Kinetics of the Two-Stage Oxidation of Sulfide by Chlorine Dioxide

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Kinetics of the Two-Stage Oxidation of Sulfide by Chlorine Dioxide György Csekö,†,‡ Changwei Pan,† Qingyu Gao,*,† and Attila K. Horváth*,‡ †

College of Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China Department of Inorganic Chemistry, Faculty of Sciences, University of Pécs, Ifjúság u. 6, Pécs H-7624, Hungary

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‡

ABSTRACT: The sulfide−chlorine dioxide reaction was found to have two distinct kinetic stages at alkaline conditions. The first stage proceeds so rapidly that it can only be measured by a stopped-flow technique at low temperature and leads to the parallel formation of polysulfide and sulfate as sulfur-containing products. At the same time, chlorite, chlorate, and chloride are produced from chlorine dioxide in detectable amounts, suggesting a complex stoichiometry. A nine-step kinetic model including short-lived intermediates like sulfide radical and •HSClO2− is proposed to describe the kinetic data in this rapid stage. In an excess of chlorine dioxide, the first stage is followed by a significantly slower one to be measured by conventional UV−vis spectroscopy at room temperature. Considering that tetrasulfide is formed during the first rapid course of the reaction, the subsequent slow kinetic stage can only be described by the direct oxidation of tetrasulfide by chlorine dioxide and, surprisingly, the tetrasulfide-catalyzed disproportionation of chlorine dioxide.

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INTRODUCTION The oxidation of sulfide has recently attracted extensive interest because of the fact that hydrogen sulfide plays a crucial role in physiological and pathological processes,1−3 in prokaryotes,4,5 and in nonlinear chemical dynamics.6−11 Various sulfur-containing intermediates produced during the oxidation of sulfide may easily react with the oxidants or other intermediates, making the reaction particularly complicated. The kinetics and mechanism of the oxidation of hydrogen sulfide are mainly studied by using different inorganic oxidants12−14 because the determination of hydrogen sulfide within living organisms is complicated when various biomolecules are used as oxidants.15−18 Furthermore, sulfide generated from wastewater systems may easily create extensive problems. Hydrogen sulfide gas present in the waste atmosphere can be adsorbed onto a series of chemical and biological reactions, resulting in corrosion and nuisance at wastewater treatment plants.19,20 The oxidation of sulfide by dioxygen in natural water is proposed to proceed via a chain mechanism, and formal kinetic orders of sulfide and oxygen were found to be 1.34 and 0.56, respectively.21 The oxidation of hydrogen sulfide by the neutrophil oxidant hypochlorous acid was shown to produce polysulfides by a second-order rate coefficient of 2 × 109 M−1 s−1 at pH = 7.4.22−24 Polysulfides were also found to be crucial intermediates during the course of oxidation of hydrogen sulfide by hydrogen peroxide in acidic solutions. The kinetics of this reaction may easily be described by a two-term rate law.25 A similar stoichiometry and mechanism was also established for the oxidation of sulfide by peroxymonosulfate but with 3−4 orders of magnitude faster rate compared to hydrogen peroxide.26 Sustained oscillations © XXXX American Chemical Society

in the pH and redox potential may as well be observed in the chlorite−sulfide reaction in a continuous-flow stirred tank reactor,8,27 and the oscillations can further be enhanced by catalytic amounts of copper(II).28 Chlorine dioxide is normally used in water treatment for removing hydrogen sulfide created from bacteria and with the advantages of avoiding the formation of colloidal sulfur. Interestingly, however, no detailed kinetic information is available on the kinetics of the sulfide−chlorine dioxide reaction because of the fact that around neutral and slightly alkaline conditions the reaction is too fast to follow conveniently even by a stopped-flow technique at room temperature. In this work, we report the most important results on the oxidation of sulfide by chlorine dioxide in an alkaline medium.

