Autocatalysis-Driven Clock Reaction II: Kinetics of the Pentathionate

Article pubs.acs.org/JPCA

Autocatalysis-Driven Clock Reaction II: Kinetics of the Pentathionate−Periodate Reaction Li Xu and Attila K. Horváth* Department of Inorganic Chemistry, University of Pécs, Ifjúság útja 6., Pécs H-7624, Hungary ABSTRACT: The pentathionate−periodate reaction has been investigated by spectrophotometrically monitoring the total amount of iodine evolved in the presence of phosphoric acid/dihydrogen phosphate buffer at 468 nm. The majority of the main characteristics of the title system is very reminiscent of that found recently in the pentathionate−iodate reaction, a system that led us to classify generally the clock reactions. Along with the pentathionate−iodate reaction the title system is proposed to belong to the autocatalysis-driven clock reactions as well. The kinetic model of the pentathionate−iodate system published recently was implemented by the necessary reactions of periodate to compose a 24-step kinetic model in which the mechanisms of the pentathionate−iodine, pentathionate−iodate, bisulfite−periodate, bisulfite− iodate, iodide−periodate, and the well-known Dushman reactions are combined. A thorough analysis revealed that the direct pentathionate− periodate reaction plays a role only to produce iodide ion via a finite sequence of reactions, and once its concentration reaches a certain level, the reaction is almost exclusively governed by the pentathionate− iodine, the iodide−periodate, and the Dushman reactions. As expected strong catalytic effect of the buffer composition is also found that can readily be explained by its well−known catalytic influence on the Dushman reaction.

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INTRODUCTION Although Landolt’s original discovery about the sulfite−iodate reaction dates back to more than a century,1,2 the system as a tool to investigate several spatial nonlinear dynamical phenomena has been living its renaissance nowadays. As a result, for instance, in the one-side-fed spatial reactor, oscillations and sustained wave patterns have been reported.3−9 The qualitative picture of the Landolt reaction has long been accepted10,11 starting with the slow direct reaction between the reactants eventually producing iodide ion 3HSO3− + IO3− → 3SO4 2 − + 3H+ + I−

and followed by the Dushman reaction

species closing up the (auto)catalytic cycle. With regard to the rapidness of the third process, there are two distinct cases: If the third step is rapid (such as in the case of the Landolt reaction), then the substrate (sulfite) and the clock species (iodine) cannot coexist. Opposite to this case, a slow third reaction provides a possibility that although the clock species appears after a well-defined time lag, it cannot be associated with the complete consumption of the substrate molecule; thus, the substrate and the clock species may coexist for a long time.13 Furthermore, this situation is also complicated by the fact that in relative excess of substrate, the reactions belonging to this category also exhibit a clock behavior. In contrast to this in an excess of substrate substrate-depletive clock reactions do not show clock behavior under this condition. It led us to classify the clock reactions into the category of substratedepletive and autocatalysis-driven clock reactions.13 Certainly, so far only a couple of real chemical examples exists belonging to the category of the autocatalysis-driven clock reactions, such as the thiocyanate−iodate,14 aminoiminomethane sulfinic acid− iodate,15 2-aminoethanethiolsulfuric acid−iodate,16 dimethylaminoiminomethane sulfinic acid−iodate,17 and the pentathionate−iodate13 systems, but the number of them is soon expected to be increased. The aim of this article is to elucidate the kinetics and mechanism of the pentathionate−periodate system as well as to

(1)

12

5I− + IO3− + 6H+ → 3I 2 + 3H 2O

(2)

The clock behavior emerges from the fact that the color of iodine appears only after the substrate sulfite is completely consumed due to the fast sulfite−iodine reaction: HSO3− + I 2 + H 2O → SO4 2 − + 3H+ + 2I−

(3)

As a result, this sequence of reactions clearly explains that the system is autocatalytic not only with respect to hydrogen ion but also to iodide ion. Generally speaking, a Landolt-type reaction consists of three critical steps: (a) a slow direct reaction between the reactants followed by (b) a reaction to be governed by one of the products of the direct reaction (usually the autocatalyst, iodide) and one of the reactants (iodate), and (c) another reaction between the product of the second step (iodine) and the substrate (sulfite) to produce the autocatalytic © XXXX American Chemical Society

Received: August 5, 2014 Revised: September 19, 2014

A

dx.doi.org/10.1021/jp507925e | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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acceptable fit was that the average deviation for the relative fit approached 5%, which is close to the experimentally achievable limit of error of the spectrophotometer.

demonstrate that it also belongs to the category of autocatalysis-driven clock reactions.

