Autocatalysis-Driven Clock Reaction III: Clarifying the Kinetics and

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Autocatalysis-Driven Clock Reaction III: Clarifying the Kinetics and the Mechanism of the Thiourea Dioxide--Iodate Reaction in an Acidic Medium György Csek#, Qingyu Gao, Li Xu, and Attila K. Horváth J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00584 • Publication Date (Web): 11 Feb 2019 Downloaded from http://pubs.acs.org on February 13, 2019

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The Journal of Physical Chemistry

Autocatalysis-Driven Clock Reaction III: Clarifying the Kinetics and Mechanism of the Thiourea Dioxide–Iodate Reaction in an Acidic Medium György Csek˝o,†,‡ Qingyu Gao,∗,† 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–iodate reaction has been reinvestigated spectrophotometrically under acidic condition using phosphoric acid–dihydrogen-phosphate buffer within the pH range of 1.1–1.8 at 1.0 M ionic strength adjusted by sodium perchlorate and at 25◦ C. The system was found to exhibit clock behavior, having a well-defined and reproducible time lag called Landolt time, though elementary iodine may even be detected in substrate excess, hence under these conditions the reaction can be classified

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as an autocatalysis-driven clock reaction. It is clearly demonstrated that the previously proposed kinetic model suffers from serious drawbacks both from theoretical and experimental point of view. The reaction may be characterized by either sigmoidalshaped or by rise-and-fall kinetic traces depending on the initial concentration ratio of the reactants. Iodide significantly accelerates the appearance of the clock species iodine acting therefore as an autocatalyst. The age of stock TDO solution also has a great, so far completely overlooked impact on the Landolt time. Based on evaluating simultaneously the kinetic curves a 16-step kinetic model including five well-known rapidly established equilibria is proposed with 7 fitted rate coefficients in which the rate coefficients of both forms of TDO were determined.

Introduction Thiourea dioxide (TDO) being as a green reducing agent has long been used in chemistry and chemical technology due its versatile properties 1,2 despite the fact that its redox chemistry in aqueous solution still provides significant challenges for future studies to fully understand its special features and transformations at molecular level. TDO is fairly stable under aqueous acidic conditions, however it decomposes relatively rapidly into sulfoxylate ion and urea depending on the alkalinity of aqueous solution. 3,4 Xu et al. has recently shown 5 that even under acidic conditions TDO relatively slowly but steadily rearranges into a more reactive form, whose reactions may be much faster with the corresponding oxidizing agent than with the original form of TDO. Although it still provides a challenge 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. The oxidation of TDO by iodate in acidic medium was first investigated by Mambo and Simoyi. 10 Unfortunately, the exact age of TDO solution used in their experiments is unclear, the only information extracted from their paper is that the stock solution was not kept for 2


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more than four hours. Our previous experience obtained from studying the TDO–chlorine dioxide 6 reaction is that the shape of the kinetic curves may even drastically change when TDO stock solution ages. The original sigmoidal characteristics of the measured kinetic curves in case of using fresh TDO stock solution may easily be lost when a 2-hour-old reagent stored in aqueous condition is used in case of using chlorine dioxide as an oxidizing agent. Thus, it seems to be quite crucial to know exactly the age of the stock TDO solution to be used in order to establish a correct chemical model. Unfortunately, this is not the only problem with Mambo and Simoyi’s report. 10 They proposed an 11-step mechanism including questionable reactions and rate coefficients to describe their kinetic data. First, very recently, Stanbury 11 has pointed out that the kinetic model includes sequence of reversible reactions whose rate coefficients assigned violate the principle of detailed balancing 12 by many orders of magnitude. Second, their proposed kinetic model includes a direct reaction between thiourea dioxide and triiodide ion, a process that is not necessary to describe the kinetic data measured directly in the TDO–iodine reaction. 5 Third, Mambo and Simoyi’s proposed kinetic model (afterwards MS model) involves direct reaction between iodine and thiourea trioxide (TTO) a process that was explicitly ruled out to occur by Makarov et al. 13 All these inadequacies appear to suggest that clarification of the intimate details of the title reaction is eagerly expected. Last but not least, it is also worthwhile to point out that the TDO–iodate system is a Landolt-type clock reaction though it is not completely clear whether it is uniquely a substrate-depletive or an autocatalysis-driven clock reaction. 14 This question arises from the fact that TTO is considered as a long-lived intermediate in the MS model. According to Mambo and Simoyi’s discussion it looks to be a substrate-depletive one though the acid- and iodide-inhibitory characteristics of the TDO–iodine reaction 5 appears to suggest that at low pHs it may rather be an autocatalysis-driven clock reaction meaning that thiourea dioxide and the clock species iodine may coexist for a fairly long-time before I2 disappears in excess of TDO. All these problems prompted us to reinvestigate the system thoroughly.

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Experimental Section Materials. All the chemicals (sodium iodate, potassium iodide, phosphoric acid, sodium dihydrogen phosphate, TDO and sodium perchlorate) were of the highest purity commercially available and were used without further purification. All stock solutions were prepared from distilled water obtained from Milli-Q water purification system having a resistivity of 18.2 MΩ·cm. The TDO stock solution was freshly prepared before each measurement. The age of the stock TDO solution was kept approximately constant at 270±4 s except otherwise stated. Argon gas was bubbled through the solution to protect it from oxygen. The ionic strength was set to 1.0 M by sodium perchlorate. The pH of the solutions was regulated between 1.1 and 1.8 by using phosphoric acid/dihydrogen phosphate buffer taking the pKa1 of phosphoric acid as 1.8. 15 The dihydrogen phosphate concentration was kept constant at 0.25 M except otherwise stated. The temperature of the reaction vessel was maintained at 25.0±0.5◦ C.