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EXPERIMENTAL SECTION

Materials. A chlorine dioxide stock solution was prepared by acidification of a sodium chlorite solution by 50% (v/v) sulfuric acid. To prepare an oxygen-free stock solution, the chlorine dioxide gas evolved was purged out from the solution by a pure nitrogen stream and redissolved in ice cold deoxygenated water. The stock solution was kept refrigerated and protected from light to prevent its photochemical decomposition.30 The purity of the chlorine dioxide solution was checked daily for chloride, chlorite, and chlorate impurities after purging out its •ClO2 content. None of these byproducts could be detected for up to 1 month. The concentrations of the stock chlorine dioxide solution and sodium chlorite were determined by a standard iodometric method and/or spectrophotoReceived: May 21, 2018

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DOI: 10.1021/acs.inorgchem.8b01386 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry metrically prior to each experiment. The accuracy of the concentration determination was found to always be better than 0.5%. In the case of chlorine dioxide, the titration process was performed with special care to avoid the loss of chlorine dioxide due to its well-known volatility. Commercially available sodium chlorite was purified as described previously.31 All of the other chemicals were of the highest purity commercially available (acetic acid, sodium acetate, sodium hydroxide, sodium sulfide, sodium sulfate, and sodium perchlorate) and were used without further purification. The purity of sodium sulfide was checked by the following method. A known amount of sodium sulfide was dissolved in oxygen-free distilled water, followed by the addition of a bromine solution in excess. The reaction mixture was left to stand for at least 5 min, which was proven to be long enough to oxidize sulfide into sulfate. Excess bromine was then removed by a nitrogen stream from the solution. H+ liberated completely by the oxidation process was determined by titrating the sample against a standard sodium hydroxide solution. All solutions were prepared by oxygen-free distilled water from a Milli-Q purification system. In the case of the equilibrium measurements, double-distilled and twice ion-exchanged water was used. The pH of sodium sulfide solutions was regulated between 12.6 and 13.5 by sodium hydroxide, and the ionic strength was adjusted to 1.0 M by the addition of the necessary amount of sodium sulfate. The ionic strength of the chlorine dioxide stock solution was also controlled at 1.0 M by sodium sulfate, but it did not contain any sodium hydroxide to avoid the well-known alkaline disproportionation of chlorine dioxide.32 When the effect of the chlorite ion was studied, the initial chlorine dioxide stock solution contained the necessary amount of sodium chlorite as well. During the equilibrium measurements, the pH of the chlorine dioxide stock solution was set to 5.55 by an acetic acid/acetate buffer, taking the pKa of acetic acid as 4.55.29 The acetate concentration was kept constant at 1.0 M. In agreement with previous studies, the acetate buffer was found to be innocent of reacting directly with chlorine dioxide.33−38 The pH of the sodium chlorite stock solution was set to 11.0 by sodium hydroxide, and the ionic strength was adjusted by sodium perchlorate to 1.0 M. All of the solutions were precooled in a refrigerator. Before each measurement, the initial solutions were left to stand more than 15 min at thermostated conditions to reach the temperature of 7.0 ± 0.5 °C. Altogether 94 kinetic runs (including the repeated ones as well) were performed in the following concentration ranges: [•ClO2]0 = 0.13− 0.96 mM, [HS−]0 = 0.05−0.4 mM, [ClO2−]0 = 0−0.2 M, and pH = 12.3−13.2. Methods and Instrumentation. The reaction was followed by an Applied Photophysics SX20 stopped-flow instrument attached to a single-wavelength spectrophotometer that provides monochromatic light. The kinetic curve was acquired at 360 nm, where the major absorbing species are chlorine dioxide and chlorite ion having molar absorbances of 1180 ± 23 and 1.60 ± 0.05 M−1 cm−1, respectively. These values were determined experimentally from the measured absorbance of the given reactant at 360 nm and its concentration obtained from iodometric titration. In exactly the same way, molar absorbances of chlorine dioxide and chlorite at 260 nm were also determined experimentally to be 51.9 ± 0.8 and 147 ± 3 M−1 cm−1, respectively. The optical path of the quartz cuvette was always 1 cm. A standard diode-array spectrophotometer (Zeiss S600) was used for equilibrium measurements and for determination of the initial concentration of the chlorine dioxide solution used for kinetic measurements. The sulfide and chlorine dioxide solutions were always mixed in a 1:1 ratio by the stopped-flow instrument. Because the reaction cannot be studied under pseudo-first-order conditions, an improved calibration of stopped-flow instrument is used. The filling time of the observation cell (3.0 ± 0.1 ms) and the hypothetical starting time of the reaction studied were determined as described previously.39 The equilibrium measurements were carried out in a tandem quartz cuvette equipped with a Teflon cap. Each subcell of the cuvette has an optical path of 4 mm, resulting in a 8 mm total optical path. The subcells were separated by a quartz wall having 2 mm width. The upper part of the quartz wall contained a hole that allowed

