On the Kinetics and Mechanism of the Thiourea Dioxide-Periodate

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A: Kinetics, Dynamics, Photochemistry, and Excited States

On the Kinetics and Mechanism of the Thiourea DioxidePeriodate Autocatalysis-Driven Iodine-Clock Reaction György Csek#, Qingyu Gao, Changwei Pan, Li Xu, and Attila K. Horváth J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b06207 • Publication Date (Web): 13 Aug 2019 Downloaded from pubs.acs.org on August 14, 2019

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The Journal of Physical Chemistry

On the Kinetics and Mechanism of the Thiourea Dioxide–Periodate Autocatalysis-Driven Iodine-Clock Reaction György Csek˝o,†,‡ Qingyu Gao,∗,† Changwei Pan,† Li Xu,¶ 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, Ifj´ uság u. 6, Pécs, Hungary, H-7624 ¶Department of Chemical Engineering and Technology, School of Chemistry, Biology and Material of Science, East China University of Technology, Nanchang 330013, Jiangxi Province, People’s Republic of China E-mail: [email protected]; [email protected]

Abstract The thiourea dioxide–periodate reaction has been investigated at acidic conditions using phosphate buffer within the pH range of 1.1–2.0 at 1.0 M ionic strength adjusted by sodium perchlorate. Absorbance–time series are monitored as a function of time at 468 nm, the isosbestic point of I2 –I3 – system. The profile of these kinetic runs follows either sigmoidal-shaped or rise-and-fall traces depending on the initial concentration ratio of the reactants. The clock species iodine appears after a well-defined but reproducible time lag even in substrate excess meaning that the system may be classified as

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an autocatalysis-driven clock reaction. It is also demonstrated that the age of thiourea dioxide solution markedly shortens the Landolt time suggesting that original form of thiourea dioxide (TDO) rearranges into a more reactive form and reacts faster than the original one. The behavior found is consistent with that of recently observed in other oxidation reactions of TDO. To characterize the system quantitatively a 22-step kinetic model is constructed from adapting the kinetic model of the TDO–iodate reaction published recently by supplementing it with six different reactions of periodate. By the help of seven fitted rate coefficients a sound agreement between the measured and calculated absorbance–time traces is obtained.

Introduction Despite the widespread practical application in paper and textile industry the redox transformation of thiourea dioxide (TDO) in aqueous solution is still not fully understood due to its unusual structure and its complex decomposition or rearrangement reactions. 1,2 TDO is fairly stable under acidic conditions, however it decomposes relatively rapidly into sulfoxylate ion and urea via a carbon–sulfur bond cleavage depending on the pH at basic conditions. 3,4 Xu et al. has recently demonstrated 5 that TDO slowly rearranges into a more reactive form, whose reactions may be considerably faster with the corresponding oxidizing agent than with the original form of TDO. Although it is still in dispute whether this rearrangement belongs to tautomerism 6,7 or an oligomer–monomer-, 8 or even an aminoimino–carbenoid slow transformation, 9 it is quite clear that this phenomenon has to be taken into consideration when studying the redox reactions of TDO. Very recently, Shao et al. has arrived at a conclusion supported by TOF-MS spectroscopy and quantum chemical calculations that in aqueous solution TDO exists in cyclic clusters containing various number of molecules of TDO and in form of aminoiminomethanesulfinic acid (NH2 NHCSO2 H). 10 We have previously illustrated in case of the TDO–chlorine dioxide reaction 6 that aging of TDO stock solution may drastically change the shape of the kinetic curves even when no notable decomposition of TDO is 2