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MATERIALS AND INSTRUMENTATION Materials and Buffers. Potassium pentathionate was prepared as described previously,18 and its purity was found to be better than 97.0%. The stock solution was checked prior to each experiment, and once the purity of the solid sample was proven to be decreased due to the formation of elementary sulfur and other sulfur species, it was discarded and new potassium pentathionate sample was prepared. Potassium metaperiodate (Reanal), phosphoric acid, sodium dihydrogen phosphate, potassium iodide and sodium perchlorate were of the highest purity commercially available and were used without further purification. Twice ion-exchanged and doubledistilled water was used to prepare all the stock solutions. Phosphoric/dihydrogen phosphate buffer was used to maintain the pH between 1.10 and 2.15 by taking the pKa of phosphoric acid as 1.80.19 Sum of the initial total concentration of dihydrogen phosphate, [H2PO4−], and phosphoric acid, [H3PO4], was always kept constant at 0.65 M, and the desired pH was adjusted by changing the ratio between [H3PO4] and [H2PO4−]. The ionic strength of all the stock solutions including pentathionate, periodate, and buffer solution was adjusted to be 0.5 M by adding the necessary amount of sodium perchlorate. Temperature of the reaction vessel was maintained at 25.0 ± 0.1 °C. Initial concentrations of pentathionate and periodate were varied in the ranges of 0.25−9.00 mM and 0.667−9.17 mM, respectively. In this experimental setup, the reaction with 159 different experimental conditions were investigated. Several experiments were also repeated that convinced us about a good reproducibility of the kinetic measurements. Methods and Instrumentation. The reaction was followed by a Zeiss S600 diode array spectrophotometer in the visible range without using the deuterium lamp of the spectrophotometer. The reaction has been carried out in a standard quartz cuvette equipped with a magnetic stirrer and a Teflon cap having 1 cm optical path. The buffer solution was first delivered into the cuvette followed by pentathionate solution and, if necessary, iodide solution. The stirring rate was controlled at 750 rpm to provide sufficiently fast mixing of the reactants before initiating reaction by injecting periodate solution from a fast delivery pipet. The spectrum of the reaction solutions at the wavelength range of 400−800 nm was acquired up to approximately 20 000−90 000 s.

RESULTS Preliminary Observation. As expected, an absorbance− time profile similar to the pentathionate−iodate system13 was recorded. It clearly indicated that iodine is formed only after a fairly long time that strongly depends on the initial concentration of the reactants as well as the pH. We also noticed another similarity to the pentathionate−iodate system, namely, that an absorbance increase at 800 nm can also be observed. It suggests that a light-scattering species must also be produced during the course of the reaction because none of the possible products have detectable absorbance at this wavelength. Furthermore, after completion of the reaction, a detectable amount of colloidal sulfur can be collected from the cuvette. It suggests that a sulfur producing reaction must be involved in the mechanism. Because a light-scattering species disturbs the quantitative absorbance detection, we concluded that for simultaneous evaluation of the kinetic curves we should truncate the kinetic curves from the time point, where colloidal sulfur precipitation occurs. Such an example can be seen in Figure 1.

Figure 1. Experimental absorbance−time series at two different wavelengths. Conditions are as follows: [S5O62−]0 = [IO4−]0 = 2.0 mM, pH = 1.94 (blue); and [S5O62−]0 = 0.8 mM, [IO4−]0 = 2.0 mM, pH = 1.94 (green). Empty circles indicate the absorbance measured at 468 nm, while the solid lines represent the measured absorbance at 800 nm.

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Another important observation has to be emphasized as well. In an excess of pentathionate, iodine appears before complete depletion of the substrate pentathionate due to the slow pentathionate−iodine reaction.18 Of course the concentration of iodine decreases once its production from the sequence of the original reactions ceases and may completely disappear at high excess of pentathionate. In addition to that, the initially added trace amount of iodide ion (shown in Figure 2) significantly decreases the time necessary for appearance of iodine. Consequently, iodide ion plays a key role in determining the kinetics of the reaction. We shall see later that iodide ion is an autocatalyst of the system; therefore, the pentathionate−periodate reaction can also be classified as an autocatalysis-driven clock reaction. The absorbance−time profiles of the measured kinetic curves suggest that initial rate studies are a noninformative way for

DATA TREATMENT In the visible range only iodine and triiodide were found to be the absorbing species; therefore, the isosbestic point of the iodine−triiodide system (λ = 468 nm) was selected for the parameter estimation by ChemMech/ZiTa program package developed to fit basically unlimited experimental series.20 Molar absorbance of iodine and triiodide ion was set to be 750 M−1 cm−1 for the calculation process. Originally, each kinetic run contained more than 500 absorbance−time data pairs; therefore, it was necessary to reduce the number of time points (40−80) to avoid unnecessary and time-consuming calculations. The essence of this method has already been described elsewhere.21 Altogether almost 9425 experimental points from the 159 kinetic series were used for the simultaneous evaluation. Our quantitative criterion for an B



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Since this value is significantly lower than unity within the concentration range studied (this observation is, however, reminiscent of that seen in the above-mentioned reaction) it refers to a complex overall effect on the formation of iodine. A conceivable explanation of this observation is that at higher pHs mainly the initial step governs the kinetics via the rate− determining formation of iodide ion followed by essentially pH independent processes like the overall pentathionate−iodine18 and iodide−periodate22 reactions. Once pH decreases the contribution of the Dushman reaction,12 the overall kinetics becomes more and more pronounced; consequently, the effect of the initial pentathionate concentration becomes negligible. As a result its formal kinetic order is decreased. Figure 4 indicates the effect of initial periodate concentration on ti, which seems to be entirely different compared to the one Figure 2. Measured absorbance−time series at 468 nm. Conditions are as follows: [S5O62−]0 = 0.6 mM; [IO4−]0 = 1.7 mM; pH = 1.8; I = 0.5 M. [I−]0/μM = 0.0 (black); 1.07 (blue); 2.67 (green); 5.33 (cyan); and 9.78 (red).

