Exact Concentration Dependence of the Landolt Time in the Thiourea

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Exact Concentration Dependence of the Landolt Time in the Thiourea Dioxide–Bromate Substrate-Depletive Clock Reaction György Csek#, Qingyu Gao, Attila Takács, and Attila K. Horváth J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02025 • Publication Date (Web): 18 Apr 2019 Downloaded from http://pubs.acs.org on April 18, 2019

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The Journal of Physical Chemistry

Exact Concentration Dependence of the Landolt Time in the Thiourea Dioxide–Bromate Substrate-Depletive Clock Reaction György Csek˝o,†,‡ Qingyu Gao,∗,† Attila Takács,¶ 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 ¶MTA-PTE Research Group for Selective Syntheses, University of Pécs, Ifj´ uság u. 6, Pécs, Hungary, H-7624 E-mail: [email protected]; [email protected] Abstract The thiourea dioxide–bromate 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 title system shows a remarkable resemblance to the classical Landolt reaction, namely the clock species (bromine) may only appear after the substrate thiourea dioxide (TDO) is completely consumed. Thus the title system can be classified as a substrate-depletive clock reaction. Despite the well-known slow rearrangement characteristic of TDO in acidic solution it is surprisingly found that the Landolt time of the title reaction does not depend at all on the age of TDO solution applied. It is, however, shown experimentally that the inverse of Landolt time linearly depends on the initial

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bromate concentration as well as on the square of the hydrogen ion concentration. In addition to this it is also noticed that dihydrogen phosphate markedly affects the Landolt time as well, and this feature may easily be taken into consideration by the H2 PO4 – dependence of the rate of bromate–bromide reaction quantitatively. Based on the experiments a simple 3-step kinetic model is proposed from which a complex formula is derived to indicate the exact concentration dependence of the Landolt time.

Introduction Chemical compounds including thioureido group are one of the most biologically active moieties. Among them the simplest one is thiourea from which several therapeutic drugs 1–3 may be derived by substitution of the hydrogen by suitable functional groups. (see: Fig0

ure S8 in the supporting information) Derivative of thiourea, like N, N -dimethylthiourea (DMTU), is for example a well-known and effective scavenger of toxic oxygen metabolites removing rapidly in vitro hydrogen-peroxide, hydroxyl radicals and hypochlorous acid. 4–8 Another medically important derivative of thiourea is guanylthiourea (GTU) which is generally used as a stimulator of intestinal peristalsis. 9 Furthermore, S-allyl-GTU has been tested as a promising immunostimulant and tumor inhibitor. 10,11 In addition to that GTU is extensively used in industry due to its special structure. It enables to be used in the synthesis of anion-caged supramolecular compounds 12 and in vulcanization of natural rubber. 13,14 As seen these species are extensively involved in biological and technological processes, and they are considered as reactive agents, therefore firm knowledge of the fundamental background of their redox transformations is eagerly expected. Strong oxidizing agents like bromate in acidic conditions are supposed to oxidize thiourea or its derivatives essentially to sulfate via the successive formation of the corresponding sulfenic, sulfinic and sulfonic acids as intermediates. The stability of these species depends on the nature of substitutes on the amino functional group. For instance thiourea trioxide (TTO) is considered to be a relatively longlived intermediate that is responsible for the delay of formation of sulfate as a final product in 2


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case of the thiourea–bromate reaction. 15 Furthermore, the guanylthiourea–bromate system was found to proceed in two different pathways, the first one includes the stepwise oxidation of GTU via the corresponding sulfenic, sulfinic and sulfonic acids, and the second one starts with the formation of ring-cyclized 3,5-diamino-1,2,4-thiadiazole followed by its successive oxidation to sulfoxide and sulfone eventually leading to produce finally sulfate and guanylurea via a ring-opening mechanism. 16 In case of the DMTU–bromate reaction ESI experiments provided no clear evidence for the detectable formation of any S-oxygenated DMTU species. 17 Similar to this, no S-oxygenated trimethylthiourea (TMTU) was detected in the TMTU–bromate reaction. 18 In contrast to this, however, when tetramethylthioura (TTTU) is oxidizied by bromate in an acidic condition then tetramethyl-aminoiminomethanesulfenic acid is found to be a relatively long-lived intermediate playing a key role in determining the nonlinearity of the reaction. 19 Since all the above mentioned reactions display clock behavior 20 it looks to be crucial to understand the kinetic role of the intermediates formed during the oxidation of substituted thioureas. Thiourea dioxide (TDO) in itself has a widespread interest in chemistry and chemical technology, 21,22 and is commercially available, clarification of the intimate details of the kinetics of TDO–bromate reaction may serve as a suitable template to resolve the problems arisen in similar systems mentioned above. The first important fact that one should take care of is that TDO — even acidic conditions — relatively slowly but steadily rearranges into a more reactive form, 23 whose reactions are reported to be much faster with the corresponding oxidants than the original form of TDO. It is still unresolved whether this rearrangement is the consequence of a tautomerism 24,25 or of an oligomer–monomer degradation 26 or even of an aminoimino–carbenoid transformation 27 it is indisputably clear that this characteristic must be taken into consideration when the kinetics of the redox transformation of TDO is designed to be investigated. Overlooking the possible kinetic effect of aging is not the only inconsistency that may be found. In studying the kinetics and mechanism of the thiourea–bromate system Simoyi et al. reported 15 the rate coefficients of the TDO–bromine

