On the complexity of kinetics and the mechanism of the thiosulfate- periodate reaction

Article abstract of DOI:10.1021/ic2006309

The thiosulfate-periodate reaction has been studied spectrophotometrically in a slightly acidic medium at 25.0 ± 0.1 °C in an acetate/acetic acid buffer by monitoring the absorbance in the 250-600 nm wavelength range at a constant ionic strength adjusted by the buffer component sodium acetate. In agreement with a previous study, we found that the reaction cannot be described by a single stoichiometric equation, tetrathionate and sulfate are simultaneously formed, and its ratio strongly depends on the pH. As expected at certain initial concentration ratios of the reactants, the reaction behaves as a clock reaction, but after its appearance, iodine is slowly consumed mainly because of the moderate tetrathionate-iodine reaction. It is also enlightened that the initial rate of the reaction is completely independent of the pH, which apparently contradicts a previous study, which postulates a "supercatalytic" behavior of the hydrogen ion on the title reaction. Significant buffer assistance that may change the absorbance-time profiles was also observed. On the basis of the kinetic data, a robust 28-step kinetic model with 22 fitted parameters is proposed and discussed to explain adequately all of the important characteristics of the kinetic curves.

Full text of DOI:10.1021/ic2006309

ARTICLE
pubs.acs.org/IC
On the Complexity of Kinetics and the Mechanism of the
ThiosulfateꢀPeriodate Reaction
00
Evelin Rauscher, Gy€orgy Cseko, and Attila K. Horvꢀath*
Department of Inorganic Chemistry, University of Pꢀecs, Ifjꢀusꢀag ꢀutja 6, H-7624 Pꢀecs, Hungary
S Supporting Information
b
ABSTRACT:
The thiosulfateꢀperiodate reaction has been studied spectrophotometrically in a slightly acidic medium at 25.0 ( 0.1 °C in an
acetate/acetic acid buffer by monitoring the absorbance in the 250ꢀ600 nm wavelength range at a constant ionic strength adjusted
by the buffer component sodium acetate. In agreement with a previous study, we found that the reaction cannot be described by a
single stoichiometric equation, tetrathionate and sulfate are simultaneously formed, and its ratio strongly depends on the pH. As
expected at certain initial concentration ratios of the reactants, the reaction behaves as a clock reaction, but after its appearance,
iodine is slowly consumed mainly because of the moderate tetrathionateꢀiodine reaction. It is also enlightened that the initial rate of
the reaction is completely independent of the pH, which apparently contradicts a previous study, which postulates a “supercatalytic”
behavior of the hydrogen ion on the title reaction. Significant buffer assistance that may change the absorbanceꢀtime profiles was
also observed. On the basis of the kinetic data, a robust 28-step kinetic model with 22 fitted parameters is proposed and discussed to
explain adequately all of the important characteristics of the kinetic curves.
’ INTRODUCTION
oscillation in closed conditions is the thiosulfateꢀperiodate
reaction.10 It was demonstrated that at certain experimental condi-
tions three extrema appeared in the pHꢀtime curves. Moreover, in a
continuously stirred flow reactor (CSTR), sustained and damped
oscillations occurred with variation of the initial concentrations of
the reactants. The unique feature of this system is that if it is in a
steady state temporary perturbation (change of the flow rate,
injection of either of the reactants, etc.) results in a rare, fairly long
transient period of damped oscillation. Such an unsustained oscilla-
tory behavior in a CSTR is rather uncommon, and by that time, no
model has yet been proposed to describe this behavior. Rꢀabai et al.
have suggested10 the simple empirical rate law model
Two decades after the 1980s have witnessed the discovery of a
rich variety of oscillatory reactions in open systems.1,2 By that time,
however, only a few chemically different systems were known to
oscillate in a batch such as the BZ reaction,3,4 the BrayꢀLiebhafsky
reaction,5 and the chloriteꢀiodideꢀmalonic acid reaction.6 All of
these systems exhibit oscillation at strongly acidic conditions at
nearly constant hydrogen ion concentration. The pH is, therefore,
adjusted by strong acids (e.g., sulfuric acid, perchloric acid, etc.) in
the systems mentioned above. Considerable efforts were devoted in
the late 1980s to search such a chemical system that provided pH
oscillation in batch. Large-amplitude pH oscillation was found in
the closed iodateꢀsulfiteꢀthiosulfate system by Rꢀabai and Beck.7
The phenomenon was explained by the cross-catalytic and inhi-
bitory effects of thiosulfate and sulfite on the sulfiteꢀiodate and
thiosulfateꢀiodate systems, respectively. Later it turned out that a
“simple” supercatalytic effect8 of the hydrogen ion on the sulfiteꢀ
iodate reaction and partial regeneration of sulfite in the thiosulfiteꢀ
iodate reaction was capable of providing a good description of the
observed kinetic traces.9 Another system reported to exhibit pH
4IO4ꢀ þ S2O32ꢀ þ H2O f 2SO42ꢀ þ 4IO3ꢀ þ 2Hþ
2
3
v1 ¼ ðk1½Hþꢁ þ k1 ½Hþꢁ Þ½IO4ꢀꢁ½S2O32ꢀꢁ
ð1Þ
0
Received: March 28, 2011
Published: May 25, 2011
r
2011 American Chemical Society
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|

Inorganic Chemistry
ARTICLE
IO3ꢀ þ 6S2O32ꢀ þ 6Hþ f 3S4O62ꢀ þ Iꢀ þ 3H2O
2
2
v2 ¼ k2½S2O32ꢀꢁ ½IO3ꢀꢁ½Hþꢁ
ð2Þ
for a qualitative explanation of the phenomena mentioned above.
Although it provides a fairly good qualitative agreement, it should
be stressed that only the rate term of eq 1 was postulated and no
direct kinetic measurements were provided to support this fact. It
is, however, not surprising at all that the authors were not able to
achieve better agreement because the system is considerably
more complicated, and it was even mentioned in their paper that
“the system is so complex that we were unable to simulate
quantitatively its kinetic behavior”. Here, we, therefore, report
our extensive study on the kinetics of the thiosulfateꢀperiodate
reaction.
Figure 1. Molar absorbance of the species present in the reaction. The
spectra of thiosulfate (black), periodate (blue), tetrathionate (green),
iodine (red), iodate (yellow), iodide (cyan), and triiodide (magenta) are
indicated by different colors. Note that the right y axis belongs uniquely
to the triiodide ion, and the spectrum of iodate (yellow) is shifted along
the y axis by 400 Mꢀ1 cmꢀ1 for better visibility.
’ EXPERIMENTAL SECTION
Materials and Buffers. All chemicals were of the highest purity
commercially available (acetic acid, sodium acetate, sodium thiosulfate,
and potassium metaperiodate) and were used without further purifica-
tion. Stock solutions were freshly prepared each day from doubly
distilled and twice ion-exchanged water. The pH of the solutions was
regulated between 4.35 and 5.70 by an acetic acid/acetate buffer, taking
the pKa of acetic acid as 4.55. The acetate concentration was always kept
constant at 0.5 M by controlling an approximately constant ionic
strength throughout the experiments, and the pH was adjusted by
the necessary amount of acetic acid. The temperature of the reaction
vessel was maintained at 25.0 ( 0.1 °C. The concentrations of
thiosulfate and periodate were in the ranges 0.5ꢀ20.0 and
0.25ꢀ4.8 mM, respectively. With this experimental setup, we investi-
gated the reaction at 82 different experimental conditions and we also
repeated our experiments in several different cases, which convinced us
about the good reproducibility of the kinetic curves (see Figure S1 in the
Supporting Information).
