Simultaneous evaluation of different types of kinetic traces of a complex system: Kinetics and mechanism of the tetrathionate - bromine reaction

Article abstract of DOI:10.1021/jp9026089

The bromine-tetrathionate reaction has been studied in the presence of phosphoric acid/dihydrogen phosphate buffer at T = 25 ± 0.1°C and at I = 0.5 M ionic strength with both stopped-flow technique and a conventional diode array spectrophotometer. The sto

Full text of DOI:10.1021/jp9026089

9988
J. Phys. Chem. A 2009, 113, 9988–9996
Simultaneous Evaluation of Different Types of Kinetic Traces of a Complex System:
Kinetics and Mechanism of the Tetrathionate-Bromine Reaction
De´nes Varga†,‡ and Attila K. Horva´th*,†
Department of Chemistry, UniVersity of Pe´cs, Ifju´sa´g u´tja 6, H-7624 Pe´cs, Hungary
ReceiVed: March 23, 2009; ReVised Manuscript ReceiVed: July 14, 2009
The bromine-tetrathionate reaction has been studied in the presence of phosphoric acid/dihydrogen phosphate
buffer at T ) 25 ( 0.1 °C and at I ) 0.5 M ionic strength with both stopped-flow technique and a conventional
diode array spectrophotometer. The stoichiometry of the reaction was found to be S4O26- + 7Br2 + 10H2O
f 4SO24- + 14Br- + 20H+ in bromine excess, but no unambiguous stoichiometry can be established in
tetrathionate excess because elementary sulfur as well as hydrogen sulfide are also present in appreciable amounts
besides the major product sulfate. It has also been shown that the reaction has two well-separable kinetic phases
in an excess of tetrathionate. Rapid disappearance of bromine was observed in the early stage of the reaction
followed by a much slower spectral change in the UV region that can be attributed to the disappearance of
an absorbing species having much stronger light absorption than that of tetrathionate in the given wavelength
range. Two different types of kinetic curves measured by two different instruments have been evaluated
simultaneously that led us to suggest and discuss a 10-step model.
Introduction
method is more preferred. The advantages of this method have
recently been summarized in our previous paper,11 though in
the case of evaluation of overlapping spectra sometimes no
unambiguous kinetic model can be offered even with the
simultaneous curve fitting method. This situation occurred in
case of the tetrathionate-hypochlorous acid system, where a
couple of mathematically equivalent but chemically different
models were proposed.8 At that time it was supposed that a
long-lived intermediate was formed (S2O3Cl-) during the
reaction based on the early observations of Awtrey and
Connick12 who assigned a relatively long lifetime to S2O3I- and
S2O3Cl- species. It was concluded from the experimental
observations that iodine slowly disappeared in the thiosulfate-
iodine reaction in an excess of iodine after the first very rapid
stage.13 Tetrathionate can, however, further react with iodine
in a relatively slow autoinhibitory reaction because the iodide
ion formed during the oxidation process retards the reaction
significantly,13,14 therefore, it is not necessary to suppose a long-
lived intermediate whose further reaction is responsible for the
slow reduction of iodine. Furthermore, it was also demonstrated
that no absorbing species was accumulated in appreciable
amounts. Nevertheless, our paper also provided a reasonable
answer14 to the question about the unexpected but experimentally
found iodide dependence of the rate coefficient of the rate law
suggested by Awtrey and Connick. To obtain more reliable
information about the possible role of the S2O3X- species (where
X can be any halogen), we decided to investigate the analogous
tetrathionate-bromine reaction. Thorough survey of the litera-
ture indicated no detailed investigation on the kinetics and
mechanism of this reaction. Recent renewed interest of further
conversion of thiosulfate and/or polythionates in microbiology,15-18
geochemistry,19 and leaching processes20 also justifies an
investigation leading to a deeper understanding of the redox
chemistry of tetrathionate.
Tetrathionate ion is known as one of the most stable low
valence sulfur-containing compounds obtained through the
oxidation of thiosulfate leading to sulfate in neutral and slightly
acidic media. Its formation as a long-lived key intermediate in
the oxidation reactions of thiosulfate is often accompanied by
the appearance of wide variety of nonlinear dynamical phe-
nomena. It has been recently shown that electrochemical
oxidation of thiosulfate leads to the formation of not only
tetrathionate but also higher polythionates in an oscillatory
fashion.1 Moreover, oxidation of thiosulfate by hypochlorous
acid also eventually gives an appreciable amount of polythion-
ates and sulfur precipitation in slightly acidic media.2 The most
studied chemical system involving the oxidation of thiosulfate
in which tetrathionate plays an important role is the thiosulfate-
chlorite reaction, which shows multistability, complex periodic
and aperiodic oscillation in a continuously stirred tank reactor
(CSTR), and a fluctuation and stirring rate effect in batch.3-6
Unfortunately, the kinetics and mechanism of the chlorite-
thiosulfate reaction is still a mystery, and no quantitative
description can therefore be offered for the explanation of such
a wide variety of dynamical behavior. The last two decades
have, however, witnessed considerable efforts to unravel the
kinetics and mechanism of reaction of tetrathionate with several
different oxidizing agents such as hydrogen peroxide,7 hy-
pochlorous acid,8 chlorine dioxide,9 and chlorite10 that may help
to contribute to a better understanding of the dynamical behavior
of the chlorite-thiosulfate parent reaction. In most of these
systems the highly overlapping spectra of the reactants and the
end products prevent the usage of simplified evaluation
techniquesssuch as the initial rate studies and the individual
exponential curve fitting methodsto obtain reliable kinetic
models; therefore, the choice of the simultaneous curve fitting
Experimental Section
* E-mail: horvatha@gamma.ttk.pte.hu.
