Kinetics and mechanism of the reaction between thiosulfate and chlorine dioxide

Article abstract of DOI:10.1021/jp981714n

The reaction between thiosulfate and chlorine dioxide in slightly alkaline medium has been studied by stopped- flow techniques. The reaction cannot be studied under pseudo-first-order condition, thus a new approach based on the improved calibration and use of stopped-flow spectrophotometers was applied. The reaction starts with irreversible formation of ^?S₂O₃ClO₂^2- radical. The main path of the reaction produces tetrathionate and chlorite through the formation of light absorbing tetrathionate radical (^?S₄O₆^3-). Any of the reactant present in excess slightly modifies the 1:1 stoichiometry, and sulfate as well as chloride ions are also formed. A detailed mechanism based on a rigorous simultaneous fitting of the experimental data is proposed.

Full text of DOI:10.1021/jp981714n

J. Phys. Chem. A 1998, 102, 7267-7272
7267
Kinetics and Mechanism of the Reaction between Thiosulfate and Chlorine Dioxide
Attila K. Horva´th† and Istva´n Nagypa´l*
Jo´zsef Attila UniVersity, Institute of Physical Chemistry, Szeged, P.O. Box 105, H-6701, Hungary
ReceiVed: March 31, 1998; In Final Form: May 27, 1998
The reaction between thiosulfate and chlorine dioxide in slightly alkaline medium has been studied by stopped-
flow techniques. The reaction cannot be studied under pseudo-first-order condition, thus a new approach
based on the improved calibration and use of stopped-flow spectrophotometers was applied. The reaction
starts with irreversible formation of •S2O3ClO22- radical. The main path of the reaction produces tetrathionate
and chlorite through the formation of light absorbing tetrathionate radical (•S4O63-). Any of the reactant
present in excess slightly modifies the 1:1 stoichiometry, and sulfate as well as chloride ions are also formed.
A detailed mechanism based on a rigorous simultaneous fitting of the experimental data is proposed.
Introduction
in order to unravel the mechanism of an unknown reaction. It
is also the first report of using ZiTa6 for numerically integrating
Among the chlorite-driven chemical oscillators,1 the thio-
sulfateschlorite reaction gives some of the most exotic dynam-
ics. The reaction is autocatalytic under batch condition,2 and
it exhibits oscillation in a CSTR.2 A propagating reaction front
may be generated in unstirred solutions3 and the reaction, in
unbuffered solution, behaves as a clock reaction. The reaction
time, however, varies irreproducibly within the first several
minutes, even in identically prepared samples.4 Only the
distribution of the reaction times is reproducible. A qualitative
explanation of the irreproducibility is the parallel formation of
SO42- and S4O62- ions accompanied by H+ and OH- formation
with only a very slight increase of pH. The further reaction of
the absorbance profile along the observation cell.5
Experimental Section
Materials. •ClO2 stock solution was prepared7 by oxidizing
NaClO2 solution in 10% H2SO4 by K2S2O8. The •ClO2 evolved
was purged out with an air stream and dissolved in cold water.
The stock solution was kept refrigerated and protected from
-
light. The stock solution was checked daily for Cl-, H+, ClO2
,
and ClO3- impurities after purging out its •ClO2 content. None
of these impurities could be detected up to 1 month. The
commercially available (Aldrich) NaClO2 was purified as
described.7 All other chemicals were the highest quality
commercially available. All solutions were prepared with
Milli-Q water, with 18.2 µS cm-1 conductivity. The ionic
strength was adjusted to 0.5 M by NaClO4 in all measurements,
except for the ion chromatographic studies. The pH of the
solutions was regulated between 7.5 and 9.5 by a boric acids
sodium hydroxide buffer.
2-
-
S4O6 with ClO2 is highly autocatalytic in H+. Thus, if the
proton formation in a small part of the reactive solution
overtakes the OH- formation because of the local fluctuations,
then it ignites the autocatalytic process and the reaction is over
instantenously. If the system avoids this in the first several
minutes, then the OH- concentration reaches a sufficient value
to suppress any local fluctuations, and the system behaves as a
regular clock reaction. The ultimate goal of the investigations
of this system is to understand and describe quantitatively the
wide range of “exotic” phenomena. For such a complex kinetic
system, we have to investigate all the conceivable and accessible
subsystems. As a part of the systematic kinetic studies on the
subsystems, we have undertaken a detailed stoichiometric and
kinetic study on the thiosulfateschlorine dioxide reaction. The
results of these investigations are presented in this paper. No
kinetic studies on this system have been reported before.