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observed. The alteration may as well be so pronounced that the original sigmoidal characteristic is completely lost when a 2-hour-old TDO is used instead of a fresh one. The apparent irreproducibility of the kinetic curves is also highlighted in the TDO–iodine reaction when a fresh or an aged TDO solution is used to perform the experiments. 5 The TDO–iodate system was shown to display a clock feature first by Mambo and Simoyi, 11 though the authors failed to report that the age of stock TDO solution significantly affects the Landolt time. 12 In contrast to this in case of the TDO–bromate reaction no aging effect was observed as reported by Csek˝o et al. 13 The lack of aging effect was explained by the fact that the key TDO–bromine reaction is so rapid in presence of fresh TDO that it hits almost the diffusion control limit, thus leaving no further place for additional increase in the reaction rate. Periodate is a strong oxidizing agent, and its speciation in aqueous solution has recently been clarified. 14 It is shown that periodate ion exists overwhelmingly in its octahedral form in presence of water thus former studies on the redox reactions of periodate ion may require reinvestigation or reevaluation. Thorough review of the literature has revealed that no systematic kinetic study on the TDO–periodate reaction has yet been reported, thus it seems to be a perfect candidate to construct its kinetic model by extension from the recently proposed kinetic model of the TDO–iodate reaction. This extension would require feasible reactions of periodate ion. As it was shown previously the TDO–iodate system was classified to be an autocatalysis-driven clock reaction 12 thus by analogy of the pentathionate–iodate 15 and pentathionate–periodate 16 systems it is expected that the title reaction may also belong to this subclass. Our aim here is to present the detailed kinetic model of the TDO–periodate system for the first time and to demonstrate how important it is to develop a feasible kinetic model of a subsystem providing a solid basis to extend it further for adequate description of its parent system.

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Experimental Section Materials. All the chemicals including sodium periodate (Sinopharm Chemical Reagent Co. Ltd. and Reanal), sodium iodide (VWR International and Aladdin Industrial Corporation), phosphoric acid (Xilong Scientic and Sigma-Aldrich), sodium dihydrogen phosphate (Sinopharm Chemical Reagent Co. Ltd. and Sigma-Aldrich), thiourea dioxide (Merck and SigmaAldrich), and sodium perchlorate (Merck) were of the highest purity commercially available and were used without further purification. All solutions were prepared by oxygen-free (argon gas was bubbled through for at least 15 min.) deionized water from a Milli-Q water purification system (having a resistivity of 18.2 MΩcm). The TDO stock solutions were freshly prepared before each kinetic experiment expect when the aging effect of TDO was investigated. Majority of the kinetic runs was performed with an age of the TDO stock solution being 300±1 s. The ionic strength in all the samples were set to 1.0 M adjusted by the necessary amount of sodium perchlorate solution. The pH of the reacting solutions was regulated between 1.1 and 2.0 by phosphoric acid/dihydrogen phosphate buffer taking the pK a1 of phosphoric acid as 1.8. 17 This value worked consistently well in a number of previous studies. 12,13,15,16 The dihydrogen phosphate concentration was kept constant at 0.25 M. The temperature of the reaction vessel was maintained at 25.0±0.1o C.

Methods and Instrumentation The reaction was followed by an Analytik Jena Specord S600 diode array spectrophotometer. Majority of the kinetic runs was performed without using the deuterium lamp of the photometer to minimize the photochemical decomposition of the light sensitive material, periodate. 14,18–22 The reaction was carried out in a standard quartz cuvette equipped with magnetic stirrer and a Teflon cap having a 10.00 mm optical path. Solutions containing the buffer components and the reagent periodate were delivered first from a pipet into the 4


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cuvette. The reaction was started with addition of the necessary amount of TDO solution from a fast delivery pipet that also contained iodide (if necessary). In a couple of samples the UV region was also used to monitor the reaction to gain additional qualitative information about the Landolt period. 13

C NMR spectra were recorded by using a Bruker Avance III 500 spectrometer (at 125.7

MHz). The chemical shifts are referenced to tetramethylsilane.

Data Treatment Evaluation of the kinetic curves was performed at the isosbestic point of I2 –I3 – system at 468 nm by the program package ZiTa/Chemmech. 23 The molar absorbance of both species was found to be 750 M−1 ·cm−1 at this wavelength. Originally each kinetic run contained more than 1000 absorbance–time data pairs, therefore it was necessary to reduce the number of time points (60–70) to avoid unnecessary time-consuming calculations. Altogether almost 5000 experimental points of 74 kinetic curves were used simultaneously for data evaluation to obtain the kinetic model and the corresponding rate coefficients.