characterization of the concentration dependence of the reactants. To visualize quantitatively the effect of the reactants and the pH, we define ti as a time necessary to reach the absorbance of 0.01 absorbance unit at 468 nm, which corresponds to [I2] = 1.33 × 10−5 M, and analyze the concentration dependence of ti. The main advantage of this definition is that it can exactly be determined experimentally, and no disturbing side reaction (precipitation of sulfur) can be taken into consideration during the analysis. Concentration Dependence of ti. Figure 3 shows the dependencies of ti on the concentration of pentathionate meanwhile keeping the rest of the conditions constant. One can easily realize that pH clearly affects the influence of the initial pentathionate concentration on the reciprocal of ti. The log−log plot suggests that the formal kinetic order of pentathionate increases with increasing pH, which seems to be a completely opposite effect observed experimentally in the case of the corresponding pentathionate−iodate reaction.13

Figure 4. Dependence of ti on the concentration of periodate. Conditions are as follows: [S5O62−]0 = 0.49 mM and pH = 1.1 (black); [S5O62−]0 = 0.55 mM and pH = 1.31 (blue); [S5O62−]0 = 0.57 mM and pH = 1.52 (green); [S5O62−]0 = 0.8 mM and pH = 1.73 (cyan); [S5O62−]0 = 1.0 mM and pH = 1.93 (red); and [S5O62−]0 = 1.0 mM and pH = 2.15 (magenta).

observed in the pentathionate−iodate reaction. We should refer to the point that, in the case of the pentathionate−iodate reaction,13 the formal kinetic order of iodate was found to be strictly one corresponding to the fact that the rate of both the initiative pentathionate−iodate and the Dushman reactions depends on the first power of [IO3−]. Opposite to that in the case of the pentathionate−periodate reaction, the formal kinetic order of periodate is significantly lower than unity, and it seems to depend on pH. The lower the pH is, the more the ti becomes independent of the periodate concentration. A feasible explanation of this experimental finding is that iodate formed during the course of the iodide−periodate reaction is a key intermediate of the pentathionate−periodate reaction. As the pH decreases, more and more significant contribution from the Dushman and the pentathionate−iodate reactions is expected to occur to the overall kinetics of the parent system. Consequently, the pH-independent iodide−periodate22 reaction becomes less and less effective to govern the reaction resulting in the cessation of the effect of periodate on ti. Elucidating further the concentration dependence of ti, Figure 5 explains that formal kinetic order of hydrogen ion is between 1 and 2, which is also a significant difference compared to what we found in the corresponding pentathionate−iodate reaction.13 This observation is the consequence of the fact that

Figure 3. Dependence of ti on the concentration of pentathionate. Conditions are as follows: [IO4−]0 = 1.5 mM and pH = 1.1 (black); [IO4−]0 = 1.5 mM and pH = 1.31 (blue); [IO4−]0 = 2.0 mM and pH = 1.52 (green); [IO4−]0 = 2.0 mM and pH = 1.73 (cyan); [IO4−]0 = 2.0 mM and pH = 1.93 (red); and [IO4−]0 = 2.5 mM and pH = 2.15 (magenta). C



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Figure 5. Dependence of ti on the concentration of hydrogen ion. Conditions are as follows: [IO4−]0 = 1.5 mM, [S5O62−]0 = 0.5 mM (black); [IO4−]0 = 5.0 mM, [S5O62−]0 = 0.5 mM (blue); [IO4−]0 = 1.5 mM, [S5O62−]0 = 1.5 mM (green); [IO4−]0 = 1.5 mM, [S5O62−]0 = 0.6 mM (red); and [IO4−]0 = 5.0 mM, [S5O62−]0 = 0.8 mM (magenta).

Figure 6. Effect of ionic strength on the formation of iodine. Conditions are as follows: [IO4−]0 = 1.7 mM, [S5O62−]0 = 0.6 mM, pH = 1.8, TPO43− = 0.65 M. I = 0.33 M (black), 0.5 M (blue), 0.7 M (green), and 1.0 M (cyan) adjusted by sodium perchlorate.