† University of Pe´cs.
‡ This paper is dedicated to the memory of De´nes Varga, who suddenly
deceased during the preparation of this manuscript.
Materials and Buffers. Bromine stock solution was prepared
by distilling bromine (Sigma-Aldrich) into 0.01 M H3PO4
10.1021/jp9026089 CCC: $40.75  2009 American Chemical Society
Published on Web 08/20/2009

Kinetic Traces of a Complex System
J. Phys. Chem. A, Vol. 113, No. 37, 2009 9989
solutions. All the other chemicals were of the highest purity
commercially availablespotassium tetrathionate (Fluka), sodium
bromide, sodium dihydrogen phosphate, phosphoric acid
(Reanal)sand were used without further purification. The purity
of the commercially available tetrathionate was checked by the
following procedure. First, the S(IV) and thiosulfate contamina-
tion was examined by standard triiodide solution. If the solution
turned out to be sulfite and thiosulfate free then the weighed
amount of tetrathionate was oxidized by bromine in excess
followed by purging the remaining bromine by N2 gas. The
liberated proton was titrated against standard sodium hydroxide
solution. The purity of tetrathionate was found to be better than
99.5%. All the stock solutions were prepared from ion-
exchanged and four-times-distilled water. The concentration of
the stock bromine solution was checked by standard iodometric
titration prior to each experiment.
experiments showed that the loss of bromine was always less
than 6% in such an experimental protocol.
Data Treatment. Seven different wavelengths (between 260
and 290 nm in every 5 nm) have been chosen for the evaluation
procedure in the case of the diode array spectrophotometer to
gain as much information about the end products as possible.
The experimental curves measured by the stopped-flow ap-
paratus and by the diode array spectrophotometer were then
evaluated simultaneously by the ZiTa program package.24
Because two different types of kinetic data (absorbance-time
and concentration-time series) were evaluated simultaneously,
a relative fitting procedure has been chosen to minimize the
average deviation between the measured and calculated data.
A relative fitting procedure means that the difference between
the measured and calculated quantities are divided by the largest
change in the experimental value for each kinetic curve and
the sum of squares of average deviation obtained this way is
minimized.
Because each kinetic curve contained at least 300 data pairs,
the number of points in each run was reduced to 40-50 to avoid
unnecessary time-consuming calculations. The essence of this
method has already been described elsewhere.10 Altogether more
than 22000 experimental points from 496 kinetic series (76
concentration-time and 7 × 60 absorbance-time series) were
used for the simultaneous evaluation. Our quantitative criterion
for an acceptable fit was that the average deviation for the
relative fit approach 6%, which is close to the experimentally
achievable limit of error, taking the maximum loss of bromine
into consideration.
In an excess of tetrathionate, colloidal sulfur precipitation
occurs (see description below). Because colloidal sulfur particles
cannot be taken into consideration as a specific entity having a
characteristic absorption spectrum, therefore we decided to
remove those parts of the kinetic curves, where absorbance
increase can be observed at longer wavelengths. The “absor-
bance” change measured at longer wavelength can be attributed
to the colloidal sulfur particles because on one hand the
reflection of the analyzing light on the particles fails to reach
the detector and on the other hand none of the sulfur-containing
species has an absorption at 600 nm. Typically it meant that
the kinetic curves were truncated at around 300 s, depending
on the initial concentration of the reactants.
Phosphoric acid-dihydrogen-phosphate buffer was used to
maintain the pH between 2.10 and 3.80. The ionic strength was
kept constant at 0.5 M with sodium dihydrogen phosphate as a
buffer component, and the pH of the solution was adjusted with
the desired amount of phosphoric acid, taking the pKa of
phosphoric acid as 1.80.21
To study the first kinetic stage of the reaction, the following
concentration ranges were used: [S4O26-]0 ) 0.001-0.008 M,
T0Br ) 0.0028-0.0075 M, [Br-]0 ) 0-0.2 M, pH ) 2.10, 2.80,
2
3.80, where T0Br ) [Br2]0 + [Br-3 ]0. Altogether 76 concentration-
2
time series were used for data evaluation. When the slower part
of the reaction was studied at the same pHs, the initial
tetrathionate and bromine concentrations were kept in the ranges
of 0.167-1.33 mM and 0.25-1.1 mM, respectively. Twenty
different initial concentration ratios at three different pHs were
used to investigate the reaction in such a way that tetrathionate
was always maintained in excess. The exact concentrations of
each kinetic run are seen in the Supporting Information.
Methods and Instrumentation. Stoichiometric Studies. In
an excess of bromine the stoichiometry of the reaction was
established by simple iodometric and acid-base titrations. In
the case of iodometric titration, iodide was added to the solution
and the iodine formed from the remaining amount of bromine
was titrated with standard thiosulfate solution.