Results Our preliminary experimental results have clearly demonstrated that the TDO–periodate reaction, not unexpectedly, features clock behavior. Figure 1 illustrates typical absorbance– time profiles under the conditions applied. These runs indicate remarkable resemblance on the kinetic curves measured in case of the TDO–iodate reaction. 11,12 Because periodate is a strong oxidizing agent one may easily expect that periodate might rapidly oxidize TDO to leave iodate behind as a reduced iodine-containing product and therefore at suitable initial conditions the present system is directly transformed into the TDO–iodate reaction. Fig. 1A, however, clearly shows that upon mixing the reactants no rapid absorbance decrease may be observed (both species absorbs the UV-light significantly at 269 nm, εTDO = 489 M−1 cm−1

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εIO4− = 497 M−1 cm−1 , determined in this work from separate measurements) thus suggesting the absence of rapid TDO–periodate reaction. Second, it is known from previous studies that periodate solution is subject to decompose by UV-light irradiation 14,18–22 thus intensity of the analyzing light of our diode-array spectrophotometer may have a substantial effect on the measured curve via opening a photocatalyzed route. Indeed, we found that applying more intense analyzing light the reaction is markedly accelerated as shown in Fig. 1B. It provides a solid support for our experimental setup to monitor the reaction only at visible spectral range to exclude the photocatalytic decomposition of periodate. Quite recently, in a number of subsequent papers, it has also been demonstrated experimentally that TDO, even in acidic aqueous conditions, ages 5 and several times the aged form of TDO is more reactive toward the corresponding oxidizing agents 6,7,12 than its original form. The only exception was found to be the TDO–bromate reaction 13 where no effect of aging was found when the TDO solution was not older than a day. The lack of aging effect is explained by the rapidness of dominant TDO–bromine reaction with either the fresh or the aged TDO. To elucidate whether the effect of aging may be pronounced or not in case of the title reaction we have performed two series of kinetic runs in excess of both reactants. The results are illustrated in Fig. 2. As it is seen in both cases the time necessary for the appearance of iodine is shortened approximately 15 %. This suggests that the aged form of TDO again is slightly more reactive toward periodate than its original form. Fig. 2 also clarifies that the title system may be classified as an autocatalysis-driven clock reaction because the clock species iodine appears transiently in substrate excess after a well-defined time lag. 24 All these experiments indicated that the TDO–periodate system may be quite sensitive to experimental errors (such as impurities, etc.) therefore it looks to be also important to highlight the reproducibility of the kinetic curves prior to elucidate the kinetics and mechanism by nonlinear parameter estimation. The random ’noises’ may easily be enlarged by the highly nonlinear nature of the system and it may thus result in a false kinetic model.

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Figure 1: (A): Absorbance–time series measured at different wavelengths in the TDO– periodate reaction in absence of initially added iodide ion. Initial conditions are as follows: [TDO]0 = 1.2 mM, [IO4 – ]0 = 0.86 mM, pH = 2.0. Selected wavelengths (nm) are 269 (black), 350 (blue) and 468 (green). Red dot corresponds to the calculated initial absorbance of solution without any reaction to occur. (B) Effect of light illumination on the TDO–periodate reaction. Initial concentrations are as follows: [TDO]0 = 0.855 mM, [IO4 – ]0 = 0.57 mM, and pH = 2.0. The following illumination protocol has been used: at constant integration time (86 ms), data accumulation was 5 and data were measured at every 35 seconds (red curve), while data accumulation was 10 and data were measured at every 22 seconds (purple curve).

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Figure 2: (A): Measured (symbols) and calculated (solid lines) absorbance–time series measured in stoichiometric excess of TDO when TDO solution ages. Initial conditions are as follows: [TDO]0 = 2.25 mM, [IO4 – ]0 = 1.0 mM, pH = 1.75. Age of the stock TDO solution (s): 290 (black), 11298 (blue), 21866 (green), 38840 (cyan), 80595 (red). (B) Measured (symbols) and calculated (solid lines) absorbance–time series measured in stoichiometric excess of periodate when TDO solution ages. Initial conditions are as follows: [TDO]0 = 1.4 mM, [IO4 – ]0 = 1.0 mM, pH = 1.75. Age of the stock TDO solution (s): 390 (black), 11381 (blue), 21958 (green), 38929 (cyan), 80691 (red).

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Fig. 3 demonstrates the reproducibility of experimental curves in both excesses. In all cases the stock solutions were prepared freshly prior to each experiment from solid reagent obtained by different manufacturers. 0.25


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Figure 3: Reproducibility of the measured kinetic curves in excesses of both reactants. Age of the TDO solution was set to 300 s in all kinetic runs presented here. Initial conditions for the black and green curves are [TDO]0 = 2.26 mM, [IO4 – ]0 = 0.779 mM and pH = 1.8, while in the case of blue and red curves [TDO]0 = 1.05 mM, [IO4 – ]0 = 1.02 mM and pH = 1.25. In the case of the black and blue curves TDO and periodate stock solutions were prepared from solid reagents obtained from Merck and Sinopharm manufacturers, repectively, while in those of green and red curves TDO and periodate stock solutions were prepared from Sigma-Aldrich and Reanal. As it is seen in both cases almost perfect reproduction may be obtained, since less than 1% difference can be detected between the measured Landolt times and even in the maximum of absorbance. From this we concluded that the aging effect is a real phenomenon and the proposed kinetic model must reflect to this observation.