Methods and Instrumentation. The reaction was followed by a
Zeiss S600 diode-array spectrophotometer. The reaction was carried out
in a standard quartz cuvette equipped with magnetic stirrer and a Teflon
cap having a 1 cm optical path. The buffer components and periodate
were delivered from a pipet first. The spectrum of these solutions
was always recorded just before starting the reaction to determine
the exact periodate concentration. The reaction was started with the
addition of the necessary amount of a thiosulfate solution from a fast-
delivery pipet. The spectrum of the reacting solutions at the wavelength
range of 250ꢀ600 nm was acquired up to approximately 8000 s in
every 10 s.
time points (60ꢀ70) to avoid unnecessary time-consuming calculations.
The essence of this method has already been described elsewhere.12 To
obtain the kinetic model and the rate coefficients, an absolute fitting
procedure has been chosen to minimize the average deviation between
the measured and calculated absorbance bands. Altogether almost
35 000 experimental points from the 90 ꢂ 7 kinetic series were used
for the simultaneous evaluation. Our quantitative criterion for an
acceptable fit was that the average deviation for the absolute fit approach
0.006, which is close to the experimentally achievable limit of error under
present experimental conditions.
’ RESULTS
Stoichiometry. The stoichiometry of the reaction was already
thoroughly investigated by Rꢀabai et al.10 It was found that in high
excess of periodate the stoichiometry can clearly be characterized
by the following equation:
S2O32ꢀ þ 4IO4ꢀ þ H2O f 2SO42ꢀ þ 4IO3ꢀ þ 2Hþ ð3Þ
If, however, thiosulfate is in excess, then periodate is reduced
to the iodide ion; meanwhile, the tetrathionate and sulfate ions
are formed as oxidation products of sulfur according to the
following limiting stoichiometric equations:
S2O32ꢀ þ IO4ꢀ þ H2O f 2SO42ꢀ þ Iꢀ þ 2Hþ ð4Þ
and
Data Treatment. Matrix rank analysis studies have revealed11 that
seven absorbing species exist in the wavelength range of 250ꢀ600 nm,
namely, the reactants thiosulfate and periodate and the long-lived
intermediates and products such as tetrathionate, iodine, triiodide ion,
iodate, and iodide ion. Spectra of these species are shown in Figure 1. It is
seen that periodate, tetrathionate, and triiodide have strong absorbance
bands in the UV range, whereas thiosulfate, iodate, iodine, and iodide
have only weak absorption bands. In addition, iodine and triiodide absorb
light in the visible range as well. Highly overlapping spectra of the
absorbing species prompted us to choose seven different wavelengths for
data evaluation to provide enough experimental information about the
absorbing species. In the selection of the wavelength, it is considered that
the measured absorbance has to be lower than 1.8 because, above this
value, the linear relationship between the absorbance and concentration
cannot be fulfilled. Therefore, we have chosen the following wave-
lengths: 275, 280, 285, 290, 350, 400, and 468 nm. Originally, each
kinetic run contained more than 700 absorbanceꢀtime data pairs at a
given wavelength; therefore, it was necessary to reduce the number of
8S2O32ꢀ þ IO4ꢀ þ 8Hþ f 4S4O62ꢀ þ Iꢀ þ 4H2O ð5Þ
The ratio of eqs 4 and 5 mainly depends on the pH; lower pH
prefers the formation of tetrathionate, and the actual stoichiom-
etry at a given experimental condition may be generated by
the appropriate linear combination of these equations. Our
preliminary investigations clearly confirmed these earlier
observations.
Preliminary Observations. The most important characteris-
tics of the measured kinetic curves can be summarized as follows:
Figure 2 shows the effect of the pH on the initial phase of the
reaction. As can be seen, a decrease of absorbance in the UV
range is independent of the pH, suggesting that the initial step of
the reaction does not depend on the pH in the pH range studied.
This result is in complete contradiction with the empirical rate
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Figure 2. Measured (symbols) and calculated (solid lines) absorbanceꢀ
time curves at [S2O32ꢀ]0 = 0.5 mM and [IO4ꢀ]0 = 2.0 mM at different
pHs: 5.70 (b); 5.55 (0); 5.10 (2); 4.65 (]); 4.35 (9).
Figure 4. Measured (symbols) and calculated (solid lines) absorbanceꢀ
time curves at constant [S2O32ꢀ]0/[IO4ꢀ]0 = 4:3 ratio at pH = 4.65.
[IO4ꢀ]0/mM = 4.9 (b), 4.5 (0), 4.0 (2), 3.5 (]), 3.0 (9), 2.5 (O), and
2.0 ([).
increase in the absolute concentration of the reactants results
in a more intense rise of the absorbance at 275 nm when
thiosulfate is consumed. The maximum in the absorbance is
then followed by a slow decrease, which can be attributed to the
tetrathionateꢀiodine reaction.
Figure 6 shows the change of shape of the measured absor-
banceꢀtime series with varying [S2O32ꢀ]0 at constant periodate
concentration and pH. It is easily seen that a minimum appears
in the measured curves as the initial [S2O32ꢀ]0/[IO4ꢀ]0 ratio
increases above 2 and the minimum even becomes lower.
It follows from the fact that the ratio of the oxidized sulfur-
containing product is shifted toward the formation of tetrathio-
nate over sulfate.
Figure 7 depicts the measured absorbanceꢀtime series with
changes in the initial periodate concentration at constant low
[S2O32ꢀ]0 and pH. It suggests that under these experimental
conditions thiosulfate is mainly oxidized to sulfate.
Figure 3. Measured (symbols) and calculated (solid lines) absorbanceꢀ
time curves at [S2O32ꢀ]0 = 10.0 mM and [IO4ꢀ]0 = 2.0 mM: 5.55 (O);
5.10 (0); 4.65 (4).
law given by Rꢀabai et al., postulating a formal kinetic order of 2
(or even 3) for the hydrogen ion.10
Initial Rate Studies. The isosbestic point of the iodineꢀ
triiodide system seems to be a good candidate for data evaluation
of the initial rate because it uniquely refers to the rate of
Figure 3 indicates the shape of the kinetic curves at a 5:1 initial
molar ratio of thiosulfateꢀperiodate at different pHs. As can be
seen, the absorbance measured in the UV range as a function
of time goes through a minimum before leveling off and its
minimum value strongly depends on the pH. The lower the pH
is, the higher the minimum value of the absorbance becomes.
This suggests that eq 5 is preferred over eq 4 at lower pHs
because the tetrathionate ion has a strong absorbance band in the
UV range.
Figure 4 shows that at certain experimental conditions iodine
is formed in a detectable amount, but it reacts further with
tetrathionate in a slow reaction,13,14 meaning that iodine is a
long-lived intermediate of the reaction. This observation is in full
accordance with an earlier investigation reported by Rꢀabai et al.10
It should also be noted that iodine can appear in the solution only
if thiosulfate is completely consumed. Therefore, this reaction
may also be treated as a Landolt-type reaction,15 although the
sudden appearance of iodine is not so pronounced because of its
low concentration in the present case. It is therefore easily con-
ceivable why the Landolt-type behavior of this system has not
been discovered yet.
formation of the total amount of iodine (TI = [I2] þ [I3ꢀ]).
2
As, however, indicated above (see Figure 4), the reaction behaves
as a clock reaction, meaning that iodine can only be observed
after a well-defined time lag. Thus, we concluded that the absor-
banceꢀtime curves measured at the visible range are not appro-
priate for the initial rate studies. Figure 1 clearly indicates that no
wavelength exists in the UV range, where the absorbance can be
designated uniquely to one of the absorbing species, but as can
be seen, the major absorbing species is periodate. Although triiodide
has a very intense absorption band in the UV range, the concentra-
tion of this species is basically zero as long as thiosulfate is present
in the solution. This means that at the initial phase of the reaction
the absorbance change at 275 nm is mainly due to a decrease of
the periodate concentration. The molar absorbance of thiosulfate
is very small compared to that of periodate and tetrathionate, and
therefore a decrease of thiosulfate negligibly contributes to the
overall absorbance change. As a result, the net effect at 275 nm is
clearly the decrease of absorbance at the beginning stage of the
reaction. Thus, we concluded that the absorbanceꢀtime series
measured at 275 nm is suitable for evaluation of the kinetic curves
by the initial rate method. Figure 8 shows the result of the initial
rate studies. This clearly indicates that the formal kinetic order
of both reactants is 1, but the initial phase of the reaction is
Figure 5 demonstrates the change of shape of the measured
absorbanceꢀtime series at a constant initial thiosulfateꢀ
periodate ratio with increasing thiosulfate concentration. An
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Figure 6. Measured (dots) andꢀcalculated (solid lines) absorbanceꢀ
[S2O32ꢀ]0/mM = 0.5 (black), 1.0 (blue), 2.0 (green), 3.0 (red), 4.0
(magenta), 6.0 (light gray), 6.66 (brown), 8.0 (purple), 10.0 (yellow),
12.0 (dark gray), 16.0 (orange), and 20.0 (cyan).