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reaction to be 100 M−1 s−1 while in the same issue of the same journal direct study of the TDO–bromate reaction 28 a value of 5×106 M−1 s−1 was assigned to the same reaction. Furthermore the supporting information contains the result of the simulation done by the Chinake’s model 28 to compare the simulated curves with their own experimental results. It is out of question that the model is not capable of providing even a semiqualitative agreement between measured and calculated data. More importantly, Chinake’s model does not work unless a small, but trace amount of initial bromide impurity is introduced. Unfortunately, no clear information is provided about it in their original report. This kind of inconsistency may as well be found after inspecting the reports on the kinetics of the DMTU–bromate 17 and 0

the N, N -dimethylaminoiminomethanesulfinic acid–bromate 29 reaction. Our motivation to reinvestigate the TDO–bromate reaction was to provide a firmly established kinetic model to describe the major characteristics of this reaction and if possible elucidate the clock feature of this system to give the exact concentration dependence of the Landolt time.

Experimental Section Materials. All the chemicals (sodium bromate (Sigam-Aldrich), sodium and potassium bromide (Reanal), cc. phosphoric acid 85 % (Xilong Scientific and Sigma-Aldrich), sodium dihydrogen phosphate dihydrate (Sinopharm Chemical Reagent Co Ltd and Sigma-Aldrich), TDO (Sigma-Aldrich), barium chloride (Reanal) and sodium perchlorate(Merck)) were of the highest purity commercially available and were used without further purification. All stock solutions were prepared by oxygen-free (argon gas was bubbled through) distilled water — having a resistivity of 18.2 MΩ cm — obtained from a Milli-Q purification system. The TDO stock solutions were freshly prepared before each measurement. The age of TDO stock solution was kept constant at 300 ± 5 s except those cases where the effect of aging was studied. The ionic strength in the stock solutions was set to 1.0 M by sodium perchlorate. 4


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The pH of solutions (pH = −log[H+ ]) was regulated between 1.1 and 1.8 by phosphoric acid/dihydrogen phosphate buffer taking the pKa1 of phosphoric acid as 1.8. 30 This value worked consistently well in a number of systems investigated previously. 31–33 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 o C.

Methods and Instrumentation The reaction was monitored 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 carried out in a standard quartz cuvette equipped with magnetic stirrer and a Teflon cap having 10.00 mm optical path. The buffer components, the bromate were delivered from a pipet first into the cuvette. In case of the TDO–bromate system, the reaction was initiated by the addition of the necessary amount of TDO solution from a fast delivery pipet. This stock solution also contained the calculated amount of bromide (if necessary). When the bromate–bromide subsystem was investigated, the reaction was initiated by introducing the necessary amount of the bromide solution from a fast delivery pipette. The spectra of reacting solution at the wavelength range of 400–800 nm 13

were acquired up to approximately one day.

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 carried out at 400 nm, where the molar absorbance of bromine and tribromide ion was found to be 174.03 M−1 cm−1 and 445.68 M−1 cm−1 , respectively. The Landolt time defined corresponds to the time when the clock event starts for each experiment. These values were determined directly from the absorbance–time curves, when the measured absorbance values statistically differed from zero for the first time at the 5



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given experiment. The nonlinear parameter estimation was performed by the program package ZiTa/Chemmech. 34 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 timeconsuming calculations. Altogether, including the TDO–bromate and the bromate–bromide systems, more than 6500 experimental points of 107 measured curves were used for data evaluation to establish the kinetic model and to determine the corresponding rate coefficients.