Proposed Kinetic Model for Simultaneous Evaluation of Kinetic Curves As it was mentioned previously in case of the TDO–iodate system the reaction starts with subsequent formal oxygen transfer processes eventually leading to the formation of iodide ion. 12 Thus it seems to be straightforward that the initiation of title reaction has to start 9




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Figure 4: Measured (dots) and calculated (solid lines) absorbance–time series profiles with varying the initial concentration of periodate at pH = 1.25 and [TDO]0 = 1.0 mM. Age of TDO stock solutions was 300 s. [IO4 – ]0 /mM = 0.43 (black), 0.52 (blue), 0.84 (green), 1.0 (cyan), 1.17 (magenta), 1.43 (red), 1.69 (brown), 1.96 (yellow), 2.08 (purple).

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Figure 5: Measured (dots) and calculated (solid lines) absorbance–time series profiles with varying the initial concentration of TDO at pH = 1.6 and [IO4 – ]0 = 0.78 mM. Age of TDO stock solutions was 300 s. [TDO]0 /mM = 0.64 (black), 0.69 (blue), 0.87 (green), 1.04 (cyan), 1.45 (red), 1.55 (magenta), 1.61 (brown), 1.69 (yellow).

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Figure 6: Measured (dots) and calculated (solid lines) absorbance–time series profiles with varying the pH at [TDO]0 = 2.25 mM and [IO4 – ]0 = 1.17 mM. Age of TDO stock solutions was 300 s. pH = 1.1 (black), 1.25 (blue), 1.4 (green), 1.6 (cyan), 1.8 (red).

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Figure 7: Measured (dots) and calculated (solid lines) absorbance–time series profiles with varying the initial concentration of iodide ion at pH = 1.8, [IO4 – ]0 = 1.0 mM and [TDO]0 = 1.0 mM. Age of TDO stock solutions was 300 s. [I – ]0 /µM = 0.0 (black), 0.38 (blue), 5.0 (green), 8.0 (cyan), 10.7 (red), 14.3 (magenta), 17.8 (brown), 26.7 (yellow).

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with a relatively slow—possibly oxygen transfer—process to yield iodate. This assumption is indirectly supported by Fig. 1 indicating that the TDO–periodate reaction cannot be considered as a rapid process due to the absence of fast drop of absorbance right after mixing the reactants. It also looks to be evident from Fig. 2 that the aged form of TDO reacts more rapidly with periodate than the original form. Thus Steps R5 and R10 have to be included in the final model. The carbon- and nitrogen containing products of the initial step are found to be the mixture ammonium ion, cyanamide and urea as indicated in Fig. 8 below (at strongly acidic conditions escape of CO2 may easily hinder its detection). The exact concentration ratios of these products are not determined from our work simply because this part of TDO does not participate in the redox process. Thus the equations involving C,Ncontaining products are not completely balanced there might be missing water molecules or H+ in either side of the reaction depending on the exact amount of ammonia, cyanamide and urea formed.

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Figure 8: 13 C-NMR spectra measured in excess of both reactants. Initial conditions are as follows: (black curve) [TDO]0 = 0.17 M; [IO4 – ]0 = 0.05 M and pH = 1.3; (red curve) [TDO]0 = 0.07 M; [IO4 – ]0 = 0.08 M and pH = 1.3. The peaks at 177.5 ppm, 162.5 ppm and 118.1 ppm belong to TDO, urea and cyanamide, respectively.

These two reactions were supplemented with the kinetic model of the TDO–iodate reaction with fixed rate coefficients determined previously 12 and the rate constants of Steps R5 and R10 were fitted. The average deviation in this case was found to be 8.7 % meaning that 12


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other reactions of periodate must also be considered. Therefore we included the reactions of periodate with all the species involved like bisulfite, iodide ion, hypoiodous acid, iodous acid and the short-lived I2 O2 species. Then we considered that the rate of these reactions is proportional to H+ , [H+ ]2 beside pH-independent pathways. The nonlinear parameter estimation was started by including all these steps followed by stepwise elimination of the unnecessary rate terms. Systematic model reduction finally led to the minimal kinetic model found to be adequate for describing simultaneously our experimental data.