Figure 5. Measured (dots) and calculated (solid lines) absorbanceꢀ
time curves at a constant [S2O32ꢀ]0/[IO4ꢀ]0 = 1:1.54 ratio at pH = 4.65.
[IO4ꢀ]0/mM = 5.0 (black), 4.5 (blue), 4.0 (red), 3.5 (green), 3.0
(magenta), and 2.0 (brown).
time curves at a constant [IO4
] = 2.0 mM ratio at pH = 4.65.
0
calculated data, were omitted step by step, but the omission was
only executed if the given parameter became insensitive again
after its resensitization. We mean for resensitization that the rate
coefficient of the given step was increased to change the value of
the average deviation at least by 5%. A slow but straightforward
model reduction led us to propose the kinetic model given in
Table 1. For the sake of completeness, the molar absorbance
of the absorbing species used in the fitting procedure is given in
Table 2. The sound agreement between the measured and calcu-
lated absorbances at seven different wavelengths (see Figures 2ꢀ7
and S2ꢀS7 in the Supporting Information) and the 0.0059
absorbance unit average deviation indicates that the proposed
model is working properly within the concentration range used
in the experiments.
completely independent of the pH. One might also argue about
the fact that the formation of tetrathionate may disturb the
evaluation of the initial rate if its formation strongly depends
on the initial concentration ratio of the reactants. More explicitly,
there might be a case when although the consumption of periodate
increases with decreasing pH at a given time, the shift between
eqs 4 and 5 with decreasing pH compensates for the absorbance
fall by an increase of the tetrathionate concentration. The net
effect may, therefore, be as if the reaction is independent of
the pH. It is easily seen that if the apparent unchange of the
absorbanceꢀtime curves as a function of the pH is a consequence
of the latter fact, then a slight pH dependence should occur at
different wavelengths just as a result of the difference of the molar
absorbance ratio of periodate and tetrathionate. Figure 8, how-
ever, indicates that the same formal kinetic order can be obtained
for the reactants and the hydrogen ion as well at both wave-
lengths; therefore, it is confirmed that the initial phase of the
reaction is independent of the pH.
Proposed Kinetic Model. The approach we have chosen to
analyze our data set has already been successfully applied in
several cases of our previous works.12,16 The method takes advan-
tage of the significant advances of computing power and resem-
blestheconstructionoflargemodelssuchasthosein atmospheric17
and combustion chemistry.18 The most critical part of this
method is to postulate the set of species (reactants, intermediates,
and products) involved in the reactions. Besides the reactants
(thiosulfate and periodate), the products (tetrathionate, sulfate,
iodate, and iodide), and the long-lived intermediates identified
by UVꢀvis spectroscopy (iodine and triiodide), several other
intermediates likely to participate in the reaction are postulated
such as HSO3ꢀ, S2O3OHꢀ, HIO2, HOI, I2O2, S2O3Iꢀ, and
S4O6Iꢀ. The next step is to find all of the conceivable reactions
among all of these species. In the present case, we found 154
different reactions, which are summarized in Table S1 in the
Supporting Information. We then considered that all of these
reactions have rate equations consisting of three terms: the first
one is independent of Hþ, and the second and third ones
are proportional to [Hþ] and [Hþ]2, respectively. This means
that we started the fitting procedure with 462 rate coefficients
(3 ꢂ 154). As a start, rate coefficients determined from inde-
pendent studies were fixed and the rest of them were fitted during
the evaluation procedure. The rate parameters, which became
insensitive for the average deviation between the measured and
’ DISCUSSION
Step 1 is the initiating equilibrium between the reactants that
probably proceeds via an O-atom transfer from periodate to
thiosulfate to produce iodate and S2O3OHꢀ. We found that
the forward and reverse reactions are both independent of the
pH and their rate coefficients were calculated as k1 = 7.36 (
0.07 Mꢀ1 sꢀ1 and kꢀ1 = 2.70 ( 0.03 Mꢀ1 ꢀ1, respectively. It
s
should be emphasized that Hþ is involved only in the stoichi-
ometry of the reactions. Step 1 may therefore be treated as an
alternative suggestion for interpreting the sudden rise of the pH
at the beginning stage of the reaction observed by Rꢀabai et al.
in an unbuffered medium.10 Separate calculations have shown
that pH increases from 5.5 to 5.8 at the initial condition used by
Rꢀabai et al. can per se be achieved using step 1 within 2 s, which
agrees well with their experimental findings. We should, however,
emphasize as well that there is not even a single fact in our
experiments indicating any sign of a pH-dependent rate term of
the thiosulfateꢀperiodate reaction. Our experiments unambigu-
ously suggest that the pH dependence has to have arisen from the
Hþ-dependent pathways of the subsystems of the thiosulfateꢀ
periodate reaction. One should also notice that step 1 is an
equilibrium, but the stoichiometry and rate laws of the forward
and backward reactions are inconsistent with the law of mass
action. This discrepancy, however, is only apparent because if
one replaces S2O3OHꢀ with S2O42ꢀ, then the inconsistency
disappears. Furthermore, the removal of Hþ can easily be
explained by the fast protolytic equilibrium between the species
S2O42ꢀ and S2O3OHꢀ. This argument is also valid in the case of
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ꢀ
Figure 7. Measured (dots) and calculated (solid lines) absorbanceꢀ
time curves at a constant [S2O32ꢀ]0 = 0.5 mM ratio at pH = 4.65.
[IO4ꢀ]0/mM = 4.8 (black), 4.0 (blue), 3.0 (green), 2.0 (cyan), 1.0 (red),
0.75 (brown), 0.5 (magenta), and 0.25 (yellow).
Figure 8. Initial rate studies at different conditions: [IO4
] =
0
2ꢀ
2.00 mM, pH = 5.55, and c0 correspond to [S2O3
] (b, O);
0
[S2O32ꢀ]0 = 0.50 mM, pH = 5.55, and c0 correspond to [IO4ꢀ]0 (0,
9); [S2O32ꢀ]0 = 0.50 mM, [IO4ꢀ]0 = 2.00 mM, and c0 correspond to
[Hþ]0 (2, 4). Filled and empty symbols belong to the measured kinetic
curves at 275 and 290 nm, respectively.
step 5 (see later). It should also be noted that periodate exists in
four different forms19 under our experimental conditions such as
H5IO6, H4IO6ꢀ, H3IO62ꢀ, and IO4ꢀ, although a more recent
conditions. Our calculation has revealed that k4 can be calculated
as (7.7 ( 0.2) ꢂ 105 Mꢀ2 sꢀ1 from our experiments. The role of
this reaction is highly confirmed because this is the main route
leading to the formation of tetrathionate.
Step 5 is the initiation of the thiosulfateꢀiodate reaction
probably proceeding via an O-atom transfer from iodate to
thiosulfate. As expected, we found that the rate of this reaction
depends on [Hþ] but not on [Hþ]2, as was found by Rieder.24
The fact that the rate of the overall thiosulfateꢀiodate reaction
depends on [Hþ]2 has recently been explained25 in terms of the
rapid pH-dependent equilibrium formation of I2O2 from iodide
and iodate ions and its subsequent reaction with thiosulfate.