Methods and Instrumentation The reaction was followed by an Analytik Jena Specord S600 diode array spectrophotometer within the wavelength range of 400–800 nm without using the deuterium lamp of the photometer. The reaction was performed in a standard quartz cuvette equipped with magnetic stirrer and a Teflon cap having 1 cm optical path. The buffer components and the reactant iodate were delivered from a pipette first. The reaction was started with addition of the necessary amount of TDO that also contained iodide (if it was necessary) from a fast delivery pipette. The spectra of reacting solution at the wavelength range of 400–800 nm was acquired up to approximately 5000 s.

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Data Treatment Evaluation of the kinetic curves was carried out at the isosbestic point of I2 –I3 – system at 468 nm by the program package ZiTa/Chemmech. 16 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 more 4000 experimental points of 70 experimental curves were used for data evaluation to obtain the kinetic model and the corresponding rate coefficients.

Results As a first step we have tried to confirm all the major experimental feature of system reported by Mambo and Simoyi. 10 First, in TDO excess and at acidic condition the total iodine concentration follows a rise and fall behavior as a function of time after a well-defined time lag that qualitatively agrees with Mambo and Simoyi’s result. Second, in excess of iodate the measured absorbance–time traces at 468 nm follows a sigmoid characteristics suggesting clearly that autocatalysis might be involved in the system. This characteristic is also in qualitative accordance with the previously published results. Furthermore, addition iodide in micro amounts significantly shortens the induction period observed meaning that iodide ion acts as an autocatalyst. This feature immediately poses quite important questions on developing a reliable kinetic model. Does the direct reaction between TDO and iodate exist at all or is the system initiated by trace iodide impurities inherently involved in stock iodate solution? 17–20 If there is indeed then which form of TDO does really react with iodate, the initial one or the aged one or even both? Since aging of TDO solution is a well-documented feature it is crucial to have reliable information on the rate coefficient of equation described

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below under the present experimental conditions: kaged

TDOinit −→ TDOaged

(1)

Aging of Thiourea Dioxide at pH = 2 Previously, it is reported 5 that between pH = 3 and 5 eq. 1 is independent of [H+ ] and kaged was found to be 1.55×10−6 s−1 . Since the experimental circumstances applied here is significantly more acidic, we performed independent studies on the stability of TDO at pH = 2. Figure 1 describes the spectral changes of TDO solution followed by UV-Vis spectroscopy.

Time intervals: 1

Every 2 hours Daily

0.8 7 102 ×Log(A269 )

Absorbance

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0.6

3

−1

0.4

−5

0.2 0 240

−9

260

280

300

0

Wavelength (nm)

2 4 6 Time (10−4 ×s)

320

8

340

Figure 1: Spectral changes of 2.0 mM TDO solution observed at pH = 2. Spectra were acquired every 2 hours within the first day (black), followed by recording UV-Vis spectrum of the aging TDO solution (red) every day. The inset shows the natural logarithm of the measured absorbance at 269.5 nm against time. The slope of the straight line was found to be (1.95±0.05)×10−6 s−1 corresponding to first-order rate coefficient of eq. 1. It is clear that decrease of pH results in a somewhat higher rate coefficients for eq. 1, though this slight change (approximately 20%) may easily be attributed to the usage of different background electrolyte (phosphate buffer) in the present case. kage = (1.95±0.05)×10−6 s−1 obtained means that the half-life of the original form of TDO is about 4.1 days under our experimental circumstances. This observation may pose a relevant question whether this

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vanishingly slow process has any crucial impact on the measured kinetic curves or not.

Effect of Aging of TDO on the TDO–Iodate reaction Kinetic traces were performed from the same stock solution within this series of runs. The age of TDO in aqueous buffered phase was recorded when the corresponding experiment is initiated. Fig. 2 displays the effect of aging, i.e. shortening the length of induction period with increasing age of TDO solution.

0.3 0.25

Absorbance at 468 nm

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0.2

0.15 0.1

0.05 0

0

400

800

1200

1600

2000

2400

Time (s)

Figure 2: Effect of aging on the measured (dots) and calculated (solid lines) absorbance– time series at [TDO]0 = 0.9 mM, [IO3 – ]0 = 1.0 mM, pH = 1.8. Age of TDO stock solutions in seconds: 266 (black), 3339 (blue), 10833 (green), 14437 (cyan), 18906 (magenta), 21139 (red), 23208 (brown), 25302 (yellow), 42985 (orange). From these studies it is quite clear that age of TDO solution plays a crucial role in determining the length of the induction period, even though the half-life of original form of TDO is as long as 4.1 days! Changes are especially significant in case of fresher TDO solution. As seen when the age of TDO solution varies from approximately 4.5 min to 55 min, the induction period decreases from 1400 s to 1000 s. In addition to that in case of a 4-hour old TDO solution the induction period is roughly halved to 700 s, which means if the age of TDO solution is not controlled correctly when studying the kinetics of the target reaction it may easily lead to a misinterpreted and false conclusion. We therefore concluded that it is important to use TDO stock solution at the same age to establish a reliable kinetic model. 7



Thus, except otherwise stated, all the experimental runs were initiated with having the age of TDO solution to be 270±4 s. At the same time this series of kinetic runs appears to suggest that the aged form of TDO is significantly more reactive than the fresh one, which is quite consistent what was observed in case of other redox reactions of TDO. 5–7