Kinetic Studies. The first relatively fast kinetic phase of the
title reaction was measured by a Hi-Tech SF-61 stopped-flow
apparatus attached to a single wavelength spectrophotometer
that provides monochromatic light. The reaction was followed
at 460 nm, the isosbestic point of Br2-Br-3 system. The
measured absorbances were converted into total bromine
concentration according to the molar absorbances of bromine
and tribromide at this wavelength (see Supporting Information,
Results
Preliminary Observations. Figure 1 shows a typical kinetic
run in an excess of tetrathionate measured by the diode array
spectrophotometer. It clearly indicates that bromine is consumed
within the time of mixing the reactants in the cuvette, but
significant changes can be observed in the UV range lasting
for approximately 10 min. Moreover, comparing the initial
spectra of the reactants with the spectrum of the reacting mixture
clearly indicates that a species having a much stronger absor-
bance band than that of tetrathionate in the given spectral range
accumulates in a detectable amount. Although it is well-known
that tribromide ion has a very intense absorbance band25 in the
UV range (λmax ) 266 nm, ε ) 39900 M-1 cm-1), as Figure 1
indicates tribromide ion cannot be responsible for this effect,
because the measured absorbance is zero at the first experimental
time point at the 460 nm (isosbestic point of Br2-Br-3 system).
A reasonable explanation would, however, be the formation of
higher polythionates or other polysulfide species that has a much
stronger absorbance band in the UV range than that of
tetrathionate.26 At first sight, the idea that oxidation of tetrathion-
ate by a strong oxidizing agent leads to the formation of higher
εBr ) εBr ) 81 M-1 cm-1). The reaction becomes too fast to
-
3
be 2measured conveniently at pseudo-first-order conditions; thus,
an improved calibration and use of a stopped-flow spectropho-
tometer has been used to unravel the kinetics and mechanism
of the title reaction. The application and the essence of this
method have already been published elsewhere.22,23
In an excess of tetrathionate, the reaction was also followed
by Zeiss S10 diode array spectrophotometer at 260-600 nm
wavelength range. The kinetic measurements were carried out
in a standard 1 cm quartz cuvette equipped with a Teflon cap
and magnetic stirrer. The buffer solution was delivered first,
followed by the bromine solution (also containing the corre-
sponding buffer). Then the spectrum of this solution was
recorded to determine the initial concentration of bromine.
Finally, the necessary amount of tetrathionate was introduced
from a fast delivery pipet to start the reaction. Separate

9990 J. Phys. Chem. A, Vol. 113, No. 37, 2009
Varga and Horva´th
Figure 1. Time-resolved spectral changes in the tetrathionate-bromine
reaction in an excess of tetrathionate after the fast disappearance of
bromine in the absence of initially added bromide ion. The initial
Figure 2. Typical absorbance change at four different wavelength.
[S4O26-]0 ) 1.33 × 10-3 M, TB0 r ) 1.1 × 10-3 M, [Br-]0 ) 0 M, pH
2
) 2.08. λ (nm) ) 270 (b), 280 (0), 290 (2), 300 ()). Note that
absorbance at t ) 0 values are calculated from the initial concentrations
of the reactants.
concentrations are as follows: [S4O26-]0 ) 0.001 M, TB0 r ) 0.001 M,
2
[Br-]0 ) 0 M, and pH ) 2.80. The dashed line indicates calculated
initial spectrum of the reactants supposing no reaction at all. The time-
resolved spectra (solid lines) were taken at t ) 5, 25, 45, 95, 195, and
495 s. The arrow indicates the direction of change in the absorbance at
the time interval given above.
TABLE 1: Determination of the Stoichiometry in an Excess
of Brominea
pH [S4O26-]0, M [Br2]0, M [Br2]∞, M [H+]∞, M SR1 SR2
polythionates or polysulfides may seem surprising, but recent
studies have already shown this phenomenon in the case of
oxidizing thiosulfate.1,2 Further discussion about the formation
of the relatively long-lived intermediate will be discussed later.
The appearance of polythionates or polysulfides also complicates
the stoichiometry of the reaction in an excess of tetrathionate
because several other sulfur-containing species may also be
formed. Separate experiments confirmed the formation of
hydrogen sulfide by its characteristic odor as well as by the
formation of a brownish black lead sulfide precipitate after
adding lead nitrate to the solution. For the sake of completeness,
it should be noted that the majority of the precipitation is due
to the formation of white lead sulfate. Besides hydrogen sulfide,
however, we ruled out the formation of thiosulfate, because
addition of Fe3+ to the reacting solution does not give the
characteristic purple color of the ferric(III) thiosulfato complex
that gradually fades away after approximately 1 min upon its
formation. It is also well-known that degradation of polythion-
ates leads to the formation of S(IV) species.27,28 Moreover, at a
huge excess of tetrathionate after the rapid disappearance of
bromine, the solution becomes pale yellow depending on the
excess of tetrathionate, suggesting the formation of some
polysulfide species29 from which elementary sulfur also pre-
cipitates. Figure 2 shows a typical measured absorbance-time
profile at the later stages of the reactions in an excess of
tetrathionate measured at several different wavelengths. As seen,
the intermediate formed in the first rapid stage of the reaction
disappears, but after a couple of minutes, a slow but steady
absorbance increase can be observed; meanwhile, the solution
gradually becomes opalescent, suggesting the formation of
colloidal sulfur. It should be emphasized that the appearance
of a wide variety of sulfur-containing compounds is definitely
the consequence of the reaction because the tetrathionate solution
is stable under these experimental conditions.