Results The qualitative picture of our preliminary studies clearly supports Chinake et al’s important finding that at suitable experimental condition the title reaction has a clock feature. The formation of bromine is delayed in stoichiometric excess of bromate, but the clock species never appears in TDO excess. It means that the TDO–bromate system may be considered as a prototype of the original Landolt reaction 35 that is classified as a substrate-depletive clock reaction. 20 The Landolt time measured therefore provides a suitable possibility to analyze the concentration dependence of the Landolt time from which a reliable kinetic model may be deduced. Figure 1 indicates the inverse of Landolt time varying the initial concentration of bromate and TDO meanwhile keeping the rest of the conditions constant in each series. As it is seen initial bromate concentration strongly affects the Landolt time, the larger the bromate concentration is the shorter is the Landolt time to be measured. This result is in complete agreement with Chinake’s report. 28 In contrast to this, however, under our experimental conditions, TDO does not have a pronounced effect on the Landolt time, it has only a subtle role, though it seems to be well-established that increase of TDO concentration slightly increases the Landolt time under our experimental conditions. Unfortunately, this feature has never been reported and analyzed in Chinake’s paper. Figure 2 shows that inverse of the Landolt time against the square of the hydrogen

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Figure 1: Inverse of the measured Landolt time against the initial concentration of the reactants in absence of initially added bromide ion. Conditions are as follows: (black) [TDO]0 = 1.3 mM, pH = 1.1, X-axis corresponds to [BrO3 – ]0 ; (blue) [BrO3 – ]0 = 1.7 mM, pH = 1.4, X-axis corresponds to [TDO]0 . [H2 PO4 – ]0 = 0.25 M and the age of the stock TDO solution was kept constant at 300 s for all the experiments. ion concentration. A nice linear relationship passing through the origin is found, agreeing soundly with Chinake’s report. 28 As expected addition of bromide significantly shortens the induction period, the inverse of Landolt time shows nonlinear characteristic against the initial bromide concentration (see: Figure 3). This behavior is in complete agreement with the results reported by Chinake et al. 28 Finally, we have also noticed that varying the concentration of the buffer components, meanwhile keeping rest of the initial conditions constant, also has a dramatic effect on the Landolt time. Figure 4 indicates that if the concentration of the buffer components is tripled then the Landolt time decreases by almost an order of magnitude. Such an unexpected huge effect of the buffer components has not been recognized so far.

Effect of the Age of TDO solution As it was previously shown aging of TDO solution has a significant effect on the kinetic runs in case of the chlorine dioxide–TDO 24,25 and iodine–TDO 23 reactions. In addition to

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Figure 2: Inverse of the measured Landolt time against the square of the hydrogen ion concentration in absence of initially added bromide ion. Conditions are as follows: [TDO]0 = 3.5 mM, [BrO3 – ]0 = 3.4 mM. [H2 PO4 – ]0 = 0.25 M and the age of the stock TDO solution was kept constant at 300 s for all the experiments.

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Figure 3: Inverse of the measured Landolt time against the bromide ion concentration. Conditions are as follows: [TDO]0 = 3.0 mM, [BrO3 – ]0 = 3.4 mM and pH = 1.4. [H2 PO4 – ]0 = 0.25 M and the age of the stock TDO solution was kept constant at 300 s for all the experiments.

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Figure 4: Inverse of the measured Landolt time against the H2 PO4 – concentration in absence of initially added bromide ion. Conditions are as follows: [TDO]0 = 3.5 mM, [BrO3 – ]0 = 3.6 mM and pH = 1.25. The age of the stock TDO solution was kept constant at 300 s for all the experiments. this our research group revealed that the same phenomenon occurs in case of the TDO– iodate reaction as well. 33 The general feature of these systems is that aging appreciably accelerates the reactions, sometimes even the shape of kinetic curves is also significantly altered. 24 Explanation of this experimental finding is that during the aging process initial form of TDO changes into a more reactive form resulting in acceleration of the reaction. We expected something similar in the title TDO–bromate system as well, therefore a series of kinetic runs is performed when the age of TDO solution was varied between 5 min and 3 days. Since the half-life of the initial form of TDO under present circumstances is around 4.1 days, 33 it means almost 40% of the initial TDO must be transformed into its more reactive form, thus significant accelerating effect could be expected. The results are presented in Figure 5. In contrast to our expectation, however, quite surprisingly we found no aging effect in the TDO–bromate system, the measured curves, regardless the age of TDO solution, coincide each other within the experimental error. A possible explanation of this observation will be discussed later.

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Absorbance at 400 nm


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Figure 5: Measured (symbols) and calculated (solid lines) absorbance–time profiles at 400 nm in the TDO–bromate reactions. Conditions are as follows: [TDO]0 = 3.5 mM, [BrO3 – ]0 = 3.4 mM and pH = 1.4. Ages of the stock TDO solution in seconds: 300 (black), 6053 (blue), 11813 (green), 81143 (cyan), 102623 (red), 162623 (magenta), 275700 (orange).