Characteristics of the Kinetic Traces as [TDO]0 is varied It is already well-known that iodine oxidizes TDO in acidic condition to eventually give sulfate and iodide ion, meanwhile producing ammonium ion and carbon dioxide from the nitrogen- and carbon part of TDO as innocent products. 5 The TDO–iodine system was established to be an iodide and hydrogen inhibitory reaction, 5 thus such a condition (at high acidity and iodide concentration produced or initially added) may easily be provided during the course of title reaction that iodine may transiently appear in excess of TDO. Final I2 concentration at the end of reaction depends of course on the extent of excess of TDO. Consequently, iodine concentration may easily be diminished to zero in huge TDO excess, but it might also be leveled off after reaching its maximum. This diversified dynamical feature is shown below in Fig. 3, when initial TDO concentration is varied while keeping rest of the reactant concentration constant. It is easy to understand that a fine balance of sequences of reactions producing and consuming iodine is necessary to not only qualitatively but also quantitatively describe the major characteristics of the system. Therefore every single intimate detail of the subsystems must first be identified to come up with a feasible model. We shall point out that for this rise and fall dynamical feature the dual effect of the well-known kinetics of the Dushman reaction 21–24 and the acid- as well as the iodide inhibitory behavior 5 of the TDO–iodine system is sufficient to characterize quantitatively this phase of the title reaction. At the same time, it will also be discussed that in MS model neither the inhibitory effect of iodide nor that of the hydrogen ion is correctly taken into consideration in the TDO–iodine reaction.

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0.3


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0.25 0.2

0.15 0.1

0.05 0

0

1000

2000

3000

4000

Time (s)

Figure 3: Effect of initial TDO concentration on the measured (dots) and calculated (solid lines) absorbance–time series at [IO3 – ]0 = 1.0 mM, pH = 1.8. Age of TDO stock solutions in 270±3 s. [TDO]0 /mM = 0.31(black), 0.51 (blue), 1.0 (green), 1.3 (cyan), 1.4 (magenta), 1.56 (red), 1.81 (brown), 1.85 (yellow), 1.91 (orange), 2.2 (light gray), 2.8 (purple), 4.2 (dark gray).

Effect of Initially Added Iodide Ion In agreement with Mambo and Simoyi’s we have also found that trace amount of iodide significantly shortens the induction period for the appearance of iodine. Although it is not stated explicitly in their paper, it is evident that iodide not just catalyzes the title reaction, it acts as an autocatalyst shown in Figure 4. Mambo and Simoyi also argued that their iodate solution was contaminated with iodide and the concentration of this species may be as high as 4 µM in their experimental conditions. In contrast to this, our study, however, showed that even if the stock iodate solution contained trace amount of iodide its concentration cannot be higher than approximately 0.005 % of the iodate concentration in agreement with our previous study. 19 It thus corresponds to 5×10−8 M, the value which is significantly smaller than the smallest initial iodide concentration used in our experiments. Consequently, in our case the inherent iodide contamination of the iodate solution could not play any decisive role in determining the characteristics of the kinetic curves. It indirectly implies that direct reaction between TDO and iodate has to exist.

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0.25 0.2

0.15 0.1

0.05 0 0

200

400

600

800

1000

Time (s)

Figure 4: Effect of initially added iodide on the measured (dots) and calculated (solid lines) absorbance–time series in iodate excess at pH = 1.6, [TDO]0 = 1.0 mM and [IO3 – ]0 = 1.0 mM. Age of TDO stock solutions in 270±3 s. [I – ]0 /µM = 0 (black), 2.0 (blue), 4.0 (green), 7.5 (cyan), 22.5 (red).

Effect of Acidity Mambo and Simoyi reported 10 that acidity has a pivotal role in determining the dynamics of the liberation of iodine, especially in TDO excess, with which we agree completely. At higher pHs iodine does not appear at all due to the fact that the iodine–TDO reaction is inversely proportional 5 to [H+ ] therefore the rate of this reaction always exceeds that of the Dushman reaction (formation of iodine). Decrease of pH, however, increases the rate of formation of iodine and simultaneously decreases the rate of TDO–iodine reaction, therefore iodine may appear in detectable amount as a transient species in excess of TDO. Consequently, it means that the maximum of transient iodine concentration has to increase with decreasing pH. Due to the above mentioned facts, the rate of iodine disappearance should also decrease with decreasing pH. This complex qualitative picture is soundly manifested in Figure 5.

Individual Evaluation of Kinetic Curves All these results appear to establish that a simple 3-step Landolt-type kinetic model, including the direct TDO–iodate reaction producing iodide ion, the Dushman- and the TDO–iodine reaction are suitable to evaluate the measured kinetic curves individually. According to the 10


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0.16


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0.12

0.08

0.04

0 0

500

1000

1500

2000

2500

3000

Time (s)

Figure 5: Effect of pH on the measured (dots) and calculated (solid lines) absorbance– time series in TDO excess in absence of initially added iodide. [TDO]0 = 1.0 mM and [IO3 – ]0 = 0.6 mM. Age of TDO stock solutions in 270±3 s. pH = 1.1 (black), 1.25 (blue), 1.4 (green), 1.6 (cyan), 1.8 (red). major experimental findings we propose the following sequence of overall processes along with their rate equations. k

I 3(NH2 )2 CSO2 + 2IO3− + 6H2 O −→ 6NH4+ + 3CO2 + 2I− + 3SO42−

(I)

vI = kI [TDO][IO3− ][H+ ]2 5I− + IO3− + 6H+ −→ 3I2 + 3H2 O

(II)

vII = kII [IO3− ][H+ ]2 [I− ]2 k

II (NH2 )2 CSO2 + 2I2 + 4H2 O −→ 2NH4+ + CO2 + 4I− + 4H+ + 4SO42−

vIII = kIII

(III)

[TDO][I2 ] u + [I− ]

Calculating all these three rate coefficients for every run (except those ones where the effect of TDO aging is studied) followed by averaging the corresponding values provided kI = 19.9±4.9 M−3 s−1 , kII = (4.72±0.94)×108 M−4 s−1 and kIII = (3.22±0.49)×10−4 s−1 (u =10−8 M has been kept constant necessarily to prevent the rate for vIII to be infinity

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at zero initial iodide concentration) meanwhile the average deviation between the measured and calculated data was found to be within the range of 0.4% to 2.0%. It means that this core model is able to describe the kinetic data quite soundly though the description is only qualitative. To indicate this fact additional calculation process was performed to simulate simultaneously all the kinetic runs by using the previously determined rate coefficients mentioned above. The average deviation for the kinetic curves used was found to be 8.2 % indicating that refinement of simplified model is necessary to describe the kinetic data quantitatively.