the overall kinetics of the title reaction is governed by the pentathionate−periodate, pentathionate−iodate, pentathionate−iodine, iodide−iodate, and iodide−periodate reactions. Significant pH dependence differences of these reactions, namely, the pH independent pentathionate−iodine and iodide−periodate reactions, first order dependence of [H+] of the initiative step in the case of the pentathionate−iodate and pentathionate−periodate reactions, and the second order H+ dependence of the Dushman reaction account for the pH effect found here. Effect of Buffer Concentration and the Ionic Strength. The hypothesis that the pentathionate−iodate and the Dushman reactions play a key role in determining the kinetic behavior of the title system can indirectly be checked via the influence of the ionic strength and the total buffer concentration. It was clearly demonstrated that rate of the Dushman reaction is strongly affected by the ionic strength and by the nature of buffer components.23 In addition to that, phosphates can efficiently catalyze the Dushman reaction.24 We also learned from our previous study that the pentathionate− iodate system is also very sensitive to the concentration of the buffer components as well as that of the ionic strength.13 Figures 6 and 7 depict the effect of the buffer components and that of the ionic strength on the kinetic runs, respectively. It is clear, as anticipated, that both the increase of the ionic strength and that of the buffer components concentration have an accelerating effect on the formation of iodine. These observations, therefore, give a further decisive evidence that the main core of the proposed kinetic model has to include both the Dushman and the pentathionate−iodate reactions. Proposed Kinetic Model. To establish the kinetic model first we took the complete kinetic model of the pentathionate− iodate reaction. This model was then supplemented by the conceivable reactions of periodate ion with the reactants, the intermediates, and the product iodide. As a start, the rate equations of all these reactions were supposed to have three terms, the first one was independent of pH and the second and third terms were set to be proportional to [H+] and [H+]2, respectively. Systematic elimination of the reactions not to have any effect on the quality of the fit finally led to the following kinetic model:

Figure 7. Effect of the concentration of buffer components on the formation of iodine. Conditions are as follows: [IO3−]0 = 1.7 mM, [S5O62−]0 = 0.6 mM, pH =1.8, and I = 0.5 M adjusted by the necessary amount of sodium perchlorate. TPO43−/M = 0.1 (black), 0.35 (blue), 0.65 (green), and 0.95 (cyan).

H3PO4 ⇌ H+ + H 2PO4 −

(E1)

H 2SO3 ⇌ H+ + HSO3−

(E2)

HIO4 ⇌ H+ + IO4 −

(E3)

I3− ⇌ I 2 + I−

(R1)

I 2 + H 2O ⇌ HOI + H+ + I−

(R2)

S5O6 2 − + I 2 ⇌ S5O6 I− + I−

(R3)

S5O6 I− + H 2O → S3O3OH− + S2 O3I− + H+

(R4)

S3O3OH− + 3I 2 + 5H 2O → 3HSO3− + 6I− + 8H+ (R5) −

S2 O3I + I 2 + 3H 2O →

2HSO3−

−

+ 3I + 4H

HSO3− + I 2 + H 2O → SO4 2 − + 2I− + 3H+ D

+

(R6) (R7)



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S5O6 2 − + IO−3 + 2H 2O → S3O3OH− + 2HSO−3 + HOI

Table 1. Fitted and Fixed Rate Coefficients of the Proposed Kinetic Model; No Error Indicates That the Given Parameter Is Fixed during the Calculation Process

(R8)

HSO3− + IO3− → SO4 2 − + HIO2 −

(R9)

+

step

HIO2 + I + H → 2HOI

(R10)

R1

HSO3− + HOI → SO4 2 − + I− + 2H+

(R11)

R2

IO3− + I− + 2H+ ⇌ I 2O2 + H 2O

(R12)

R2′

H+ + I− + I 2O2 + H 2O → 3HOI

(R13)

R3

I 2O2 + H 2O → HOI + HIO2

(R14)

−

S2 O3OH +

IO3−

+ H 2O → HIO2 +

2HSO−3

R4 R5 R6 R7 R8 R9 R9′ R10 R11 R12

(R15)

S5O6 2 − + HIO4 + H 2O → S2 O3OH− + S3O3OH− + IO3− + H+

(R16)

I− + IO4 − + H+ → HOI + IO3− −

−

(R17)

+

I + IO4 + 2H → 2HIO2

(R18)

IO4 − + HSO3− → SO4 2 − + IO3− + H+

(R19)

R13 R14 R15 R16 R17 R17′ R18 R19 R20 R21 R22 R23 R24

IO4 − + S2 O3OH− + H 2O → HOI + 2SO4 2 − + 2H+ (R20)

IO4 − + S3O3OH− + 2H 2O → H+ + HOI + 3HSO3− (R21) −

−

−

IO4 + S2 O3I + H 2O → I 2 + 2SO4 + 2H

+

(R22)

HIO4 + S5O6 I− + 5H 2O → 6H+ + 2I− + 5HSO−3 (R23) −

IO4 + HIO2 →

2IO3−

+H

+

(R24)

Rate coefficients determined by nonlinear simultaneous parameter estimation are illustrated in Table 1. The average deviation was found to be 4.9% by a relative fitting procedure. Altogether only 13 fitted parameters were used, and the rest of the parameters was either fixed or directly taken from previous reports. Figures 8−10 demonstrate the quality of the fit for representative examples and also support the fact that the proposed kinetic model is working properly under our experimental conditions.