Individual evaluation of the kinetic curves All these experimental results appear to suggest that a simple Landolt-type kinetic model is able to describe all the characteristics of the measured curves. Therefore the following kinetic model is used to evaluate the experimental data individually: k

i1 3TDO + 2BrO3− −→ N, C−containing products + 3SO42− + 2Br−

(1)

v1 = ki1 [TDO][BrO3− ][H+ ]2 k

i2 5Br− + BrO3− + 6H+ −→ 3Br2 + 3H2 O

(2)

v2 = ki2 [Br− ][BrO3− ][H+ ]2 k

i3 TDO + 2Br2 −→ SO42− + 4Br− + N, C−containing products

(3)

v3 = ki3 [TDO][Br2 ] − Br2 + Br− − )− −* − Br3

v4 = ki4 [Br2 ][Br− ] − k−i4 [Br3− ] 10


(4)

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Step 1 is of course a complex reaction that leads eventually to the formation of bromide ion. The nitrogen- and carbon containing end-products of this reaction is not unambiguous. 13

C-NMR studies clearly showed that in excess of bromate cyanamide is the main product,

however, in TDO excess a major peak appears at 162.57 ppm belonging to urea, but characteristics shift of cyanamide as well as that of dissolved carbon dioxide may also be visible (see: Figure S3 of the Supporting Information). Since the nitrogen- and carbon-containing products do not participate in the redox transformation hereafter they are mentioned as N,C-containing products. The key species, bromide, is then oxidized by bromate to form bromine in Step 2 and finally bromine reacts with TDO in a rapid reaction to reform bromide and thus closing the autocatalytic cycle. The pH dependence of Step 1 may be deduced from Figure 2 that indicates a perfect linear relationship between the Landolt time and the inverse of [H+ ]2 . It should be noted, however, that Chinake et al. suggested 28 this initiation with just a [H+ ]-dependence in its rate law. Since this is one of the rate-determining step of their kinetic model one would straightforwardly pose a question how this proposal may be augmented with their experimental findings that agrees well with our ones. The explanation is simple, they included trace impurities of bromide ion (5×10−6 M) which is enough to drive the overall reaction via sequence of Steps 2 and 3, consequently Step 1 was not needed anymore to initiate the reaction. Certainly, the rate determining step in their kinetic model is therefore Step 2 whose rate law is proportional to the square of hydrogen ion concentration as it was established previously by numerous research groups independently. 36–39 Step 3 is a very rapid process that is way out of the timescale of a stopped-flow instrument, therefore the rate coefficient of this reaction cannot be determined under our experimental condition, so it was fixed at a value of 106 M−1 s−1 during the whole calculation procedure.

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C-NMR

studies revealed that in excess of TDO after the reaction is completed, again mixture of urea, cyanamide and dissolved carbon dioxide may as well be detected. (see: Supporting Information, Figure S2) Therefore part of the products of the TDO–bromine reaction is given in general as nitrogen- and carbon-containing end-products.

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All the kinetic measurements were evaluated by the simple Steps 1–3 kinetic model with two fitted (ki1 and ki2 ) parameters. The values were then averaged to come up with ki1 = 361 ± 77 M−3 s−1 and ki2 = 27.7 ± 7.2 M−3 s−1 as overall rate coefficients. The fit was found to be very sound, the average deviation of the kinetic curves was varied between 0.3 % to 2.8 % though some trends may be observed in case of the individually determined ki2 values. This trend was found to be more pronounced in case of those kinetic curves where the effect of pH and that of the buffer components concentration were investigated. Lower pHs and higher [H2 PO4 – ] values result in a larger ki2 value. Thus we concluded that the apparent ki2 value has to depend on the buffer concentration as well. In order to unravel it unambiguously the bromide–bromate reaction was studied independently under the same experimental condition as in case of the title reaction.

