General pathway of sulfur-chain breakage of polythionates by iodine confirmed by the kinetics and mechanism of the pentathionate-iodine reaction

Article abstract of DOI:10.1021/ic300895c

The pentathionate-iodine reaction has been studied spectrophotometrically at T = 25.0 ± 0.1 °C and at an ionic strength of 0.5 M in both the absence and presence of an initially added iodide ion at the pH range of 3.95-5.15. It was found that the pH does not affect the rate of the reaction; however, the iodide ion produced by the reaction strongly inhibits the oxidation. Therefore, it acts as an autoinhibitor. The kinetic curves also support the fact that iodide inhibition cannot be explained by the formation of the unreactive triiodide ion, and S₅O₆I^- along with the iodide ion has to be involved in the initiating rapid equilibrium being shifted far to the left. Further reactions of S₅O₆I ^-, including its hydrolysis and reaction with the iodide ion, lead to the overall stoichiometry represented by the following equation: S ₅O₆^2- + 10I₂ + 14H₂O → 5SO₄^2- + 20I^- + 28H⁺. A nine-step kinetic model with two fitted parameters is proposed and discussed, from which a rate equation has also been derived. A brief discussion about the general pathway of sulfur-chain breakage of polythionates supported by theoretical calculations has also been included.

Full text of DOI:10.1021/ic300895c

Article
pubs.acs.org/IC
General Pathway of Sulfur-Chain Breakage of Polythionates by
Iodine Confirmed by the Kinetics and Mechanism of the
Pentathionate−Iodine Reaction
Li Xu, Gyo
̈
̈
́ ́ ́
rgy Cseko, Tamas Kegl, and Attila K. Horvath*
Department of Inorganic Chemistry, University of Pec
́
́ ́
́
s, Ifjusag utja 6, H-7624 Hungary
Jan
́
os Szentag
́
othai Research Center, Pecs, Ifjusag utja 34, H-7624 Hungary
́
́
́
́
*
S Supporting Information
ABSTRACT: The pentathionate−iodine reaction has been studied
spectrophotometrically at T = 25.0 ± 0.1 °C and at an ionic
strength of 0.5 M in both the absence and presence of an initially
added iodide ion at the pH range of 3.95−5.15. It was found that
the pH does not affect the rate of the reaction; however, the iodide
ion produced by the reaction strongly inhibits the oxidation.
Therefore, it acts as an autoinhibitor. The kinetic curves also
support the fact that iodide inhibition cannot be explained by the
−
formation of the unreactive triiodide ion, and S O I along with the
5
6
iodide ion has to be involved in the initiating rapid equilibrium
−
being shifted far to the left. Further reactions of S O I , including
5
6
its hydrolysis and reaction with the iodide ion, lead to the overall
2
−
stoichiometry represented by the following equation: S O + 10I2
5
6
2−
−
+
+
14H O → 5SO + 20I + 28H . A nine-step kinetic model with
2 4
two fitted parameters is proposed and discussed, from which a rate equation has also been derived. A brief discussion about the
general pathway of sulfur-chain breakage of polythionates supported by theoretical calculations has also been included.
INTRODUCTION
The oxidation of thiosulfate by different oxidizing agents exhibits
several exotic nonlinear dynamical phenomena, such as
nate, however, significantly less information is available in the
■
literature about the oxidation of pentathionate. We could track
19
only a single study by Read et al. that directly investigates the
oxidation of pentathionate by the ferrate ion. Although little
information is known about the redox reactions of pentathionate,
we may expect similar kinetic behavior of polythionates because
of their similar chemical structure. The reaction of pentathionate
with iodine may be a good candidate to check this idea because,
on the one hand, the reaction can easily be followed by UV−
visible spectroscopy and, on the other hand, the kinetics of
1
autocatalysis under batch conditions, bistability and oscilla-
1
,2
3,4
tions or complex periodic and aperiodic (chaotic) behavior,
5
and multistationary states in a continuously stirred tank reactor
CSTR), as well as the appearance of different kinds of reaction-
diffusion patterns (chemical waves and chemical reaction fronts)
in an unstirred system.
many sulfur-containing intermediates (mainly polythionates
with a considerably long half-life) may be produced during the
oxidation of thiosulfate.
