Kinetics and Mechanism of the Concurrent Reactions of Hexathionate

Article Cite This: J. Phys. Chem. A 2019, 123, 5418−5427

pubs.acs.org/JPCA

Kinetics and Mechanism of the Concurrent Reactions of Hexathionate with S(IV) and Thiosulfate in a Slightly Acidic Medium Changwei Pan,† Fengpeng Lv,† Tamaś Keǵ l,‡ Attila K. Horvat́ h,*,§ and Qingyu Gao*,† †

College of Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China Department of Inorganic Chemistry, Faculty of Sciences and MTA-PTE Research Group for Selective Chemical Syntheses, and § Department of Inorganic Chemistry, Faculty of Sciences, University of Pécs, Ifjúság u. 6, Pécs H-7624, Hungary

‡

Downloaded via NOTTINGHAM TRENT UNIV on August 13, 2019 at 11:20:57 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Reactions of hexathionate with thiosulfate and sulfite have been investigated by high-performance liquid chromatography via monitoring the concentration−time series of tetrathionate, pentathionate, hexathionate, and thiosulfate simultaneously within the pH range of 4.0−5.0. In both reactions, elementary sulfur forms; more significant sulfur precipitation may be observed in the case of the hexathionate− thiosulfate reaction, but slight turbidity in the other system means that elementary sulfur also appears in a detectable amount in the hexathionate−sulfite reaction. Initial rate studies have revealed that the formal kinetic orders of both reactants in both systems are clearly unity but pH-dependence can only be observed in the case of the hexathionate−sulfite reaction. The proposed kinetic model appears to suggest that nucleophilic attack of sulfite and thiosulfate may also occur on the β- or γ-sulfur of the polythionate chain and breakages of the α−β, β−γ, and γ−γ′ bonds are all conceivable possibilities to drive the reactions. Consequently, the generally accepted sulfur-chain elongating effect of thiosulfate on longer polythionates is also proven to be accompanied by sulfur-chain shortening pathways, eventually leading to the formation of elementary sulfur.

■

INTRODUCTION Polythionates are well-known long-lived intermediates produced from the oxidation of thiosulfate by different oxidants, leading eventually to sulfate ion.1,2 Their further reactions with the corresponding oxidants sometimes display fascinating kinetics3 and may contribute to the appearance of a rich variety of exotic nonlinear dynamical phenomena.4−9 Hexathionate, being one of the important intermediates in redox transformations or metabolism of sulfur-containing compounds in various environmental, industrial, and biological systems,10,11 is often reported to be produced in numerous oxidation processes of thiosulfate.1,2 It is also well-known that hexathionate is unstable in weakly alkaline conditions and degradation of the sulfur−sulfur bond eventually leads mainly to the formation of elemental sulfur and thiosulfate.12 Compared to tetrathionate and pentathionate, significantly less information is available in the literature about redox transformation of hexathionate. Hexathionate can readily be degraded by the attack of nucleophilic reagents such as cyanide, sulfide, and sulfite ions via heterolytic cleavage of sulfur−sulfur bonds. These reactions are generally offered for quantitative determination of hexathionate.13,14 The sulfur chain of polythionates may as well be attacked by thiosulfate;12,15−21 thus, decomposition of polythionates is usually accompanied by catalytic rearrangement of polythionates even in a nearly neutral medium.19,22−24 Heterolysis selectivity of the divalent sulfur−sulfur bond plays a key role in © 2019 American Chemical Society

modulating the distribution of sulfur species in the case of thiosulfatolysis and sulfitolysis of pentathionate as the attack of thiosulfate or sulfite may take place on the inequivalent divalent sulfur atoms of hexathionate formed.25 In the present work, the concurrent reactions of hexathionate with thiosulfate and sulfite were investigated in a slightly acidic medium where decomposition of polythionates does not have any significant contribution to the rearrangement reaction. This study is performed to determine the individual rate coefficients of the polythionate−thiosulfate and polythionate−sulfite reactions in order to establish the relationship between the reactivity and structure of polythionates. It may as well provide a reasonable explanation of the sulfur formation during the course of reactions, exhibiting nonlinear characteristics.26−28

■

EXPERIMENTAL SECTION Materials. Commercially available reagents such as potassium tetrathionate (Sigma-Aldrich), sodium sulfite (Sigma-Aldrich), and sodium thiosulfate (Sigma-Aldrich) were of the highest purity and used without further purification. Potassium trithionate was prepared as described previously29 and its purity was found to be better than 99.0%.