Preliminary stopped-flow experiments showed that the reaction
could not be studied using the usual approach of pseudo-first-
order conditions. The reaction is too fast in large thiosulfate
excess and the change of the absorbance is too small if chlorine
dioxide is in large excess. The only way of studying the reaction
was by the application of comparable concentration of both
reactants. The use of comparable concentrations posed many
questions which led us to develop an improved calibration and
use of stopped-flow instruments.5 The present paper is our first
report of using the improved use of the stopped-flow method
Methods. The stoichiometry of the reaction was studied
spectrophotometrically by measuring the spectra of the products
up to 10 min after mixing the reactants directly in a 10 mm
quartz cuvette equipped with Teflon cap. The chlorine dioxide
stock solution was introduced directly into the cuvette from a
fast delivery pipet as the last component, just before the cuvette
was closed. The spectra of the solutions of the products were
detected by Zeiss S10 diode array spectrophotometer between
266 and 450 nm up to 10 min in every minute. No detectable
change in the spectra was detected after 1 min. The expected
absorbing species in the product solution were the reagent in
excess, as well as S4O6 and ClO2-. (Cl- and SO4 do not
absorb light in the given range.) We have determined the molar
absorbance of these species prior to stoichiometric measure-
ments. In separate series of experiments we checked if a linear
algebraic decomposition of their composite spectra is an
appropriate tool for precise analytical determination of their
concentration. Figure 1 shows the molar absorbance of the
species in question calculated from the spectrum of at least five
2-
2-
solutions with different concentrations.
† E-mail: horvatha@chem.u-szeged.hu.
* To whom all correspondence should be addressed. E-mail: nagypal@
chem.u-szeged.hu.
2-
No change in the spectra of the prepared mixtures of S2O3
,
S4O62-, and ClO2- in the given pH range was observed for 20
S1089-5639(98)01714-9 CCC: $15.00 © 1998 American Chemical Society
Published on Web 08/25/1998

7268 J. Phys. Chem. A, Vol. 102, No. 37, 1998
Horva´th and Nagypa´l
TABLE 1: The Initial [S2O32-]0, [•ClO2]0 and the
2-
Spectrophotometrically Determined [S4O6
] as Well as
[ClO2
]
∞
Concentrations in Excess Thiosulfa∞te. SR )
-
([S2O32-]0 - [S2O32-]∞)/[•ClO2]0
2-
[S4O6
]
∞
[•ClO2]0 [S4O6
(mM)
]
∞
[ClO2 ]
2-
2-
-
∞
[S2O3
]
0
-
run
(mM)
(mM)
(mM)
[ClO2
]
SR
∞
1
2
3
4
5
6
7
8
6.06
6.67
7.75
8.76
9.70
3.49
3.97
4.42
2.21
2.41
2.24
2.22
2.17
1.67
1.61
1.56
0.870
0.964
0.910
0.902
0.881
0.681
0.665
0.647
1.360
1.470
1.370
1.350
1.310
0.980
0.915
0.881
0.640
1.006
1.020
1.030
1.032
1.034
1.045
1.064
1.068
0.656
0.664
0.668
0.673
0.694
0.727
0.734
Figure 1. Molar absorbances of thiosulfate (long dashed line),
tetrathionate (dots), and chlorite (dot-dashed line) ions and chlorine
dioxide (solid line).
TABLE 2: The Initial [S2O32-]0, [•ClO2]0 and the
-
Spectrophotometrically Determined [ClO2
] Concentrations
∞
in Excess Chlorine Dioxide. SR ) ([S2O32-]0)/([•ClO2]0 -
[•ClO2]∞)
min. A systematic study of the linear algebraic decomposition
of the spectra of many mixtures with known concentration
showed that the accuracy of concentration determination for
chlorite and tetrathionate ions is within 1% and for thiosulfate
is within 8%. The reason for the inaccuracy of thiosulfate
concentration is its low molar absorbance compared to the other
two ions (see: Figure 1). To check the result of the stoichi-
ometry established from the photometric experiments, several
solutions of the products were analyzed by a WATERS
Ionchromatograph. Kinetic measurements were carried on a
Hi-Tech SF -61 stopped-flow instrument attached to M300
monochromator. Most of the runs were followed at 360 nm,
where chlorine dioxide has its absorption maximum. In some
cases (see below) the reaction was followed at four additional
wavelengths (350, 380, 400, and 420 nms).