us to mix the separated solution by turning the cuvette upside down several times. The capillary electrophoresis (CE) experiments were performed as described by Lu et al.40 on a P/ACE MDQ Capillary Electrophoresis System (Beckman Coulter Inc., Fullerton, CA) equipped by a diodearray detector. The instrument was used in an indirect detection mode,41,42 and the running solutions were composed of 5 mM KH2PO4, 5 mM (NH4)2SO4, and 0.5 mM KNO3. The voltage applied was 30 kV, and the absorbance was detected at 214 nm. Data Treatment. Each original kinetic run initially contained 1000 absorbance−time data pairs. Therefore, it was necessary to reduce the number of time points (35−50) to avoid unnecessary time-consuming calculations. The data reduction was carried out in such a way that the arch length between two neighboring data had to be approximately equal along the whole kinetic curve.43 Altogether more than 3500 data pairs of 94 experiments were used for the simultaneous data evaluation by the program package Chemmech/ Zita.44

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RESULTS AND DISCUSSION Preliminary Studies. A thorough review of the literature revealed that no detailed investigation has yet been reported on the title system. Therefore, preliminary investigations were found to be necessary for unraveling the major characteristics of the reaction. Figure 1 displays the UV−vis spectra upon

Figure 1. UV−vis spectrum of the sulfide−chlorine dioxide reaction. Conditions are as follows: [S2−]0 = 0.333 mM, [•ClO2]0 = 1.6 mM, and pH = 11.75 adjusted by a buffer containing potassium phosphate (33.3 mM) and dipotassium−hydrogen phosphate (33.3 mM).

mixing of the sulfide solution [the predominant form of sulfur(II−) species is a hydrogen sulfide ion (HS−) under our experimental circumstances because the pK1 and pK2 values of hydrogen sulfide (H2S) are 6.9 and 17.1, respectively;33 thus, when the term “sulfide” is used below, it rather reflects its most dominant form the hydrogen sulfide ion (HS−) under the conditions studied] with chlorine dioxide in a closely sealed quartz cuvette. As is clearly seen, the reaction can be divided into two separate kinetic stages. The first stage is very fast and completed within mixing of the reactants, while the second one can conveniently be followed by conventional UV−vis spectroscopy. During the first stage, an extremely rapid rise of the absorbance is observed around 260 nm; meanwhile, a simultaneously very fast fall is clearly seen around 360 nm, where chlorine dioxide has an absorption maximum. In the second stage, however, around both 260 and 360 nm, a relatively slow decrease of the absorbance may be realized. Because alkaline decomposition of chlorine dioxide is wellB


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Inorganic Chemistry known from the literature,45,46 as a first step, one should check whether the decay of chlorine dioxide really belongs to the second stage of the reaction or it is simply due to the alkaline degradation of chlorine dioxide described by the following reaction: k1 2ClO2 + 2OH− → ClO2− + ClO3− + H 2O

sulfide. A typical UV−vis spectrum of the end product is illustrated in Figure 3. As is indicated, the characteristic

(1)

This equation explicitly shows that, during the course of alkaline decomposition, chlorite ion must form, which means that near 260 nm, where chlorite has a significant molar absorbance (εClO2− = 147 ± 3 M−1 cm−1, which agrees soundly with the one determined by Furman and Margerum47), the absorbance should have increased (chlorate does not have any significant absorption at this wavelength, and chlorine dioxide just slightly absorbs the light, having a molar absorptivity of ε·ClO2 = 51.9 ± 0.8 M−1 cm−1). Instead of that, we observed a slight decrease in the second slower stage of the reaction (as seen in Figure 1), which indirectly rules out the possibility that in this stage the undesired side reaction of • ClO 2 decomposition occurs alone. Furthermore, Figure 2 indicates