The fitting procedure also indicated that the rate coefficient of
the back-reaction of step 5 can also be calculated from our
study suggests20 the appearance of dimer H2I2O10 in an
4ꢀ
alkaline solution of periodate whose concentration is negligible
at pH = 4.35ꢀ5.55. Those species, however, are rapidly equili-
brated with each other, and periodate is mainly in a singly charged
form (either H4IO6ꢀ or IO4ꢀ) under the present experimental
conditions. Because there is a fast equilibrium between these
forms and the ratio of [IO4ꢀ]/[H4IO6ꢀ] is 29.5,21 it looks
reasonable to suppose IO4ꢀ to be the reactive species despite the
fact that our experiments do not provide any solid basis for
establishing the kinetically active form of periodate. Thus, in the
proposed kinetic model, IO4ꢀ is supposed in all of those steps in
which periodate is involved as a reactant.
Steps 2 and 3 are further oxidations of S2O3OHꢀ by the
periodate ion. An interesting result of our calculation is that
periodate can react with S2O3OHꢀ in two different pathways.
The structure of S2O3OHꢀ is supposed to be HOSSO3ꢀ, and
attack of periodate on the sterically preferable S atom may be
followed by scission of the SꢀS bond, leading to either sulfate
experiments as kꢀ5 = (3.6 ( 0.1) ꢂ 107 Mꢀ1 sꢀ1
.
Step 6 is a comproportionation that produces iodate from the
periodate ion and iodous acid via a simple O-atom transfer. The
role of this reaction is to prevent the accumulation of iodous acid
under those experimental conditions, where the concentration
of the iodide ion is negligible. We also found this step to be
pH-independent within the experimental conditions studied.
The value of k6 = (2.1 ( 0.1) ꢂ 105 Mꢀ1 sꢀ1 has worked
consistently well in fitting the experimental traces, but it differs by
a factor of 2 from that determined recently in the iodideꢀ
periodate reaction.26 As we shall see later, this is not the only rate
coefficient that works consistently well with values different from
those reported previously. We have also tried to seek experi-
mental evidence to explain these differences adequately. Figure 9
shows absorbanceꢀtime series measured at different buffer
concentrations, keeping all of the other conditions unchanged.
It clearly shows that the shape of the kinetic curves significantly
changes with variation of the buffer concentration, meaning that
at the later stages of the reaction strong buffer assistance must
be involved in one or maybe more subsystems. This phenom-
enon frequently accompanies several reactions of oxyhalogen
species.27 Consequently, this means that the application of
different buffer concentrations results in a notable difference in
the determination of the value of the apparent rate coefficient of
the given step.
ꢀ
and hypoiodous acid (step 2) or HSO3 and iodate (step 3).
This observation is not a unique feature of this species; in the
chloriteꢀtetrathionate reaction, this effect was already observed
and reported.12 To strengthen the roles of k2 and k3, additional
fitting procedures have been carried out to indirectly support
the necessity of these parallel steps. Eliminating them individu-
ally from the fitting procedure resulted not only in an unaccep-
tably high increase of the average deviation (0.0106 and 0.0080,
respectively) but also in a systematic deviation between the
measured and calculated kinetic curves. Thus, we concluded that
the role of these steps along with the given rate equations is
confirmed.
Step 4, which eventually leads to the formation of tetrathio-
nate, was already suggested by several independent research
groups.22,23 It is found that the rate of this process is proportional
to [Hþ], in agreement with the experimental findings that the
formation of tetrathionate is preferred at lower pHs. We have
also found that our value for k4 is lower than that used by
Schreiber et al.23 in simulating the dynamical behavior of the
tetrathionateꢀhydrogen peroxide reaction. In addition, we have
not found any evidence that the rate equation of this reaction
may have a pH-independent term under our experimental
Step 7 is the oxidation of hypoiodous acid by the periodate ion
to produce iodate and iodous acid. The rate coefficient of this
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Table 1. Fitted and Fixed Rate Coefficients of the Proposed Kinetic Modela
no.
1
chemical equation
rate equation
parameter
k1 = 7.36 ( 0.07 Mꢀ1 sꢀ1
S2O32ꢀ þ IO4ꢀ þ Hþ h S2O3OHꢀ þ IO3
k1[S2O32ꢀ][IO4
]
ꢀ
ꢀ
ꢀ
k
ꢀ1[S2O3OHꢀ][IO3
]
k
ꢀ1 = 2.70 ( 0.03 Mꢀ1 sꢀ1
2
3
4
5
IO4ꢀ þ S2O3OHꢀ þ H2O f HOI þ 2SO42ꢀ þ 2Hþ
IO4ꢀ þ S2O3OHꢀ þ H2O f 2HSO3ꢀ þ IO3ꢀ þ Hþ
S2O32ꢀ þ S2O3OHꢀ þ Hþ f S4O62ꢀ þ H2O
S2O32ꢀ þ IO3ꢀ þ 2Hþ h S2O3OHꢀ þ HIO2
k2[IO4ꢀ][S2O3OHꢀ]
k3[IO4ꢀ][S2O3OHꢀ]
k2 = 0.89 ( 0.04 Mꢀ1 sꢀ1
k3 = 1.50 ( 0.03 Mꢀ1 sꢀ1
k4[Hþ][S2O32ꢀ][S2O3OHꢀ]
k5[S2O32ꢀ][IO3ꢀ][Hþ]
k4 = (7.7 ( 0.2) ꢂ 105 Mꢀ2 sꢀ1
k5 = (2.1 ( 0.1) ꢂ 105 Mꢀ2 sꢀ1
k
ꢀ5[S2O3OHꢀ][HIO2]
k
ꢀ5 = (3.6 ( 0.1) ꢂ 107 Mꢀ1 sꢀ1
6
7
8
9
IO4ꢀ þ HIO2 f 2IO3ꢀ þ Hþ
IO4ꢀ þ HOI f IO3ꢀ þ HIO2
IO4ꢀ þ Iꢀ þ Hþ f IO3ꢀ þ HOI
IO3ꢀ þ Iꢀ þ 2Hþ h I2O2 þ H2O
k6[IO4ꢀ][HIO2]
k7[IO4ꢀ][HOI]
k8[IO4ꢀ][Iꢀ]
k6 = (2.1 ( 0.1) ꢂ 105 Mꢀ1 sꢀ1
k7 = 39.2 ( 1.5 Mꢀ1 sꢀ1
k8 = 5.4 ( 0.3 Mꢀ1 sꢀ1
k9[IO3ꢀ][Iꢀ][Hþ]2
k9 = (3.9 ( 0.2) ꢂ 108 Mꢀ3 sꢀ1
k
ꢀ9 = 100 sꢀ1
10
11
12
I2 þ I2O2 þ 2H2O f 2HIO2 þ 2Iꢀ þ 2Hþ
HIO2 þ Iꢀ þ Hþ f 2HOI
k10[I2][I2O2][Hþ]
k11[HIO2][Iꢀ][Hþ]