3.8
3.8
3.8
3.8
3.8
2.8
2.8
2.8
2.8
2.8
0.001
0.0015
0.002
0.003
0.005
0.001
0.0015
0.002
0.003
0.005
0.001
0.0015
0.002
0.003
0.005
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.0331
0.0293
0.0258
0.01915
0.0049
0.0328
0.0294
0.0262
0.01915
0.00475
-
-
-
6.90
7.13
7.10
6.95
7.02
7.20
7.07
6.90
6.95
7.05
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
b
-
0.0202
0.0300
0.0398
0.0597
0.1005
20.2
20.0
19.9
19.9
20.1
b
-
-
-
b
-
-
-
-
b
-
-
b
-
-
-
a SR1 and SR2 are defined as the ([Br2]0-[Br2]∞)/[S4O26-
]
and
0
[H+]∞/[S4O62-]0 ratios. b Without buffer.
1. In excess of tetrathionate, however, our attempt to establish
a uniform stoichiometry failed. This fact is not surprising if
one takes the number of different sulfur-containing species
detected in an excess of tetrathionate into account.
MRA Studies. To determine the number of absorbing species,
matrix rank analysis (MRA)30 has been executed on all the
measured series simultaneously where the measured values did
not exceed 1.0 absorbance unit. Those time points where
absorbance increase could be observed at longer wavelenghts
(500-600 nm) due to the light reflection on colloidal sulfur
particles have been eliminated from the evaluation. It typically
meant that time points up to 300-600 s were taken into account
depending on the initial concentration of the reactants. This study
has clearly revealed three independent absorbing species, namely
tetrathionate, a color intermediate, and “sulfur”. The present
study is, however, unable to distinguish between the possible
forms of “sulfur” that may be HS(OH), etc., from which the
gradual sulfur precipitation occurs. The polysulfide species as
a form of “sulfur”, however, can clearly be ruled out because
acidification of polysulfide solution immediately leads to the
formation of elementary sulfur precipitation.
Stoichiometry. Iodometric titration showed that the stoichi-
ometry of the reaction can be characterized in an excess of
bromine as follows:
S4O26- + 7Br2 + 10H2O f 4SO24- + 14Br- + 20H+
Proposed Kinetic Model. Early Stage: The method leading to
the best fitting model has already been published elsewhere.9,10,23,31,32
The most critical part of this procedure is to choose the set of
species involved in the mono- and bimolecular reactions. This
group consists of S4O26-, Br2, Br-, Br3-, SO42-, H2O, H+, and
(1)
This stoichiometry was also verified in absence of buffer by
simple acid-base titration. The results are summarized in Table

Kinetic Traces of a Complex System
J. Phys. Chem. A, Vol. 113, No. 37, 2009 9991
P(x), where P(x) is a sulfur-containing end product at the
stopped-flow time scale, but it is an intermediate at longer
periods. Further discussion on P(x) will be continued later in
this paper. Additionally the S4O6Br-, S2O3Br-, S2O3OH-, HSO-3
intermediates have also been chosen for the following reasons:
• The role of S4O6I- and S2O3I- has already been well-
established in the tetrathionate-iodine reaction.13,14 By analogy
one can assume that the corresponding bromine-containing
species may also be involved in the tetrathionate-bromine
reaction.
over a longer time scale. Decay of P(x) results in formation of
another absorbing speciessmost probably it is HS(OH)sfrom
which elementary sulfur gradually precipitates. The simplicity
of the kinetic curves suggests that the description of the second
kinetic phase requires only two fitted rate coefficients (the OH-
dependent and independent R10) and 2 × 7 molar absorbances
of P(x) and HS(OH) at seven different wavelengths.
P(x) f (3 - y)SO24- + 2HS(OH) + H2S (R10)
• The S2O3OH- species is a well-known key intermediate of
the tetrathionate-hydrogen peroxide reaction7 as well as the
tetrathionate-iodine reaction.13,14 Therefore, it must also be
included as an intermediate of the tetrathionate-bromine
reaction.
The average deviation was found to be 4.8% for the 7 × 60
absorbance-time series in the case of evaluating only the later
stage of the reaction. The final results (rate coefficients and
molar absorbances) can be found in the last column of Tables
2 and 3, respectively.
To set up the initial kinetic model as a first step, all the
conceivable mono- and bimolecular reactions of these species
were considered along with their H+- and OH--catalyzed
pathways, meaning that more than 100 reactions were included
in the start of the evaluational process. By eliminating the
processes step by step that do not have any effect on the quality
of fit we finally arrive at the core of the kinetic model in which
all the steps are necessary for description of the kinetic data
for the early stage of the reaction. After this long, but
straightforward, calculation procedure, the following kinetic
model emerged
Evaluation of Two Kinetic Stages Simultaneously: As seen,
evaluation of the two distinct, well-separable kinetic phases led
to a reasonable kinetic model for both stages. The connection
between them is the color intermediate P(x) formed in step R9.