Proposed Kinetic Model for Simultaneous Evaluation of Kinetic Curves To extend the simplified kinetic model the following modifications were found to be necessary. We included all those equilibria that should undoubtedly be involved under our experimental condition and thus having notable effect on the calculated kinetic curves. These rapidly established equilibria are shown below in eqs. E1, R1, R2, R3, R8 and R11. Furthermore, the slow transformation reaction of TDO being experimentally confirmed to occur as well must be a central part of the extended model. As a next step eqs. I–III were divided into elementary and quasielementary processes. Eq. I is the overall complex initiating reaction leading eventually to the formation of iodide ion. This complicated stoichiometric equation was divided into three consecutive steps, in which TDO reduces iodate in a stepwise fashion via formal oxygen-transfer processes. These reactions are indicated in eqs. R5–R7. It should also be noted that both forms of TDO were considered to be reacted with the major iodinecontaining species (iodate, iodine, iodous acid and hypoiodous acid) at the beginning of the evaluation process. It is also evident that eq. II, the well-known Dushman reaction may also be rationalized by elementary steps indicated by eqs. R11–R13 supplemented by the well-known rapidly established equilibria eqs. R1, R2 and R3. Finally, the recently 12


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published sequence of reaction in case of the TDO–iodine reaction was also considered here to divide eq. III into elementary and quasielementary steps. Finally, the well-known rapid reaction between HSO3 – and iodine 25 has to be considered as well to establish the correct stoichiometry. The evaluation procedure was eventually started from a 70-step kinetic model followed by reducing the number unnecessary processes in a stepwise fashion. This procedure has been applied successfully in many cases to come up with a feasible and relatively simple kinetic model. 26–28 As a result the following kinetic model was 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 + IO3− + 2H2 O + 2H+ −→ 2NH4+ + CO2 + HSO3− + HIO2

(R5)

TDO + HIO2 + H+ + 2H2 O −→ 2NH4+ + CO2 + HSO3− + HOI

(R6)

TDO + HOI + 2H2 O −→ 2NH4+ + CO2 + HSO3− + I−

(R7)

− + TDO + I2 − )− −* − TDOI + I + H

(R8)

TDOI + 3H2 O −→ 2NH4+ + CO2 + HSO3− + I−

(R9)

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

(R10)

H+ + I− + HIO3 − )− −* − I2 O2 + H2 O

(R11)

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I− + H+ + I2 O2 −→ I2 + HIO2

(R12)

I− + H+ + HIO2 −→ 2HOI

(R13)

TDOaged + IO3− + 2H2 O + 2H+ −→ 2NH4+ + CO2 + HSO3− + HIO2

(R14)

TDOaged + I2 −→ TDO2+ + 2I−

(R15)

TDO2+ + TDO + 4H2 O −→ 4NH4+ + 2CO2 + SO42− + S

(R16)

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 1.0 % which is close to the experimentally achievable error limit of absorbance measurements. It therefore provides a very sound agreement between the measured and calculated data. Figures 2–5 nicely demonstrate that the proposed kinetic model is working exceptionally well. Because the simultaneous evaluation was performed when the age of TDO solution was not longer than half a day and it was already shown 5 that the degradation process of TDO is more complex at a longer time scale it straightforwardly means the limitation of the kinetic model used for quantitative description. At longer time scale the kinetic model must certainly be extended but the extension must wait for clear understanding of the degradation process.

Discussion Step E1 is only an auxiliary process necessary to take the slight pH changes into consideration during the calculation. This process has to be established rapidly (kE1 = 1.58×105 s−1 and k−E1 = 107 M−1 s−1 values were used) and the ratio of these rate coefficients was set to give the pKa1 value of phosphoric acid at the current conditions to be 1.8. 15 This value worked consistently well in a number of previous systems investigated. 27,28 Step R1 is the generally well-known fast equilibrium formation of triiodide ion studied by

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Table 1: Rate equations used and rate coefficients obtained from evaluating simultaneously the kinetic data of the TDO–iodate reaction. 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] (R5) kR5 [TDO][IO3 – ][H+ ]2 (R6) kR6 [TDO][HIO2 ] (R7) kR7 [TDO][HOI] (R8) kR8 [TDO][I2 ] (−R8) k−R8 [H+ ][[I – ]][TDOI] kR9 [TDOI] (R9) 0 kR9 [TDOI][H+ ]−1 (R10) kR10 [HSO3 – ][I2 ] (R11) kR11 [H+ ][I – ][HIO3 ] (−R11) k−R11 [I2 O2 ] kR12 [I2 O2 ][I – ] (R12) 0 kR12 [I2 O2 ][I – ][H+ ] (R13) kR13 [I – ][HIO2 ][H+ ] (R14) kR14 [TDOaged ][IO3 – ][H+ ]2 (R15) kR15 [TDOaged ][I2 ] (R16) kR16 [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 29.7±0.3 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±2 s−1 2.22±0.05 M s−1 3.1×109 M−1 s−1 107 M−2 s−1 108 s−1 (4.67±0.10)×108 M−1 s−1 (6.29±0.05)×1010 M−2 s−1 109 M−2 s−1 7608±301 M−3 s−1 104 M−1 s−1 105 M−1 s−1

independent research groups. 29,30 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 well-established acid dissociation process of iodic acid. Ka = 0.156±0.002 M was established independently by Ramette and Palmer, 31 as well as by Strong and Pethybridge 32 at zero ionic strength. Considering that it is 1.0 M in our experiments we used Ka = 0.32 M throughout the whole calculation process.