k12[I2]
k10 = (9.2 ( 1.1) ꢂ 1010
M
ꢀ2 sꢀ1
k11 = 109 Mꢀ2 sꢀ1
I2 þ H2O h HOI þ Iꢀ þ Hþ
k12 = 5.52 ꢂ 10ꢀ2 sꢀ1
k
ꢀ12[HOI][Iꢀ][Hþ]
k
ꢀ12 = 1.02 ꢂ 1011
M
ꢀ2 sꢀ1
I2 þ Iꢀ h I3
k13[I2][Iꢀ]
k13 = 5.6 ꢂ 109 Mꢀ1 sꢀ1
ꢀ
13
ꢀ
kꢀ13[I3
]
k
ꢀ13 = 8.5 ꢂ 106 sꢀ1
14
15
16
17
18
19
20
21
22
23
24
25
26
HIO2 þ I2 þ H2O f IO3ꢀ þ 2Iꢀ þ 3Hþ
S2O32ꢀ þ I2 f S2O3Iꢀ þ Iꢀ
k14[HIO2][I2]
k15[S2O32ꢀ][I2]
k16[S2O3Iꢀ][Hþ]
k14 = (1.4 ( 0.1) ꢂ 108 Mꢀ1 sꢀ1
k15 = (2.0 ( 0.1) ꢂ 109 Mꢀ1 sꢀ1
S2O3Iꢀ þ H2O f S2O32ꢀ þ HOI þ Hþ
IO4ꢀ þ S2O3Iꢀ þ 2H2O f 2SO42ꢀ þ Iꢀ þ HOI þ 3Hþ
S2O32ꢀ þ HOI f S2O3OHꢀ þ Iꢀ
k16 = (2.4 ( 0.2) ꢂ 1011
M
ꢀ1 sꢀ1
k17[IO4ꢀ][S2O3Iꢀ]
k18[S2O32ꢀ][HOI][Hþ]
k19[S2O3OHꢀ][S2O3Iꢀ][Hþ]
k20[HSO3ꢀ][I2]
k21[HSO3ꢀ][HOI]
k22[IO4ꢀ][HSO3ꢀ][Hþ]
k23[S2O32ꢀ][HIO2][Hþ]
k24[S2O3OHꢀ]2
k17 = (1.7 ( 0.1) ꢂ 106 Mꢀ1 sꢀ1
k18 = (2.1 ( 0.2) ꢂ 107 Mꢀ2 sꢀ1
S2O3OHꢀ þ S2O3Iꢀ f S4O62ꢀ þ HOI
HSO3ꢀ þ I2 þ H2O f SO42ꢀ þ 2Iꢀ þ 3Hþ
HSO3ꢀ þ HOI f SO42ꢀ þ Iꢀ þ 2Hþ
IO4ꢀ þ HSO3ꢀ f SO42ꢀ þ IO3ꢀ þ Hþ
S2O32ꢀ þ HIO2 þ Hþ f S2O3OHꢀ þ HOI
2S2O3OHꢀ þ H2O f S2O32ꢀ þ 2HSO3ꢀ þ 2Hþ
S2O3OHꢀ þ IO3ꢀ þ H2O f 2HSO3ꢀ þ HIO2
S4O62ꢀ þ I2 h S4O6Iꢀ þ Iꢀ
k19 = (4.7 ( 0.2) ꢂ 1012
k20 = 3.1 ꢂ 109 Mꢀ1 sꢀ1
k21 = 107 Mꢀ1 sꢀ1
M
ꢀ2 sꢀ1
k22 = (1.6 ( 0.1) ꢂ 1010
M
M
ꢀ2 sꢀ1
ꢀ2 sꢀ1
k23 = (3.9 ( 0.3) ꢂ 1010
k24 = 6.66 ( 0.51 Mꢀ1 sꢀ1
k25[S2O3OHꢀ][IO3ꢀ][Hþ]
k26[S4O62ꢀ][I2]
k25 = (2.2 ( 0.2) ꢂ 105 Mꢀ2 sꢀ1
k26 = 1.92 Mꢀ1 sꢀ1
k
ꢀ26[S4O6Iꢀ][Iꢀ]
k
ꢀ26 = 107 Mꢀ1 sꢀ1
27
28
S4O6Iꢀ þ H2O f S2O3OHꢀ þ S2O3Iꢀ þ Hþ
k27[S4O6Iꢀ]
k27 = 214 sꢀ1
I
ꢀ þ S4O6Iꢀ f 2S2O3Iꢀ
k28[Iꢀ][S4O6Iꢀ]
k28 = 1.28 ꢂ 105 Mꢀ1 sꢀ1
a No error indicates that the value in question was fixed during the fitting procedure.
reaction was found to be 39.2 ( 1.5 Mꢀ1 sꢀ1, indicating that the
oxidation of hypoiodous acid by periodate is orders of magnitude
slower than that of iodous acid. It also explains the fact that
iodine can slowly be oxidized by periodate in an indirect way. The
removal ofꢀiodine by periodate is, therefore, a consequence of the
HOIꢀIO4 reaction, followed by a shift in the well-known
relatively rapid hydrolysis of iodine28 in which HOI is involved
(see later).
Step 8 is the well-known oxidation of iodide by the periodate
ion. Present experiments indicate approximately half of the
value of k8 determined in previous independent studies26,29 but
worked consistently during the fitting procedure here. These
studies, however, also reported no direct buffer assistance in the
iodideꢀperiodate reaction, meaning that the apparent difference
cannot be simply explained by this fact. However, as can be seen,
the iodide ion is not an initial reactant in the present system; it is
produced via a finite sequence of reactions. If the formation of the
iodide ion is affected by the presence of buffer components and
the absorbanceꢀtime series (which mainly corresponds to the
Table 2. Molar Absorbance (Given in Mꢀ1 cmꢀ1 Units) of
the Absorbing Species Used in the Fitting Procedure
λ (nm) εS O 2ꢀ
εIO
ꢀ
εS O 2ꢀ
εIO
ꢀ
εIꢀ
εI
εI ꢀ
3
2
3
4
4
6
3
2
275
280
285
290
350
400
468
8.51
4.54
2.60
1.64
0
370.5
317.1
272.5
231.9
222.5
158.4
110.8
75.5
0
11.9
5.95 0.87 260.6 32725
3.1 0.76 264.9 37605
1.76 0.70 251.5 38129
1.14 245.2 25055
3.46
0
0
0
0
0
0
119.4 25489
0
0
0
0
241.8
754.6
6124
747.1
0
0
consumption of periodate) is at least partly determined by the
iodideꢀperiodate reaction, then one may observe a notable differ-
ence in the determination of the (apparent) rate coefficient of the
given reaction. Certainly, this is a possible but not the only
explanation of the experimental fact that we have found; conse-
quently, more research is required to explore it more thoroughly.
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experimental conditions (different initial concentrations, lower
pH, etc.), but present experiments do not provide a solid basis to
confirm its decisive contribution to the kinetics.
Step 11 is the well-known relatively fast comproportionation
of iodous acid and the iodide ion to produce hypoiodous acid.
The rate coefficient of this process was fixed at k11 = 109 Mꢀ2sꢀ1
,
as proposed by Lengyel and co-workers.31
Step 12, the well-known iodine hydrolysis, was already thor-
oughly studied by several research groups.28 We adopted the
forward and reverse rate coefficients determined by Lengyel
et al.31
Step 13 is the rapid equilibrium formation of the triiodide ion
investigated by several research groups independently.32,33 The
rate coefficients of the forward and reverse reactions were set to
k13 = 5.7 ꢂ 109 Mꢀ1 sꢀ1 and kꢀ13 = 8.5 ꢂ 106 sꢀ1, respectively,
Figure 9. Measured absorbanceꢀtime curves at 275 nm with different
buffer concentrations. Conditions: [S2O32ꢀ]0 = 3.68 mM, [IO4ꢀ]0 =
4.49 mM, pH = 4.65. The ionic strength is adjusted by sodium
perchlorate to 0.5 M. [acetate]0/M = 0.5 (black), 0.192 (blue), 0.1
(green), 0.042 (cyan), and 0.025 (red).
to give log βI
ꢀ
= 2.83, where βI is the formation constant of the
ꢀ
3
3
triiodide ion.34
Step 14 is the oxidation of iodous acid by iodine to produce
iodate and iodide ions. This reaction plays an important role at
the later stages of the reaction. Omitting this step from the final
model would result in not only a 0.0097 absorbance unit average
deviation but also the appearance of a systematic deviation at
those conditions, where iodine appears after Landolt time;
therefore, its kinetic role was confirmed indirectly.