Figure 3. UV−vis spectrum of the end product of the sulfide− chlorine dioxide reaction. Conditions are as follows: [S2−]0 = 100 mM, [•ClO2]0 = 15 mM, and pH = 13.

absorption band of tetrasulfide appears at around a maximum of 370 nm, although the amount of tetrasulfide formed seems to be subtle compared to the amount of chlorine dioxide that disappeared from the solution. The data obtained suggested that approximately 0.3 mM tetrasulfide (εS42− = 1140 M−1 cm−1 7) formed when 15 mM •ClO2 was used to oxidize 0.1 M sulfide. Consequently, the major sulfur-containing species of the oxidation has to be sulfate because sulfite48,49 and thiosulfate43,50 are rapidly oxidized further by chlorine dioxide as well and polythionates are not stable species under these experimental circumstances. The appearance of the characteristic absorption band around 260 nm clearly suggests that chlorite ion certainly forms during the course of the first very rapid stage, although it may not be the only chlorinecontaining product. Therefore, CE studies were also performed to identify whether chlorate or chloride ions may as well be produced by the end of the reaction. Table 1 displays the results of quantitative analysis of chlorine-containing species. The amount of chlorite ion was first determined by UV−vis spectroscopy, and then 2.0 mL of sample was withdrawn from the cuvette and injected into CE for calculation of the amount of chlorate and chloride.

Figure 2. Comparison of the decay of chlorine dioxide during the second stage of the sulfide−chlorine dioxide reaction (blue curve) and in the case of its alkaline decomposition (black curve) using the same buffer, as indicated in the caption of Figure 1. The blue curve is the section of absorbance−time profiles at 360 nm (Figure 1), while in the case of the black curve, [•ClO2]0 = 0.488 mM was used.

a direct comparison of the absorbance−time profiles during the course of the second stage of the sulfide−chlorine dioxide reaction and in the alkaline decomposition of chlorine dioxide at the same pH. From this figure, it is evident that, although alkaline decomposition of chlorine dioxide cannot be avoided, the major process responsible for the decay of chlorine dioxide is the second stage of the title reaction. From the rate equation proposed by Bray45 (v1=k1[•ClO2]2[OH−]), our measurements provided k1 = 160 ± 20 M−2 s−1 taking into consideration that pKa3 of phosphoric acid is 11.75.29 At the same time, it means that the correct quantitative evaluation of the kinetic curves at the second stage of the sulfide−chlorine dioxide reaction requires consideration of this process as well (see later the quantitative description of the second stage of the reaction). The results presented above appear to suggest that, in the first stage of the reaction, a long-lived sulfurcontaining intermediate must form that can react further with the excess of chlorine dioxide in a significantly slower reaction. Therefore, UV−vis studies were also performed in an excess of

Table 1. Representative Examples Indicating the Measured Amount of Chlorine-Containing Species by the Sulfide− Chlorine Dioxide Reactiona [S2−]0/ mM

[•ClO2]0/ mM

[ClO2−]∞/ mM

[Cl−]∞/ mM

[ClO3−]∞/ mM

1.0 0.333 0.667 0.5 0.333 0.833 1.0 1.0 1.0 1.0

4.90 1.78 3.37 3.22 3.10 3.27 3.27 4.47 5.54 7.0

2.97 1.08 2.07 1.96 1.62 2.25 2.06 2.41 3.18 3.98

0.81 0.26 0.52 0.37 0.29 0.64 0.84 0.92 0.83 0.78

1.18 0.44 0.78 0.84 1.16 0.47 0.44 1.12 1.47 2.06

a

The pH was adjusted by a 1:1 phosphate/hydrogen phosphate buffer.