Compared to trithionate and tetrathionate, pentathionate is
less stable in aqueous solution, especially at alkaline conditions,
(
6
−9
Besides the major product, sulfate,
2
0,21
22
tetrathionate−iodine
as well as that of trithionate−iodine
1
0,11
reactions have already been available for comparison. The main
outcome of these papers indicates that the oxidation of
polythionates eventually leading to sulfate starts with an initiating
12
+
equilibrium (a formal I transfer to the inner sulfur of the sulfur
but it is relatively stable at pH < 8.0 and may therefore be a
conceivable candidate as one of the sulfur-containing inter-
mediates during the oxidation of thiosulfate. Recent researches
have been shown that not only chemical but also electrochemical
oxidation of thiosulfate leads to the formation of higher
−
chain to produce S O I ) in which the iodide ion is also involved.
x
6
Our aim in this paper is to obtain an additional support about the
nontriiodide”-based iodide inhibition, as well as to unravel the
“
kinetics and mechanism of the analogous pentathionate−iodine
reaction. As a result, it may also provide a better understanding
and insight into the nature of the sulfur-chain-breaking reactions
of pentathionate that may be helpful as a guide in unraveling
more complex oxidation reactions of pentathionate.
1
3,14
polythionates.
Moreover, the kinetic studies of hydrogen
10
11
peroxide−thiosulfate, chlorite−thiosulfate, and hypochlo-
15
rous acid−thiosulfate systems have clearly demonstrated that
pentathionate is formed in detectable amounts and may thus
contribute to the appearance of a rich variety of kinetic
4
,6−9,16−18
phenomena
found experimentally in the oxidation
Received: May 2, 2012
Published: June 28, 2012
reactions of thiosulfate. Compared to trithionate and tetrathio-
©
2012 American Chemical Society
7837
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Materials and Instrumentation. Materials. The potassium
pentathionate was first prepared by the reaction of sodium
thiosulfate with hydrochloric acid and arseneous oxide followed
by ion exchange with a slurry of finely crystalline potassium
for nonlinear parameter estimation by the ZiTa program
25
package Altogether 23000 experimental points from 176
kinetic runs were used for simultaneous fitting. To obtain the
kinetic model and the individual reaction rate coefficients, an
absolute fitting procedure has been chosen to minimize the
average deviation between measured and calculated concen-
trations. Our quantitative criterion for an acceptable fit was that
the average deviation for the absolute fit approached 0.005
absorbance units, which is close to the experimentally achievable
limit of error of the spectrophotometer.
23
acetate as described previously. To confirm the purity of
potassium pentathionate, Raman spectroscopy was carried out
by a NXR Fourier transform Raman spectrometer. Its exact
purity was checked by the following method. A known amount of
potassium pentathionate was dissolved in pure distilled water
followed by the addition of a bromine solution in excess. The
reaction mixture was left to stand for at least 5 min, which was
proven to be enough to oxidize pentathionate into sulfate
completely. The excess of bromine was then removed by boiling
the solution for a couple of minutes. The hydrogen ion, liberated
by the oxidation of pentathionate by bromine according to the
equation
Computational Details of Theoretical Calculations. For
all of the calculations, the PBE0 functional was selected, i.e., the
26
zero-parameter hybrid functional by Adamo and Barone based
on the generalized gradient approximation exchange and
27
correlation functionals by Perdew, Burke, and Ernzerhof. For
all atoms, the def2-TZVPD triple-ζ basis set with polarization
28
and diffuse basis functions were employed. This model
2
−
+ 10Br + 14H O → 5SO + 28H + 20Br−
2−
+
S5O
6
2
2
4
chemistry exhibited a reasonable agreement with the exper-
29
2−
(
1)
imental geometrical parameters for all species of the S O
x 6
type (x = 3−5). Optimized geometries were identified by the
absence of negative eigenvalues in the vibrational frequency
analysis. Geometry optimizations were completed with solvent
effects taken into account by employing the polarizable
was determined by titrating the sample against a standard sodium
hydroxide solution. The purity of the solid potassium
pentathionate sample was found to be better than 97.0% and
checked prior to each experiment. No thiosulfate, sulfite, and
elementary sulfur impurities could be detected up to 2−4 weeks.
30
continuum model methodology with dielectric constant ε =
2
3
7
8.355 for water. For all of the calculations, the Firefly 7.1.G
Because the composition of solid pentathionate
is
31
1
quantum chemical package was used. Natural bond orbital
K S O · / H O, this means that it may contain only a trace
2
5
6
2
2
32
(
NBO) analyses have been performed by the module NBO 5.G
amount of sulfate or tetrathionate besides crystalline water. Once
the purity of the solid sample was proven to be decreased because
of the formation of elementary sulfur and other sulfur species, it
was discarded and a new solid potassium pentathionate sample
was prepared. All of the other chemicals (iodine, potassium
iodide, acetic acid, sodium acetate, and sodium perchlorate) were
of the highest purity commercially available and were used
without further purification. The stock solutions were prepared
from twice ion-exchanged and double-distilled water. The initial
concentration of the iodine solution was determined by titration
of the stock solutions with standardized thiosulfate and/or
spectrophotometrically before each experiment.
implemented in Firefly.
RESULT
■
Stoichiometry. The stoichiometry of the reaction was
established by visible spectroscopy from the end of the kinetic
measurements in an excess of iodine. The calculation indicated
that the ratio of iodine and pentathionate is 10 and the only
sulfur-containing product of the reaction is the sulfate ion.