Kinetics of the bromide–bromate reaction The kinetics of bromide–bromate reaction was first studied by Judson and Walker, 40 who reported the widely accepted rate law for this reaction including a first order dependence on bromide as well as bromate ion concentrations and a second-order dependence on hydrogen ion concentration. Later, it was also shown that this rate law, especially at higher bromide concentrations, has to be supplemented by a second term that is second order with respect to bromide ion. 41–44 Furthermore, Cortes and Faria have recently proven 39 that this rate law is even much more complex and buffer catalysis in case of acetate should also be taken into consideration. One therefore easily conclude if the bromate–bromide reaction is subject to general acid catalysis then phosphoric acid/dihydrogen phosphate buffer may as well enhance the rate of this reaction. We have therefore performed additional experiments to unravel quantitatively the dihydrogen phosphate catalysis and to determine the corresponding rate coefficients by nonlinear parameter estimation. Substantial effect of the dihydrogen phosphate concentration is demonstrated in Figure 6. As it is clearly seen five times higher H2 PO4 – concentration enhances the rate of formation 12


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Figure 6: Measured (symbols) and calculated (solid lines) absorbance–time profiles at 400 nm in the bromate–bromide reaction. Conditions are as follows: [Br – ]0 = 9.38 mM, [BrO3 – ]0 = 1.88 mM and pH = 1.6. [H2 PO4 – ]/mM = 86.9 (black), 158 (blue), 227 (green), 295 (cyan), 364 (red), 477 (magenta). of bromine quite substantially. To quantify its effect and to establish a suitable rate equation describing the kinetics of the bromate–bromide reaction initial rate studies have also been performed and the results are shown in Figure 7. Figure 7A indicates that the formal kinetic orders of bromate and bromide ions are clearly unity in a complete agreement with previous studies, but that of hydrogen ion was found to be 2.19 ± 0.06. The latter value indicates a bit higher one than the generally accepted 2. In addition to that the dependence of initial rate on the H2 PO4 – concentration is illustrated in Figure 7B. The measured data may only be fitted by a second-order polynomial function meaning that the effect of H2 PO4 – seems to be quite complex. This observation is in a sound accordance with the results published by Cortes and Faria. 39 They found even a much more complicated effect of acetate buffer resulting in a six-term rate law. The measured absorbance–time series (at 67 different initial conditions) can soundly be fitted by eqs. 2 and 4, where 00

0

v2 = (k2 + k2 [H2 PO4− ] + k2 [H+ ][H2 PO4− ]2 )[H+ ]2 [Br− ][BrO3− ].

(5)

Nonlinear parameter estimation leads to the following rate coefficients: k2 = 4.01 ± 0.26 M−3 s−1 , 0

00

k2 = 25.97 ± 1.71 M−4 s−1 and k2 = 5573 ± 161 M−6 s−1 . Comparing these results with 13



A

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Figure 7: A: Results of the initial rate studies to determine the formal kinetic orders of the reactants. Conditions are as follows: Black curve: [Br – ]0 = 2.81 mM, pH = 1.8, the logarithm of initial bromate concentration is indicated in the X-axis. Blue curve: [BrO3 – ]0 = 0.376 mM, pH = 1.25, the logarithm of initial bromide concentration is indicated in the X-axis. Green curve: [Br – ]0 = 3.75 mM, [BrO3 – ]0 = 0.751 mM, the logarithm of hydrogen ion concentration is indicated in the X-axis. The slopes of straight lines were found to be 1.01 ± 0.02, 1.06 ± 0.03 and 2.19 ± 0.06, respectively in case of the black, blue and green curves. B: Plot of the initial rate versus H2 PO4 – concentration. The solid line represents the second-order polynomial fit of the experimental points.

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the one reported by Cortes and Faria 39 it is important to note that all these terms may also be found in their rate law suggesting that general buffer assistance has a substantial role in determining the kinetics of the bromate–bromide reaction. Comparing the value of k2 (buffer independent rate coefficient) presented here and the ones reported by Cortes and Faria 39 as well as by Schmitz 44 or Rábai 43 — being respectively 4.12 M−3 s−1 , 2.18 M−3 s−1 and 3.6 M−3 s−1 — supports the present kinetic model. The quality of fit is illustrated in Figures 8A, 8B and 8C as the initial concentration of bromate, bromide and the pH are varied.

Proposed Kinetic Model Combining the results of individual evaluation of the kinetic curves in the TDO–bromate reaction and that of the simultaneous evaluation performed in the bromate–bromide reaction a simple kinetic model is proposed to describe quantitatively all the measured kinetic curves in case of the TDO–bromate and the bromate–bromide reactions. The kinetic model used for simultaneous data evaluation is summarized in Table 1. The rate coefficients of the bromide– bromate reaction were also fitted along with k1 when all the measured kinetic curves in these system were used for data evaluation. As a result all the measured (117) kinetic traces can be described by 1.5% average deviation indicating a sound agreement between the measured and calculated data in both systems. The quality of fit is illustrated in Figures 9, 10, 11, 12 and 13. It should be noted that the formation constant of tribromide ion was fixed as 18.06 M−1 used successfully in a tetrathionate–bromine system 45 and this value is a sound agreement with the values found by independent research groups. 46,47 (E2) equilibrium is rapidly established, rate coefficient of the reverse reaction was fixed 48 as reported previously, and the value of the forward rate coefficient was set to 9.03×108 M−1 s−1 to provide the formation constant of tribromide ion as shown above.