C


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Inorganic Chemistry

conditions. The absorbance−time curves obtained in this way, however, do not follow exponential decay, which means that a single-exponential individual fit, along with the conventional dead-time determination,52 is not suitable for the simultaneous evaluation of the kinetic curves. Therefore, a new, integrated approach, including the starting time of the reaction and filling time of the observation cell, has been chosen to evaluate the kinetic curves. Details of this concept can be found elsewhere.39 As a first step, evaluation of the individual kinetic curves was performed by using single stoichiometric equations (eqs 2−4) one by one, supposing that the formal kinetic orders of both reactants are 1. Not surprisingly, we found that neither of these equations alone is capable of even individual evaluation of the kinetic curves. The best result with an average deviation of 0.007 absorbance unit can be achieved by using eq 3, although evidently it does not work properly in a high excess of chlorine dioxide, where the consumed chlorine dioxide/sulfide ratio is significantly higher than 4. However, when we combined eqs 2 and 4, an acceptable fit is obtained in the case of the individual evaluation of the kinetic curves. k4 = 180000 ± 35000 M−1 s−1 and k2 = 88000 ± 8200 M−1 s−1 are calculated, and the measured data could be described by this simplified model by 0.005 au (note that the formal kinetic orders of both reactants in both reactions are supposed to be unity). This fitting appears to suggest that the proposed model describing all of the kinetic data simultaneously is more likely to proceed via a branching mechanism. This idea is also supported by the complex stoichiometry observed. A plausible possibility of the presence of a branching mechanism is that the reaction starts with parallel electron- and oxygen-atom-transfer processes as an analogy of sulfite and thiosulfate oxidation performed by chlorine dioxide.43,48−50 In these systems, it is shown that the reaction starts with electron transfer from the substrate to chlorine dioxide and with oxygen transfer from chlorine dioxide to the substrate, simultaneously. To check whether the initiation step

These data evidently clarify that indeed chlorate and chloride ions form in a significant amount during the course of the reaction. Stoichiometry. Qualitative and quantitative analyses of the products performed by CE and UV−vis spectroscopy support a complex stoichiometry that cannot be augmented with a single equation. The simultaneous formation of chlorite, chlorate, and chloride as well as sulfate and tetrasulfide suggests that the actual stoichiometry of the first stage of the reaction can be described by an appropriate linear combination of the following equations: k2 HS− + 8ClO2 + 9OH− → SO4 2 − + 8ClO2− + 5H 2O (2)

HS− + 4ClO2 + 5OH− → SO4 2 − + 2ClO3− + 2Cl− + 3H 2O k4 HS− + 2ClO2 + OH− → S + 2ClO2− + H 2O

(3) (4)

where S may represent any polysulfide species. According to Giggenbach’s study in an aqueous alkaline condition, the composition of Sx2− may vary from disulfide to pentasulfide depending on the experimental condition.51 Taking into consideration the formation constant of different polysulfide ions and the experimental circumstances applied here, approximately 80% of the total polysulfide species is calculated to be in the form of tetrasulfide. The rest has to be in the form of trisulfide. Therefore, S in eq 4 corresponds to the mixture of trisulfide and tetrasulfide. These stoichiometric equations are evidenced by the following facts: (1) the major sulfurcontaining species is sulfate; however, some polysulfides also form during the course of the reaction that may react further with the excess of chlorine dioxide in a significantly slower reaction; (2) chlorate and chloride ions also form in a detectable amount besides the chlorite ion. One should also note that if eqs 2−4 are responsible for establishing the stoichiometry, then the amount of chlorate and chloride should approximately be equal to each other. According to our measurements, this is certainly not the case. This deviance can be rationalized by the fact that disproportionation of chlorine dioxide evidently contributes to the product distribution (see the preliminary studies) accounting for generating more chlorate than chloride. In the opposite case, when more chloride ion formed compared to the amount of chlorate, a side reaction augmented by

HS− + •ClO2 F • HS + ClO2−

(6)

proceeds or not, we first investigated the effect of the chlorite ion on the measured kinetic curves. It is conceivably expected that the presence of a chlorite ion may inhibit the reaction, when the backward direction of the electron-transfer process plays a notable role. We therefore performed experiments in the presence of a huge excess of chlorite, and the result is presented in Figure 4. As is clearly seen, a positive absorption shift may be realized with increasing chlorite concentration, which may pose an immediate question. Gordon and Emmenegger suggested53 that a weak adduct complex forms upon the interaction of a huge excess of chlorite ion on chlorine dioxide. Later, Körtvélyesi and Gordon reported even the formation constant of this complex along with its visible spectrum.54 Because it is a key issue to correctly describe the measured absorbance−time series, we tried to reproduce their experiments to obtain the exact molar absorbance and formation constant of this complex under our experimental conditions. However, any attempt to reproduce their results has completely failed. Our typical result is illustrated in Figure 5. As is unambiguously indicated, the spectrum does not change at all when the same amounts of chlorite ion and chlorine dioxide are separated or mixed. Consequently, Gordon’s result cannot be confirmed, and it is more likely that an experimental artifact has led these authors to come up