rate equation kR1[I3−]

k−R1[I2][I−] kR2[I2] k−R2[HOI][I−][H+] kR2′[I2][H+]−1 k−R2′[HOI][I−] kR3[S5O62−][I2] k−R3[S5O6][I−] kR4[S5O6I−] kR5[S3O3OH−][I2] kR6[S2O3I−][I2] kR7[HSO3−][I2] kR8[S5O62−][IO3−][H+] kR9[HSO3−][IO3−][H+] kR9′[HSO3−[IO3−][H+]2 kR10[HIO2][I−][H+] kR11[HSO3−][HOI] kR12[IO3−][I−][H+]2 k−R12[I2O2] kR13[I2O2][I−] kR14[I2O2][H+] kR15[S2O3OH−][IO3−][H+] kR16[S5O62−][HIO4] kR17[I−][IO4−] kR17′[I−][HIO4] kR18[I−][IO4−] kR19[HSO3−][IO4−] kR20[S2O3OH−][HIO4][H+] kR21[S3O3OH−][IO4−] kR22[S2O3I−][IO4−] kR23[S5O6I−][HIO4] kR24[IO4−][HIO2]

parameter value 8.5 × 106 s−1 5.6 × 109 M−1 s−1 0.0552 s−1 1.023 × 1011 M−2 s−1 1.98 × 10−3 M s−1 3.67 × 109 M−1 s−1 10 M−1 s−1 106 M−1 s−1 4.83 ± 0.39 s−1 104 M−1 s−1 104 M−1 s−1 3 × 109 M−1 s−1 0.0205 M−2s−1 8800 M−2s−1 108 M−3s−1 109 M−2s−1 109 M−1 s−1 107 M−3s−1 106 s−1 (1.10 ± 0.11) × 107 M−1 10670 ± 990 M−1 s−1 (4.60 ± 0.29) × 104 M−2 0.0121 ± 0.0022 M−1 s−1 5.52 ± 0.39 M−1 s−1 15.2 ± 0.9 M−1 s−1 0.792 ± 0.061 M−1 s−1 (1.16 ± 0.15) × 106 M−1 95.2 ± 8.9 M−2 s−1 0.093 ± 0.008 M−1 s−1 1.7 × 106 M−1 s−1 2410 ± 185 M−1 s−1 (5.19 ± 0.35) × 105 M−1

s−1 s−1

s−1

s−1

and kR14 differ by approximately a factor of 2 from the previously determined ones that can readily be explained by the different experimental circumstances applied. As shown in our previous paper, both values are very sensitive to the concentration of the buffer components as they are linearly proportional to [H2PO4−].13 In contrast to this, in the case of kR4, we found here a notably higher value than compared to the previous ones.13,18 It seems to suggest that the pentathionate− iodine reaction must also be sensitive to the quality of the buffer applied as well as the absolute concentration of the buffer components. Step R15 has already been proposed previously, but the rate coefficient kR15 was found to be slightly less (approximately 5 times) here compared to a report of a previous study.25 A feasible explanation of this fact would be the difference between the qualities of the buffer applied giving rise to an appearance of specific catalytic effect of acetate buffer on the S2O3OH−− iodate reaction. In lack of pure S2O3OH−, however, it can therefore be treated only as a hypothesis. Step R16 is the initiation of the title reaction to breakup the sulfur chain of the pentathionate resulting in the formation of S2O3OH−, S3O3OH−, and iodate. S2O3OH− and S3O3OH− are intermediates of the reaction to be oxidized further by periodate/periodic acid eventually resulting in the formation of iodide ion in a finite sequence of reactions. We also found

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DISCUSSION Step E1 is only an auxiliary process, necessary to take the slight pH change into consideration during the course of reaction. Steps E2 and E3 were also included because both HSO3−and IO4− are protonated within the pH range studied, and the reactivity difference of their forms may also have influence on the kinetic runs. The ratio of rate coefficients of the rapid forward and reverse reactions was adjusted to give the corresponding pKa of phosphoric, sulfurous, and periodic acid to be 1.80, 1.85, and 1.64, respectively.19 As mentioned previously steps R1−R14 were directly taken from our previous study.13 Majority of the rate coefficients was fixed during the calculation process except for kR4, kR13, and kR14. In case of kR4, kR13, and k14, the values calculated here were found to be in a very reasonable agreement with those reported previously.13,18 It is, however, worthwhile to note that both kR13 E



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Figure 9. Experimental (dots) and fitted (solid lines) absorbance− time curves at 468 nm with respect to changing the concentration of periodate. Conditions are as follows: (A) [S5O62−]0 = 0.8 mM; pH = 1.73; [IO4−]0/mM = 7.0 (blue); 5.0 (green); 3.4 (cyan); 2.0 (red); 1.46 (magenta); 1.0 (brown); and 0.68 (gray). (B) [S5O62−]0 = 1.0 mM; pH = 1.94; [IO4−]0/mM = 8.33 (blue); 6.0 (green); 4.0 (cyan); 2.09 (red); 1.53 (magenta); 1.27 (brown); and 0.83 (gray).