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Step R3 is the well-known hydrolytic equilibrium of iodine taking place in aqueous solution. The rate coefficients of the forward and backward processes including the H+ -inhibited pathway were determined previously. 33–35 This equilibrium is established rapidly under our experimental circumstances that enables us to simplify the kinetic model with elimination of H2 OI+ species. Consequently, the rate coefficient of k−R3 has to be recalculated from the values reported by Lengyel et al. 35 All the rate coefficients regarding to the iodine hydrolysis were used as fixed ones during the fitting procedure. Step R4 is responsible for the aging effect of TDO in aqueous acidic solution. The rate coefficient of this reaction was calculated to be (1.95±0.05)×10−6 s−1 from independent measurements and thus it was used as a fixed value during majority of the evaluation procedure. In the final rate coefficient refinement process, however, it was also allowed to be fitted and this calculation resulted in kR4 = (1.87±0.09)×10−6 s−1 indirectly supporting the fact, that indeed this rearrangement process plays a crucial role in the redox transformation of TDO. Step R5 is the initiation of the title reaction leading eventually to the breakage of C–S bond and the formation of bisulfite and iodous acid. Our calculation has revealed that the rate of this reaction has to depend on the square of the hydrogen ion concentration. The rate coefficient optimized was found to be 29.7±0.3 M−3 s−1 . Previously it was mentioned that the stock iodate solution may also contain trace amount of iodide, consequently the dynamics of the system may easily be described without Step R5. We therefore performed an additional calculation process in which kR5 = 0 M−3 s−1 was considered and trace amount of iodide impurity was introduced in the stock iodate solution. Since all the experiments were performed from the same iodate stock solution in all individual experimental curves the iodide impurity must be directly proportional to the initial iodate concentration applied. The best fit was achieved by 0.005 % iodide impurity but the average deviation was found to be over 9.0 % indicating that Step R5 is a necessary part of the kinetic model. Additional fitting procedure was also performed to elucidate the hydrogen dependence of the rate of this reaction. Considering that vR5 does not depend on [H+ ] 6.5 % average deviation was

16


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obtained between the measured and calculated data, which is definitely much higher than the experimentally achievable error limit of absorbance measurement. If, however, we suppose that vR5 is linearly proportional to [H+ ] a significantly better, though still an unacceptable 3.1 % average deviation is obtained. All these calculations led us to conclude that vR5 is proportional to the square of [H+ ] by which 1.0 % average deviation is obtained indicating an almost perfect agreement between the measured and calculated data. Steps R6 and R7 are rapid reactions between TDO and iodous acid as well as between TDO and hypoiodous acid producing hypoiodous acid and iodide ion respectively besides CO2 , ammonium ion and bisulfite. The rate coefficients of these processes cannot be calculated unambiguously from our experiments, therefore kR6 = 106 M−1 s−1 and kR7 = 106 M−1 s−1 were fixed during the calculation procedure. As it is seen linear combination of (R5)+(R6)+(R7)+(R11)+(R12)+(R13)+2×(R3)+3×(R10) gives the overall stoichiometry indicated by eq. I. Step R8 is a rapidly established equilibrium of the TDO–iodine reaction that was first proposed by Xu et al. 5 to produce a short-lived iodinated-TDO intermediate. As it is seen this equilibrium is responsible for the hydrogen- and iodide inhibition of this reaction. The equilibrium constant of this process cannot be determined from our experiments, therefore KR8 was set to a small 10−6 M value to provide a low level steady-state concentration for TDOI. It should also be noted that Mambo and Simoyi interpreted the hydrogen- and iodide inhibition of the TDO–iodine system by the fast TDO–HOI reaction along with the rapidly established iodine hydrolysis. As it is seen these reactions are also included in our proposed model. Thus, if they are right a reduced model via eliminating Steps R8 and R9 might also describe our experimental data. In contrast to this we found that the average deviation increased well above 10 % meaning that these steps cannot be omitted from the model. Consequently, these processes are indeed responsible for the hydrogen- and iodide inhibition of the TDO–iodine reaction. Step R9 is the rapid decomposition of TDOI leading to bisulfite and iodide as well as

17



to the chemically inactive ammonium ion and carbon dioxide. In complete agreement with Xu et al. 5 we found that this decomposition occurs in parallel pathways a pH-independent one and a hydroxide-assisted route. Both rate coefficients could be determined from our 0

measurements as kR9 = 200±2 s−1 and kR9 = 2.22±0.05 M s−1 , respectively. Comparing these rate coefficients with the ones published recently 5 one may easily see a factor of 2fold and 50-fold difference. These deviations, however, may easily be explained by using different medium accompanied by buffer assistance as well. In case of the Dushman reaction it is a well-known phenomenon 22 thus it is also a conceivable possibility here to occur. In order to support this idea we have also performed additional experiments where the pH, the ionic strength and the initial concentration of the reactants were kept constant in absence of initially added iodide ion meanwhile [H2 PO4 – ]0 (and at the same time [H3 PO4 ]0 as well) was varied. The results are shown below in Figure 6.