Received: January 10, 2019 Revised: May 24, 2019 Published: June 10, 2019 5418

DOI: 10.1021/acs.jpca.9b00276 J. Phys. Chem. A 2019, 123, 5418−5427

Article

The Journal of Physical Chemistry A Potassium pentathionate was prepared by following the procedure reported by Kelly and Wood,30 and its purity (better than 98.5%) was checked by high-performance liquid chromatography (HPLC) or capillary electrophoresis (CE) and by titration with HgCl2. Potassium hexathionate was synthesized following the description reported by Goehring and Feldmann,31 and its purity was checked by HPLC or CE methods and by titration with bromine. All these measurements indicated the purity of potassium hexathionate to be 94.3%, with 2.5% impurity of pentathionate. This small but constant impurity of pentathionate was taken into consideration during the course of simultaneous data evaluation in such a way that the measured concentration of pentathionate was corrected by the concentration of pentathionate originating from the impurity of hexathionate. The stability of hexathionate in aqueous solution in the presence of acetate buffer (the pH was set to 4.5) was checked for a month, and less than 0.05% loss of hexathionate could be detected from which we concluded that hexathionate is stable enough to perform kinetic runs lasting several days. All solutions were prepared by Milli-Q distilled water having a resistivity of 18.2 MΩ·cm. Water was deoxygenated with bubbling N2 for at least 30 min to remove oxygen completely from the solutions. It was necessary because dissolved O2 may cause series side effects via its reaction with sulfite during the course of kinetic runs lasting for several days. Acetic acid/ acetate buffer was used to stabilize the pH between 4.0 and 5.0. The ionic strength was maintained at 0.06 M in all solutions by the buffer component sodium acetate, and the pH of the solution was adjusted by the addition of the desired amount of acetic acid taking its pKa as 4.55.32 Initial concentrations of reagents hexathionate, thiosulfate, and sulfite were all varied between 0.05 and 0.56 mM. Altogether, 45 kinetic runs were collected in case of both, studying the hexathionate−sulfite and hexathionate−thiosulfate reactions. Methods and Instrumentation. The HPLC separation experiments were performed on a Thermo UltiMate 3000 instrument equipped with a DAD-3000 multiple-wavelength detector, a Phenomenex Genimi C18 separation column (5.0 μm, 46 μm × 250 mm), and an LPG-3400SD pump with four pistons. The mobile phase consisted of 7 mM tetra(nbutyl)ammonium hydroxide (TPAOH) as an ion-pair agent and acetonitrile. The pH of the mobile phase was adjusted by phosphoric acid. The separation performance was optimized to the ratios of 72:25 (Vwater/Vacetonitrile) for sulfitolysis of hexathionate and 85:15 (Vwater/Vacetonitrile) for studying the thiosulfatolysis of hexathionate. All the experiments, including the reaction and separation processes, were conducted at (25.0 ± 0.1) °C and the samples were filtered through a 0.45 μm membrane filter prior to injecting it into the automatic sampling device. Data Treatment. Calibration curves were obtained to describe the relationships between the concentrations and peak area of each species to be monitored. Our experimental setup allowed us to follow the concentrations of hexathionate, pentathionate tetrathionate, and thiosulfate during the course of the reactions. The integrated areas of the peaks representing thiosulfate, tetrathionate, pentathionate, and hexathionate possessed excellent linear correlations (R > 0.99) with their concentrations. The experimental curves (concentration−time series of hexathionate, pentathionate, tetrathionate, and thiosulfate) were then analyzed simultaneously with the program package Chemmech.33

More than 11 000 experimental points from 90 kinetic runs for studying both the reactions of thiosulfatolysis and sulfitolysis of hexathionate were used for simultaneous data evaluation. Our quantitative criterion for an acceptable fit was that the average deviation for the relative fit approached 2%, which is close to the experimentally achievable error limit of the concentration determination under the present experimental circumstances. Computational Details. Full geometry optimizations have been performed with the PBE0 functional, which is a zeroparameter hybrid functional by Adamo and Barone34 based on the gradient-corrected exchange and correlation functionals developed by Perdew, Burke, and Ernzerhof.35 The stationary points were characterized by frequency calculations in order to verify that they have zero imaginary frequencies. For all atoms, the triple-ζ def2-TZVPD basis set36 was employed, which is augmented with diffuse functions. Natural bond orbital analyses have been performed by the GENNBO 5.0 program.37 Quantum theory of atoms in molecules analyses of the wave function38 were carried out with the AIMAll software.39 Solvent effects were taken into account during the geometry optimization, invoking the solvation model based on density implicit model,40 with the polarizable continuum model continuum approach for the electrostatic part, using water as solvent (ε = 78.355). For all the calculations the Gaussian 09 D.01 suite of programs41 was used.

■

RESULTS Identification of Sulfur-Containing Species. Figure 1 displays typical chromatograms during the course of sulfitolysis and thiosulfatolysis of hexathionate. As it is clearly seen, in both cases, concentration−time profiles of thiosulfate,

Figure 1. Detection of sulfur-containing species in the sulfitolysis (a) and thiosulfatolysis (b) of hexathionate by HPLC: [S6O62−]0 = 0.06 mM, pH = 4.25, [SO32−]0 = 0.10 mM at 106 min in Figure 1a and [S2O32−]0 = 0.10 mM at 220 min in Figure 1b. 5419


Article

The Journal of Physical Chemistry A tetrathionate, pentathionate, and hexathionate can conveniently be obtained under our experimental circumstances. Furthermore, at longer retention times even heptathionate may also be detected. However, our effort to synthesize solid potassium heptathionate with a purity higher than 90% has failed; therefore, peak areas of heptathionate were not converted into concentrations. In addition to this, it has recently been shown that during the course of thiosulfatolysis of pentathionate25 turbidity of the reaction mixture appears at the beginning stage of the reaction and then it later disappears. In the case of the thiosulfatolysis of hexathionate because of the presence of γ and γ′-sulfur it is expected that this feature becomes more profound at the beginning stage, which may lead to the appearance of significant amounts of sulfur precipitation. Indeed, Figure 2 shows snapshots of turbidity on the reacting solution in the case of thiosulfatolysis followed by sulfur deposition by the end of the reaction.

Figure 3. Plots of logarithm of the initial rate of the hexathionate− sulfur(IV) reaction against log([S(IV)]0) at pH = 4.0 and at [S6O62−]0 = 0.1 mM (black curve); log([S6O62−]0) at pH = 4.25 and at [S(IV)]0 = 0.1 mM (blue curve); and log([H+]) at [S6O62−]0 = 0.1 mM and [S(IV)] = 0.18 mM (green curve).

kinetic orders of the reactants are 1 for hexathionate and sulfur(IV) species. When the logarithm of the initial rate is plotted against log[H+] a straight line having a slope of −0.68 was obtained meaning that among the sulfur(IV) species SO32− must be considered as the kinetically active form during the course of the reaction. Figure 4 displays the log−log plots of the initial rate against the logarithm of initial hexathionate, thiosulfate, and H+

Figure 2. Snapshots of the reaction mixture in the case of thiosulfatolysis (upper ones) and sulfitolysis (lower ones) of a hexathionate ion. Initial conditions are as follows: [S6O62−]0 = 0.1 mM; pH = 4.5; [S2O32−]0 = 0.1 mM (upper pictures); [S6O62−]0 = 0.1 mM; pH = 4.5; [S(IV)]0 = 0.1 mM (lower pictures).