Step 15 is the initiating step of the well-known thiosulfateꢀ
iodine reaction.35 Our calculation indicated that its rate
coefficient has to be somewhat smaller [k15 = (2.0 ( 0.1) ꢂ
109 Mꢀ1 sꢀ1] than that of the corresponding hydrogen sulfiteꢀ
iodine reaction. We also noticed a strong correlation between
k15 and k20; therefore, our measurements provided enough
information to determine only the ratio of k15/k20. Because
k20 was reported by an independent study (see the discussion
later), it allowed us to calculate the actual value of k15 as well. It
should also be noted that inclusion of its back-reaction results in a
small decrease in the average deviation by 2%. Although its role
cannot be decisive in the overall kinetics,
Step 9 is the well-known initiating step of the Dushman
reaction30 with the reversible formation of a short-lived intermedi-
ate I2O2. We found that the absolute value of the forward rate
coefficient (k9) could be determined from our experiments, but
the reverse one is in total correlation with k10, which means that
we, in fact, could calculate only the ratio k10/kꢀ9. Our calculation
has only provided a lower limit of 0.1 sꢀ1 for kꢀ9. Because I2O2 is
a short-lived intermediate, we set kꢀ9 to 100 sꢀ1, which strictly
fulfills this criterion, and calculated k10. It is also interesting that
no value is available for the forward and reverse rate coefficients
of the initiating equilibrium of the Dushman reaction, although
the rate coefficient of the global Dushman reaction was deter-
mined by several research groups. A good survey can be found in
Schmitz’s paper.27 It is accepted that the rate equation of the
Dushman reaction is given as r = (4.2 ( 0.8) ꢂ 108[Hþ]2[Iꢀ]2-
[IO3ꢀ] at [Iꢀ]0 > 5 ꢂ 10ꢀ6 M. Considering the reaction
ꢀ
Iꢀ þ I2O2 þ H2O þ Hþ f 3HOI v ¼ kI ½I ꢁ½I2O2ꢁ ð6Þ
ꢀ
S2O3Iꢀ þ Iꢀ f S2O32ꢀ þ I2
ð8Þ
and step 12 gives us the overall stoichiometry of the Dushman
reaction. If I2O2 is treated as a short-lived steady-state inter-
the reaction may also be treated as a tentative step that may have a
significant role at different experimental conditions. Therefore,
we are inclined not to include it in the proposed model.
mediate with kIꢀ = 100 Mꢀ1 ꢀ1, our measurements would
s
provide a value of (3.9 ( 0.2) ꢂ 108 Mꢀ4 sꢀ1 for the overall rate
coefficient of the Dushman reaction, which is in excellent
agreement with the data reported by Schmitz.27 Unfortunately,
as can be seen below, the role of eq 6 is negligible under our
experimental conditions, because eq 6 with a low iodide ion
concentration is not able to compete with other reactions of
I2O2.
Step 16 is the pH-dependent hydrolysis of S2O3Iꢀ that
produces thiosulfate and hypoiodous acid. Because S2O3Iꢀ was
found to be a short-lived intermediate, one would expect that
only the ratio of the rate coefficients of their further reactions
could be calculated. Our calculations, however, resulted a clear
minimum in the average deviation as a function of k16, k17, and
k19 as well, from which we concluded that the absolute value of
k16 as well as that of k17 and k19 could be determined. A possible
explanation of this fact is that one of the reactants forms back
Step 10 is the only reaction of I2O2 that is necessary for a
quantitative description of the measured absorbanceꢀtime series
especially after Landolt time. As described above, the individual
rate coefficient cannot be calculated because of the appearance of
a total correlation between k10 and kꢀ9. We also found that the
rate of this reaction is proportional to [Hþ] within the pH range
studied. We have also tried to include the reaction of I2O2 by
thiosulfate
through step 16, and the wide initial concentration range in
2ꢀ
[S2O3
] carries enough experimental information for the
0
simultaneous evaluation of the kinetic curves to calculate the
absolute value of k16. It is also interesting to note that this process
is autocatalytic with respect to Hþ and plays a significant role in
the first stage of the reaction, where the appropriate amount of
HOI is produced.
S2O32ꢀ þ I2O2 þ H2O f S2O3OHꢀ þ HIO2 þ Iꢀ ð7Þ
and by the iodide ion (eq 6) with no success. The latter reaction
was completely unnecessary, but inclusion of eq 7 resulted in a
small change in the average deviation by less than 3%. Therefore,
we concluded that eq 7 might play a significant role at different
Step 17 is the other manner of conversion of the short-lived
intermediate S2O3Iꢀ that has a significant contribution at period-
ate excess, whereas step 16 has a greater influence at lower
periodate concentrations. As pointed out before, because the
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absolute value of k16 could be determined from the experiments,
that of k17 could also be calculated.
equivalently well):
2S2O3OHꢀ f S2O32ꢀ þ S2O4OHꢀ þ Hþ
ð9Þ
ð10Þ
Step 18 is the pH-dependent oxidation of thiosulfate by
hypoiodous acid probably proceeding via an O-atom transfer.
This reaction prevents buildup of hypoiodous acid in thio-
sulfate excess. To strengthen the role of step 18 in the final
model, we have also carried out an additional fitting procedure
by eliminating k18 from the proposed model. The evaluation
resulted in a significant increase of the average deviation
(0.0263 absorbance unit) as well as in an appearance of the
systematic deviation between the measured and calculated
data. Therefore, we concluded that the role of step 18 is
strongly confirmed.
Step 19 is another route to produce tetrathionate at lower pHs
from S2O3OHꢀ and S2O3Iꢀ. The reason why the absolute value
of k19 can be determined was already discussed previously. The
role of this step was also confirmed by an additional fitting
procedure, where k19 was omitted from the proposed model. The
average deviation was increased unacceptably (0.0168 absor-
bance unit); therefore, its role is also highly established in the
proposed model.
fast
S2O4OHꢀ þ H2O
s
2HSO ꢀ þ Hþ
f
3
where the rate-limiting process is eq 9. It is also interesting to
note that the relatively low value of k24 = 6.66 ( 0.51 Mꢀ1 sꢀ1
indicates that S2O3OHꢀ is a long-lived intermediate of the
reactions. This fact is not surprising at all because a significant
role of S2O3OHꢀ is already established in a different chemical
system.25 If this is true, one might also expect that in the UV
range this species must have significant molar absorbance to
contribute to the overall absorbance. As can be seen, the fitting
procedure was executed in the wavelength range of 275ꢀ468 nm.
Because we were able to achieve a sound quantitative agreement
between the measured and calculated absorbances, it is con-
cluded that within this range S2O3OHꢀ does not have significant
absorption. Probably at lower wavelengths, this conclusion is no
longer valid, but under our experimental conditions, it is not
necessary to include S2O3OHꢀ in the final model as an absorbing
species. The reason is simple because in this case the reactants
already have enough absorbance contribution (especially the
periodate ion) to the overall absorbance to exceed the 1.8 limit,
where the linearity between the concentration and the measured
signal is not fulfilled. That is why no fitting was executed below
275 nm. Of course, one might argue that lowering the initial
concentration of the reactants allows us to calculate the molar
absorbance of S2O3OHꢀ from the kinetic curves but lowering
the initial concentration would also result in a lower S2O3OHꢀ
concentration, meaning that its contribution to the overall
absorbance becomes commensurable with the error of the
absorbance measurements. Omitting this step from the model
yields an average deviation of 0.0092 absorbance unit and
systematic deviations between the measured and calculated
kinetic curves; therefore, we concluded this reaction to be
strongly confirmed.
Step 25 is the pH-dependent oxidation of the long-lived
intermediate S2O3OHꢀ by the iodate ion, producing hydrogen
sulfite and iodous acid. We confirmed the role of this step
indirectly by eliminating k25 from the final model. The simulta-
neous evaluation of the kinetic curves indicated a large increase in
the average deviation (0.0104), from which we concluded that
the role of this step is well-justified.