Therefore, the stoichiometry of this reaction can be expressed as
follows:
The pH of the solutions was maintained between 3.95 and 5.15
2−
2−
−
+
S5O6 + 10I + 14H O → 5SO + 20I + 28H
2
2
4
by acetic acid/acetate buffer by taking the pK of acetic acid as
a
2
4
(2)
4
0
.55. The acetate concentration was always kept constant at
.05 M, and the pH was adjusted by the necessary amount of
Individual Curve-Fitting Method. Survey of the exper-
imental curves in the pentathionate−iodine reaction reveals two
important characteristics of this system. On the one hand, the
decay of iodine is independent of the pH within the pH range
used in the experiments, as seen in Figure 1. The same
phenomenon has also been reported in the tetrathionate−
acetic acid. The ionic strength was adjusted to be 0.5 M by adding
the necessary amount of sodium perchlorate. The temperature of
the reaction vessel was maintained at 25.0 ± 0.1 °C. The initial
concentrations of the reactants were varied in the ranges of
.063−0.768, 0.0293−1.40, and 0−1.897 mM in the cases of
iodine, pentathionate, and iodide, respectively.
0
2
0,21
22
iodine
and trithionate−iodine systems, meaning that this
Methods and Instrumentation. The reaction was followed by
a Zeiss S600 diode-array spectrophotometer at the wavelength
range of 400−800 nm without using the deuterium lamp of the
photometer. 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. First, the buffer components, the
reactant iodine, and iodide (if necessary) were delivered from a
pipet. The spectrum of the solution was always recorded before
injection of the pentathionate solution to determine the exact
initial concentration of iodine. The reaction was started with the
addition of the necessary amount of a pentathionate solution
from a fast-delivery pipet.
feature is a general phenomenon of the polythionate−iodine
reactions. On the other hand, Figure 2 describes the effect of the
initially added iodide ion on the consumption of the total amount
of iodine. It clearly demonstrates that an increase of the initial
iodide concentration significantly inhibits the pentathionate−
iodine reaction. Therefore, the iodide ion acts as an autoinhibitor
of the system because its concentration monotonously increases
during the course of the reaction. To account for all of these
observations, our first effort to evaluate the kinetic curves
individually was, therefore, based on the following apparent rate
equation:
2
−
Data Treatment. In the visible range, only iodine and
triiodide were found to absorb light; therefore, the isosbestic
point of the iodine−triiodide system (λ = 468 nm) was selected
dTI2
[S O ]TI2
5 6
− 11
= kapp
−
0 dt
[I ]
(3)
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Table 1. Apparent Rate Coefficients of Representative
Examples Determined by the Individual Curve-Fitting
Method
S5O62−]0/mM
[I ] /mM
[I ] /mM
−
pH
kapp × 105 s−1
[
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.03
0.455
0.43
0
3.95
3.95
3.95
3.95
3.95
3.95
3.95
4.85
4.85
4.85
4.85
4.85
4.85
4.85
3.95
4.25
4.55
4.85
5.15
4.55
4.55
4.55
4.55
4.55
4.55
4.55
3.73
3.48
3.17
3.15
3.23
3.25
3.13
3.78
3.67
3.33
3.38
3.25
3.37
3.76
3.35
3.20
3.17
3.09
3.25
3.02
2.66
2.54
2.25
2.14
1.95
1.83
.06
0
.121
.251
.5
0.445
0.45
0
0
0.45
0
.8
0.41
0
.401
.05
0.42
0
0.064
0.096
0.18
0
.05
0
.05
0
Figure 1. Measured (dots) and calculated (solid lines) absorbance−
.05
0.245
0.355
0.509
0.732
0.533
0.543
0.533
0.538
0.533
0.520
0.520
0.520
0.515
0.512
0.515
0.520
0
2−
time curves at [S O ] = 0.201 mM and [I ] = 0.511 mM at different
5
6
0
2 0
.05
0
pH values in the absence of the initially added iodide ion. pH = 3.95
black), 4.25 (blue), 4.55 (green), 4.85 (cyan), and 5.15 (red).
.05
0
(
.05
0
.061
.061
.061
.061
.061
.489
.489
.489
.489
.489
.489
.489
0
0
0
0
0
0
0.100
0.499
0.999
1.300
1.600
1.897
second-order reaction, having the formal kinetic order of both
reactants as 1. This kinetic model fits all of the data with an
unacceptably high average deviation of 0.046 absorbance units.
We therefore concluded that inhibition of the iodide ion cannot
be taken into account only by the formation of the triiodide ion.