+ − H3 PO4 − )− −* − H + H2 PO4

(E1)

− −− I− + I2 ) −* − I3

(R1)

+ − HIO3 − )− −* − H + IO3

(R2)

− + I2 + H2 O − )− −* − HOI + I + H

(R3)

TDO −→ TDOaged

(R4)

TDO + H4 IO6− −→ C, N−containing products + IO3− + HSO3−

(R5)

HSO3− + H4 IO6− −→ SO42− + IO3− + 2H2 O + H+

(R6)

2I− + H4 IO6− + 2H+ −→ IO3− + I2 + 3H2 O

(R7)

H4 IO6− + I2 O2 −→ IO3− + 2HIO2 + H2 O

(R8)

HIO2 + H4 IO6− −→ 2IO3− + H+ + 2H2 O

(R9)

TDOaged + H4 IO6− −→ C, N−containing products + IO3− + HSO3−

(R10)

TDO + IO3− −→ C, N−containing products + HSO3− + HIO2

(R11)

TDO + HIO2 −→ C, N−containing products + HSO3− + HOI

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TDO + HOI −→ C, N−containing products + HSO3− + I−

(R13)

− + −− TDO + I2 ) −* − TDOI + I + H

(R14)

TDOI −→ C, N−containing products + HSO3− + I−

(R15)

HSO3− + I2 + H2 O −→ SO42− + 2I− + 3H+

(R16)

−− H+ + I− + HIO3 ) −* − I2 O2 + H2 O

(R17)

I− + H+ + I2 O2 −→ I2 + HIO2

(R18)

I− + H+ + HIO2 −→ 2HOI

(R19)

TDOaged + IO3− −→ C, N−containing products + HSO3− + HIO2

(R20)

TDOaged + I2 −→ TDO2+ + 2I−

(R21)

TDO2+ + TDO −→ C, N−containing products + SO42− + S

(R22)

Rate coefficients calculated from simultaneous evaluation of all the kinetic runs are indicated in Table 1. The average deviation in terms of relative fitting procedure was found to be 1.8 % which is close to the experimentally achievable error limit of absorbance measurements providing a sound agreement between the measured and calculated data. Figs. 2, 4–7 clearly indicate that the proposed kinetic model is working adequately. It should also be noted that the kinetic model may be used to evaluate the kinetic data when the age of the stock TDO solution is not longer than a day. If follows from the fact that the degradation process of TDO at a longer timescale was found to be more complex shown by Xu et al. 5 Therefore when the age of TDO stock solution is older then the kinetic model presented here must certainly be extended, though the extension must first await for clear understanding of the degradation process.

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Table 1: Rate equations used and rate coefficients obtained from evaluating simultaneously the kinetic data of the TDO–periodate reaction. Those rate coefficients where no standard deviation is given are fixed during the whole calculateion process. No. (E1) (−E1) (R1) (−R1) (R2) (-R2)

Rate equation kE1 [H3 PO4 ] k−E1 [H+ ][H2 PO4 – ] kR1 [I2 ][I – ] k−R1 [I3 – ] kR2 [HIO3 ] k−R2 [H+ ][IO3 – ] kR3 [I2 ] (R3) 0 kR3 [I2 ]/[H+ ] k−R3 [H+ ][I – ][HOI] (−R3) 0 k−R3 [I – ][HOI] (R4) kR4 [TDO] kR5 [TDO][H4 IO6 – ] (R5) 0 kR5 [TDO][H4 IO6 – ][H+ ] (R6) kR6 [HSO3 – ][H4 IO6 – ] kR7 [I – ][H4 IO6 – ] (R7) 0 kR7 [I – ][H4 IO6 – ][H+ ] (R8) kR8 [I2 O2 ][H4 IO6 – ][H+ ]2 (R9) kR9 [HIO2 ][H4 IO6 – ] (R10) kR10 [TDOaged ][H4 IO6 – ] (R11) kR11 [TDO][IO3 – ][H+ ]2 (R12) kR12 [TDO][HIO2 ] (R13) kR13 [TDO][HOI] (R14) kR14 [TDO][I2 ] (−R14) k−R14 [H+ ][[I – ]][TDOI] kR15 [TDOI] (R15) 0 kR15 [TDOI]/[H+ ] (R16) kR16 [HSO3 – ][I2 ] (R17) kR17 [H+ ][I – ][HIO3 ] (−R17) k−R17 [I2 O2 ] kR18 [I2 O2 ][I – ] (R18) 0 kR18 [I2 O2 ][I – ][H+ ] (R19) kR19 [I – ][HIO2 ][H+ ] (R20) kR20 [TDOaged ][I2 ] (R21) kR21 [TDO2+ ][TDO]