Steps 26ꢀ28 were directly adopted from our previous
work without any change and fixed throughout the whole
fitting procedure.14 It is clear that this set of reactions has a
major influence on the later phase of the reaction after the
Landolt time, where tetrathionate and iodine are present
simultaneously. Under our experimental conditions, how-
Step 20 is the well-known fast reaction between hydrogen
sulfite and iodine, and its kinetics were thoroughly studied by
Yiin and Margerum36 and even the rate coefficient of this process
was determined to be 3.1 ꢂ 109 Mꢀ1
s
ꢀ1. Therefore, we have
fixed k20 at this value during the fitting process.
Step 21 is the rapid oxidation of hydrogen sulfite by hypoio-
dous acid. Our calculation indicated that this reaction has to
be fast to treat HSO3ꢀ as a steady-state intermediate. The actual
rate coefficient cannot be determined from our experiments
because there is a strong correlation between k21 and k22. Any
fixed value higher than 107 Mꢀ1 sꢀ1 would result in the same
average deviation; therefore, we decided to use the lower limit of
the value for k21.
Step 22 is the oxidation of hydrogen sulfite by the period-
ate ion via an O-atom transfer. We found that this reaction is
pH-dependent and our calculation has provided a value of
(1.6 ( 0.1) ꢂ 1010 Mꢀ2 sꢀ1 for k22 if k21 is fixed at 107 Mꢀ1
s
ꢀ1, meaning that the ratio of k22/k21 = 1600 ( 100 Mꢀ1
.
This means that under our experimental conditions step 22 is
a very rapid reaction and it cannot be studied by a conven-
tional diode-array spectrophotometer. This point was
strengthened by preliminary experiments indicating that
the hydrogen sulfiteꢀperiodate reaction is, in fact, com-
pleted within less than a tenth of a second. Unfortunately,
no research paper is available in the literature to provide
independent information about the rate coefficient of this
reaction that would also provide us a possibility to calculate
the actual value of k21.
Step 23 is the pH-dependent oxidation of thiosulfate by
iodous acid, producing S2O3OHꢀ and hypoiodous acid, that
probably proceeds via an O-atom transfer. As expected, it is a
fast process that governs the reaction in the initial phase
where a significant amount of thiosulfate is present. Omitting
this reaction would lead to an increase of 0.0151 in the
average deviation; therefore, we concluded that this step
is also necessary for a quantitative description of the kinetic
curves.
ever, the amount of iodine formed is not significant (TI
=
2
[I2] þ [I3ꢀ] < 9 ꢂ 10ꢀ5 M); therefore, we concluded that
there is not enough experimental information to refine these
parameters.
Finally, we shall point out how the complex absorbanceꢀtime
profiles along with the changing stoichiometry can be under-
stood by the proposed model. Figure 10 shows the measured
absorbanceꢀtime profiles at 275 and 468 nm. At the beginning
stage of the reaction, thiosulfate is oxidized simultaneously to
tetrathionate and sulfate; meanwhile, periodate reduced to
iodate, hypoiodous acid, and the iodide ion. The concentration
ratio of these species mainly depends on the pH and on the initial
Step 24 is a second-order decomposition of S2O3OHꢀ,
producing thiosulfate and hydrogen sulfite. We suggest that
it probably proceeds through the following sequence of
reactions (although any other alternative suggestion works
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• A total of 18 steps of the proposed model have already been
reported in previous studies. Either the majority of the rate
coefficients were fixed to a known value during calculation
or the values determined here were in sound agreement with
the ones previously found. In some cases (such as steps 1, 9,
and 22), no rate coefficient was available in the literature.
• The majority of the remaining steps are the reactions of
periodate with different intermediates such as S2O3OHꢀ,
S2O3Iꢀ, and HSO3ꢀ, which are evidently necessary to
prevent the accumulation of these species at high excess of
periodate.
• Necessity of the newly proposed reactions such as steps 10,
14, 16, 18, 19, and 23 has been confirmed indirectly by the
simultaneous evaluation of the kinetic curves. In each case,
not only did the average deviation increased significantly but
also the systematic deviation occurred between the mea-
sured and calculated kinetic data with the elimination of a
given step.
• The proposed model also adequately explains the experi-
mental fact that only small amounts of iodine can be
accumulated during the reaction. This fact is due to the fine
balance of iodide and hypoiodous acid formed during the
Landolt time. For the appearance of iodine, the initial
concentration ratio of the reactants has to be in a very
narrow range. An increase of thiosulfate increases the
amount of iodide but decreases that of hypoiodous acid,
resulting in a cessation of the formation of iodine after a
critical [S2O32ꢀ]0/[IO4ꢀ]0 ratio. In the opposite manner,
an increase of periodate decreases the amount of iodide and
leads to the exclusive formation of iodate.
It should also be mentioned that at first sight in the visible
range the deviation between the measured and calculated data
seems to be relatively large (see Figures 4 and S6G and S7G in
the Supporting Information. It should be taken into considera-
tion that in all of these cases the measured absorbance is relatively
low and the average deviation of these kinetic curves is still
around 0.006 absorbance unit, which is within the criterion of the
acceptable fit defined in the Data Treatment section. Therefore,
we concluded that the proposed model predicts the absorbanceꢀ
time series at the visible range well within the error of the
absorbance measurement. Further refinement of those para-
meters that are mainly responsible for the later phase of the
reaction is only possible if the measured absorbance is enlarged
approximately by an order of magnitude. As was seen previously,
it is very difficult (if it is possible at all) to increase experimentally
the amount of iodine to such an extent.
Finally, but not least, it has to be admitted that the proposed
model in its present form is not able to explain all of the
experimental findings (including the rare, fairly long transient
period of damped oscillation) reported by Rꢀabai et al.10 Further
work is still underway in our laboratory to improve the model to
be able to describe the most important dynamical feature of this
system in a CSTR.
Figure 10. Three different stages of a complex absorbanceꢀtime curve.
Conditions: [IO4ꢀ]0 = 4.90 mM; [S2O32ꢀ]0 = 3.68 mM; pH = 4.65. The
left y axis belongs to symbols O, and the right y axis belongs to 9.