On the basis of the remarkable resemblance of the kinetic
Figure 2. Measured (dots) and calculated (solid lines) absorbance−
2
−
time curves at [S O ] = 0.11 mM, [I ] = 0.56 mM, and pH = 4.55 in
5
6
0
2 0
−
the presence of the initially added iodide ion. [I ] /mM = 0.0 (black),
0
0.101 (blue), 0.399 (green), 0.699 (cyan), 0.998 (red), 1.397 (magenta),
and 1.796 (brown).
20−22
behavior of the polythionate−iodine reactions,
we suggest
−
where T = [I ] + [I ]. The surprising results of our calculation
the kinetic models R1−R9 similar to the reactions mentioned
I
2
2
3
above:
is that eq 3 is able to fit all of the 176 kinetic curves with k equal
app
−
5 −1
to (3.15 ± 0.50) × 10
s
within an acceptable error, although
−
+
I + H O ⇌ HOI + I + H
(R2)
(R3)
2
2
we also noticed that kapp slightly decreases as the initial
concentration of iodide increases. This feature is illustrated in
Table 1. Later we shall see that this feature can easily be explained
by the proposed model.
2−
−
−
S5O6 + I ⇌ S O I + I
2
5 6
−
−
−
+
S O I + H O → S O I + S O OH + H
(R4)
(R5)
5
6
2
2
3
3
3
Proposed Kinetic Model. Because the overall reaction
produces a relatively huge amount of proton (see eq 2), the
protonation and deprotonation processes of the buffer
components would seem to be necessary to follow the slight
change of the pH during the course of the reaction:
−
−
I− + S
−
S
O
I + I → S
O
O I
5
6
2
3
3 3
fast
S O OH + 3I + 5H O ⎯ ⎯→ 3HSO + 8H + 6I−
−
−
+
3
3
2
2
3
(R6)
+
−
CH COOH ⇌ H + CH COO
(4)
fast
3
3
S O I + I + 3H O ⎯ ⎯→ 2HSO + 4H + 3I−
−
−
+
2
3
2
2
3
(R7)
(R8)
(R9)
However, as shown above, the pH does not affect the reaction;
therefore, this equilibrium was only taken into consideration for
the sake of completeness. Our first effort was to describe all of the
76 kinetic curves simultaneously based on eq 2, which was
augmented by the well-known triiodide formation equilibrium:
fast
−
−
+
−
S O I + 3I + 6H O ⎯ ⎯→ 3HSO + 9H + 7I
3
3
2
2
3
fast
1
−
2−
−
+ 2I + 3H+
HSO3 + I + H O ⎯ ⎯→ SO
2
2
4
−
−
Table 2 contains the parameter set determined by the
simultaneous evaluation of the kinetic curves, and the results
are illustrated in Figures 1−4. (Supporting Information is also
available to show the results of the fits for all of the 176 measured
kinetic curves.) By the proposed kinetics, we were able to
I + I ⇌ I
(R1)
2
3
In this model, the iodide inhibition was taken into consideration
simply by the formation of the kinetically inactive triiodide ion
and the rate equation of eq 2 was considered to be an overall
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Table 2. Fitted and Fixed Rate Coefficients of the Proposed
Kinetic Model
describe all of the 176 kinetic curves by 0.0048 absorbance unit
average deviation, suggesting the plausibility of our kinetic
model.
a
step
R1
rate equation
parameter
5.7 × 109 M−1s−1
Discussion. Step R1 is the well-known fast equilibrium of the
−
33,34
k [I ][I ]
R1
2
formation of the triiodide ion studied by several authors.
The
k−R1[I3−]
8.5 × 10 s
6
−1
rate coefficients of the forward and reverse reactions were set to
2
R2
k [I ]
5.52 × 10− s−1
1.023 × 10 M−2 s−1
9
−1 −1
6 −1
−
R2
2
k = 5.7 × 10 M
s and k−R1 = 8.5 × 10 s to give log β =
R1
I
3
+
−
11
k−R2[HOI][H ][I ]
24
2.83, where βI3− is the formation constant of the triiodide ion.
+
−3
−1
k′ [I ]/[H ]
1.98 × 10 M s
R2
2
−
3.67 × 10 M s−1
9
−1
Step R2 is the hydrolytic equilibrium of iodine in an aqueous
solution. The rate coefficients of the forward and reverse
reactions including the hydroxide-driven pathway were deter-
mined previously; therefore, we used these values as fixed ones
k′−R2[HOI][I ]
2
−
1
−1 −1
R3
k [S O ][I ]
10 M
s
R3
5
6
2
−
−
6
−1 −1
k−R3[S O I ][I ]
10 M
s
5
6
−
−1
R4
R5
R6
R7
R8
R9
k [S O I ]
3.29 ± 0.06 s
R4
5
6
35−37
−
−
310 ± 66 M s−1
−1
k [S O I ][I ]
throughout the whole fitting procedure.