Although there are two types of kinetic traces (concentration-time
for the first phase and absorbance-time for the second phase),
the comprehensive program package ZiTa24 is capable of
determining the rate coefficients of the combined system,
evaluating different types of the kinetic curves simultaneously.
The results of the simultaneous evaluation can be seen in Tables
2 and 3; the average deviation was found to be 4.9%. It is clear
that the kinetic parameters and the molar absorbances deter-
mined from the two different calculation procedures agree well
within their standard deviation. Therefore, it is concluded that
the parameter set obtained from both evaluational procedures
is reliable and consistent. Nevertheless, the powerful ability of
the comprehensive program package ZiTa to determine the
kinetic parameters of an unknown system is also highlighted.
H+ + H2PO-4 h H3PO4
Br2 + Br- h Br-3
(E1)
(R1)
(R2)
S4O62- + Br2 h S4O6Br- + Br-
S4O6Br- + H2O f S2O3Br- + S2O3OH- + H+
Discussion
(R3)
(R4)
S4O6Br- + Br- f 2S2O3Br-
The rapid de- and reprotonation process E1 was taken into
account with a known equilibrium constant21 to follow the
change in pH during the reaction especially at pH ) 3.8, where
the phosphate buffer has weak capacity (pKE1 ) 1.80). This
acid dissociation equilibrium may be regarded as an auxiliary
process, necessary for the detailed calculation, but it is not a
central part of the proposed model.
S2O3Br- + Br2 + 3H2O f 2HSO-3 + 3Br- + 4H+
(R5)
S2O3Br- + Br3- + 3H2O f 2HSO-3 + 4Br- + 4H+
(R6)
Step R1 is the well-known formation of tribromide ion. This
equilibrium is established rapidly; therefore, the fast forward
S2O3OH- + Br2 + 2H2O f 2HSO-3 + 2Br- + 3H+
(R7)
(kR1 ) 1.81 × 109 M-1 s-1) and the reverse (k-R1 ) 108 s-1
)
rate coefficients of step R1 were fixed during the calculation to
give the known formation constant of tribromide ion as 18.1
HSO-3 + Br2 + H2O f 2Br- + SO24- + 3H+
M-1 33
.
(R8)
Step R2 is a formal Br+ transfer from bromine to one of the
inner sulfur atoms of tetrathionate. The back reaction was found
to be fast; any value higher than k-R2 ) 107 M-1 s-1 would
S4O26- + S2O3Br- + H2O f P(x) + Br- + 2H+ +
ySO24- (R9)
lead to the same final result. Therefore, we fixed it to k-R2
107 M-1 s-1. The forward reaction (kR2) is, however, in total
correlation with k-R2; therefore, only the ratio of kR2/k-R2
)
where y can be 1, 2, or 3.
)
The average deviation was found to be 4.6% for the 76
concentration-time series with six fitted rate coefficients in the
case of only the stopped-flow measurements. The final results
of the calculation can be seen in the fourth column of Table 2.
Later Kinetic Stage: As seen in Figure 2, the reaction has a
slower kinetic phase in an excess of tetrathionate. To evaluate
the second kinetic stage, all the kinetic parameters determined
from the first stage of the reaction were fixed. It means that
P(x) formed in step R9 can only be treated as an intermediate
KR2 ) 1.68 ( 0.26 could be determined. Figure 3 shows the
first rapid stage of the reaction as the initial concentration of
tetrathionate varies. As one can see at t ) 0 s, the concentration
of bromine significantly decreases with increasing tetrathionate
concentration, apparently indicating that the KR2 ) kR2/k-R2 value
would be determined by a simple linear fit of the measured
bromine concentration at t ) 0 s plotting against the inverse of
initial tetrathionate concentration (see Supporting Information).
However, it would only be true if the decrease of the bromine

9992 J. Phys. Chem. A, Vol. 113, No. 37, 2009
Varga and Horva´th
S10
TABLE 2: Fitted and Fixed Rate Coefficients of the Proposed Kinetic Modela
parameterb
SF
step
R1
(-R1)
R2c
(-R2)
R3
R4
R5
R6
R7
rate equation
simultaneous
kR1[Br2][Br-] (M-1 s-1 × 10-9
)
1.81
1.81
-
k-R1[Br-3 ] (s-1
)
108
108
-
kR2[S4O62-][Br2] (M-1 s-1 × 10-7
)
1.68 ( 0.26
2.11 ( 0.49
-
k-R2[S4O6Br-][Br-] (M-1 s-1
)
107
107
-
kR3[S4O6Br-] (s-1
)
141 ( 13
8.83 ( 1.64
2.27 ( 0.20
1.03 ( 0.33
109
121 ( 12
5.87 ( 0.90
1.80 ( 0.30
1.72 ( 0.82
109
-
kR4[S4O6Br-][Br-] (M-1 s-1 × 10-3
)
)
-
kR5[S2O3Br-][Br2] (M-1 s-1 × 10-5
kR6[S2O3Br-][Br3-] (M-1 s-1 × 10-6
)
-
-
kR7[S2O3OH-][Br2] (M-1 s-1
)
-
-
R8
R9
R10
R10′
kR8[HSO-3 ][Br2] (M-1 s-1
)
3 × 108
3 × 108
1.98 ( 0.60
-
kR9[S4O62-][S2O3Br-] (M-1 s-1 × 10-5
kR10[P(x)] (s-1 × 102)
)
1.82 ( 0.32
1.33 ( 0.10
1.92 ( 0.22
-
1.32 ( 0.10
1.93 ( 0.23
k′R10[H+]-1 [P(x)] (M ·s-1 × 105)
-
a No error indicates that the value in question was fixed during the fitting procedure. b The value of the rate coefficients determined from
only the first kinetic phase (SF), the second kinetic phase (S10), and simultaneously (simultaneous) from both measurements, respectively.
c Note that the kR2/k-R2 ratio can only be determined from the experiments.