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10000 20000 30000 40000 50000 60000 70000

Time (s)

Figure 8: Measured (symbols) and calculated (solid lines) absorbance–time series in the bromate–bromide reaction at 400 nm. Conditions are as follows: (A) [Br – ]0 = 3.75 mM, pH = 1.6, [BrO3 – ]0 /mM = 0.376 (black); 0.751 (blue); 1.50 (green); 2.25 (cyan); 3.01 (red); 4.51 (magenta). (B) [BrO3 – ]0 = 1.5 mM, pH = 1.4, [Br – ]0 /mM = 1.88 (black); 3.75 (blue); 7.51 (green); 11.3 (cyan); 15.0 (red); 18.8 (magenta). (C) [Br – ]0 = 3.75 mM , [BrO3 – ]0 = 0.751 mM, pH = 1.1 (black); 1.25 (blue); 1.4 (green); 1.6 (cyan); 1.8 (red).

16


Page 17 of 32


0.08

0.06

0.04

0.02

0 0

500

1000

1500

2000

2500

3000

Time (s)

Figure 9: Measured (symbols) and calculated (solid lines) absorbance–time profiles at 400 nm in the TDO–bromate reaction in absence of initially added bromide ion. Conditions are as follows: [TDO]0 = 1.6 mM and pH = 1.4. [BrO3 – ]0 /mM = 5.63 (black), 3.76 (blue), 3.01 (green), 2.25 (cyan), 1.69 (red).


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


0.16

0.12

0.08

0.04

0 0

2000

4000

6000

8000

Time (s)

Figure 10: Measured (symbols) and calculated (solid lines) absorbance–time profiles at 400 nm in the TDO–bromate reaction. Conditions are as follows: [TDO]0 = 3.0 mM, [BrO3 – ]0 = 3.4 mM and pH = 1.4. [Br – ]0 /mM = 0.0 (black), 0.052 (blue), 0.104 (green), 0.172 (cyan), 0.259 (red), 0.345 (magenta), 0.431 (brown), 0.603 (yellow), 0.689 (purple).

17


Page 18 of 32

0.2

0.15

0.1

0.05

0 0

10000

20000

30000

40000

Time (s)

Figure 11: Measured (symbols) and calculated (solid lines) absorbance–time profiles at 400 nm in the TDO–bromate reaction in absence of initially added bromide ion. Conditions are as follows: [TDO]0 = 1.6 mM and [BrO3 – ]0 = 3.8 mM. pH = 1.8 (black), 1.6 (blue), 1.4 (green), 1.25 (cyan), 1.1 (red).

0.2


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



0.16 0.12 0.08 0.04 0 0

2000

4000

6000

8000

Time (s)

Figure 12: Measured (symbols) and calculated (solid lines) absorbance–time profiles at 400 nm in the TDO–bromate reaction in absence of initially added bromide ion. Conditions are as follows: [TDO]0 = 3.5 mM and [BrO3 – ]0 = 3.4 mM, pH = 1.4. [H2 PO4 – ]/M = 0.0976 (black), 0.166 (blue), 0.229 (green), 0.291 (cyan).

18


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Table 1: Rate equations used and rate coefficients obtained from evaluating simultaneously the kinetic data of the TDO–bromate and the bromate–bromide reaction. Note that water and H+ may be missing for (M1) and (M3) equation because the end-products are a mixture of different C,N-containing products. No.

Step

(E1)

+ – −− H3 PO4 ) −* − H +H2 PO4

(E2)

– Br2 +Br – − )− −* − Br3

(M1)

3TDO+2BrO3 – →3SO42 – +2Br – +C,N−containing products –

–

+

(M2) 5Br +BrO3 +6H →3Br2 +3H2 O (M3)

TDO+2Br2 →SO42 – +4Br – +C,N−containing products

Rate equation kE1 [H3 PO4 ] k−E1 [H+ ][H2 PO4 – ] kE2 [Br2 ][Br – ] k−E2 [Br3 – ]

Rate coefficient 1.585×105 s−1 107 M−1 s−1 9.03×108 M−1 s−1 5×107 s−1

k1 [TDO][BrO3 – ][H+ ]2

365±3 M−3 s−1

k2 [Br – ][BrO3 – ][H+ ]2 0 k2 [Br – ][BrO3 – ][H+ ]2 [H2 PO4 – ] 00 k2 [Br – ][BrO3 – ][H+ ]3 [H2 PO4 – ]2