Figure 8. Experimental (dots) and fitted (solid lines) absorbance− time curves at 468 nm with respect to changing the concentration of pentathionate. Conditions are as follows: (A) [IO4−]0 = 2.0 mM; pH = 1.52; [S5O62−]0/mM = 3.27 (blue); 1.60 (green); 1.07 (cyan); 0.80 (red); 0.57 (magenta); 0.445 (brown); and 0.314 (gray). (B) [IO4−]0 = 2.0 mM; pH = 1.94; [S5O62−]0/mM = 3.2 (blue); 2.0 (green); 1.33 (cyan); 1.0 (red); 0.80 (magenta); 0.667 (brown); and 0.307 (gray).

ion and periodic acid are the kinetically active species, respectively (kR17, kR17′). Step R19 is the oxidation of hydrogen sulfite by periodate ion. Unfortunately, no direct research paper has yet been published determining directly the kinetics of this reaction. According to ref 25, this step is a fast reaction in the time scale of the title reaction. Indeed, we found kR19 to be (1.16 ± 0.15) × 106 M−1 s−1 indicating a rapid reaction taking place probably via an oxygen transfer process. Steps R20 and R21 are further oxidations of the intermediates S2O3OH− and S3O3OH− by periodate ion. On the basis of our experiments, both rate coefficients could be determined as indicated in Table 1. Step R22 was also proposed in a previous study of the reaction between thiosulfate and periodate ions. This reaction was found to be a fast second order reaction; therefore, we directly adopted its rate coefficient to be kR22 = 1.7 × 106 M−1 s−1 from the literature.25 Step R23 has not been proposed so far. It is well-known that, during the reaction of pentathionate and iodine, intermediate S5O6I− forms. In an excess of periodate, it is also conceivable that periodate can readily oxidize this ion into hydrogen sulfite meanwhile being reduced to iodide ion. We found kR23 to be 2410 ± 185 M−1 s−1.

that the periodic acid is more reactive to break up the sulfur chain; hence, the rate of this reaction is proportional to [HIO4]. Its rate coefficient kR16 was found to be 0.0121 ± 0.0022 M−1 s−1. In additional calculations we also checked whether the rate of this reaction is further proportional to [H+] or [OH−]. These calculations, however, indicated that in both cases simultaneous evaluation of the kinetic curves provided significantly higher average deviations (6.5% and 7.7%, respectively) resulting in the necessity of the rate equation indicated in Table 1. Steps R17 and R18 are the well-known oxidation of iodide ion by periodate. It has been well-established that the reaction is governed by two limiting stoichiometries and that the rate of formation of iodine is independent of pH.22 One of the limiting stoichiometries leads exclusively to the formation of iodine (see the sequence of steps R18, R10, and R2), while the other one produces iodate and iodine (see the sequence of steps R17 and R2). As seen, this feature evidently appears in our present system as well. It is also known that at strongly acidic conditions (below pH = 2), the rate of the iodide−periodate reaction becomes pH-dependent.26,27 This feature is also reflected in our present model because in step R17 periodate F



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determining the formation of iodine. Consequently, we see no option to decrease the number of parameters without preserving the ability of the model to describe quantitatively the experimental curves simultaneously as well as to be in harmony with the models of related systems. It should be mentioned that the model presented here is not complete as it is unable to explain the precipitation of sulfur during the course of the reaction. We suggest that the S3O3OH− → S2 O3OH− + S

(4)

reaction is a conceivable possibility to explain it. Indeed, including this reaction into the model leads to a slightly less average deviation (4.8%). However, as we pointed out previously sulfur precipitation prevents the quantitative absorbance determination due to light scattering of the colloid particles; therefore, the truncated kinetic curves are noninformative for determining the pathway leading to the formation of sulfur. This led us to conclude that the rate coefficient of eq 4 cannot be determined unambiguously from our experiments. Finally, we believe that the autocatalytic effect of iodide ion and the clock behavior of the reaction should also be enlightened from this complex model. As can be seen, the initial reaction produces the intermediates S 2 O 3 OH − , S3O3OH−, and iodate ion. Periodate can then further oxidize the former ions (steps R20 and R21) to produce hypoiodous acid and hydrogen sulfite. These two species react further to give iodide ion via step R11. Once iodide ion is produced, steps R12−R14, R17, and R18 along with steps R2 and R10 lead to the formation of iodine. Iodine is then removed via the pentathionate−iodine reaction to produce iodide ion autocatalytically. As long as the concentration of iodide ion is low, the direct pentathionate−iodate reaction also plays a key role to increase its concentration level. Once the level of iodide ion reaches a certain value, pentathionate is not able to eliminate iodine anymore; consequently, it rings the bell for the clock behavior. Of course the appearance of iodine is also enhanced by the fact that the pentathionate−iodine reaction is autoinhibitory with respect to iodide ion. From this point the role of the initial pentathionate−periodate and the pentathionate− iodate reactions is gradually lost, and the periodate−iodide reaction and the Dushman reaction along with the pentathionate−iodine reaction govern mainly the formation and loss of iodine depending on the initial concentration ratio of the reactants. Special kinetic feature of the pentathionate− iodine reaction makes it possible that the clock species iodine and the substrate pentathionate coexist for a relatively long time. It makes a significant difference between the clockcharacteristics of the title reaction compared to the original Landolt reaction. This is why we believe that the title reaction is better to be classified as an autocatalysis-driven clock reaction, similarly to the pentathionate−iodate reaction,13 while the Landolt reaction is a substrate-depletive clock reaction. We should also mention that periodic acid and periodate ion exist in aqueous solution in octahedral (H5IO6, H4IO6−) and tetrahedral forms (HIO4, IO4−).28 On the basis of our experiments, however, it is impossible to differentiate whether the octahedral or the tetrahedral form is more reactive in those reactions where periodate or periodic acid are involved as reactants because in aqueous solution the concentration ratio of these forms is constant.