Rate coefficient 1.585×105 s−1 107 M−1 s−1 5.7×109 M−1 s−1 8.5×106 s−1 108 s−1 3.125×108 M−1 s−1 5.52×10−2 s−1 1.98×10−3 M s−1 1.023×1011 M−2 s−1 3.67×109 M−1 s−1 (1.87±0.09)×10−6 s−1 0.088±0.005 M−1 s−1 3.33±0.009 M−2 s−1 104 M−1 s−1 11 M−1 s−1 4882±98 M−2 s−1 (1.01±0.04)×1010 M−3 s−1 (2.97±0.05)×106 M−1 s−1 1.38±0.07 M−1 s−1 29.7 M−3 s−1 106 M−1 s−1 106 M−1 s−1 104 M−1 s−1 1010 M−2 s−1 200 s−1 2.22 M s−1 3.1×109 M−1 s−1 107 M−2 s−1 108 s−1 4.67×108 M−1 s−1 6.29×1010 M−2 s−1 1011 M−2 s−1 104 M−1 s−1 105 M−1 s−1

Discussion Step E1 is only an auxiliary reaction that takes into consideration the slight pH change during the whole calculation process. Because this equilibrium is established very rapidly 15 ACS Paragon Plus Environment


the rate coefficients of both the forward and the reverse reactions are set to relatively large values, kE1 = 1.585×105 s−1 and k−E1 = 107 M−1 s−1 , respectively. The ratio of these rate coefficients provides the pKa1 of phosphoric acid to be 1.8. 17 This value worked consistently well in a number of previous systems investigated. 12,13,15,16 Step R1 is the well-known rapidly established equilibrium between iodine and triiodide ion studied by independent research groups. 25,26 The individual rate coefficients of the forward and backward processes were set to be kR1 = 5.7×109 M−1 s−1 and k−R1 = 8.5×106 s−1 , respectively to provide logβI3− = 2.83, where βI3− is the formation constant of triiodide ion. Step R2 is the acid dissociation process of iodic acid. Ka = 0.156±0.002 M was established independently by Ramette and Palmer, 27 as well as by Strong and Pethybridge 28 at zero ionic strength. Considering that the ionic strength is set to 1.0 M in our experiments Ka = 0.32 M is used throughout the whole calculation process. The rate coefficient of the forward and reverse processes is fixed such a way to provide a rapidly established equilibrium and at the same time their ratio should give Ka mentioned above. Step R3 is the long-established hydrolytic equilibrium of iodine. The rate coefficients of the forward and backward processes including the H+ -inhibited pathway were determined previously 29–31 and these rate coefficients were adopted directly. As it is well-known this equilibrium is established relatively rapidly under our experimental circumstances that enables us to eliminate H2 OI+ species from the model. Consequently, the rate coefficient of k−R3 has to be recalculated from the values reported by Lengyel et al. 31 The fixed rate coefficients used throughout the whole calculation process are indicated in Table 1. Step R4 is responsible for the aging effect of TDO in aqueous acidic solution as already shown in our previous work. 12 The rate coefficient of this reaction was calculated to be (1.95±0.05)×10−6 s−1 from independent measurements 5 and thus it was used as a fixed value during majority of the evaluation procedure. When the final kinetic model was carried out, this rate coefficient was also allowed to be fitted and this calculation resulted in kR4 = (1.87±0.09)×10−6 s−1 indicating a sound consistency with our previously published