Data Treatment. Only the experimental data measured up
to an absorption maximum of 1.4 have been used for the
evaluation of the kinetic runs. Because all the kinetic curves
contained 512 data points, the number of points in each run
was reduced to about 100 to avoid unnecessary and time-
consuming calculations. The point reduction was based on the
principle of equivalent arclength in order to avoid loosing any
important chemical information. The next step of the evaluation
was to carry out the matrix rank analysis on the absorbances
time data series to determine the number of absorbing species.
The experimental curves were analyzed with the program
package ZiTa,6 developed recently for fitting kinetic data.
Altogether, 12 852 experimental points of the 131 absorbances
time series data points were used for simultaneous fitting. The
sum of squares of the deviation between the experimentally
measured and calculated absorbances was selected as a param-
eter to be minimized.
run [S2O32-]0 (mM) [•ClO2]0 (mM) [•ClO2]∞ (mM)
SR
1
2
3
4
5
6
7
1.291
1.906
1.380
2.035
0.968
0.822
1.112
2.475
2.492
2.658
2.595
1.374
3.021
2.127
1.056
0.502
1.244
0.535
0.335
2.150
0.976
0.910
0.958
0.976
0.988
0.932
0.944
0.966
adjusted to 9.7 by N,N-diethylethanolamine. Besides the
thiosulfate in excess, only tetrathionate could be detected. The
quantitative evaluation of a large series of ionchromatographic
measurements was in complete agreement with the results of
the spectrophotometric studies (see below), therefore they are
not given in detail. Table 1 summarizes the results of the
photometric analysis of the products in excess thiosulfate.
•
•
In excess ClO2, the unreacted ClO2 was determined from
•
that range of the spectra where ClO2 is the only absorbing
species. Table 2 summarizes the results.
The data in Table 1 and 2 convincingly show that the basic
stoichiometry is 1:1, i.e.,
2 S2O32- + 2•ClO2 f S4O62- + 2 ClO2
(1)
-
but this stoichiometry is slightly shifted toward the reactant in
excess. The photometric and ionchromatographic analysis of
the products showed that only tetrathionate and sulfate, as well
as chlorite and chloride ions, are formed in both conditions.
Since no other sulfur- and chlorine-containing oxyanion could
be detected, these observations imply that the stoichiometry is
3 S2O32- + 2•ClO2 + H2O f
S4O62- + 2SO42- + 2Cl- + 2H+ (2)
Results
Stoichiometric Studies. Ionchromatographic analysis was
used to identify the sulfur-containing products formed in excess
thiosulfate. The ionchromatographic column available under
our condition (slightly alkaline pH) and for our possible products
(sulfate, tetrathionate, polythionates, and excess thiosulfate) was
Polyspher IC AN-1. The chlorine and sulfur-containing prod-
ucts cannot be determined simultaneously because of the huge
difference in their retention times. Moreover, the chlorine-
containing products can only be eluted in measurable retention
time by acidic eluent on the given column, thus the further
oxidation of tetrathionate and thiosulfate by chlorite4,8 would
falsify the results. Therefore the eluent was chosen to be 2.5
mM parahydroxybenzoic acid dissolved in 10 volume-percent-
age methanolswater mixture. The pH of the eluent was
in excess thiosulfate and that the stoichiometry
S2O32- + 4•ClO2 + 3H2O f
2SO42- + Cl- + 3 ClO2- + 6 H+ (3)
in excess chlorine dioxide should also be considered; and an
appropriate linear combination of the three reactions may explain
the results.
The most important characteristics of the kinetic curVes. (1)
In excess chlorine dioxide the reaction is completed within a
few seconds as demonstrated in Figures 2 and 3. The
preliminary data fitting showed that all the experimental curves
can be fitted, in chlorine dioxide excess, as a sum of a second

Thiosulfate and Chlorine Dioxide
J. Phys. Chem. A, Vol. 102, No. 37, 1998 7269
Figure 2. Experimental curves (symbols) in excess of chlorine dioxide.