3.11±0.19 M−3 s−1 36.34±0.92 M−4 s−1 5534±58 M−6 s−1

k3 [TDO][Br2 ]

106 M−1 s−1

Discussion The most surprising result reported here is certainly the highly unexpected experimental observation that the kinetic traces measured in the title reaction — within the aging time range studied — do not depend on the age of the TDO stock solution in contrast to our previous reports on the TDO–chlorine dioxide, 24,25 TDO–iodine 23 and TDO–iodate 33 reactions. Actually, this is the first reaction of TDO investigated by our research group where, even though the aging of TDO solution in acidic condition is a well-established feature, no effect was found. In all the previously measured systems the aging effect is attributed to a slow but steady rearrangement of TDO upon dissolving along with the fact that the reactivity of original form of TDO and that of the aged one significantly differ from each other. In case of the TDO–iodate reaction 33 we found that the aged form of TDO reacts significantly more rapidly with iodate and iodine resulting in shorter and shorter Landolt time. The present system, however, suggests that there is no difference between the reactivities of the aged and the original form of TDO towards bromate and bromine as well. Because the TDO– bromine reaction is very fast even in very fresh TDO solution there supposed to be no room 19



0.06


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

0.05 0.04 0.03 0.02 0.01 0 0

2000

4000

6000

Time (s)

Figure 13: Measured (symbols) and calculated (solid lines) absorbance–time profiles at 400 nm in the TDO–bromate reaction in absence of initially added bromide ion. Conditions are as follows: [BrO3 – ]0 = 1.8 mM and pH = 1.4. [TDO]0 /mM = 0.5 (black), 0.77 (blue), 1.12 (green), 1.70 (cyan), 1.91 (red), 2.28 (magenta), 2.59 (brown). for further acceleration when TDO is aging. The most important outcome of the present experiments that the reactivity of the two different forms of TDO does not differ too much towards bromate ion. The other remarkable characteristics of the kinetic curves is that the buffer concentration notably affects the Landolt time. This feature, however, can quantitatively be explained by the buffer dependence of the bromate–bromide reaction as shown previously. A word is also in an order here to highlight that Chinake et al. 28 suggested that TTO can be accumulated at the beginning stage of the reaction and sulfate may only appear simultaneously with bromine. Unfortunately, we provided an experimental proof that sulfate forms well in advance bromine would appear as shown in the Supporting Information (see: Figures S4 and S7). Furthermore, in TDO excess our 13 C-NMR studies gave no evidence for an appearance of TTO as a long-lived intermediate. Thus we concluded that TTO can only be a short-lived intermediate of the title reaction. Finally, it was also shown previously that the inverse of the measured Landolt times depends linearly on the concentration of bromate and on [H+ ]2 . In addition to that the TDO–bromate system is a substrate-depletive clock reaction 20 because the substrate (TDO)

20


Page 20 of 32

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has to be totally consumed before the clock species bromine appears. Therefore it is possible to deduce an analytical formula of the concentration dependence of the Landolt time just like in case of the classical Landolt reaction. 49

Concentration dependence of the Landolt time To derive a formula indicating the exact concentration dependence of the Landolt time one should consider the following simple kinetic model: k

L1 3 A + 2 B −→ 2 C + 6 H + P;

k

L2 5 C + B + 6 H −→ 3 D;

k

L3 A + 2D −→ 4 C + 4 H,

vR1 = kL1 [A][B]

(R1)

vR2 = kL2 [C][B]

(R2)

vR3 = kL3 [A][D]

(R3)

where A, B, C, D, H and P correspond to TDO, bromate, bromide, bromine, hydrogen ion and products. According to Table 1 it is easy to see that the following equalities stand:

kL1 = k1 [H+ ]2

(6)

and 0

00

kL2 = (k2 + k2 [H2 PO4− ] + k2 [H+ ][H2 PO4− ]2 )[H+ ]2 .