Figure 4. Plots of logarithm of the initial rate of the hexathionate− thiosulfate reaction against log([S2O32−]0) at pH = 4.5 and at [S6O62−]0 = 0.1 mM (black curve); log([S6O62−]0) at pH = 5.0 and at [S2O32−]0 = 0.1 mM (blue curve); and log([H+]) at [S6O62−]0 = 0.1 mM and [S(IV)] = 0.1 mM (green curve). The blue data were shifted by −0.1 unit along the y-axis for better visibility.

Furthermore, in the case of the sulfitolysis of hexathionate turbidity may also be observed at the beginning stage of the reaction although its appearance is not as significant as found during the course of thiosulfatolysis. Eventually, elementary sulfur deposits on the bottom of the flask by the end of the reaction. Initial Rate Studies. Figure 3 shows the logarithm of the initial rate defined as v0 = −d[S6O62−]/dt against the logarithm of initial hexathionate, sulfur(IV), and H+ concentrations, respectively, in the case of the hexathionate−sulfur(IV) reaction. As it is seen, linear relationships are clearly established with slopes being unity, indicating that the formal

concentrations, respectively, in the case of the hexathionate− thiosulfate reaction. From this figure it may easily be concluded that the formal kinetic order of hexathionate and thiosulfate is clearly 1. Furthermore, within the pH range studied the reaction is independent of pH. Proposed Kinetic Model. A similar approach was used to develop the kinetic model for the thiosulfatolysis and sulfitolysis of hexathionate as published previously in the cases of those of tetrathionate and pentathionate.25,42 As expected the most comprehensive kinetic model, working 5420


Article

The Journal of Physical Chemistry A soundly when studying the sulfitolysis and thiosulfatolysis of pentathionate, published recently by Ji et al.25 was unable to describe quantitatively our present kinetic data. Although the average deviation between the measured and calculated data was found to be 3.9%, systematic deviation was noticed at the [S5O62−]−time and [S4O62−]−time curves at higher initial sulfite concentrations when studying the sulfitolysis of hexathionate. Therefore, we concluded that some important processes are missing from that model for adequately describing our data simultaneously. Considering that thiosulfate and sulfite as nucleophilic species may attack either the β- or γ-sulfur of the hexathionate or pentathionate and upon this attack the chain breakage may also occuralthough not an equal probabilityat both sides of the sulfur atom it may result in the formation of a short-lived intermediate S3O32− that is capable of producing elemental sulfur. As a result, the following model is proposed to describe the measured kinetic data H+ + SO32 − F HSO3−

(R1)

S4 O6 2 − + SO32 − F S3O6 2 − + S2 O32 −

(R2)

S4 O6 2 − + S2 O32 − F S5O6 2 − + SO32 −

(R3)

S5O6

2−

+ S2 O3

2−

F S6O6

2−

+ SO3

2−

(R5)

S5O6 2 − + S2 O32 − → S3O32 − + S4 O6 2 −

(R6)

S6O6 2 − + S2 O32 − → S3O32 − + S5O6 2 −

(R7)

S6O6 2 − + SO32 − → S3O32 − + S4 O6 2 −

(R8)

S3O32 − + H 2O → S2 O32 − + HS(OH)

(R9)

no.

rate equation

(R1) (−R1) (R2) (−R2) (R3) (−R3) (R4) (−R4) (R5) (−R5) (R6) (R7) (R8) (R9) (R10) (−R10)

kR1[H+][SO32−] k−R1[HSO3−] kR2[S4O62−][SO32−] k−R2[S3O62−][S2O32−] kR3[S4O62−][S2O32−] k−R3[S5O62−][SO32−] kR4[S5O62−][S2O32−] k−R4[S6O62−][SO32−] kR5[S6O62−][S2O32−] k−R5[S7O62−][SO32−] kR6[S5O62−][S2O32−] kR7[S6O62−][S2O32−] kR8[S6O62−][SO32−] kR9[S3O32−] kR10[HS(OH)] k−R10

rate coefficient 1.585 × 1010 M−1 s−1 103 s−1 3.13 ± 0.09 M−1 s−1 3 × 10−5 M−1 s−1 (4.10 ± 0.45) × 10−4 M−1 41.3 ± 1.1 M−1 s−1 (5.09 ± 0.05) × 10−2 M−1 584 ± 4 M−1 s−1 0.0772 ± 0.004 M−1 s−1 1180 ± 53 M−1 s−1 (1.25 ± 0.11) × 10−3 M−1 (8.71 ± 0.34) × 10−2 M−1 128 ± 2 M−1 s−1 104 s−1 0.2 s−1 10−8 M s−1