TABLE 3: Measured and Calculated Molar Absorbancea of the Absorbing Species Used in the Fitting Procedure
P(x)
simultaneousc εcalcd
HS(OH)
simultaneous εcalcd
S10c εcalcd
S10 εcalcd
S4O26- εmeasd
S5O26- εmeasd
b
λ (nm)
260
265
270
275
280
285
290
2034 ( 44
1724 ( 37
1439 ( 31
1174 ( 25
936 ( 20
727 ( 15
549 ( 12
2033 ( 42
1724 ( 36
1439 ( 30
1174 ( 24
936 ( 19
727 ( 14
549 ( 11
374 ( 14
314 ( 11
267 ( 10
227 ( 8
189 ( 7
153 ( 6
122 ( 5
375 ( 12
314 ( 11
267 ( 10
227 ( 8
189 ( 6
153 ( 5
122 ( 4
552
416
309
225
161
112
76.3
2100
1800
1500
1150
940
720
544
a Molar absorbances are given in the M-1 cm-1 unit. b See ref 26. c Molar absorbance determined from only the second kinetic phase (S10)
and simultaneously (simultaneous) from both measurements, respectively.
concentration in the dead-time of the stopped-flow instrument
is solely due to the rapid establishment of equilibrium R2. Partial
contribution of the extent of the reaction to the concentration
decrease of bromine during the dead-time cannot be ruled out;
therefore, we do not have solid basis to determine KR2 by this
way.
dence of the kinetic curves. The reaction proposed here is the
bromine analogy of that reaction, which proceeds via the attack
of bromide ion on the empty inner sulfur of S4O6Br- followed
by splitting of the S-S bond of the intermediate. As a result,
S4O6Br- is converted to S2O3Br- that can either be oxidized
by bromine eventually to sulfate or can react with tetrathionate
to produce the absorbing intermediate P(x). The necessity of
this step can be supported by the fact that its elimination would
result in a significant increase in the average deviation (8.0%).
The majority of the increase in the average deviation arises from
the difference between the measured and calculated curves in
the presence of initially added bromide ion; therefore, we
concluded that this step is essential for quantitative description
of the kinetic curves.
Similar initiating process was proposed in the corresponding
tetrathionate-iodine reaction13,14 with two important differences.
First, the forward reaction of the initiating equilibrium could
be calculated independently; second, kR2 is many orders of
magnitude lower in case of the tetrathionate-iodine reaction
than that of the present one. It directly indicates that the initiating
equilibrium is not shifted as much to the left in the tetrathionate-
bromine reaction. Also taking into consideration that the
formation constant of tribromide ion is more than 1 order of
magnitude lower than that of the triiodide ion, it directly means
that the inhibitory effect of halide ion cannot be so pronounced
as that observed in the latter system. The inhibitory or more
precisely the autoinhibitory effect of bromide ion in the
tetrathionate-bromine reaction is illustrated in Figure 4.
A reaction similar to step R3 was already suggested to take
place in the tetrathionate-iodine system.13,14,34 By analogy one
can assume that S4O6Br- formed in the initiating equilibrium
reacts with water to produce S2O3Br- and S2O3OH- by splitting
the inner sulfur bond. Our fitting procedure has provided a value
of (141 ( 13) s-1 for the rate coefficient of step R3. Omitting
this step from the proposed model would yield a 26% average
deviation from which we concluded this step to be essential
for the quantitative description of the simultaneous evaluation
of the kinetic curves.
Step R5 is the oxidation of S2O3Br- by bromine yielding
sulfite and bromide ions. The individual rate coefficient kR5 was
found to be (2.27 ( 0.20) × 105 M-1 s-1. Omitting this step
from the final model would increase the average deviation to
6.2%, indicating systematic deviation between the measured and
calculated data in the absence of initially added bromide ion;
therefore, we found the role of this step to also be important in
the final model.
Step R6 is the oxidation of S2O3Br- by tribromide ion
yielding sulfite and bromide ions. It is interesting to note that
this is the only reaction of tribromide ion which is necessary
for fitting the kinetic data. It plays a significant role at a larger
initial bromide concentration and eventually helps to use up
the total bromine amount more quickly. Although elimination
of this step from the final model increases the average deviation
from 4.9% to only 5.9%, systematic deviation can be observed
between the measured and calculated data at high initial bromide
concentration in the stopped-flow time-scale; therefore, we
A similar process to step R4 has recently been proposed in
the tetrathionate-iodine reaction to explain the iodide depen-

Kinetic Traces of a Complex System
J. Phys. Chem. A, Vol. 113, No. 37, 2009 9993
Figure 3. Measured (symbols) and calculated (solid lines) kinetic
curves at different tetrathionate concentrations in the early stage of the
reactions. TB0 r ) 0.006 M, pH ) 2.08, [Br-]0 ) 0 M. [S4O26-] /M )
Figure 5. Measured (symbols) and calculated (solid lines) kinetic
curves at different pHs in the early stage of the reaction. [S4O26-]0 )
0.006 M, T0Br ) 0.006 M, [Br-]0 ) 0 M. pH ) 2.08 (b), 2.80 (0),
0
2
2
0.002 (b), 0.003 (0), 0.004 (2), 0.006 ()), 0.008 (9).