(7)

Considering that steady-state approximation holds for species D (bromine) during the course of the induction period we obtain:

2kL3 [A][D] = 3kL2 [C][B]

21


(8)


Page 22 of 32

According to Steps R1–R3 the concentration of C (bromide) is governed by the following differential equation after substitution of eq. 8: dC = 2vR1 − 5vR2 + 4vR3 = 2kL1 [A][B] + kL2 [C][B] dt

(9)

If concentration of hydrogen ion is kept constant during the course of the reaction, i.e. buffer is applied, then eq. 9 may be rewritten as follows: dx 3 = 2kL1 ([A]0 − x)([B]0 − x) + kL2 x([B]0 − x) dt 2

(10)

where x is the reaction coordinate, and subscript zero means the initial concentration of the given species. Taking into consideration that bromine appears only when species A is totally consumed (i.e. x reaches 2/3[A]0 ) then rearrangement of eq. 10 leads to Z

2 [A]0 3

0

1 dx = (2kL1 [A]0 + (kL2 − 3kL1 )x)([B]0 − x)

Z

tL

dt

(11)

0

After integrating eq. 11 followed by some algebraic manipulation finally we arrive at the following expression:

tL

1 = ln 2kL1 [A]0 + (kL2 − 3kL1 )[B]0

kL2 [B]0 3kL1 ([B]0 − 23 [A]0 )

,

(12)

If bromide ion is initially added then eq. 10 is modified to the following expression dx 3 = 2kL1 ([A]0 − x)([B]0 − x) + kL2 ([C]0 + x)([B]0 − x) dt 2

(13)

leading to Z 0

2 [A]0 3

1 dx = (2kL1 [A]0 + kL2 [C]0 + (kL2 − 3kL1 )x)([B]0 − x)

22


Z

tL

dt 0

(14)

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Finally, integration and a subsequent algebraic rearrangement results in the following expression: 1 ln tL = 2kL1 [A]0 + kL2 [C]0 + (kL2 − 3kL1 )[B]0

kL2 ([C]0 + 32 [A]0 )[B]0 (2kL1 [A]0 + kL2 [C]0 )([B]0 − 32 [A]0 )

, (15)

where [C]0 is the initial bromide concentration. Upon deriving eqs. 12 and 15 the following statements may be obtained: • Since kL1 and kL2 are both proportional to the square of the hydrogen ion concentration, the inverse of Landolt must as well be proportional to [H+ ]2 as found experimentally. • The dependence of Landolt time on [H2 PO4 – ] may directly be understood via the dihydrogen phosphate concentration dependence of kL2 . • If bromate is applied in high excess then eq. 12 may be simplified to

tL =

1 kL2 ln (kL2 − 3kL1 )[B]0 3kL1

from which anyone can straightforwardly conclude that the inverse of Landolt time is linearly proportional to the initial bromate concentration as shown experimentally. • Applying bromide in high excess eq. 15 may be rearranged to

tL =

[B]0 1 ln kL2 [C]0 [B]0 − 32 [A]0

from which one can easily see that the inverse of Landolt time has to be proportional to the initial bromide concentration.

23



Conclusion In this paper the kinetics and mechanism of the TDO–bromate reaction was reinvestigated. It has been illustrated that the title system is a substrate-depletive clock reaction and a relatively simple kinetic model is able to explain the main kinetic features found experimentally. Surprisingly, in contrast to previous studies 23–25,33 the shape of the measured curves or Landolt necessary for the sudden appearance of clock species does not depend at all on the age of stock solution. This feature may easily be interpreted by the following way. Reactivity of the two different forms of TDO towards bromate does not differ from each other and the reaction between fresh form of TDO with elemental bromine in itself is fast enough not to make any further difference if we compare it with the rapidness of the aged TDO–bromine reaction. This may happen when the original reaction is close to the diffusion control limit. As a result even though TDO ages, it does not have any influence on the kinetic curves measured in case of the TDO–bromate reaction. The most important consequence of the results presented here is that depending on the nature of the oxidizing agent redox reactions may or may not be affected by the age of TDO solution, thus it is advisable to check this possibility prior to start any detailed investigation of any oxidation reactions of TDO. Although this report does not provide an unambiguous answer of the aging process but at the same time it is strongly believed that the information detailed above provides further insight into the chemical background of the secret, but so far undiscovered nature of the aging process of TDO.

Supporting Information Comparison of the measured and simulated absorbance–time traces in case of the Chinake et al.’s model, as well as the results of

13

C NMR studies can be found in the supporting

information.

24


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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 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. A. T. is thankful for the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The authors thank K. V. Csek˝o for her expertise programming assistance provided during data processing.

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nique. A Non-Diffusion-Controlled Ion-Molecule Reaction. J. Phys. Chem. 1986, 90, 4382–4388. (49) Horváth, A. K.; Nagypál, I.; Csek˝o, G. Theoretical Investigation on the Concentration Dependence of the Landolt Time. J. Phys. Chem. A 2008, 112, 7868–7872.

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TOC Graphic

Substrate-Depletive Clock Reaction zz

Absorbance

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

Page 32 of 32

Time (s)

32


??

Exact Concentration Dependence of the Landolt Time in the Thiourea

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