5HS− + 8ClO2 + 13OH− → 5SO4 2 − + 8Cl− + 9H 2O (5)

might also have a contributory effect. Kinetics. Our preliminary study clearly showed that the reaction designed to be performed under pseudo-first-order condition and at 25 °C is still too fast to be measured by a stopped-flow technique because the time scale of the reaction is in the submillisecond range. Even though the pH was raised to around 13, the reaction was still completed within the dead time of the instrument. However, when the temperature was decreased to 7 °C and the initial reactant concentrations were chosen to be commensurable, the reaction time may be prolonged to the 20−100 ms time scale, which is thus suitable for stopped-flow measurements. Therefore, the first stage of the reaction was investigated under these experimental D


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Inorganic Chemistry

As Figure 6 suggests within the pH range studied, no kinetic effect of the hydroxide ion can be observed.

Figure 4. Measured and calculated kinetic curves at different initial chlorite concentrations. Conditions are as follows: [S2−]0 = 0.0526 mM, [•ClO2]0 = 0.35 mM, and pH = 13. [ClO2−]0/mM = 0.0 (black), 48.9 (blue), 122 (green), and 195 (cyan). In each case, filled and empty symbols correspond to a reproduction.

Figure 6. Measured (symbols) and calculated kinetic curves with respect to the different hydroxide ion concentrations using the kinetic model established in steps R1−R9. Conditions are as follows: (A) [HS−]0 = 0.053 mM; [ClO2]0 = 0.33 mM. (B) [HS−]0 = 0.53 mM; [•ClO2]0 = 0.81 mM. [OH−]/M = 0.156 (blue), 0.0975 (green), 0.0546 (cyan), 0.0312 (red), and 0.0195 (magenta) for both A and B.

Kinetic Model for the First Stage. On the basis of the experiments performed, the following kinetic model is finally proposed: HS− + •ClO2 F • HSClO2− Figure 5. Typical equilibrium measurement in a tandem quartz cuvette. Conditions are as follows: pH = 5.55; I = 1.0 M. In the case of the red curve, 0.50 M NaClO2 without using a buffer was introduced into one of the cells of the tandem cuvette, while the other cell contained an acetic acid/acetate buffer. The spectrum was recorded without mixing of the contents of the cells. In the case of the yellow curve, 0.50 M NaClO2 was introduced in one of the cells of the tandem cuvette, while the other one contained 0.95 mM •ClO2 in a buffer. The spectrum indicated by yellow was recorded without mixing of the components. The black curve indicates the spectrum of the mixed sample.

•

(R1)

HSClO2− + OH− → •S− + ClO2− + H 2O

• −

(R2)

S + •ClO2 → S + ClO2−

(R3)

•

HSClO2− → SO2 H− + •Cl

(R4)

•

Cl + •ClO2 + 2OH− → ClO3− + Cl− + H 2O

(R5)

SO2 H− + 2•ClO2 + 3OH− → SO4 2 − + ClO3− + Cl− + 2H 2O •

with this false conclusion. A further indirect confirmation of this result is that the shift of the kinetic curves observed in Figure 4 can conveniently be explained by the 1.6 M−1 cm−1 molar absorbance of chlorite at 360 nm. (Note that this value was also confirmed by independent measurements.) At the same time, the curvature of these kinetic runs remains unchanged (with an appropriate shift along the y axis resulting in a complete overlap of these curves), meaning explicitly the lack of a chlorite effect. As a result, our main conclusion is that the backward direction of eq 6 cannot compete effectively with other fast processes to observe any inhibitory effect of the chlorite ion and the application of the chlorite ion even in huge excess does not lead to the formation of a •Cl2O4− complex. Before a suitable model for simultaneously describing the measured absorbance−time series is proposed, it is also worthwhile to check the pH dependence of the kinetic curves.