0.3


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0.25 0.2

0.15 0.1

0.05 0 0

400

800

1200

1600

2000

Time (s)

Figure 6: Effect of [H2 PO4 – ] on the dynamics of the measured (dots) and calculated (solid lines) absorbance–time series in TDO excess in absence of initially added iodide. [TDO]0 = 1.3 mM and [IO3 – ]0 = 1.0 mM, pH = 1.6. Age of TDO stock solutions in 270±3 s. [H2 PO4 – ]0 = 0.09 (black), 0.18 (blue), 0.27 (green), 0.315 (cyan), 0.36 (red), 0.405 (magenta). Not surprisingly, very strong accelerating effect of buffer concentration may be realized that maybe augmented with the fact that the individual rate coefficients of some processes involved should be influenced by the buffer concentration itself. To quantify these dependencies is out of the scope of present study and is therefore left for future investigations. 18


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Step R10 is the rapid, essentially diffusion-controlled reaction of iodine with bisulfite studied by Yiin and Margerum. 25 The rate coefficient 3.1×109 M−1 s−1 was directly adapted from their work and was used as a fixed one throughout the whole fitting process. It should, however, be noted that this reaction proceeds via a short-lived intermediate ISO3 – , whose further hydrolysis is also a fast process. Step R11 is also a rapidly established equilibrium to produce the short-lived intermediate I2 O2 . The equilibrium constant cannot be unambiguously determined from our experiments, therefore we fixed KR11 = 0.1 M2 to provide a sufficiently low concentration level for I2 O2 to treat it as a steady-state intermediate. Because Schmitz 23 also considered the following possibility, I2 O2 + H2 O −→ HIO2 + HOI

(2)

we tried to include this reaction into the final kinetic model with an adjustable rate coefficient. The quality of the fit, however, did not change at all, therefore we concluded that this process is not necessary to describe our kinetic data. Step R12 is the further transformation of the short-lived intermediate to produce iodine and iodous acid as proposed by Schmitz 23 and Agreda et al. 24 As it is seen we found that a two-term rate law including a pH-dependent and a pH-independent pathways is necessary to describe quantitatively the kinetic data. The rate coefficients of this reaction could be calculated from our experiments as kR12 = (4.67±0.10)×108 M−1 s−1 and 0

kR12 = (6.29±0.05)×1010 M−2 s−1 . To support that both terms are indeed necessary we have performed extended calculation with eliminating first the pH-independent route (kR12 = 0 M−1 s−1 ) 0

then the pH-dependent (k12 = 0 M−2 s−1 ) pathway. The average deviations were found to be 2.2 % and 3.3 %, respectively, meaning that omitting either of these pathways would increase the average deviation to significantly larger values. It thus provides an indirect but sound support to include both routes for adequate description of the kinetic data. Step R13 is also a very fast reaction whose rate coefficient cannot be calculated from our experiments. Our calculation has revealed that any value higher than kR13 = 109 M−2 s−1 19



would lead to the final average deviation, therefore we fixed this rate coefficient during the course of the whole calculation process. This value is in complete agreement with the value reported by Lengyel et al., 35 but it is also worthwhile to mention that Furrow 36 used a significantly higher value (5×109 M−1 s−1 ) with no [H+ ] dependence on the rate equation interpreting the most important kinetic feature of the iodate–hydrogen peroxide reaction. Step R14 is basically the same reaction as is found in Step R5, but in this reaction the aged form of TDO is one of the reactants. Our calculation provided kR14 to be 7608±301 M−3 s−1 , which means that the reactivity of the aged form of TDO is significantly larger towards iodate ion than the fresh one. This finding is in complete coincidence what is published in case of the TDO–chlorine dioxide 6 and the TDO–iodine 5 systems. Step R15 is the other important reaction of the aged TDO with iodine to produce TDO2+ and iodide ions. Formation of ion pairs of halide ions with thiourea was recently suggested by Biesiada et al. 37 Here, as an analogy, we propose a similar opportunity but it may only occur in case of the aged TDO. Since the rate coefficient of this reaction cannot even be determined in studying the TDO–iodine system, it is not surprising that only a lower limit could be calculated for kR15 . We found that kR15 104 M−1 s−1 inequality should be valid therefore it is fixed at this value during the course of the whole evaluation process. Step R16 was already suggested previously 5 and is responsible for the appearance of trace amount of elementary sulfur in case of the TDO–iodine reaction. Consequently, it means that change in the stoichiometry of title reaction appears to be related to the wellknown slight stoichiometric change in the TDO–iodine reaction 5 as TDO stock solution ages. The rate coefficient of this reaction has to be large enough as well to ensure that TDO2+ can be treated as a steady-state intermediate. It should also be noted that the amount of elementary sulfur formed via this pathway is marginal and does not disturb the quantitative absorbance measurements, thus the kinetic curves were not truncated like in the cases of the pentathionate–iodate 27 and the pentathionate–periodate 28 reactions. But at the same time it has to be kept in the final model to be consistent with the major characteristics of the

20


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TDO–iodine reaction. 5 A paragraph is also in an order here to demonstrate even more explicitly why sometimes a complete reinvestigation of a system may be more important than it is generally thought, even though the basic core of the previously published kinetic model is more or less resolved. We have already pointed out that even prior to the beginning of reinvestigation of the system some inconsistencies may be realized in the original work Mambo and Simoyi. Part of them—like aging effect and erroneous usage of those reactions that do not occur at all under the conditions studied—can easily be avoided with carefully designed experiments. Another part—like violation of the principle of detailed balancing—can as well be overcome by doublechecking the parameter set to be used. If all these problems are properly handled then it is also worthwhile to check whether the proposed kinetic model is able to describe the major tendencies measured in case of series kinetic runs. This is exactly what we did with the kinetic model proposed by Mambo and Simoyi. 10 According to Tables II and III of the cited paper (see: top of page no. 13666) we tried to simulate the measured absorbance–times series of Figures 1, 3, 4 and 5 (see: pages 13663 and 13664). The results are seen in the Supporting Information along with the original experimental curves published there. As it is clearly seen the model is not capable of even providing qualitative agreement (not mentioning the substantial difference in the absorbance values) in case of all these Figures. Currently, we could not allocate explicitly the problem, it may be the consequence of mistyped rate coefficients or rate equations published in Tables II and III, 10 or there is an unnoticed integration problem in Simoyi’s work. This seems to be not a unique appearance, since very recently Stanbury has clearly pointed out 11 a similar inconsistency in Sexton’s et al. paper. 38