[•ClO2]0 ≈ 9.3 × 10-4 M, pH ) 8.55; [S2O32-]0 × 104 M ) 2.90 (b),
3.77 (0), 4.84 (2), 5.77 (]), 6.44 (9), 6.88 (3). Calculated curves are
illustrated by solid line.
Figure 5. Experimental curves (symbols) in excess of thiosulfate.
[S2O32-]0 ) 1.95 × 10-3 M, [•ClO2]0 ≈ 9.7 × 10-4 M, pH ) 7.48 (b),
8.60 (0), 9.27 (2). Calculated curves are illustrated by solid line.
Figure 6. Experimental curves (symbols) in excess of thiosulfate.
[•ClO2]0 ≈ 7.2 × 10-4 M, pH ) 9.27; [S2O32-]0 × 103 M ) 1.28 (b),
1.51 (0), 1.59 ([), 1.71 (4). Calculated curves are illustrated by solid
line.
Figure 3. Experimental curves (symbols) in excess of chlorine dioxide.
[S2O32-]0 ) 3.70 × 10-4 M, pH ) 8.55; [•ClO2]0 × 104 M ) 7.59 (b),
9.34 (0), 11.9 (2), 12.6 (]). Calculated curves are illustrated by solid
line.
on the sets of experimental data measured at five different
wavelengths. The rank of the matrixes was found to be 2 in
both excesses. It follows that a species absorbing light in the
350-420 wavelength range is formed during the reaction. The
residual absorbancestime curve, visual illustration of matrix
rank analysis, is a deciding evidence of the presence of an
absorbing intermediate, as can be seen in Figure 8. Dogliotti
and Hayon14 reported the flash photolysis study, while Scho¨ne-
sho¨fer15 the pulse radiolysis of thiosulfate solution. It was found
in these works that radiation of thiosulfate solution yielded a
relatively long-lived, with a lifetime of some milliseconds,
transient species with a strong absorbance band in the 340-
440 nm wavelength range. The maximum of this band was
between 370-380 nm with a 1650-1720 M-1cm-1 molar
absorbance.14,15 Essential difference in the interpretation of the
results is that Dogliotti and Hayon identified this transient as
thiosulfate radical, while Scho¨nesho¨fer as tetrathionate radical.
The results of kinetic measurements in Scho¨nesho¨fer’s paper
showed that the thiosulfate radical was yielded by a first, rapid
step of irradiation, followed the thiosulfate radical reacting
further with thiosulfate ion to result in a tetrathionate radical.
These results are generally accepted,16 thus it seems to be logical
to assume that tetrathionate radical is the second absorbing
intermediate species in the thiosulfateschlorine dioxide system.
Another important result of Scho¨nesho¨fer’s work is that the
thiosulfate ion catalyzes the decomposition of tetrathionate
radical. The catalytic effect will be analyzed and compared to
our results later.
Figure 4. Experimental curves (symbols) in excess of chlorine dioxide.
[S2O32-]0 ) 7.9 × 10-4 M, [•ClO2]0≈1.3 × 10-3 M, pH ) 7.58 (b),
8.55 (0), 9.31 (1). Calculated curves are illustrated by solid line.
and third-order rate law (both of them first order with respect
to chlorine dioxide, first and second order with respect to
thiosulfate). (2) Figure 4 shows that the reaction in chlorine
dioxide excess is slightly dependent on pH. However, no pH-
dependence was observed in excess thiosulfate, as depicted in
Figure 5. (3) The sigmoidal-shaped kinetic curves are the most
important feature in kinetic data in excess thiosulfate (Figures
6 and 7). Moreover, the increase thiosulfate by 1 order of
magnitude decreases dramatically the reaction time by almost
2 orders of magnitude.
Matrix Rank Analysis (MRA). Matrix rank analysis9-12 was
carried out, and the residual absorbance curves13 were calculated
Proposed Mechanism. The mechanism proposed is based on
a rigorous simultaneous fitting of 131 experimental curves. The

7270 J. Phys. Chem. A, Vol. 102, No. 37, 1998
Horva´th and Nagypa´l
TABLE 3: Initial Concentrations and Concentration Ranges
of the Reactants in the Kinetic Experiments Given in mM
dm-3 Unit
2-
[•ClO2]0
[S2O3
]
0
pH
runs
0.33-1.35
0.50-1.22
0.38-1.34
0.55-1.18
0.42-1.34
0.50-1.17
0.211-0.908
1.32-1.97
0.215-1.09
1.28-1.98
0.191-1.06
1.21-1.89
7.58
7.48
8.55
8.60
9.31
9.27
21
17
31
14
32
17
concentration ranges of the reactants in the samples are collected
in Table 3. Several hundred models have been used to try
quantitatively describe the experimental curves. Some of the
trials will be dealt with in the discussion. The following reaction
mechanism was suggested, which is in qualitative and quantita-
tive agreement with all experiments:
Figure 7. Experimental curves (symbols) in excess of thiosulfate.