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results. Step R5 is one of the initiation of the title reaction leading eventually to the breakage of C– S bond and the formation of bisulfite and iodate. Our calculation revealed that the rate law of this process has to contain two different terms. The first term is independent of pH and the other one is proportional to H+ . This complex rate law suggests that both orthoperiodate ion (H4 IO6 – ) and orthoperiodic acid (H5 IO6 ) are reactive species. Because pK1 of orthoperiodic acid is 0.98±0.18 14 it means that under our experimental conditions, especially at lower pHs, significant amount of periodate may be found in completely protonated form. The rate coefficients optimized were found to be 0.088±0.005 M−1 s−1 and 3.33±0.01 M−2 s−1 . To prove that both terms are necessary for adequate description of the kinetic curves simultaneously, additional calculation processes have been performed by setting first kR5 = 0 M−1 s−1 and 0

then kR5 = 0 M−2 s−1 meanwhile rest of the rate coefficients is allowed to be optimized. These calculations revealed that the average deviation of the best fit becomes to be 3.3 % 0

and 3.8 %, respectively when kR5 or kR5 is separately eliminated from the model. Besides the significant increase in the average deviation systematic differences may be observed between the measured and calculated kinetic curves especially when the pH is varied. Thus we concluded that both terms are necessary to describe soundly all the kinetic data. One may also note that periodate solution may contain trace amount of iodide impurities that may drive the reaction without Step R5 via the sequence of Steps R7, R14, R15 and R16. We therefore performed an additional calculation process in which kR5 = 0 M−1 s−1 and 0

kR5 = 0 M−2 s−1 (along with kR10 = 0 M−1 s−1 ) were considered and trace amount of iodide impurity was introduced in the stock periodate solution. Because all the experiments were performed from the same periodate stock solution in all individual experimental curves the iodide impurity must be directly proportional to the initial periodate concentration applied. The best fit was achieved by 0.004 % iodide impurity but the average deviation was found to be over 8.0 % indicating that Step R5 (as well as Step R10) is a necessary part of the kinetic model and iodide impurity alone is not able to describe the measured data simultaneously.

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Step R6 is the fast oxidation of bisulfite by periodate. Unfortunately, no kinetic data is available in the literature on this reaction. Our preliminary experiments clearly showed that this oxidation process is completed within the mixing time of a stopped-flow instrument, therefore we set this rate coefficient to be 104 M−1 s−1 throughout the whole calculation process. Step R7 is the well-known oxidation of iodide by periodate. The kinetics of this reaction was studied by several research groups. In slightly acidic medium the rate of this reaction is independent of pH 32–34 but at more acidic condition below pH = 3 a [H+ ]-dependent term also appears in the rate law. 35 In agreement with these studies the rate coefficient of the pH-independent term was fixed at 11 M−1 s−1 as determined previously 33,34 and that of the pH-dependent term was determined to be 4882±98 M−2 s−1 . Step R8 was found to be necessary to describe the measured data. In this reaction short-live intermediate I2 O2 is oxidized by periodate ion leading to the formation of iodate and iodous acid. Rate law of this reaction was found to depend on the square of [H+ ] and this rate coefficient was determined to be (1.01±0.04)×1010 M−3 s−1 . It should, however, be noted that actually kR8 /k−R17 = 101±4 M−2 could be calculated from our experiments because there is a total correlation between these parameters. To prove that this step is also necessary for adequate description of the kinetic data additional calculation process was performed where Step R8 was eliminated from the kinetic model. The average deviation in this case was found to be 6.2 % indicating a significant difference between the measured and calculated kinetic curves from which we concluded that this step is indeed indispensable. Step R9 is the comproportionation reaction of iodous acid and periodate to produce iodate. Thorough survey of the literature has revealed no direct kinetic report on this reaction. However, this process was found to be necessary to describe the kinetic data of iodide–periodate reaction. 34 In that work a value of (1.23±0.34)×105 M−1 s−1 has been reported. However it was also pointed out that this rate coefficient was found to be in total correlation with kR19 thus kR9 /kR19 = (1.23±0.34)×10−4 M. Note that in the previous work