R5
5
6
−
2
−1 −1
k [S O OH ][I ]
>10 M
s
Step R3 is a rapid initiating equilibrium between the reactants,
R6
3
3
2
−
−
2
−1 −1
k [S O I ][I ]
>10 M
s
producing S O I and the iodide ion. Later we shall see that the
5
6
R7
2
3
2
−
3
−1 −1
k [S O I ][I ]
>10 M
s
attack of the iodine molecule is likely to occur on the β (or β′)-
sulfur of pentathionate. Our calculation has provided only a
R8
3
3
2
kR9[HSO3−][I2]
3.1 × 10 M s−1
9
−1
a
higher limit for KR3 = k /k = 0.01; any value lower than that
No error indicates that the value in question was fixed during the
R3 −R3
leads to the same average deviation, meaning that this
equilibrium is shifted far to the left. To provide a low steady-
fitting procedure.
−
state concentration for the species S O I , we have set k = 10
5
6
R3
−1
−1
6
−1 −1
−5
M
s
and k−R3 = 10 M
s
to provide K = 10 during the
R3
calculation process.
Step R4 is one of the possible pathways of S O I to produce
−
5
6
additional sulfur-containing short-lived intermediates via the
breakup of the sulfur chain. The solvent water molecule probably
attacks the γ-sulfur of the sulfur chain (an attack on β′-sulfur
−
−
cannot be ruled out entirely), resulting in S O I and S O OH .
2
3
3
3
Because both species are short-lived intermediates, our kinetic
measurements do not provide a solid basis to distinguish
between step R4 and the following reaction:
−
−
−
+
S O I + H O → S O I + S O OH + H
(5)
5
6
2
3
3
2
3
−
One should keep in mind that iodine in S O I is placed on the
3
3
Figure 3. Measured (dots) and calculated (solid lines) absorbance−
inner sulfur and not on the terminal one to be in agreement that
time curves at [I ] = 0.51 mM and pH = 4.55 in the absence of the
2
0
iodine attacks the β-sulfur of the sulfur chain. If further reaction
2
−
initially added iodide ion. [S O6 ]0/mM = 0.03 (black), 0.06 (blue),
−
5
of S O OH with iodine is considered to be a rapid reaction
2
3
0.101 (green), 0.201 (cyan), 0.400 (red), 0.800 (magenta), and 1.401
resulting in the formation of hydrogen sulfite as well, step R4 can
easily be replaced by eq 5 kinetically. However, as we show later,
the attack of the oxygen atom of the solvent molecule most likely
(
brown).
−
takes place on the γ-sulfur of S O I ; therefore, we are rather
5
6
−5
inclined to keep step R4 in the final model. If K = 10 is used to
provide a low steady-state concentration for S O I , we could
calculate kR4 = 3.29 ± 0.06 s . Our fitting also indicated that k
R3
−
5
6
−1
R4
and KR3 cannot be determined independently because of the
strong correlation between these kinetic parameters; only their
product could be calculated. Later we shall see that this fact can
conveniently be explained by the overall rate equation obtained
from the proposed kinetic model.
−
Step R5 is the other important conversion reaction of S O I
5
6
in which the iodide ion probably attacks one of the inner sulfurs
of the sulfur chain, resulting in the breakup of the sulfur−sulfur
−
bond as well. Such a reaction of the intermediate S O I with the
x
6
iodide ion was already proposed in the tetrathionate−iodine
Figure 4. Measured (dots) and calculated (solid lines) absorbance−
21
2
−
reaction and turns out to be necessary to describe adequately
time curves at [S O ] = 0.05 mM and pH = 4.85 in the absence of the
5
6
0
the polythionate−iodine reactions. It was found that the
individual rate coefficient of this reaction cannot be determined
as well because of the strong correlation between the rate
initially added iodide ion. [I ] /mM = 0.064 (black), 0.096 (blue), 0.18
2
0
(
green), 0.245 (cyan), 0.355 (red), 0.509 (magenta), and 0.732
(
brown).
coefficients of k , k , and k ; only the product of K and k
can be calculated unambiguously. As a result, if KR3 = 10 was
R3 −R3
R5
R3
R5
−5
considered in the calculation process, we obtained k = 310 ± 66
R5
−
1 −1
M
s .
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SxO62 + I ⇌ S O I + I
−
−
−
Steps R6−R8 are fast processes in which the short-lived
2
x 6
(11)
−
−
−
intermediates S O OH , S O I , and S O I are oxidized by
3
3
2
3
3
3
where x = 3−5. This equilibrium is shifted far to the left and
established rapidly compared to the time scale of the reaction in
question. Should these reactions start with formal I , the
inhibitory effect of the iodide can easily be explained by eq 11. As
iodine, resulting in hydrogen sulfite and the iodide ion. All of
these reactions were found to be rapid processes, and only the
lower limits of k , k , and k (indicated in Table 2) could be
+
R6 R7
R8
determined from our measurements.