concentration ratio of the reactants. The net effect is that the
absorbance steadily decreases at 275 nm. As long as the thio-
sulfate ion is present, iodine formed from step 12 is quickly
removed to produce the iodide ion and hypoiodous acid through
step 17. Eventually, this cycle increases the concentration of
iodide and hypoiodous acid, and we shall see that the key species
is hypoiodous acid in determining the kinetics of the following
stage of the reaction. The first stage is finished when thiosulfate is
completely removed from the solution. This time is usually
defined as the Landolt time. Because iodine formed from step
12 is no longer consumed, it suddenly appears in the solution
along with the triiodide ion. The amount of iodine is mainly
determined by the amount of hypoiodous acid formed in the first
stage of the reaction. This effect results in a sudden rise in
absorbance at both 275 and 468 nm. Once hypoiodous acid is
removed, the absorbance at 468 nm reaches its maximum. One
may also notice that the maxima of the absorbanceꢀtime curves
at 275 and 468 nm are shifted by approximately 200 s. This
follows from the fact that the concentration of iodide is alsꢀo
decreased in the second stage, and as a result, the I2ꢀI3
equilibrium is shifted toward the formation of iodine. Conse-
quently, the amount of triiodide starts to decrease before all of
hypoiodous acid is transformed to iodine. The third stage of the
reaction starts after HOI is completely consumed. In this phase,
the tetrathionateꢀiodine and iodideꢀperiodate reactions slowly
decrease the concentration of tetrathionate and periodate to
produce sulfate and iodate. It is also interesting to note that the
complex stoichiometry can also be understood via the proposed
kinetic model. In high excess of periodate, steps 1, 2, 3, 6, 7, and
22 account for the stoichiometry given by eq 3, while in high
excess of thiosulfate, steps 1, 4, 5, 18, and 23 completely explain
the limiting stoichiometry given by eq 5. If the pH is higher and
the excess of thiosulfate is moderate, then the net effect of steps 1,
9, 10, 11, 12, 20, 21, and 24 gives the stoichiometry characterized
by eq 4. It should be emphasized, however, that these sequences
of reactions cannot be separated experimentally; thus, it is quite
difficult to reach each limiting stoichiometry, as noticed by Rꢀabai
et al.10
’ CONCLUSION
One might also argue that such a robust model can be
described by almost any complex type of kinetic curve, and it is
an overestimation of the number of kinetic parameters needed
for an adequate description of the kinetic curves. To support the
validity of our kinetic model, the following facts should be
considered:
The work presented here may be considered as the first
comprehensive effort to unravel the kinetics and mechanism of
the complex thiosulfateꢀperiodate reaction, although it is clear
that we are only a step further in understanding the overall
chemistry of this fascinating system. It is indubitably demon-
strated that the initial phase of the reaction is completely
5801
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Inorganic Chemistry
ARTICLE
independent of the pH, and strong pH dependence can only be
observed in the later phase of the reaction, where the role of the
thiosulfateꢀperiodate reaction is negligible. It is, therefore,
expected that the rate law model of the thiosulfateꢀperiodate
reaction explaining the (oligo)oscillatory behavior in CSTR will
further be refined in the near future for an adequate description
of the experimental observations reported previously. It is
demonstrated as well that strong buffer assistance plays a
significant role in the later phase of the overall reaction. The
present kinetic model, however, is not yet able to take this
phenomenon into account but may pave the way for further
investigations mainly focusing on the problems to be solved.
(18) Broadbelt, L. J.; Stark, S. M.; Klein, M. T. Chem. Eng. Sci. 1994,
49, 4991–5010.
(19) Crouthhamel, C. E.; Hayes, A. M.; Martin, D. S. J. Am. Chem.
Soc. 1951, 73, 82–87.
(20) Weavers, L. K.; Hua, L.; Hoffmann, M. R. Water Environ. Res.
1997, 69, 1112–1119.
(21) Kustin, K.; Liebermann, E. C. J. Phys. Chem. 1964, 68,
3869–3873.
(22) Kurin-Cs€orgei, K.; Orbꢀan, M.; Rꢀabai, G.; Epstein, I. R. J. Chem.
Soc., Faraday Trans. 1996, 92, 2851–2855.
(23) Voslar, M.; Matejka, P.; Schreiber, I. Inorg. Chem. 2006, 45,
2824–2834.
(24) Rieder, R. J. Phys. Chem. 1930, 34, 2111–2116.
(25) Varga, D.; Nagypꢀal, I.; Horvꢀath, A. K. J. Phys. Chem. A 2010,
114, 5752–5758.
(26) Horvꢀath, A. K. J. Phys. Chem. A 2007, 111, 890–896.
(27) (a) Urbansky, E. T.; Cooper, B. T.; Margerum, D. W. Inorg.
Chem. 1997, 36, 1338–1344. (b) Furman, C. S.; Margerum, D. W. Inorg.
Chem. 1998, 37, 4321–4327. (c) Jia, Z. J.; Margerum, D. W.; Francisco,
J. S. Inorg. Chem. 2000, 39, 2614–2620. (d) Schmitz, G. Phys. Chem.
Chem. Phys. 1999, 1, 1909–1914. (e) Schmitz, G. Phys. Chem. Chem.
Phys. 2000, 2, 4041–4044.
’ ASSOCIATED CONTENT
S
Supporting Information. Listing of all of the chemical
b
reactions taken into consideration prior to the start of the fit,
presentation of the reproducibility of the kinetic curves, and
additional measured and calculated kinetic curves. This material
is available free of charge via the Internet at http://pubs.acs.org.
(28) (a) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84,
1355–1361. (b) Palmer, D. A.; van Eldik, R. Inorg. Chem. 1986,
25, 928–931. (c) Lengyel, I.; Epstein, I. R.; Kustin, K. Inorg. Chem.
1993, 32, 5880–5882.
(29) Marques, C.; Hasty, R. A. J. Chem. Soc., Dalton Trans. 1980,
111, 1269–1271.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: horvatha@gamma.ttk.pte.hu.
(30) Dushman, S. J. Phys. Chem. 1904, 8, 453–482.
(31) Lengyel, I.; Li, J.; Kustin, K.; Epstein, I. R. J. Am. Chem. Soc.
1996, 118, 3708–3719.
(32) Turner, D. H.; Flynn, G. W.; Sutin, N.; Beitz, J. V. J. Am. Chem.
Soc. 1972, 94, 1554–1559.
’ ACKNOWLEDGMENT
This work was supported by Hungarian Research Fund Grant
K68172. A.K.H. is grateful for the financial support of the Jꢀanos
Bolyai Research Scholarship of the Hungarian Academy of
Sciences.
(33) Ruasse, M.; Aubard, J.; Galland, B.; Adenier, A. J. Phys. Chem.
1986, 90, 4382–4388.
(34) IUPAC Stability Constant Database; Royal Society of Chemis-
try: London, 1992ꢀ1997.
’ REFERENCES
(35) Awtrey, A. D.; Connick, R. E. J. Am. Chem. Soc. 1951,
73, 1341–1348.
(1) Field, R. J., Burger, M., Eds. Oscillations and Traveling Waves in
Chemical Systems, 1st ed.; Wiley-Interscience: London, 1985.
(2) Ross, J., Schreiber, I., Vlad, M. O., Eds. Determination of Complex
Reaction Mechanisms, 1st ed.; Oxford University Press: Oxford, U.K.,
2005.
(36) Yiin, B. S.; Margerum, D. W. Inorg. Chem. 1990, 29, 1559–1564.
(3) Belousov, B. P. Ref. Radiats. Med. 1958, Medgiz, Moscow
1959, 145.
(4) Zhabotinsky, A. M. Biofizika 1964, 9, 306.
(5) Bray, W. C. J. Am. Chem. Soc. 1921, 43, 1262–1267.
(6) DeKepper, P.; Epstein, I. R.; Kustin, K.; Orbꢀan, M. J. Phys. Chem.
1982, 86, 170–171.
(7) (a) Rꢀabai, G.; Beck, M. T. J. Phys. Chem. 1988, 92, 2804–2807.
(b) Rꢀabai, G.; Beck, M. T. J. Phys. Chem. 1988, 92, 4831–4835.
(8) Nagypꢀal, I.; Epstein, I. R. J. Phys. Chem. 1986, 90, 6285–6292.
(9) Horvꢀath, A. K. J. Phys. Chem. A 2008, 112, 3935–3942.
(10) Rꢀabai, G.; Beck, M. T.; Kustin, K.; Epstein, I. R. J. Phys. Chem.
1989, 93, 2853–2858.
(11) Peintler, G.; Nagypꢀal, I.; Epstein, I. R.; Kustin, K. J. Phys. Chem.
A 2002, 105, 3899–3904.
(12) Horvꢀath, A. K.; Nagypꢀal, I.; Epstein, I. R. Inorg. Chem. 2006,
45, 9877–9883.
(13) Awtrey, A. D.; Connick, R. E. J. Am. Chem. Soc. 1951, 73,
4546–4549.
(14) Kerek, A.; Horvꢀath, A. K. J. Phys. Chem. A 2007, 111,
4235–4241.
(15) Landolt, H. Chem. Ber. 1885, 18, 249.
(16) Horvꢀath, A. K.; Nagypꢀal, I.; Peintler, G.; Epstein, I. R.; Kustin,
K. J. Phys. Chem. A 2003, 107, 6966–6973.
(17) Jenkin, M. E.; Sanders, S. M.; Pilling, M. J. Atmos. Environ. 1997,
31, 81–104.
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