3.80 (2).
Any appropriately chosen sulfur-containing species will lead
to the same average deviation, meaning that we do not have a
solid basis to differentiate among the possible forms of P(x) by
the simple evaluation procedures. This situation has already been
reported in the tetrathionate-hypochlorous acid reaction.8 As
a result, we may easily interpret our results by using three
different feasible possibilities for the intermediate P(x) as if it
was pentathionate, S4O2OH-, or S32-.
P(x) as pentathionate: If we suppose that the intermediate
P(x) is pentathionate, then R9 must be modified as
S4O62- + S2O3Br- + H2O f S5O26- + SO24- + Br- +
Figure 4. The disappearance of total bromine (TBr ) [Br2] + [Br-3 ])
in presence of initially added bromide ion in the 2early stage of the
2H+ (2)
reaction. [S4O62-]0 ) 0.002 M, TB0 r ) 0.007 M, pH ) 2.80. [Br-]0/M
2
) 0 (b), 0.04 (0), 0.12 (2), 0.2 ()). Measured and calculated curves
are indicated by symbols and solid lines, respectively.
Although this step is not an elementary reaction, one may
easily suggest reasonable consecutive elementary processes to
decompose it as follows:
concluded this step to be necessary for quantitative description
of the kinetic data.
Step R7 is also a rapid reaction that converts S2O3OH- into
HSO-3 . The individual rate coefficient of kR7 cannot be deter-
mined from our experiments. Any value higher than 108 M-1
s-1 leads to the same final results, which means that this rate
coefficient has to be near to the diffusion control limit.
Therefore, we have set kR7 to an arbitrary but reasonable value
S4O62- + S2O3Br- f S5O62- + SO3Br-
(3)
(4)
SO3Br- + H2O f SO24- + Br- + 2H+
of 109 M-1 s-1
.
Step R8 is a very rapid oxidation of hydrogen sulfite by
bromine. The analogous hydrogen sulfite-iodine reaction was
studied by Yiin and Margerum,35 who determined its rate
coefficient to be 3.1 × 109 M-1 s-1. Because bromine is a more
powerful oxidizing agent than iodine, the rate coefficient of the
hydrogen sulfite-bromine reaction is expected to be higher than
that of the previous reaction. Troy and Margerum36 also
determined the rate constant between sulfite and hypobromite
ion to be 1.0 × 108 M-1 s-1, suggesting that the rate coefficient
of the bromine-S(IV) reaction must be higher than that.
Therefore, we fixed kR8 ) 5 × 109 M-1 s-1 during the fitting
procedure, though the calculation requires only a value higher
than 108 M-1 s-1 for kR8.
Step R9 is responsible for the formation of the colored sulfur-
containing intermediate P(x). As Figure 5 clearly indicates, the
first phase of the reaction is basically independent of pH in the
pH range studied; therefore, the rate equations of steps R1-R9
cannot have [H+] or [OH-] dependent terms. The surprising
result of our calculation is, however, that the formal oxidation
number of sulfur in P(x) cannot be determined unambiguously.
where eq 3 is the rate-determining step.
A reaction similar to eq 2 has already been proposed in the
kinetic model of the thiosulfate-hypochlorous acid reaction;2
hence, by analogy we may propose this reaction as a source of
pentathionate in the reaction studied. Formation of pentathionate
during the oxidation of tetrathionate by a strong oxidizing agent
such as bromine may seem to be astonishing, but several pieces
of indirect evidence can be aligned to support this fact. First,
as mentioned above, Figure 1 clearly shows the formation of
an absorbing intermediate having a much stronger absorption
band in the UV range than that of tetrathionate. Second, Table
3 indicates a considerably good agreement between the calcu-
lated molar absorbance of pentathionate compared with the
values measured by independent research more than 40 years
ago.26 Third, not only chemical but also electrochemical
oxidation of thiosulfate leads to the formation of pentathionate
as shown by other researchers recently.1
P(x) as S4O2OH-: Supposing that P(x) is S4O2OH-, then R9
may be modified as

9994 J. Phys. Chem. A, Vol. 113, No. 37, 2009
S4O26- + S2O3Br- + 2H2O f S4O2OH- + 2SO42-
Varga and Horva´th
+
Br- + 3H+ (5)
This reaction can also be decomposed into an elementary
reaction such as
S4O62- + S2O3Br- f S6O92- + Br-
(6)
(7)
S6O92- + H2O f SO24- + S5O6OH- + H+
S5O6OH- + H2O f SO42- + S4O2OH- + 2H+ (8)
Figure 6. Measured (symbols) and calculated (solid lines) kinetic
curves in the later stage of the reaction at different pHs in an excess of
tetrathionate after the disappearance of bromine. [S4O26-]0 ) 6.67 ×
0
10-4 M, T ) 7.0 × 10-4 M, [Br-]0 ) 0 M. pH ) 2.08 (b), 2.80
where eq 6 is the rate-determining step. As mentioned previ-
ously, this possibility also leads to the same final result. The
reason why alternative solutions are presented for P(x), although
pentathionate seems to be a very reasonable suggestion, can be
understood based on the rate coefficients of step R10 (see later).