20−22
shown previously,
the formation of the kinetically inactive
Step R9 is the rapid, essentially diffusion-controlled, reaction
of hydrogen sulfite and iodine studied thoroughly by Yiin and
triiodide formation in itself is not able to explain the inhibitory
effect of the iodide ion. From these studies, it was also
enlightened that the following rate equation describes well the
kinetic curves of all of the polythionates−iodine reactions:
3
8
9
−1 −1
Margerum. The kR9 = 3.1 × 10 M
s value was determined
in their work for its rate coefficient, and we fixed it throughout
the whole calculation process.
Formal Kinetics. Because no intermediates were found in a
detectable amount during the course of the reaction, a rate
equation can easily be deduced from the proposed model.
Considering that
2−
[
SxO6 ]TI2
v = kx
−
[
I ]
(12)
5
−1
where 10 k = 82.7, 4.1, and 3.15 s in the case of tritihionate,
x
2
−
tetrathionate, and pentathionate, respectively. From these values,
one can easily calculate that the half-lives of the corresponding
trithionate−iodine, tetrathionate−iodine, and pentathionate−
iodine reactions are 840, 16900, and 22000 s, respectively. In
other words, this means that a longer sulfur chain of
polythionates corresponds to a more sluggish reaction toward
iodine. It raises an important question about the attack of iodine
on polythionates at a molecular level. Figure 5 indicates the
dTI2
d[S O
]
− 11
= −
5
6
0 dt
dt
2
−
−
−
=
k [S O ][I ] − k [S O I ][I ]
(6)
R3
5
6
2
−R3
5 6
−
and applying a steady-state approximation for species S O I
5
6
yield
2
−
k [S O ][I2]
−
R3
5 6
[
S O I ] =
5
6
−
kR4 + (k−R3 + k )[I ]
(7)
R5
Upon substitution of eq 7 into eq 6, followed by some algebraic
manipulation, we arrive at
2
−
dTI2
d[S O
]
− 11
0 dt
dt
5
6
= −
2
−
−
=
[S O ]T (k k + k k [I ])
5
6
I
R3 R4
R3 R5
2
−
/
{kR4 + (k−R3 + kR5 + k K )[I ]
R4 R1
−
2
+
K (k
+ k )[I ] }
(8)
R1 −R3
R5
where KR1 is the formation constant of triiodide. Taking into
account that the k ≫ k + k K inequality is fulfilled and
−
R3
R5
R4 R1
−
k−R3[I ] ≫ k holds apart from the very beginning stage of the
reaction, the following equation is obtained:
R4
−
2−
dTI2
K k + K k [I ] [S O ]TI2
5 6
− 11
R3 R4
R3 R5
=
−
−
0 dt
1 + K [I ]
[I ]
(9)
R1
Comparing eq 9 with eq 3, one can easily see that kapp slightly
depends on the actual iodide concentration.
−
K k + K k [I ]
R3 R4
R3 R5
kapp
=
−
1
+ K [I ]
(10)
R1
Substituting the rate coefficients determined here at low initial
−
5 −1
iodide concentration, we can calculate 3.15 × 10
s
for k ,
s can
app
−
5 −1
while at high initial iodide concentration, kapp = 0.6 × 10
be obtained. Comparing these values with the experimentally
−
Figure 5. Molecular structures of polythionates and S O I species
x
6
calculated at the PBE0/TZVPD level of theory. Bond distances are given
in angstroms and bond angles in degrees. Natural charges are written in
italics.
determined kapp values at different initial conditions (see Table
1), we find that the results strongly support our proposed kinetic
model as well. This equation also helps to understand why only
the products of KR3kR4 and KR3kR5 can be calculated from our
experiments.
−
calculated structures of polythionates and S O I species. It is
x
6
General Pathway of the Sulfur-Chain Breakage of
seen that among the polythionates the β-sulfur of trithionate has
the most negative partial charge (−0.411). Compared to this, the
partial charge of the β (and β′)-sulfur atom decreases to −0.203
in the case of tetrathionate, but a further increase of the sulfur
chain results in a minor change only (to −0.199) for the partial
22
Polythionates. Previous studies of trithionate and tetrathio-
2
0,21
nate
oxidation by iodine as well as our present results suggest
the fact that the sulfur-chain breakage of polythionates starts
generally with the same equilibrium:
7
841
dx.doi.org/10.1021/ic300895c | Inorg. Chem. 2012, 51, 7837−7843

Inorganic Chemistry
Article
charge of β-and β′-sulfur atoms in the case of pentathionate.
Because the β (and β′)-sulfur of the polythionate sulfur chain is
negatively charged, this site is a possible candidate to be attacked
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: horvatha@gamma.ttk.pte.hu.