s−1 s−1

s−1 s−1

contributory effect to the overall kinetics of the reaction. Thus, we concluded that this process can safely be omitted from the final model. This fact is further evidenced by obtaining a perfectly unity overall kinetic order of S(IV) for the hexathionate−sulfite reaction. It is easy to see that if the dimerization process has any decisive or even marginal role, then the formal kinetic order would have been deviated from unity to higher values. Step R2 is the well-known sulfitolysis process of tetrathionate studied first by Kurtenacker and Goldbach.43 Later, it was reported to be useful to determine different polythionates.44 The procedure was then modified by Koh et al. for quantitative purposes to analyze micro-amounts of polythionates.45 A couple of years ago our research group reported the rate coefficients of the forward and the backward processes by using HPLC techniques to track the concentration of polythionates, thiosulfate, and S(IV) species simultaneously.42 As discussed there kR2 = 3.85 M−1 s−1 and k−R2 = 3 × 10−5 M−1 s−1 were found to consistently describe the measured kinetic data. Therefore, we used these values as fixed ones at the beginning stage of the evaluation process. When we arrived at the final model at the end we fitted kR2 as well and the fitted value was found to be 3.13 ± 0.09 M−1 s−1, which confirms completely our previous result. Of course, k−R2 cannot be refined and therefore it was fixed during the whole calculation procedure because the backward process is a vanishingly slow reaction, and its rate coefficient can only be extrapolated from Naito et al.’s temperature-dependent experiments.15 It is worthwhile to note that despite the strongly positive partial charge of the sulfur, sulfite ion may also act as a genuine nucleophilic agent according to its electron density distribution, featuring a pronounced charge concentration in the vicinity of the sulfur atom (see Figure S1 in the Supporting Information). Step R3 is the well-known reaction between tetrathionate and thiosulfate to produce pentathionate and sulfite. The existence of the forward reaction was first mentioned by Foerster and Centner but they were unable to obtain the rate coefficient of this process.46 Therefore, Fava and Bresadola reinvestigated the system at an elevated temperature and at a

(R4)

S6O6 2 − + S2 O32 − F S7 O6 2 − + SO32 −

HS(OH) F S + H 2O

Table 1. Rate Equations Used and Rate Coefficients Obtained from Evaluating Simultaneously the Kinetic Data of Hexathionate−Sulfite and Hexathionate−Thiosulfate Reactions

(R10)

By the help of this kinetic model, all the concentration−time series (more than 11 000 experimental points) mentioned previously can be described by 2.2% average relative deviation providing a very sound agreement between the experimental and fitted data. Table 1 summarizes the rate coefficients fixed and fitted during the evaluation procedure. When no standard deviation is given the corresponding rate coefficients were fixed. Figures 5 and 6 depict the measured and calculated concentration−time curves in case of the hexathionate− thiosulfate reaction with varying the initial concentration of the reactants in separate series. Furthermore, Figures 7 and 8 indicate the measured and calculated kinetic curves in the case of the hexathionate−sulfite reaction. All these figures clearly support the adequacy of the proposed model.

■

DISCUSSION Step R1 is a rapidly established equilibrium responsible for setting the proper [HSO3−]/[SO32−] ratio at the pH range studied. It was necessary because among these S(IV) species only sulfite is an active agent kinetically. kR1 and k−R1 were fixed as shown in Table 1 to provide pKa2 = 7.2 for sulfurous acid. It is also well-known that HSO3− is able to dimerize into S2O52−; therefore, we considered this possibility at the beginning of the detailed calculations. However, we found no 5421


Article

The Journal of Physical Chemistry A

Figure 5. Measured (dots) and calculation (solid lines) concentration−time series in the case of the hexathionate−thiosulfate reaction. The initial conditions are as follows: [S6O62−]0 = 0.1 mM; pH = 5.0; [S2O32−]0/mM = 0.06 (black); 0.1 (blue); 0.18 (green); 0.32 (cyan); 0.56 (mM) (red).

Figure 6. Measured (dots) and calculation (solid lines) concentration−time series in the case of the hexathionate−thiosulfate reaction. The initial conditions are as follows: [S2O32−]0 = 0.1 mM; pH = 4.75; [S6O62−]0/mM = 0.06 (black); 0.1 (blue); 0.18 (green); 0.32 (cyan); 0.56 (mM) (red).

determined42 kR3 as 3.1 × 10−4 M−1 s−1 and it was in sound agreement with the values reported by Varga and Horváth18 (2.0 × 10−4 M−1 s−1) as well as by Zhang and Jeffrey (4.24 × 10−4 M−1 s−1).19 Actually, kR3 = (4.10 ± 0.45) × 10−4 M−1 s−1

relatively high ionic strength and obtained a value of 3.9 × 10−3 M−1 s−1.24 Later, Foss and Kringlebotn47 came to a similar conclusion, obtaining kR3 to be 1.3 × 10−3 M−1 s−1 at 1.15 M ionic strength. Our research group has recently 5422


Article


Figure 7. Measured (dots) and calculation (solid lines) concentration−time series in the case of the hexathionate−S(IV) reaction. The initial conditions are as follows: [S6O62−]0 = 0.1 mM; pH = 4.0; [S(IV)]0/mM = 0.06 (black); 0.1 (blue); 0.18 (green); 0.32 (cyan); 0.56 (mM) (red).

Figure 8. Measured (dots) and calculation (solid lines) concentration−time series in the case of the hexathionate−S(IV) reaction. The initial conditions are as follows: [S(IV)]0 = 0.1 mM; pH = 4.25; [S6O62−]0/mM = 0.06 (black); 0.1 (blue); 0.18 (green); 0.32 (cyan); 0.56 (mM) (red).