Figure 10. Experimental (dots) and fitted (solid lines) absorbance− time curves at 468 nm with respect to changing pH. Conditions are as follows: (A) [S5O62−]0 = 0.5 mM; [IO4−]0 = 1.5 mM; pH = 1.1 (blue); 1.31 (green); 1.52 (cyan); 1.73 (red); 1.94 (magenta); and 2.15 (brown). (B) [S5O62−]0 = 0.8 mM; [IO4−]0 = 5.0 mM; pH = 1.1 (blue); 1.31 (green); 1.52 (cyan); 1.73 (red); 1.94 (magenta); and 2.15 (brown).

Step R24 was already proposed in our previous works,22,25 and the rate coefficient found here is in a reasonable agreement with those obtained there. A word is in order here regarding the explanation of the number of parameters used in the fitting procedure. We have already mentioned that altogether 13 fitted parameters were used to characterize the experimental curves, which may seem to be an unreasonably large number. Ten of those, however, belong to the reactions that were either directly studied in independent researches or indirectly proposed as necessary processes to describe the kinetic behavior of a reaction related to the title system. The fixed parameters used here in the fitting procedure were also reported from previous studies. It means that we proposed only three new reactions, R16, R21, and R23, and all these reactions are connected to the reactant periodate ion or periodic acid. Among them, of course, step R16 is mandatory because without it no reaction takes place at all, and steps R21 and R23 are reactions of periodate and periodic acid with different intermediates whose reactions are difficult to study individually at all. Removing these two reactions from the model, however, leads to an unacceptably high average deviation with an appearance of systematic errors between the measured and calculated kinetic curves, from which we concluded that these processes play significant roles in

KD

H4IO6− ⇌ IO4 − + 2H 2O G

(5)



Article

Reactor with Conical Geometry. J. Chem. Phys. A 2006, 110, 14043− 14049. (4) Szalai, I.; Kepper, P. D. Spatial Bistability, Oscillations and Excitability in the Landolt Reaction. Phys. Chem. Chem. Phys. 2006, 8, 1105−1110. (5) Pojman, J. A.; Komlósi, A.; Nagy, I. P. Double-Diffusive Convection in Traveling Waves in the Iodate−Sulfite System Explained. J. Phys. Chem. 1996, 100, 16209−16212. (6) Keresztessy, A.; Nagy, I. P.; Bazsa, G.; Pojman, J. A. Traveling Waves in the Iodate−Sulfite and Bromate−Sulfite Systems. J. Phys. Chem. 1995, 99, 5379−5384. (7) Horváth, J.; Szalai, I.; Kepper, P. D. Pattern Formation in the Thiourea−Iodate−Sulfite System: Spatial Bistability, Waves, and Stationary Patterns. Phys. D 2010, 239, 776−784. (8) Takács, N.; Horváth, J.; Szalai, I. Spatiotemporal Dynamics of Mixed Landolt Systems in Open Gel Reactors: Effect of Diffusive Feed. J. Phys. Chem. A 2010, 114, 7063−7069. (9) Horváth, J. Sustained Large-Amplitude Chemomechanical Oscillations Induced by the Landolt Clock Reaction. J. Phys. Chem. B 2014, 118, 8891−8900. (10) Eggert, J. Landolt Reaction. Z. Elektrochem. Angew. Phys. Chem. 1917, 23, 8−19. (11) Skrabal, A. Landolt’s Reaction. Z. Elektrochem. Angew. Phys. Chem. 1922, 28, 224−244. (12) Dushman, S. The Rate of the Reaction Between Iodic and Hydriodic Acids. J. Phys. Chem. 1903, 8, 453−482. (13) Xu, L.; Horváth, A. K. A Possible Candidate To Be Classified as an Autocatalysis-Driven Clock Reaction: Kinetics of the Pentathionate−Iodate Reaction. J. Phys. Chem. A 2014, 118, 6171−6180. (14) Simoyi, R. H.; Manyonda, M.; Masere, J.; Mtambo, M.; Ncube, I.; Patel, H.; Epstein, I. R.; Kustin, K. Kinetics and Mechanism of the Oxidation of Thiocyanate by Iodate. J. Phys. Chem. 1991, 95, 770−774. (15) 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. (16) Mundoma, C.; Simoyi, R. H. Oxyhalogen-Sulfur Chemistry Oxidation of 2-Aminoethanethiolsulfuric Acid by Iodate In Acidic Medium. J. Chem. Soc., Faraday Trans. 1997, 93, 1543−1550. (17) Otoikhian, A.; Simoyi, R. H.; Petersen, J. L. Oxidation of a Dimethylthiourea Metabolite by Iodine and Acidified Iodate: N,N′Dimethylaminoiminomethanesulfinic Acid (1). Chem. Res. Toxicol. 2005, 18, 1167−1177. (18) Xu, L.; Csekö, G.; Kégl, T.; Horváth, A. K. General Pathway of Sulfur-Chain Breakage of Polythionates by Iodine Comfirmed by the Kinetics and Mechanism of the Pentathionate−Iodine Reaction. Inorg. Chem. 2012, 51, 7837−7843. (19) IUPAC Stability Constant Database; Royal Society of Chemistry: London, 1992−1997. (20) Peintler, G. ChemMech/ZiTa, A Comprehensive Program Package for Fitting Parameters of Chemical Reaction Mechanism; Attila József University: Szeged, Hungary, 1989−2011. (21) 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. (22) Horváth, A. K. Pitfall of an Initial Rate Study: On the Kinetics and Mechanism of the Reaction of Periodate with Iodide Ions in a Slightly Acidic Medium. J. Phys. Chem. A 2007, 111, 890−896. (23) Schmitz, G. Kinetics and Mechanism of the Iodate−Iodide Reaction and Other Related Reactions. Phys. Chem. Chem. Phys. 1999, 1, 1909−1914. (24) Barton, A. F. M.; Wright, G. A. Kinetics of the Iodate−Iodide Reaction: Catalysis by Carboxylate and Phosphate Ions. J. Chem. Soc. A 1968, 2096−2103. (25) Rauscher, E.; Csekö, G.; Horváth, A. K. On the Complexity of the Kinetics and Mechanism of the Thiosulfate−Periodate Reaction. Inorg. Chem. 2011, 50, 5793−5802. (26) Abel, E.; Siebenschein, R. Ermittlung Zeitlich Unzuganlicher Reaktionskinetik Durch Reaktionsverteilung. Z. Phys. Chem. 1927, 130, 631−657.

