClO2 2 − ⇌ (S5O6 )2 ClO2 4 −

(4)

(S5O6 )2 ClO2 4 − → S5O6 2 − + S5O6− + ClO2−

(5)

This kind of behavior seems to be also general because the same catalytic effect of polythionate was also observed in the case of the tetrathionate−chlorine dioxide reaction.20 Step R3 is an alternative route of decomposition of S5O6ClO22− leading to the formation of short-lived intermediates S5O72− and ClO radical. Eventually, combination of step R1 with step R3 means a formal oxygen transfer between the reactants. Role of steps R2 and R3 can easily be understood because they provide a possibility for shifting the stoichiometry 1297



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where K1 = k1/k−1. Equation 10 clearly shows that the equilibrium constant K1 cannot be determined from our measurements; only the products of K1 and the corresponding rate coefficient can be obtained. Moreover, the nonunity formal kinetic orders of the reactants as well as that of hydrogen and chloride ions can also be understood. Derivation of the formal rate equation has a series consequence; namely, even though the reaction is driven via short-lived intermediates like S5O72−, S5O82−, S5O92−, and S5O102−, this is not the only possibility. Any other sequences of reaction having the same rate determining step but containing other sets of conceivable intermediates that may lead to the same stoichiometries can equally well describe our data; therefore, the proposed kinetic model can only be treated as a reasonable feasibility.

type of kinetic curves was not observed. The autocatalytic feature of the hydrogen ion is completely suppressed by application of buffer; therefore, its appearance is not anticipated. However, the autocatalytic effect of chloride ion may be enlarged where the S-shaped curve appears, but so far all of our efforts have failed to find such conditions. The reason may be explained by the fact that the effect of chloride ion can only be anticipated at higher pHs, but at these conditions pentathionate is not stable anymore due to its well-known alkaline decomposition.19,29

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FORMAL KINETICS It has been shown that no long-lived intermediates formed in a detectable amount during the course of reaction. Therefore, a formal rate equation can be derived from the proposed mechanism. Applying steady-state approximation for species S5O6ClO22− leads to the following expression:

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CONCLUSION Our report may be treated as a first comprehensive effort to unravel the kinetics and mechanism of the pentathionate− chlorine dioxide reaction that shows several similarities as well as differences with the relevant trithionate−chlorine dioxide and tetrathionate−chlorine dioxide reactions. It was clearly demonstrated that two limiting stoichiometries exist and the initial conditions such as the concentration of the reactants, chloride ion, and pH shift the balance between them. In that sense, the polythionate−chlorine dioxide reactions do not differ from each other. However, we have noticed significant differences in the formal kinetic order of the reactants. In the previous reactions the formal kinetic order of at least one reactant is unity, but in the case of the pentathionate−chlorine dioxide reaction, neither the formal kinetic order of the reactants nor that of H+ was found to be an integer number. It clearly suggests a more complex kinetic behavior with increasing length of the sulfur chain. It is also interesting to note that the otherwise sluggish chloride ion was found to have an accelerating effect on the rate of all the polythionate− chlorine dioxide reactions indicating a general phenomenon. The most pronounced effect can, however, be measured in the case of the pentathionate−chlorine dioxide reaction due to the highest formal kinetic order of chloride ion found.

[S5O6 ClO2 2 −] = k1[S5O6 2 −][ClO2 ] k −1 + (k 2 + k 2′[H ])[Cl ] + k 2″[H+][S5O6 2 −] + k 3 + k 3′[H+] + k4[ClO2 ] +

−

(6)

According to the proposed model the consumption of chlorine dioxide can be expressed as −

d[ClO2 ] = k1[S5O6 2 −][ClO2 ] − k −1[S5O6 ClO2 2 −] dt + k4[S5O6 ClO2 2 −][ClO2 ] + k6[S5O6−][ClO2 ] + 2k 7[S5O29 −][ClO2 ] + k 8[ClO][ClO2 ] + 8k 9[S5O82 −][ClO2 ]

(7)

The steady-state concentrations of short-lived intermediates like S5O6−S5O92−, ClO, and S5O82− can also be obtained relatively easily. Substituting them into eq 7 followed by some straightforward algebraic manipulations finally leads to the following equation: −

d[ClO2 ] = k1[S5O6 2 −][ClO2 ] dt

■

− [S5O6ClO2 2 −](k −1 − 3((k 2 + k 2′[H+])[Cl−] + k 2[H+][S5O6 2 −]) − 9(k 3 + k 3′[H+]) − 9k4[ClO2 ])

(8)

*A. Horváth: e-mail, [email protected].

Substituting eq 6 into eq 8 followed by some simplifications, we arrive at the expression of

Notes

The authors declare no competing financial interest.

d[ClO2 ] − = k1[S5O6 2 −][ClO2 ]{4((k 2 + k 2′[H+])[Cl−] dt + k 2″[H+][S5O6 2 −]) + 10((k 3 + k 3′[H+]) + k4[ClO2 ])}

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ACKNOWLEDGMENTS The authors are grateful for the financial support of Chinese− Hungarian Cooperative Grant No. K-TÉT-CN-1-2012-0030 as well as that of the project SROP No. 4.2.2./A-11/1/KONV2012-0065.

÷ {k −1 + (k 2 + k 2′[H+])[Cl−] + k 2″[H+][S5O6 2 −] + (k 3 + k 3′[H+]) + k4[ClO2 ]} −1

(9)

■

−

Taking into account that the k ≫ (k2 + k′2[H ])[Cl ] + k″2 [H+][S5O62−] + k3 + k′3[H+] + k4[ClO2] inequality is fulfilled under our experimental conditions, we finally obtain a relatively simple rate equation: −

+

REFERENCES

(1) Orbán, M.; Kepper, P. D.; Epstein, I. R. An Iodine-Free ChloriteBased Oscillator. The Chlorite−Thiosulfate Reaction in a Continuous Flow Stirred Tank Reactor. J. Phys. Chem. 1982, 86, 431−433. (2) Rauscher, E.; Csekő , G.; Horváth, A. K. On the Complexity of Kinetics and the Mechanism of the Thiosulfate-Periodate Reaction. Inorg. Chem. 2011, 50, 5793−5802. (3) Wang, Z.; Gao, Q.; Pan, C.; Zhao, Y.; Horváth, A. K. BisulfiteDriven Autocatalysis in the Bromate-Thiosulfate Reaction in a Slightly Acidic Medium. Inorg. Chem. 2012, 51, 12062−12064.

d[ClO2 ] = K1((4(k 2[Cl−] + k 2′[H+][Cl−] dt + k 2″[H+][S5O6 2 −]) + 10(k 3 + k 3′[H+]))[S5O6 2 −] [ClO2 ] + 10k4[S5O6 2 −][ClO2 ]2 )

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Kinetics and Mechanism of the Oxidation of Pentathionate Ion by

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