M−1 s−1. The next step toward the elucidation of this rate coefficient appeared to be Fava and Bresadola’s result who were only able to calculate k−R3/kR2 to be 18.1. Recently, as a result of a combined HPLC experimental technique along with

evaluated from the present experiments agrees very soundly with the result of both studies. The rate coefficient of the backward reaction was first reported by Foerster and Centner46 and at 0 °C they could determine the value for k−R3 as 3.88 5423


Article


Figure 9. Computed structures and calculated partial charges of thiosulfate (a), trithionate (b), tetrathionate (c), pentathionate (d), hexathionate (e), and heptathionate (f) anions at the PBE0/def2-TZVPD level of theory. Selected S−S bond distances are given in Å, Wiberg bond indices are written in italics, natural population analysis charges are given in italics in gray.

simultaneous data evaluation a value of 101 ± 9 M−1 s−1 was reported by Ji et al.42 Our recent result provides k−R3 = 41.3 ± 1.1 M−1 s−1 value, which soundly agrees with the results of all the reports mentioned above. Step R4 is the thiosulfate−sulfite group displacement equilibrium of pentathionate leading to the formation of hexathionate and sulfite studied first by Ji e al.25 They were able to determine kR4 and k−R4 values as 0.0165 and 1050 M−1 s−1, respectively. As it is seen, this reaction has to be a central part of our model as it must certainly be the initiating equilibrium when studying the hexathionate−sulfite reaction. As it is seen in Table 1 our recent experiments led to evaluating kR4 and k−R4 to be 0.0509 ± 0.0005 and 584 ± 4 M−1 s−1, respectively; both are in a fairly good agreement with Ji et al.’s result.25 Step R5, that is, the hexathionate−thiosulfate reaction, leading to formation of heptathionate and sulfite, has not been studied directly so far. The kinetic model of thiosulfatolysis and sulfitolysis of shorter polythionates was shown to be built up successfully from a bottom-up construction in a stepwise fashion25,42 because they cannot be studied individually excluding completely the contributory side effect of other polythionates. Therefore, the most reliable determination of the rate coefficients of the forward and backward processes is expected to be obtained from studying experimentally the most closely related system. Taking into consideration the literature data, so far, it was the pentathionate−thiosulfate reaction studied by Ji et al.25 They reported kR5 and k−R5 to be 0.105 ± 0.009 and 15 000 M−1 s−1, respectively. Our calculation here provided a somewhat lower value in the case of the forward reaction (kR5 = 0.0772 ± 0.004 M−1 s−1) and an order of magnitude lower k−R5 = 1180 ± 53 M−1 s−1 value for the backward reaction. Step R6 is an irreversible displacement reaction when thiosulfate, as a nucleophilic agent, attacks the β(β′)-sulfur of the polysulfur chain of pentathionate, which then weakens the β−γ bond, leading to its breakage, resulting in the formation of tetrathionate and a short-lived intermediate S3O32−. Interestingly, Ji et al. excluded this possibility in their paper25 even though Foss raised the feasibility of this process,48 but at that time there was no direct experimental information available whether this pathway may occur or not. Our calculation provided a value of kR6 = (1.25 ± 0.11) × 10−3 M−1 s−1, indicating that indeed breakage of the β−γ-sulfur bond is a conceivable opportunity for rearranging the sulfur chain. To indirectly confirm the necessity of this step we performed additional calculations when this step was eliminated from the

model. The average deviation is increased from 2.2 to 2.8%, which may be regarded as a sound fit as well, but in particular cases when the concentration of pentathionate was high enough systematic deviation may be found between the measured and calculated curves. From this point of view, step R6 has to be kept in the final model. Step R7 has already been suggested by Ji et al.25 and here it is confirmed that without this step the complete kinetic model would collapse. Our calculation provided a value of (8.71 ± 0.34) × 10−2 M−1 s−1, which is approximately three times higher than the one published elsewhere.25 In the molecular level thiosulfate attacks the γ(or γ′)-sulfur atom, weakening the γ−γ′ sulfur-bond, eventually resulting in its breakage. As a consequence, pentathionate and the short-lived S3O32− species will form. This route was also tried to be substituted partially or completely by the following sequence of reactions S6O6 2 − + S2 O32 − → S4 O32 − + S4 O6 2 −

(R11)

fast S4 O32 − + 2H 2O ⎯⎯⎯→ S2 O32 − + 2HS(OH)

(R12)

with no success. We therefore concluded that attack of thiosulfate on the γ-S of the sulfur chain results in the breakage of the γ−γ′ sulfur-bond more preferably than that of the β−γ bond. Step R8 is an irreversible displacement of S3O32− to a sulfite group, leading to formation of tetrathionate. The possibility of this reaction occurring was also suggested by Foss48 decades ago but it has never been confirmed whether it really plays any role in the rearrangement of hexathionate. To indirectly prove that this step is a necessary part of the kinetic model we performed an additional calculation when this step was omitted from the model. The final result indicated 7.5% average deviation, clearly supporting the indispensability of this reaction. Step R9 is a rapid hydrolysis of the short-lived intermediate S3O32− to produce HS(OH) and sulfite ions. A similar reaction was already considered and discussed when interpreting the major characteristics of the dithionite−pentathionate reaction.49 Furthermore, this intermediate is also believed to play a substantial role in the acidic decomposition of thiosulfate not only to produce elementary sulfur but various polythionates as well.50 Our calculations indicated that the rate coefficient of this reaction cannot be determined from the present experiments, and this process has to be treated as a fast reaction compared to the timescale of thiosulfatolysis and sulfitolysis of hexathionate. 5424


Article


not likely to occur because of a lack of preferable interaction of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) molecular orbitals of thiosulfate and pentathionate shown in Figure 10.

Step R10 is the conversion of HS(OH) leading to the formation elementary sulfur. The rate coefficient of the forward and reverse reactions was directly adopted from Ji et al.’s previous work25 considering that this process is a heterogeneous dissolution reaction of the sulfur precipitated. One paragraph here is also in order to highlight a crucial impact of the present kinetic model. Figure 9 indicates the calculated partial charges appearing on the sulfur atoms of various polythionates and thiosulfate. From this, it is clear that the attack of sulfite is preferable on the almost neutral γ-S of the sulfur chain of polythionate whenever it exists. In the case of tetrathionate there are only β and β′ sulfur atoms, having a partially negatively charged sulfur to be attacked which is, of course, less favorable for initiating a sulfur-chain breakage reaction, resulting in shortening the sulfur-chain of tetrathionate. As Table 2 indicates the rate coefficient belonging to this

Figure 10. Frontier molecular orbital interaction between the HOMO of thiosulfate and the LUMO of hexathionate (a) or pentathionate (b). Green arrows designate the preferred whereas red arrows show the not preferred orbital orientations.