Conclusion In this work the kinetics and mechanism of the thiourea dioxide–iodate reaction was presented. It has been shown that the previously established kinetic model along with the

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published rate coefficients as well as the experimental setup suffers from substantial deficiencies making it dubious to be used for further studies. At low pHs the title system may be classified as an autocatalysis-driven clock reaction 14,27,28 since the clock species appears even in substrate excess due to the H+ - and iodide-inhibited TDO–iodine reaction. 5 It is clearly demonstrated as well that aging of stock TDO solution affects greatly the time lag necessary for the appearance of clock species (iodine). The overall system is shown to be autocatalytic with respect to iodide. A 16-step kinetic model is constructed from the previously studied TDO–iodine and the Dushman reaction augmented by the stepwise reduction iodate by TDO producing eventually iodide ion. The experimental setup and usage of simultaneous evaluation of the kinetic curves allowed us to determine the rate coefficients of both forms of TDO, the fresh and the aged ones. The latter one is found to be more reactive, though the chemistry behind the aging process is still unclear and requires further, extended investigations. To our opinion revision of the MS model presented here means significantly more than just being a simple correction. It provides an additional example that reliably established kinetic models of a subsystem are eagerly expected and may serve as a solid background of correct interpretation for newly discovered characteristics of more complicated reaction systems.

Supporting Information Comparison of the measured and simulated absorbance–time traces in case of the Mambo and Simoyi’s model can be found in the supporting information.

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. 2015XKZD09), the Natural Science Foundation of Jiangsu Province (Grant No. BK20171186). This work 22


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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 Human Capacities in Hungary, within the framework of the 20765-3/2018/FEKUTSTRAT 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.

References (1) Makarov, S. V.; Horváth, A. K.; Silaghi-Dumitrescu, R.; Gao, Q. Recent Developments in the Chemistry of Thiourea Oxides. Chem. Eur. J. 2014, 20, 14164–14176. (2) Makarov, S.; Horváth, A.; Silaghi-Dumitrescu, R.; Gao, Q. Sodium Dithionite, Rongalite and Thiourea Oxides: Chemistry and Application; World Scientific Publishing Co. Pte Ltd: Singapore, 2016; pp 1–219. (3) Miller, A. E.; Bischoff, J. J.; Pae, K. Chemistry of Aminoiminomethanesulfinic and -Sulfonic Acids Related to the Toxicity of Thioureas. Chem. Res. Toxicol. 1988, 1, 169–174. (4) Svarovsky, S. A.; Simoyi, R. H.; Makarov, S. V. Reactive Oxygen Species in Aerobic Decomposition of Thiourea Dioxides. J. Chem. Soc. Dalton Trans. 2000, 511–514. (5) Xu, L.; Valkai, L.; Kuznetsova, A. A.; Makarov, S. V.; Horváth, A. K. Kinetics and Mechanism of the Oxidation of Thiourea Dioxide by Iodine in a Slightly Acidic Medium. Inorg. Chem. 2017, 56, 4679–4687.

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(6) Csek˝o, G.; Hu, Y.; Song, Y.; Kégl, T. R.; Gao, Q.; Makarov, S. V.; Horváth, A. K. Kinetic Evidence of Tautomerism of Thiourea Dioxide in Aqueous Acidic Solutions. Eur. J. Inorg. Chem. 2014, 2014, 1875–1879. (7) Hu, Y.; Horváth, A. K.; Duan, S.; Csek˝o, G.; Makarov, S. V.; Gao, Q. Mechanism Involving Hydrogen Sulfite Ions, Chlorite Ions, and Hypochlorous Acid as Key Intermediates of the Autocatalytic Chlorine Dioxide–Thiourea Dioxide Reaction. Eur. J. Inorg. Chem. 2015, 2015, 5011–5020. (8) Shao, J.; Liu, X.; Chen, P.; Wu, Q.; Zheng, X.; Pei, K. Structure and Property Investigations of TDO in Aqueous Phase by Density Functional Theory, UV Absorption, and Raman Spectroscopy. J. Phys. Chem. A 2014, 118, 3168–3174. (9) Lewis, D.; Mama, J.; Hawkes, J. An Investigation into the Structure and Chemical Properties of Formamidine Sulfinic Acid. Appl. Spect. 2014, 68, 1327–1332. (10) Mambo, E.; Simoyi, R. H. Kinetics and Mechanism of the Complex Oxidation of Aminoiminomethanesulfinic Acid by Iodate in Acidic Medium. J. Phys. Chem. 1993, 97, 13662–13667. (11) Stanbury, D. M. Comment on the Principle of Detailed Balancing in Complex Mechanisms and Its Application to Iodate Reactions. J. Phys. Chem. A 2018, 122, 3956–3957. (12) Fowler, R. H. Statistical Mechanics, 2nd ed.; Cambridge University Press: London, 1936; pp 659–663. (13) Makarov, S. V.; Mundoma, C.; Penn, J. H.; Petersen, J. L.; Svarovsky, S. A.; Simoyi, R. H. Structure and Stability of Aminoiminomethanesulfonic Acid. Inorg. Chim. Acta 1999, 286, 149–154. (14) Horváth, A. K.; Nagypál, I. Classification of Clock Reactions. ChemPhysChem 2015, 16, 588–594. 24