+
by iodine and, furthermore, supports a formal I transfer to the β-
sulfur of the polythionate chain. Moreover, the increase of the
Notes
−
partial charge of the β-sulfur of S O I compared to those of the
The authors declare no competing financial interest.
x
6
corresponding polythionates (0.237, 0.219, and 0.217 electrons
for the trithionate, tetrathionate, and pentathionate, respec-
tively) may also explain why the trithionate−iodine reaction is
faster by more than 1 order of magnitude compared to the
tetrathionate−iodine and pentathionate−iodine reactions and
why there is not much difference between the rates of the
tetrathionate−iodine and pentathionate−iodine reactions. The
central kinetic role of the β (and β′)-sulfur of the sulfur chain is
also supported by the well-known catalytic effect of thiosulfate on
ACKNOWLEDGMENTS
■
This work was supported by the Hungarian Research Fund
Grant CK78553). The authors are grateful to Dr. Andrea Petz
for her helpful assistance in the Raman measurements. L.X. is
thankful for financial support from the China Scholarship
Council.
(
39
−
REFERENCES
the rearrangement of tetrathionate. Once S O I forms, one
■
4
x
6
may easily see that the length of the bond between the α- and β-
sulfur atoms increases in each polythionate in the range of
(1) Orban
́
, M.; Kepper, P. D.; Epstein, I. R. J. Phys. Chem. 1982, 86,
31−433.
(
2) Rab
́
ai, G.; Beck, M. T.; Kustin, K.; Epstein, I. R. J. Phys. Chem. 1989,
0
.152−0.212 Å, facilitating an attack of the solvent molecule to
−
93, 2853−2858.
finally break up the sulfur chain. The fate of S O I , however,
x
6
(
(
(
(
3) Orban
4) Maselko, J.; Epstein, I. R. J. Chem. Phys. 1984, 80, 3175−3178.
5) Orban, M.; Epstein, I. R. J. Am. Chem. Soc. 1987, 109, 101−106.
6) Nagypal, I.; Bazsa, G.; Epstein, I. R. J. Am. Chem. Soc. 1986, 108,
́
, M.; Epstein, I. R. J. Phys. Chem. 1982, 86, 3907−3910.
differs in the case of trithionate compared to those of the higher
−
polythionates. In the former case, S O I has two different routes
3
6
́
22
for sulfur-chain breakup: hydrolysis and the reaction of iodine.
́
In the other cases, however, besides the hydrolysis, the attack of
3
635−3640.
(7) Szirovicza, L.; Nagypal
101.
(8) Zhivotniko, V. V.; Koptyug, I. V.; Sagdeev, R. Z. J. Phys. Chem. A
−
the iodide ion is also a possible route for S O I to be converted.
́ ́
, I.; Bardi, I. Int. J. Chem. Kinet. 1991, 23, 99−
x
6
−
The lack of attack of the iodide ion on S O I may easily be
3
6
explained by the lack of a sterically not hidden positively charged
sulfur atom of the molecule. Our present study of the
2
007, 111, 4122−4124.
(9) Koptyug, I. V.; Zhivotniko, V. V.; Sagdeev, R. Z. J. Phys. Chem. B
−
pentathionate−iodine reaction reveals that S O I can also be
5
6
2
(
4
(
008, 112, 1170−1176.
10) Lu, Y.; Gao, Q.; Xu, L.; Zhao, Y.; Epstein, I. R. Inorg. Chem. 2010,
9, 6026−6034.
11) Xu, L.; Horvat
Chem. A 2011, 115, 1853−1860.
12) (a) Christiansen, J. A.; Drost-Hansen, W.; Nielsen, A. Acta Chem.
attacked by the iodide ion to break up the sulfur chain. As can be
seen, the β- and γ-sulfur atoms are partially positively charged
parts of the molecule that can be attacked by the electron-rich
iodide ion. This further attack (which probably takes place on the
γ-sulfur because of its slightly more positive partial charge)
increases the length of the β-sulfur−γ-sulfur bond, resulting in its
immediate breakup. Once the sulfur chain breaks up, the
following rapidly oxidizing processes eventually lead to the
formation of sulfate.
́
h, A. K.; Hu, Y.; Ji, C.; Zhao, Y.; Gao, Q. J. Phys.
(
Scand. 1952, 6, 333−340. (b) Goehring, M.; Heibing, W.; Appel, I. Z.
Anorg. Chem. 1947, 254, 185−200. (c) Wagner, H.; Schreier, H.
Phosphorus Sulfur Relat. Elem. 1978, 4, 281−284. (d) Wagner, H.;
Schreier, H. Phosphorus Sulfur Relat. Elem. 1978, 4, 285−286. (e) Pan, C.
́
W.; Wang, W.; Horvath, A. K.; Xie, J.; Lu, Y.; Wang, Z.; Ji, C.; Gao, Q.
Inorg. Chem. 2011, 50, 9670−9677.