HSClO2− + •ClO2 → HSClO2 + ClO2−

(R6) (R7)

HSClO2 + •ClO2 + OH− → •SClO2 + ClO2− + H 2O (R8) •

SClO2 + 3•ClO2 + 5OH− → SO2 H− + 3ClO2− + ClO3− + 2H 2O

(R9)

Step R1 is a rapidly established equilibrium formation of a weak adduct. The equilibrium constant of this process cannot be determined from our measurements. Therefore, we set KR1 as 0.1 M−1 to provide such a condition that the concentration of •HSClO2− remains at a low level (106 M−1 s−1 (3.42 ± 0.03) × 106 s−1 >106 M−1 s−1 >107 M−1 s−1 (1.04 ± 0.03) × 109 M−1 s−1 >3 × 106 M−1 s−1 >5 × 106 M−1 s−1 6

−1

2•ClO2 + 2OH− → ClO3− + ClO2− + H 2O

summarizes the rate coefficients fixed and fitted during the course of the evaluation procedure. The agreement between the measured and calculated data may be seen in Figures 4, 6 and 7. When no standard deviation is given, the corresponding rate coefficients were fixed during the evaluation procedure. To prove that all of the steps presented in the kinetic model are necessary, we have carried out additional fitting procedures to remove in a step-by-step fashion the rate-determining steps

(R10)

S4 2 − + 10•ClO2 + 16OH− → 4SO4 2 − + Cl products + 8H 2O 2•ClO2 → Cl products

(R11) (R12)

where step R12 was the tetrasulfide-catalyzed decomposition of chlorine dioxide. It should be noted that, in steps R11 and R12, the chlorine-containing products are not given; it consists of a mixture of chlorite, chlorate, and chloride to obey the electron conservation balance. Their exact composition can only be given if the concentration of these products is also followed simultaneously during the course of the reaction by high-performance liquid chromatography, CE, or another analytical method. At this time, we were unable to set a suitable condition to fulfill this criterion because the second stage of the reaction was still found to be too rapid to follow them conveniently by the chromatographic techniques mentioned above. Table 3 shows the rate equations used and the rate coefficients obtained from the simultaneous evaluation. Most surprisingly, our calculation showed that, under our experimental condition, although the direct tetrasulfide−chlorine dioxide reaction proceeds steadily, tetrasulfide can very efficiently catalyze the decomposition of chlorine dioxide. The catalytic effect of hypohalite ions on the decomposition of chlorine dioxide is well-known,32,59 but to our knowledge, this is the first time that sulfur species is reported to catalyze the disproportionation of •ClO2. Unfortunately, the preparation of a pure tetrasulfide solution is still not resolved completely, and it may also contain certain amounts of other polysulfides. Therefore, although a more thorough kinetic study is eagerly required to completely elucidate this effect, further progress on this issue is expected when a pure tetrasulfide solution can be prepared.

Figure 7. Measured (symbols) and calculated kinetic curves at different initial chlorine dioxide concentrations using the kinetic model established in steps R1−R9. Initial conditions are as follows: (A) [HS−]0 = 0.053 mM; [OH−]0 = 97.5 mM; [•ClO2]0/mM = 0.13 (blue), 0.285 (green), 0.375 (cyan), and 0.635 (red); (B) [HS−]0 = 0.15 mM; [OH−]0 = 97.5 mM; [•ClO2]0/mM = 0.146 (red), 0.285 (green), 0.61 (blue), and 0.93 (cyan). G


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Inorganic Chemistry

Figure 9. Measured (symbols) and calculated (solid lines) kinetic curves at the second stage of the sulfide−chlorine dioxide reaction at pH = 11.75 using the kinetic model established in steps R10−R12. The initial conditions are as follows: (black) [S2−]0 = 1.0 mM and [•ClO2]0 = 6.61 mM for the first stage; [S42−]0 = 0.0445 mM and [•ClO2]0 = 1.176 mM for the second stage; (blue) [S2−]0 = 1.0 mM and [•ClO2]0 = 5.70 mM for the first stage; [S42−]0 = 0.0543 mM and [•ClO2]0 = 0.605 mM for the second stage; (green) [S2−]0 = 1.4 mM and [•ClO2]0 = 9.3 mM for the first stage; [S42−]0 = 0.0567 mM and [•ClO2]0 = 1.29 mM for the second stage; (cyan) [S2−]0 = 0.75 mM, [•ClO2]0 = 3.69 mM for the first stage; [S42−]0 = 0.0457 mM and [•ClO2]0 = 0.17 mM for the second stage; (red) [S2−]0 = 1.3 mM and [•ClO2]0 = 8.3 mM for the first stage; [S42−]0 = 0.0586 mM and [•ClO2]0 = 1.034 mM for the second stage; (magenta) [S2−]0 = 2.0 mM and [•ClO2]0 = 15.2 mM for the first stage; [S42−]0 = 0.064 mM and [•ClO2]0 = 2.57 mM for the second stage.