[S2O32-]0 ) 1.55 × 10-3 M, pH ) 9.27; [•ClO2]0 × 104 M ) 5.34 (b),
7.39 (0), 9.35 (2), 11.0 (]). Calculated curves are illustrated by solid
line.
•ClO2 + S2O32- f •S2O3ClO2
(R1)
2-
2-
V1 ) k1[•ClO2][S2O3
]
2•S2O3ClO22- f S4O6(ClO2)2
(R2)
4-
2- 2
V2 ) k2[•S2O3ClO2
]
S4O6(ClO2)24- + S2O32- + H2O fast8
2 SO42- + 2 Cl- + S4O62- + 2 H+ (R3)
S2O32- + •S2O3ClO22- f •S4O63- + ClO2
(R4)
-
Figure 8. The residual absorbance13 as a function of time in case of
pH ) 8.51, [S2O32-]0 ) 1.02 × 10-3 M, [•ClO2]0 ) 5.38 × 10-4 M.
V4 ) k4[S2O32-][•S2O3ClO2
]
2-
2•S4O63- f S4O62- + 2 S2O3
(R5)
2-
the average absorbance deviation with less than 2% (i.e., it is
not justified by the calculations). Any attempt to replace step
R1 with either reversible or irreversible initial step of a possible
3- 2
V5 ) k5[•S4O6
]
•ClO2 + S2O32- f •S2O3- + ClO2
(4)
-
•S4O63- + S2O32- f 2S2O32- + •S2O3
(R6)
(R7)
-
reation failed. We have also tried to assign absorbance to
•S2O3ClO22-, but the average deviation only slightly decreased
and the molar absorption coefficient calculated was less than
100 M-1 cm-1. Therefore, this radical was considered in the
final calculations as a nonabsorbing species at 360 nm. The
high rate constant calculated for the first step means that the
reactant, which is not in excess, practically disappears from the
solution within 100 ms and that the further change (see Figures
2-4) is determined by the proceeding steps between the
2-
V6 ) k6[•S4O63-][S2O3
]
•S4O63- + •S2O3 fast8 S4O62- + S2O3
-
2-
•ClO2 + •S2O3ClO22- f S2O3ClO2- + ClO2 (R8)
-
V8a ) k8a[•ClO2][•S2O3ClO2
]
2-
•
2-
V
8b ) k8b[•ClO2][•S2O3ClO22-][OH-]
•ClO2 + S2O3ClO2- + 2H2O f
2SO24- + Cl- + 4 H+ + •ClO (R9)
intermediates and the reactant in excess. The S2O3ClO2
formed in the first step has three paths for the further
transformation. Step R2 is its dimerization followed by a fast
step R3. (The fast steps R3, R7, and R10 were taken into
account with fixed rate constants of 109 M-1 s-1.) Steps R1-
R3 together lead to the stoichiometry given by eq 2 (i.e., to the
stoichiometry which is responsible for the slight deviation of
1:1 stoichiometric ratio in thiosulfate excess (Table 1)). Any
trial to replace step R3 by the reaction 5
V9 ) k9[S2O3ClO2 ][OH-][•ClO2]
-
•ClO2 + •ClO + H2O fast8 2 ClO2- + 2 H+ (R10)
-
S4O6(ClO2)24- f S4O62- + 2ClO2
(5)
Discussion
The crucial steps in the proposed mechanism are emphasized
by bold face printing. The initial step R1 is an irreversible
association of the reactants yielding •S2O3ClO22- radical. The
inclusion of the reverse reaction of (R1) into the model decreases
or to add to it the final model failed. Neither rate coefficient
for eq 5 nor its ratio to k3 could be calculated. If steps R2 and
R3 are omitted from the proposed mechanism, then the average
deviation of the best fit increases to 0.0250 absorbance unit.