This ratio could be shifted experimentally upon the addition of other solvents (for example, methanol, ethanol, etc.) into pure water, which is out of the scope of this study.

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CONCLUSIONS In this article we reported the kinetics and mechanism of the pentathionate−periodate reaction for the first time. The proposed model is constructed from several known subsystems, such as the pentathionate−iodine, the pentathionate−iodate, the iodide−periodate, and the Dushman reactions. Key feature of the title reaction is the autocatalytic production of iodide ion that is well-controlled by the above-mentioned subsystems. We have also shown that the reaction is a clock reaction as the clock species iodine appears after a well-defined reproducible time lag depending on the initial concentration range of the reactants. Because substrate pentathionate and iodine coexist for a relatively long period of time even in relative pentathionate excess, this reaction, besides other systems,13−17 serves as an additional example of the so-called autocatalysisdriven clock reactions. Experimental evidence that sulfur precipitation cannot be avoided at the final stage of the reaction might also be taken into consideration with the addition of eq 4 meaning that the proposed model should be extended to describe the kinetic feature of the title reaction at longer time scales. Last, but not least, it looks to be worth mentioning a future perspective of the application of the autocatalysis-driven clock reactions (such as the pentathionate−iodate and pentathionate−periodate reactions) in studying spatiotemporal phenomena. As seen, these systems are painfully slow reactions above pH = 3; therefore, strongly acidic conditions are a necessary requirement for a possible production of spatiotemporal structures. At this condition, the key to control the reaction is the concentration level of the autocatalyst iodide ion. It straightforwardly means that the main driving force of the reaction is rather the autocatalytic buildup of iodide ion than that of the increase of H+ observed in the original Landolt reaction. Since the diffusion constant of iodide ion is significantly lower compared to that of hydrogen ion, it may provide an inherent control for a slower diffusion of the autocatalyst. It may therefore be anticipated that several different spatiotemporal structures might be observed without the binding part of the autocatalyst reversibly or irreversibly to decrease its mobility.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.X. is thankful for the financial support from the China Scholarship Council. This work was supported by the ChineseHungarian Cooperative Grant (No. K-TÉT-CN-1-2012-0030).

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REFERENCES

(1) Landolt, H. Ueber die Zeitdauer der Reaction Zwischen Jodsäure und Schwefliger Säure. Chem. Ber. 1886, 23, 1317−1365. (2) Landolt, H. Einige Laboratoriumsapparate. Chem. Ber. 1885, 18, 56−57. (3) Labrot, V.; Hochedez, A.; Cluzeau, P.; Kepper, P. D. Spatiotemporal Dynamics of the Landolt Reaction in an Open Spatial H



Article

(27) Indelli, A.; Ferranti, F.; Secco, F. A Kinetic Study of the Reaction of Periodate with Iodide Ions. J. Phys. Chem. 1966, 70, 631− 636. (28) Crouthamel, C. E.; Hayes, A. M.; Martin, D. S. Ionization and Hydration Equilibria of Periodic Acid. J. Am. Chem. Soc. 1951, 73, 82− 87.

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Autocatalysis-Driven Clock Reaction II: Kinetics of the Pentathionate

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