Table 2. Comparison of the Calculated Rate Coefficients in the Case of the Sulfitolysis and Thiosulfatolysis of Various Polythionatesa SO32−

S2O32−

S3O62− S4O62− S5O62−

n.r. 3.13 (β) [β−β′] 41.3 (γ) [β−γ]

S6O62−

584 (β) [β−γ] 128 (γ) [γ−γ′] 1180 (γ) [β−γ]

3 × 10−5 (β) [α−β] 4.10 × 10−4 (β) [α−β] 0.0509 (β) [α−β] 1.25 × 10−3 (β) [β−γ] 0.0772 (β) [α−β] 0.0871 (γ) [γ−γ′] n.a

S7O62−

In contrast to this, in the case of hexathionate both the βand the γ-sulfur atoms can readily be attacked by thiosulfate. The former route leads to the breakage of the α−β bond, resulting in elongating the sulfur-chain whereas the latter one takes control of the sulfur-chain shortening pathway and at the same time precipitating elementary sulfur. Interestingly, the rate coefficients of both directions were found to be quite close to each other, making it clear that these possibilities are major routes for transforming the sulfur chain of hexathionate. It is, as well, directly supported by frontier molecular orbital orientations in the cases of the HOMO of thiosulfate and that of the LUMO of hexathionate shown in Figure 10.

a

In brackets sulfur atom of the polythionate chain to be attacked are indicated, whereas in square brackets the sulfur−sulfur bond to be broken is shown. The unit of all rate coefficients is M−1 s−1.

■

reaction is almost 2 orders of magnitude lower than those in the case of higher polythionates. In the case of trithionate, when the partial charge of the β-sulfur is significantly higher than in the case of tetrathionate no reaction may be observed. Note that rate coefficients of sulfite- or thiosulfate exchange reactions to be observed only by isotopic labeling51 are not included as these processes are completely invisible under our experimental circumstances. It is, however, interesting to note that attack of sulfite on the γ-S of hexathionate may result in weakening either the β−γ and γ−γ′ bonds to be broken. The former one looks to be more preferable leading to the formation of pentathionate and thiosulfate, but the concurrent route is also available and leads to the appearance of tetrathionate and S3O32−. The latter one is unstable and decomposes rapidly into elementary sulfur and sulfite. The necessity of this less preferable route is supported experimentally by observing sulfur precipitation in the sulfite− hexathionate reaction. The situation becomes more complicated when thiosulfate acts as a nucleophilic agent. The proposed kinetic model suggests that in the case of pentathionate upon attack of thiosulfate on the β-sulfur atom both the α−β and β−γ S−S bonds of the chain may be weakened. The first pathway seems to be more preferable, though the parallel route may also play a minor role to drive the reaction toward precipitating sulfur and shortening the sulfur-chain of pentathionate. The higher rate of the α−β cleavage is also in line with the lower computed bond strength of that bond as compared to that of the β−γ and γ−γ′ bonds (see Figures 9, and S2 in the Supporting Information). At the same time, however, the attack of γ-sulfur of the chain is

CONCLUSIONS It is generally accepted that thiosulfatolysis of polythionates leads eventually to the formation of higher polythionates, whereas sulfitolysis results in the formation of lower polythionates in a slightly acidic medium. The present model, however, suggests that the case of a nucleophilic attack of thiosulfate on the inner sulfur atoms may also open up a possibility of such a sulfur-chain breakage where lower polythionates and short-lived intermediate S3O32− form. The latter species gives rise to the formation of elementary sulfur. The feasibility of this sulfur-chain shortening pathway was first postulated in Foss’s work48 and interpreted here in the case of hexathionate. Furthermore, it is also shown that in the case of hexathionate attack of sulfite opens up a minor pathway, leading to the direct formation of tetrathionate and S3O32−, resulting in the appearance of elementary sulfur precipitation as well. The rate coefficients obtained from the proposed kinetic model for the simultaneous routes of sulfur-chain breakage of pentathionate and hexathionate in the case of thiosulfatolysis may easily be rationalized in terms of the strength of sulfur−sulfur bonds to be broken, the electron density around the inner sulfur atom to be attacked by thiosulfate, and sterical effects to orientate the direction of attack of the nucleophilic agent.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b00276. 5425