Thiosulfate and Chlorine Dioxide
J. Phys. Chem. A, Vol. 102, No. 37, 1998 7271
seemed to be plausible in excess chlorine dioxide. Its rate
coefficient was found to be about 1300 M-1 s-1. Because the
average deviation of the data decreased by less than 3% and
the standard error of this parameter was found to be too large
compared to the others, this process was not proposed in the
final model. If the main path (steps R4-R7) was omitted from
the model the average absorbance deviation increased dramati-
cally from 0.0089 to 0.0605. If either step R5 or step R6 (with
R7) was omitted then the average deviation also increased
significantly in both cases from 0.0089 to 0.0350 and 0.0432,
respectively. For the sake of completeness, the molar absor-
bance of tetrathionate radical was also omitted from the model,
and 0.0400 average absorbance deviation was found. Step R8
is the third path of the reaction of the •S2O3ClO22- radical with
chlorine dioxide to form in pH-independent (k8a) and pH-
Figure 9. Concentration of the species as a function of time in excess
thiosulfate [•ClO2]0 ) 8.45 × 10-4 M, pH ) 9.27, [S2O32-]0 ) 1.23 ×
10-3 M. •ClO2 (solid line), S2O32- (long dashed line), •S2O3ClO22- (dot
dashed line), •S4O63- (dot-dot dashed line), S4O62- (short dashed line),
ClO2- (dots). Note that the acquisition starts at t ) 0. The concentrations
between -ts and 0 are calculated by integration back from the measured
range.5
-
dependent (k8b) processes a nonabsorbing species S2O3ClO2
analogous to the intermediate S2O3ClO- proposed in the
chloritesthiosulfate system.4 This path is responsible for the
slight deviation of the stoichiometric ratio from 1:1 in chlorine
dioxide excess. It is followed by a rate-determining pH-
dependent step R9 and a fast reaction R10. Steps R8-R10 are
responsible for the slight pH-dependence in chlorine dioxide
excess and gives back the stoichiometry (eq 3). If the whole
path is omitted from the model, a significant increase (0.0530)
can be experienced in the average absorbance deviation.
Omitting either the k8a or the k8b from the model leads to the
average absorbance deviation 0.0580 and 0.0121, respectively.
A new way of calculation to evaluate the data provided by the
stopped-flow instrument has been suggested recently.5 The
calculation requires the filling time of the observation cell (tf)
and the hypothetical starting time (ts). The filling time was
determined physically as described.5 ts was fitted together with
the parameters of the proposed model. The hypothetical starting
time of the reaction was found to be in good agreement with
the results obtained in different chemical systems5,18 investigated
by our stopped-flow instrument. Omitting both the hypothetical
starting time and filling time from the final model leads to a
0.0107 average absorbance deviation. The calculated rate
constants, the molar absorbance of the tetrathionate radical, and
their standard deviations are shown in Table 4.
The main path in thiosulfate excess starts with step R4,
producing tetrathionate radical. Its calculated molar absorbance
of 2115 M-1 cm-1 at 360 nm is in good agreement with
Scho¨nesho¨fer’s data, who obtained a value of 1650 M-1 cm-1
at 370 nm based on pulse radiolysis experiments. Its decom-
position proceeds through the rate determining steps R5 and
R6. In step R5 the recombination of the absorbing tetrathionate
radical takes place and the reactant thiosulfate is formed back.
Step R6 is a catalytic process with respect to thiosulfate ion
forming thiosulfate radical which disappears rapidly in step R7.
The stoichiometry of step R5 as well as of steps R6 and R7 are
the same, but steps R6 and R7 have a significant role only in
thiosulfate excess. Steps R5 and R6 with R7 are responsible
for the increase of the thiosulfate ion concentration in the final
stage of the reaction, which is illustrated in Figure 9.
This overshoot-undershoot behavior17 frequently occurs in
exotic reaction systems. It should be mentioned that the
catalytic decomposition of the tetrathionate radical was earlier
suggested by Scho¨nesho¨fer,15 but the specified products ac-
cording to his work were hexathionate and sulfite ions. Our
ionchromatographic results indicated that these ions are not
formed in detectable amount under our experimental conditions.