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(15) IUPAC Stability Constant Database. Royal Society of Chemistry: London, 1992-1997. (16) Peintler, G. Zita/Chemmech, A Comprehensive Program Package for Fitting Parameters of Chemical Reaction Mechanisms. University of Szeged: Szeged, Hungary, 19892017. (17) Kepper, P. D.; Epstein, I. R.; Kustin, K. Bistability in the Oxidation of Arsenite by Iodate in a Stirred Flow Reactor. J. Am. Chem. Soc. 1981, 103, 6121–6127. (18) Papsin, G. A.; Hanna, A.; Showalter, K. Bistability in the Iodate Oxidation of Arsenous Acid. J. Phys. Chem. 1981, 85, 2575–2582. (19) Csek˝o, G.; Valkai, L.; Horváth, A. K. A Simple Kinetic Model for Description of the Iodate–Arsenous Acid Reaction: Experimental Evidence of the Direct Reaction. J. Phys. Chem. A 2015, 119, 11053–11058. (20) Valkai, L.; Horváth, A. K. Compatible Mechanism for a Simultaneous Description of the Roebuck, Dushman, and Iodate–Arsenous Acid Reactions in an Acidic Medium. Inorg. Chem. 2016, 55, 1595–1603. (21) Dushman, S. The Rate of the Reaction Between Iodic and Hydroiodic Acids. J. Phys. Chem. 1904, 8, 453–482. (22) Schmitz, G. Kinetics and Mechanism of the Iodate–Iodide Reaction and Other Related Reactions. Phys. Chem. Chem. Phys. 1999, 1, 1909–1914. (23) Schmitz, G. Kinetics of the Dushman reaction at Low I – Concentrations. Phys. Chem. Chem. Phys. 2000, 2, 4041–4044. (24) Agreda, J. A.; Field, R. J.; Lyons, N. J. Kinetic Evidence for Accumulation of Stoichiometrically Significant Amounts of H2 I2 O3 during the Reaction of I – with IO3 – . J. Phys. Chem. A 2000, 104, 5269–5274.

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(25) Yiin, B. S.; Margerum, D. W. Non-Metal Redox Kinetics: Reaction of Iodine and Triiodide with Sulfite and Hydrogen Sulfite and the Hydrolysis of Iodosulfate. Inorg. Chem. 1990, 29, 1559–1564. (26) Horváth, A. K.; Nagypál, I.; Epstein, I. R. Three Autocatalysts and Self-Inhibition in a Single Reaction: A Detailed Mechanism of the Chlorite–Tetrathionate Reaction. Inorg. Chem. 2006, 45, 9877–9883. (27) Xu, L.; Horváth, A. K. A Possible Candidate to Be Classified as an AutocatalysisDriven Clock Reaction: Kinetics of the Pentathionate–Iodate Reaction. J. Phys. Chem. A 2014, 118, 6171–6180. (28) Xu, L.; Horváth, A. K. Autocatalysis-Driven Clock Reaction II: Kinetics of the Pentathionate–Periodate Reaction. J. Phys. Chem. A 2014, 118, 9811–9819. (29) Turner, D. H.; Flynn, G. W.; Sutin, N.; Beitz, J. V. Laser Raman Temperature-Jump Study of the Kinetics of the Triiodide Equilibrium. Relaxation Times in the 10−8 –10−7 Second Range. J. Am. Chem. Soc. 1972, 94, 1554–1559. (30) Ruasse, M.; Aubard, J.; Galland, B.; Adenier, A. Kinetic Study of the Fast HalogenTrihalide Ion Equilibria in Protic Media by the Raman-Kaser Temperature-Jump Technique. A Non-Diffusion-Controlled Ion-Molecule Reaction. J. Phys. Chem. 1986, 90, 4382–4388. (31) Ramette, R. W.; Palmer, D. A. Thallium(I) Iodate Solubility Product and Iodic Acid Dissociation Constant from 2 to 75 ◦ C. J. Sol. Chem. 1984, 13, 637–646. (32) Strong, L. E.; Pethybridge, A. D. Aqueous Iodic Acid: Conductance and Thermodynamics. J. Sol. Chem. 1987, 16, 841–855. (33) Eigen, M.; Kustin, K. The Kinetics of Halogen Hydrolysis. J. Am. Chem. Soc. 1962, 84, 1355–1361. 26


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(34) Lengyel, I.; Epstein, I. R.; Kustin, K. Kinetics of Iodine Hydrolysis. Inorg. Chem. 1993, 32, 5880–5882. (35) Lengyel, I.; Li, J.; Kustin, K.; Epstein, I. R. Rate Constants for Reactions between Iodine- and Chlorine-Containing Species: A Detailed Mechanism of the Chlorine Dioxide/Chlorite-Iodide Reaction. J. Am. Chem. Soc. 1996, 118, 3708–3719. (36) Furrow, S. Reactions of Iodine Intermediates in Iodate–Hydrogen Peroxide Oscillators. J. Phys. Chem. 1987, 91, 2129–2135. (37) Biesiada, M.; Kourkoumelis, N.; Kubicki, M.; Owczarzak, A. M.; Balas, V.; Hadjikakou, S. K. Fundamental Chemistry of Iodine. The Reaction of Di-Iodine Towards Thiourea and Its Methyl-Derivative: Formation of Aminothiazoles and Aminothiadiazoles Through Dicationic Disulfides. Dalton Trans. 2014, 43, 4790–4806. (38) Sexton, A.; Mbiya, W.; Morakinyo, M. K.; Simoyi, R. H. Kinetics and Mechanism of the Oxidation of N-Acetyl Homocysteine Thiolactone with Aqueous Iodine and Iodate. J. Phys. Chem. A 2013, 117, 12693–12702.

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Table of Contents Synopsis The thiourea dioxide (TDO)–iodate system was found to be an autocatalysis-driven clock reaction. The Landolt time depends on the concentration of the reactants, the pH and that of the iodide as well as the age of TDO stock solution. A 16-step kinetic model is proposed to describe the kinetic data quantitatively.

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TOC Graphic Autocatalysis-driven Clock Reaction Formation of Iodine Low and High pH, Excess of Iodate Absorbance at 468 nm

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


t1 t1

t2

t2

t

t1

t2

t

Low pH, Excess of TDO t

High pH, Excess of TDO

Time (s)

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Autocatalysis-Driven Clock Reaction III: Clarifying the Kinetics and

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