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mentioned above a fix kR19 = 109 M−2 s−1 value was used. The calculation presented here also confirmed that only the ratio of kR9 /kR19 can be obtained from our recent kinetic data providing a value of 2.97×10−5 M. Comparing this value with the one mentioned above agrees very soundly, the approximately fourfold difference may easily be taken into consideration by the different experimental conditions like ionic strength and the buffer components applied. Step R10 is the reaction of periodate with the aged TDO. As it is seen the rate coefficient of this reaction was found to be more than an order of magnitude higher than that of Step R5. Our calculation has revealed that kR10 = 1.38±0.07 M−1 s−1 is necessary to take the effect of aging into consideration quantitatively. As seen the observation that the aged form of TDO is more reactive towards the oxidizing agent is not unique, similar effect has been found in case of the TDO–iodine 5 and TDO–iodate 12 reactions as it was already highlighted previously. Steps R11–R22 were directly taken from our previous report 12 by exactly the same set of rate coefficients. The only exception is kR19 , which is 2 orders of magnitude higher than reported in our previous paper. For the sake of completeness it should be mentioned that in case of the TDO–iodate reaction any value higher than 109 M−2 s−1 would have led to the same final result as it was emphasized there. 12 Here, we found that kR19 has to be at least 1011 M−2 s−1 to obtain the best agreement between the measured and calculated data. This value is pretty close to the one reported by Furrow interpreting the most important kinetic feature of the iodate–hydrogen peroxide reaction, 36 though Furrow used a pH-dependent rate law for the iodide–iodous acid reaction. Finally, a word is also in an order here to emphasize how important it is to develop a feasible kinetic model of a subsystem from which the necessary extension may almost straightforwardly be performed to arrive at the comprehensive kinetic model of the parent system. The story has begun with elucidating the kinetic model of the TDO–iodine system. 5 The most important features of this reaction were explained by a 9-step kinetic model that was able to describe quantitatively the effect of aging as well as the inhibitory characteristics

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of the hydrogen and iodide ions. This model was then adopted completely to the kinetic model of the TDO–iodate reaction. 12 This system is, however, strongly autocatalytic with respect to iodide ion, thus the dual role of iodide ion is crucial in explaining the kinetic feature of the TDO–iodate reaction. As it was mentioned previously this system was found to exhibit clock feature and the most important characteristics of the TDO–iodine reaction mentioned above straightforwardly led to classify the TDO–iodate system as an autocatalysis-driven clock reaction. The strong inhibitory effect of iodide ion observed meant that the clock species iodine appears well before the substrate (TDO) is depleted. In order to explain all the most important characteristics of the TDO–iodate reaction the kinetic model of the TDO–iodine system was supplemented by seven more processes. As a result this complete sequence of reaction was directly taken into consideration to develop eventually the 22-step kinetic model of the TDO–periodate system by replenishing it with 6 necessary reactions of periodate ion eventually leading to such a comprehensive model that is able to preserve all the quantitative features of its subsystems.

Conclusion In this work the kinetics and mechanism of the thiourea dioxide–periodate reaction was elucidated for the first time. It is demonstrated that the title system may be classified as an autocatalysis-driven clock reaction because the clock species iodine may as well appear, although just transiently, in substrate excess after a well-defined and reproducible time lag. It is also highlighted that the Landolt time depends on the age of the stock TDO solution in case of the TDO–periodate reaction likewise in those of the TDO–iodine, 5 TDO– chlorine dixoide 6,7 and TDO–iodate 12 reactions. As it was shown the kinetic model of the overall system was gradually built-up from those of its subsystems like the TDO–iodine and the TDO–iodate reactions. At the same it provides a strong support how powerful the simultaneous data evaluation is in producing strongly reliable kinetic models from which the

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mechanism of the parent system may relatively easily be established. It is therefore strongly recommended to utilize this option in case of studying the kinetics and mechanism of an unknown complex system.

Acknowledgment This work is supported by the National Natural Science Foundation of China (Grant No. 21773304), the Fundamental Research Funds for the Central Universities (Grant No. 2015XKMS045), the Natural Science Foundation of Jiangsu Province (Grant No. BK20171186). This work was as well supported by the GINOP-2.3.2-15-2016-00049 grant. The study was also financed by the Higher Education Institutional Excellence Programme of the Ministry of Innovation and Technology in Hungary, within the framework of the innovation for sustainable and healthy living and environment thematic programme of the University of Pécs. The project has been supported by the European Union, co-financed by the European Social Fund Grant no.: EFOP-3.6.1.-16-2016-00004 entitled by Comprehensive Development for Implementing Smart Specialization Strategies at the University of Pécs. Financial support of the Hungarian Research Fund NKFIH-OTKA Grant No. K116591 is also acknowledged.

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TOC Graphic

Autocatalysis-driven Clock Reaction

Formation of Iodine

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Time (s)

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On the Kinetics and Mechanism of the Thiourea Dioxide-Periodate

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