Article


■

(9) Rábai, G.; Hanazaki, I. Chaotic pH Oscillations in the Hydrogen Peroxide−Thiosulfate−Sulfite Flow System. J. Phys. Chem. A 1999, 103, 7268−7273. (10) Kelly, D. P. Thermodynamic Aspects of Energy Conservation by Chemolithotrophic Sulfur Bacteria in Relation to the Sulfur Oxidation Pathways. Arch. Microbiol. 1999, 171, 219−229. (11) Druschel, G. K.; Hamers, R. J.; Banfield, J. F. Kinetics and Mechanism of Polythionate Oxidation to Sulfate at Low pH by O2 and Fe3+. Geochim. Cosmochim. Acta 2003, 67, 4457−4469. (12) Pan, C.; Liu, Y.; Horváth, A. K.; Wang, Z.; Hu, Y.; Ji, C.; Zhao, Y.; Gao, Q. Kinetics and Mechanism of the Alkaline Decomposition of Hexathionate Ion. J. Phys. Chem. A 2013, 117, 2924−2931. (13) Koh, T.; Taniguchi, K. Spectrophotometric Determination of Total Amounts of Polythionates (Tetra-, Penta-, and Hexathionate) in Mixtures with Thiosulfate and Sulfite. Anal. Chem. 1973, 45, 2018− 2022. (14) Koh, T.; Taniguchi, K. Spectrophotometric Determination of Micro Amounts of Hexathionate in Mixtures with Thiosulfate and Sulfite by Means of Its Sulfitolysis. Anal. Chem. 1974, 46, 1679−1683. (15) Naito, K.; Hayata, H.; Mochizuki, M. The reactions of polythionates. J. Inorg. Nucl. Chem. 1975, 37, 1453−1457. (16) Rolia, E.; Chakrabarti, C. L. Kinetics of Decomposition of Tetrathionate, Trithionate, and Thiosulfate in Alkaline Media. Environ. Sci. Technol. 1982, 16, 852−857. (17) Zhang, H.; Dreisinger, D. B. The kinetics for the decomposition of tetrathionate in alkaline solutions. Hydrometallurgy 2002, 66, 59− 65. (18) Varga, D.; Horváth, A. K. Kinetics and Mechanism of the Decomposition of Tetrathionate Ion in Alkaline Medium. Inorg. Chem. 2007, 46, 7654−7661. (19) Zhang, H.; Jeffrey, M. I. A Kinetic Study of Rearrangement and Degradation Reactions of Tetrathionate and Trithionate in NearNeutral Solutions. Inorg. Chem. 2010, 49, 10273−10282. (20) Wagner, H.; Schreier, H. Investigations on the Sulfite Degradation of Polythionates. Phosphorus Sulfur Relat. Elem. 1978, 4, 285−286. (21) Pan, C.; Wang, W.; Horváth, A. K.; Xie, J.; Lu, Y.; Wang, Z.; Ji, C.; Gao, Q. Kinetics and Mechanism of Alkaline Decomposition of the Pentathionate Ion by the Simultaneous Tracking of Different Sulfur Species by High-Performance Liquid Chromatography. Inorg. Chem. 2011, 50, 9670−9677. (22) Goehring, M.; Helbing, W.; Appel, I. Ueber die Sulfoxylsäure. III. Die spontane Zersetzung von Polythionatlösungen. Z. Anorg. Chem. 1947, 254, 185−200. (23) Foss, O.; Brune, K.; Brotzen, O. Thiosulphate Catalysis on Mixtures of Tetrathionate and Monoselenotrithionate. Acta Chem. Scand. 1950, 4, 866−869. (24) Fava, A.; Bresadola, S. Kinetics of the Catalytic Rearrangement of Tetrathionate. J. Am. Chem. Soc. 1955, 77, 5792−5794. (25) Ji, C.; Yan, X.; Pan, C.; Lv, F.; Gao, Q. The Key Heterolysis Selectivity of Divalent Sulfur-Sulfur Bonds for a Unified Mechanistic Scheme in the Thiosulfatolysis and Sulfitolysis of the Pentathionate Ion. Eur. J. Inorg. Chem. 2016, 5497−5503. (26) Csekő , G.; Ren, L.; Liu, Y.; Gao, Q.; Horváth, A. K. A New System for Studying Spatial Front Instabilities: The Supercatalytic Chlorite−Trithionate Reaction. J. Phys. Chem. A 2014, 118, 815−821. (27) Liu, Y.; Zhou, W.; Zheng, T.; Zhao, Y.; Gao, Q.; Pan, C.; Horváth, A. K. Convection-Induced Fingering Fronts in the ChloriteTrithionate Reaction. J. Phys. Chem. A 2016, 120, 2514−2520. (28) Liu, Y.; Ren, X.; Pan, C.; Zheng, T.; Yuan, L.; Zheng, J.; Gao, Q. Chlorine dioxide-induced and Congo red-inhibited Marangoni effect on the chlorite-trithionate reaction front. Chaos 2017, 27, 104610. (29) Csekő , G.; Horváth, A. K. Non-Triiodide Based Autoinhibition by Iodide Ion in the TrithionateIodine Reaction. J. Phys. Chem. A 2010, 114, 6521−6526. (30) Kelly, D. P.; Wood, A. P. Synthesis and determination of thiosulfate and polythionates. Methods Enzymol. 1994, 243, 475−501.

Cartesian coordinates and internal energies of the computed studies, HOMO and the Laplacian of the electron density for sulfite, as well as the electron density values at bond critical points of hexathionate (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (A.K.H.). *E-mail: [email protected] (Q.G.). ORCID

Tamás Kégl: 0000-0002-4642-1703 Attila K. Horváth: 0000-0002-1916-2451 Qingyu Gao: 0000-0002-5520-0240 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS 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. BK20160240). This work was also 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 20765-3/2019/ 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.: EFOP3.6.1.-16-2016-00004 entitled by Comprehensive Development for Implementing Smart Specialization Strategies at the University of Pécs. The authors highly appreciated the expert comments of one of the anonymous reviewers on the submissions to interpret the kinetic data correctly.