P(x) as S23-: Supposing that the polysulfide species is the
intermediate P(x), then Step R9 has to be modified as
Br2
(0), 3.80 (2).
S4O26- + S2O3Br- + 3H2O f 3SO42- + Br- + 6H+ +
S23- (9)
This reaction is also a complex one that can be decomposed
into elementary processes via eqs 6-8 supplemented by
Figure 7. Measured (symbols) and calculated (solid lines) kinetic
S4O2OH- + H2O f SO42- + S32- + 3H+
(10)
curves at different bromine concentrations in the early stage of the
reactions. [S4O62-]0 ) 0.002 M, pH ) 2.08, [Br-]0 (M) ) 0. TB0 r /M )
2
0.0028 (b), 0.004 (0), 0.006 (2), 0.0072 ()).
Step R10 is responsible for the degradation of the intermediate
formed in step R9. As Figure 6 suggests, the slower kinetic
phase of the reaction clearly depends on pH: the lower the
acidity, the faster the disappearance of the intermediate. Our
predicted values of kR10 and kR′ 10 means that the half-life of the
intermediate is between 6 and 52 s under our experimental
conditions and cannot be longer than 1 min. The feasibility of
P(x) to be pentathionate is in question because it is well-known
that only the alkaline decomposition of pentathionate proceeds
very quickly;37 under mild acidic conditions, pentathionate is
believed to be adequately stable. Again if we consider that P(x)
is pentathionate, S4O2OH-, or S23-, then step R10 can be
rewritten as
Figure 8. Measured (symbols) and calculated (solid lines) kinetic
S5O26- + 4H2O f 2SO42- + 2HS(OH) + H2S + 2H+
curves in the later stage of the reaction at different tetrathionate
concentrations after the disappearance of bromine. pH ) 2.80, TB0 r
)
(11)
2
4.0 × 10-4 M. [S4O26-]0 (mM) ) 0.167 (b), 0.333 (0), 0.500 (2), 0.667
()), 1.00 (9), 1.33 (O).
or
S4O2OH- + 3H2O f SO42- + 2HS(OH) + H2S + H+
Tables 2 and 3 summarize the fitted and fixed rate coefficients,
as well as the molar absorbances used in the simultaneous
evaluation procedure. Figures 3-9 clearly demonstrate that the
model is capable of providing an acceptable description of the
experimental data over wide concentration ranges of the
reactants. The average deviation between the measured and
calculated data was found to be 4.9%, which is close to the
experimentally achievable limit of error. One must also question
which of the above-mentioned intermediates is more likely to
be P(x). From a mathematical point of view, no decision can
(12)
or
S23- + 2H2O + 2H+ f 2HS(OH) + H2S
respectively.
(13)

Kinetic Traces of a Complex System
J. Phys. Chem. A, Vol. 113, No. 37, 2009 9995
kinetic curves is applied in two different types of kinetic curves
(absorbance-time and concentration-time series) measured by
two different instruments, indicating the power of the compre-
hensive program package ZiTa24 in unraveling the kinetics and
mechanism of an unknown system. Taking the complexity of
this system into consideration, we find the result presented here
quite promising; therefore, the use of the simultaneous curve-
fitting method to determine the kinetics and the mechanism of
an unknown system is strongly recommended.
The present study may be helpful as well to understand the
intimate details of the reaction of tetrathionate, a compound that
is involved in many complex chemical systems exhibiting
temporal and spatial nonlinear dynamical behavior as well as
in microbiological, geochemical, and leaching processes.
Figure 9. Measured (symbols) and calculated absorbances (solid lines)
at different wavelengths in the later stage of the reaction. pH ) 2.08,
[S4O26-]0 ) 1.00 × 10-3 M, TB0 r ) 1.1 × 10-3 M, [Br-]0 ) 0 M.
Acknowledgment. This work was supported by the Hungar-
ian Research Fund (OTKA) grant no. K68172. A.K.H. is grateful
for the financial support of the Ja´nos Bolyai Research Scholar-
ship of the Hungarian Academy of Sciences. The authors are
indebted to Professor Istva´n Nagypa´l for his valuable sugges-
tions after he read the manuscript.
2
Wavelengths (nm) ) 260 (b), 265 (0), 270 (2), 275 ()), 280 (9), 285
(O), 290 (().
be made; however, chemically the most feasible choice seems
to be pentathionate if one compares the calculated and the
independently measured molar absorbance of pentathionate (see
Table 3) despite the fact that pentathionate is considerably less
stable than expected under our experimental conditions. It is,
however, easily conceivable that one of the products H2S,
HS(OH), or Br- catalyzes the decomposition of pentathionate,
making its lifetime much shorter under the present experimental
conditions than in pure water.
Supporting Information Available: A table containing the
conditions of each kinetic run and additional information on
the molar absorbance of the Br2/Br-3 system. This material is
available free of charge via the Internet at http://pubs.acs.org.
References and Notes
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