CONCLUSION
■
(13) Du, Z.; Gao, Q.; Feng, J.; Lu, Y.; Wang, J. J. Phys. Chem. B 2006,
110, 26098−26104.
The work presented here is the first trial to describe the kinetics
and mechanism of the pentathionate−iodine reaction. As shown,
it is demonstrated that the reaction is independent of the pH
within the pH range studied and exhibits strong iodide
autoinhibition that emerges from the initiating equilibrium
(
(
2
14) Jeffrey, M. I.; Brunt, S. D. Hydrometallurgy 2007, 89, 52−60.
́ ́
15) Varga, D.; Horvath, A. K.; Nagypal, I. J. Phys. Chem. B 2006, 110,
467−2470.
16) Yuan, L.; Gao, Q.; Zhao, Y.; Tang, X.; Epstein, I. R. J. Phys. Chem.
A 2010, 114, 7014−7020.
17) Kurin-Csorgei, K.; Orban
Faraday Trans. 1996, 92, 2851−2855.
18) Rabai, G.; Hanazaki, I. J. Phys. Chem. A 1999, 103, 7268−7273.
(
−
between the reactants, resulting in the formation of S O I and
5
6
(
̈
́ ́
, M.; Rabai, G.; Epstein, I. J. Chem. Soc.,
the iodide ion. As pointed out throughout a comparison of the
studies of trithionate−iodine and tetrathionate−iodine as well,
this phenomenon seems to be general among the sulfur-chain-
breaking reaction of polythionate with the mild oxidizing agent
iodine. We also hope that the present study will inspire some
further theoretical investigations to obtain deeper insight into the
nature of sulfur-chain-breaking reactions of polythionates.
Understanding these reactions more thoroughly may contribute
to better descriptions of nonlinear exotic phenomena in which
polythionates, mainly tetrathionate, are seriously involved.
(
́
(19) Read, J. F.; Bewick, S. A.; Donaher, S. C.; Ealman, M. D.; Oakey,
J.; Schaubel, C.; Tam, N. C.; Theriault, A.; Watson, K. J. Inorg. React.
Mech. 2005, 5, 281−304.
(
(
4
(
(
20) Kerek, A.; Horvat
21) Awtrey, A. D.; Connick, R. E. J. Am. Chem. Soc. 1951, 73, 4546−
́
h, A. K. J. Phys. Chem. A 2007, 111, 4235−4241.
549.
22) Cseko
̈
, G.; Horvat
́
h, A. K. J. Phys. Chem. A 2010, 114, 6521−6526.
23) Kelly, D. P.; Wood, A. P. Methods Enzymol. 1994, 243, 475−501.
24) IUPAC Stability Constant Database; Royal Society of Chemistry:
(
London, 1992−1997.
ASSOCIATED CONTENT
(25) Peintler, G. ZiTa, version 5.0; a comprehensive program package for
■
fitting parameters of chemical reaction mechanism; Attila Joz
́
sef University:
*
S
Supporting Information
Szeged, Hungary, 1989−1998.
Table containing the conditions of each kinetic run and figures
containing the measured and fitted data. This material is available
free of charge via the Internet at http://pubs.acs.org.
(
26) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158−6170.
(27) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77,
3865−3868.
7
842
dx.doi.org/10.1021/ic300895c | Inorg. Chem. 2012, 51, 7837−7843

Inorganic Chemistry
Article
(
28) Rappoport, D.; Furche, F. J. Chem. Phys. 2010, 133, 134105−
34115.
29) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd
ed.; Butterworth-Heinemann: New York, 1997.
1
(
(
(
30) Tomasi, J.; Persico, M. Chem. Rev. 1994, 94, 2027−2094.
31) Granovsky, A. A. Firefly, version 7.1.G, http://classic.chem.msu.
su/gran/firefly/index.html.
32) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88,
99−926.
33) Turner, D. H.; Flynn, G. W.; Sutin, N.; Beitz, J. V. J. Am. Chem.
Soc. 1972, 94, 1554−1559.
34) Ruasse, M.; Aubard, J.; Galland, B.; Adenier, A. J. Phys. Chem.
(
8
(
(
1
(
(
986, 90, 4382−4388.
35) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84, 1355−1361.
36) Lengyel, I.; Epstein, I. R.; Kustin, K. Inorg. Chem. 1993, 32, 5880−
5882.
(
37) Lengyel, I.; Li, J.; Kustin, K.; Epstein, I. R. J. Am. Chem. Soc. 1996,
1
(
(
18, 3708−3719.
38) Yiin, B. S.; Margerum, D. W. Inorg. Chem. 1990, 29, 1559−1564.
39) Fava, A.; Bresadola, S. J. Am. Chem. Soc. 1955, 77, 5792−5794.
7
843
dx.doi.org/10.1021/ic300895c | Inorg. Chem. 2012, 51, 7837−7843