■

REFERENCES

(1) Lu, Y.; Gao, Q.; Xu, L.; Zhao, Y.; Epstein, I. R. Oxygen−Sulfur Species Distribution and Kinetic Analysis in the Hydrogen Peroxide− Thiosulfate System. Inorg. Chem. 2010, 49, 6026−6034. (2) Xu, L.; Horváth, A. K.; Hu, Y.; Ji, C.; Zhao, Y.; Gao, Q. High Performance Liquid Chromatography Study on the Kinetics and Mechanism of Chlorite−Thiosulfate Reaction in Slightly Alkaline Medium. J. Phys. Chem. A 2011, 115, 1853−1860. (3) Horváth, A. K.; Nagypál, I.; Peintler, G.; Epstein, I. R. Autocatalysis and Self-Inhibition: Coupled Kinetic Phenomena in the Chlorite−Tetrathionate Reaction. J. Am. Chem. Soc. 2004, 126, 6246−6247. (4) Maselko, J.; Epstein, I. R. Chemical Chaos in the Chlorite− Thiosulfate Reaction. J. Chem. Phys. 1984, 180, 3175−3178. (5) Szirovicza, L.; Nagypál, I.; Bárdi, I. Propagating reaction front in “frozen” phase. Int. J. Chem. Kinet. 1991, 23, 99−101. (6) Zhivonitko, V. V.; Koptyug, I. V.; Sagdeev, R. Z. Temperature Changes Visualization during Chemical Wave Propagation. J. Phys. Chem. A 2007, 111, 4122−4124. (7) Kurin-Csörgei, K.; Orbán, M.; Rábai, G.; Epstein, I. R. Model for the Oscillatory Reaction between Hydrogen Peroxide and Thiosulfate Catalysed by Copper(II) Ions. J. Chem. Soc., Faraday Trans. 1996, 92, 2851−2855. (8) Yuan, L.; Gao, Q.; Zhao, Y.; Tang, X.; Epstein, I. R. Temperature-Induced Bifurcations in the Cu(II)-Catalyzed and Catalyst-Free Hydrogen Peroxide-Thiosulfate Oscillating Reaction. J. Phys. Chem. A 2010, 114, 7014−7020. 5426


Article

The Journal of Physical Chemistry A (31) Goehring, M.; Feldmann, U. Neue Verfahren zur Darstellung von Kaliumpentathionat und von Kaliumhexathionat. Z. Anorg. Chem. 1948, 257, 223−226. (32) IUPAC Stability Constant Database; Royal Society of Chemistry: London, 1992−1997. (33) Peintler, G. ChemMech-ZiTa, version 5.99g; a Comprehesive Program Package for Fitting Parameters of Chemical Reaction Mechanism; Attila József University: Szeged, 1989−2017. (34) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158−6170. (35) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (36) Rappoport, D.; Furche, F. Property-optimized Gaussian Basis Sets for Molecular Response Calculations. J. Chem. Phys. 2010, 133, 134105. (37) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Landis, C. R.; Weinhold, F. NBO 5.0; Theoretical Chemistry Institute, University of Wisconsin: Madison, 2001. (38) Bader, R. F. W. Atoms in MoleculesA Quantum Theory; Oxford University Press: Oxford, 1990. (39) Keith, T. A. AIMAll, version 15.05.18; TK Gristmill Software: Overland Park KS, USA, 2015 aim.tkgristmill.com. (40) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378−6396. (41) Frisch, M. J.; et al. Gaussian 09, Revision D.01; Gaussian Inc.: Wallingford CT, 2009. (42) Ji, C.; Yan, X.; Horváth, A. K.; Pan, C.; Zhao, Y.; Gao, Q. Comprehensive Simultaneous Kinetic Study of Sulfitolysis and Thiosulfatolysis of Tetrathionate Ion: Unravelling the Unique pH Dependence of Thiosulfatolysis. J. Phys. Chem. A 2015, 119, 1238− 1245. (43) Kurtenacker, A.; Goldbach, E. Ü ber die Analyse von Polythionatlösungen. Z. Anorg. Allg. Chem. 1927, 166, 177−189. (44) Goehring, M.; Feldmann, U.; Helbing, W. Quantitative Bestimmung der Polythionate (Trithionat, Tetrathionat, Pentathionat und Hexathionat) Nebeneinander. Z. Anal. Chem. 1949, 129, 346− 352. (45) Koh, T.; Taniguchi, K.; Iwasaki, I. Determination of Micro Amounts of Polythionates. X. Spectrophotometric Determination of Micro Amounts of Pentathionate in Mixtures with Thiosulfate and Sulfite by Means of Its Sulfitolysis. Bull. Chem. Soc. Jpn. 1978, 51, 164−168. (46) Foerster, F.; Centner, K. Beiträge zur Kenntnis der schwefligen Säure und ihrer Salze. IV. Ü ber die Einwirkung der schwefligsauren Salze auf Polythionate. Z. Anorg. Chem. 1926, 157, 45−82. (47) Foss, O.; Kringlebotn, I.; Buchardt, O.; Olsen, G. E.; Pedersen, C.; Toft, J. Displacement of Sulphite Groups of Polythionates by Thiosulphate. Acta Chem. Scand. 1961, 15, 1608−1609. (48) Foss, O.; Bjerrum, J.; Woldbye, F.; Grönvall, A.; Zaar, B.; Diczfalusy, E. Remarks on the Reactivities of the Penta- and Hexathionate Ions. Acta Chem. Scand. 1958, 12, 959−966. (49) Münchow, V.; Steudel, R. The Decomposition of Aqueous Dithionite and Its Reactions with Polythionates SnO2−6 (n = 3−5) Studied by Ion-pair Chromatography. Z. Anorg. Allg. Chem. 1994, 620, 121−126. (50) Davis, R. E. Displacement Reactions at the Sulfur Atom. I. An Interpretation of the Decomposition of Acidified Thiosulfate. J. Am. Chem. Soc. 1958, 80, 3565−3569. (51) Ritter, R. D.; Krueger, J. H. Nucleophilic Substitution at Sulfur. Kinetics of Displacement Reactions Involving Trithionate Ion. J. Am. Chem. Soc. 1970, 92, 2316−2321.

5427


Kinetics and Mechanism of the Concurrent Reactions of Hexathionate

Recommend Documents