Table 3. Rate Equations Used and Rate Coefficients Obtained from the Simultaneous Evaluation of the Kinetic Data of the Second Stage of the Sulfide−Chlorine Dioxide Reaction

Figure 8. Measured (symbols) and calculated kinetic curves at different initial sulfide concentrations using the kinetic model established in steps R1−R9. Conditions are as follows: (A) [•ClO2] ≈ 0 0.38 mM; [OH−] = 97.5 mM; [HS−]0/mM = 0.05 (blue), 0.1 (green), 0.15 (cyan), 0.25 (red), and 0.4 (magenta); (B) [•ClO2] ≈ 0 0.42 mM; [OH−] = 97.5 mM; [HS−]0/mM = 0.05 (magenta), 0.1 (red), 0.15 (cyan), 0.25 (blue), and 0.4 (green); (C) [•ClO2] ≈ 0 0.17 mM; [OH−] = 97.5 mM; [HS−]0/mM = 0.05 (blue), 0.1 (green), 0.15 (cyan), 0.25 (red), and 0.4 (magenta).

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step

rate equation

rate coefficient

R10 R11 R12

kR10[•ClO2]2[OH−] kR11[S42−][•ClO2] kR12[•ClO2][S42−]

160 ± 20 M−2 s−1 6.95 ± 0.06 M−1 s−1 107 ± 8 M−1 s−1

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CONCLUSION In this work, the kinetics and mechanism of sulfide oxidation by chlorine dioxide was studied in a strongly alkaline solution. The species distribution during the chlorine dioxide−sulfide reaction depends on the ratio and on the absolute concentration of the reactants (e.g., Figures 3 and 8) and on the pH as well. We proposed the reaction mechanism including subsequent electron- and oxygen-atom-transfer processes, which give the sulfur for Sx2− and for sulfate, respectively. This two-stage oxidation of sulfide by chlorine dioxide having two distinct time-scale processes may easily lead to nonlinear spatiotemporal dynamics such as oscillations and waves. Furthermore, this mechanism could be extended to other oxidants such as Ox (x = 2 and 3), H2O2, or other halogen compounds to be capable of parallel electron- and oxygen-atom-tranfer processes as well as for reaction control and environmental protection. Another important message of this work is that it is highly recommended to develop the new tracking tools for reactions with simultaneous multiple time scales involving many reactive species, in order to obtain an accurate and thorough mechanistic scheme.

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Qingyu Gao: 0000-0002-5520-0240 Attila K. Horváth: 0000-0002-1916-2451 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant 21773304), the Fundamental Research Funds for the Central Universities (Grant 2015XKZD09), and the Natural Science Foundation of Jiangsu Province (Grant BK20171186). A.K.H. is grateful for financial support of the Hungarian Research Fund NKFIH-OTKA (Grant K116591). This work was also supported by Grant GINOP-2.3.2-15-2016-00049. The study was also financed by the Higher Education Institutional Excellence Programme of the Ministry of Human Capacities in Hungary, within the framework of the 20765-3/2018/FEKUTSTRAT Innovation H


Article

Inorganic Chemistry

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for Sustainable and Healthy Living and Environment Thematic Programme of the University of Pécs. The project was also supported by the European Union, cofinanced by the European Social Fund (Grant EFOP-3.6.1.-16-2016-00004), entitled by Comprehensive Development for Implementing Smart Specialization Strategies at the University of Pécs.

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Kinetics of the Two-Stage Oxidation of Sulfide by Chlorine Dioxide

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