It is interesting that our suggested k6 agrees perfectly with the
value of 7.3 × 104 M-1 s-1 determined by Scho¨nesho¨fer for
the same reaction. Another consequence of the catalytic effect
of thiosulfate is that the lifetime of tetrathionate radical is much
longer in chlorine dioxide than in excess thiosulfate. Therefore
the following reaction
The average deviation between the measured and calculated
absorbances using all the 10 fitted (8 rate coefficients, 1 molar
absorbance, and the hypothetical starting time5) and 4 fixed
parameters (the filling time of the observation cell, k3, k8, and
k10) on the whole 131 absorbancestime series data points was
found to be 0.0089 absorbance unit, which is close to the
experimentally achievable limit of error with our stopped-flow
spectrophotometer. The filling time was determined indepen-
dently in an earlier work,5 therefore it was fixed to be 0.0039
s during the calculations. Typical results are illustrated in
Figures 2-7.
•ClO2 + •S4O63- f S4O62- + ClO2
(6)
-
TABLE 4: Rate Constants Calculated by the Different Fitting Methods and the Suggested Results with Their Standard
Deviations
absolute fit
relative fit
orthogonal fit
suggested value
k1 × 10-5 (M-1 s-1
k2 × 10-3 (M-1 s-1
k4 × 10-5 (M-1 s-1
k5 × 10-4 (M-1 s-1
k6 × 10-4 (M-1 s-1
)
)
)
)
)
)
)
1.82 ( 0.01
7.21 ( 0.10
2.80 ( 0.03
4.37 ( 0.02
7.18 ( 0.05
5.45 ( 0.05
1.12 ( 0.01
1.99 ( 0.02
2115 ( 14
1.83 ( 0.01
6.72 ( 0.07
2.76 ( 0.03
4.73 ( 0.03
7.26 ( 0.06
5.10 ( 0.04
1.00 ( 0.01
2.11 ( 0.01
2130 ( 17
1.67 ( 0.02
6.82 ( 0.07
2.62 ( 0.04
5.07 ( 0.03
7.56 ( 0.08
5.12 ( 0.04
1.13 ( 0.01
2.03 ( 0.01
2326 ( 22
1.8 ( 0.1
6.9 ( 0.3
2.7 ( 0.1
4.7 ( 0.4
7.3 ( 0.2
5.2 ( 0.2
1.1 ( 0.1
2.0 ( 0.1
k8a × 10-3 (M-1 s-1
k8b × 10-8 (M-2 s-1
k9 × 10-7 (M-2 s-1
ts × 10-3 (s)
)
ꢀtetr.rad. (M-1 cm-1
)
-5.60 ( 0.04
-5.42 ( 0.05
-6.53 ( 0.08

7272 J. Phys. Chem. A, Vol. 102, No. 37, 1998
Horva´th and Nagypa´l
program package, ZiTa,6 suitable for simultaneous evaluation
of many curves characterized by the same kinetic model and
parameter set; (2) the use of matrix rank analysis in order to
determine the residual absorbances13 for the demonstration of
the presence of an absorbing intermediate; and (3) an improved
calibration and use of stopped-flow spectrophotometers based
on the filling time and the hypothetical starting time.5 Combined
application of the methods revealed that the reaction proceeds
through three intermediates, namely, •S2O3ClO22-, •S4O63-, and
S2O3ClO2-. Among these, the tetrathionate radical has signifi-
cant absorbance at 360 nm. A mechanism is proposed which
describes 12 852 points in 131 different experimental curves
with an average deviation of less than 0.010 absorbance unit.
Acknowledgment. The help of Ga´bor AÄ cs in the ionchro-
matographic measurements, as well as the many helpful
discussions with Ga´bor Peintler, is gratefully acknowledged.
This work was supported by the National Science Foundation
of Hungary (OTKA) (Grant T017257).
Figure 10. Histogram of the residual absorbances.
Figure 10 illustrates the histogram constructed from the
deviations of all the points together with the best fitting error
function. The almost regular distribution of the deviations
convincingly shows that the model error cannot be significant.
The standard errors of the parameters calculated by minimizing
the sum of the squares of absolute deviations between the
measured and calculated absorbances seem to be unrealistically
small. To check the reliability of these data we also carried
out relative and orthogonal fittings with the proposed model.
Relative fitting means that the deviation between the measured
and calculated data is normalized to the largest change of the
absorbance in the given experiment and that the square-sum of
these is minimized. Orthogonal fitting means that every
experimental absorbancestime series is transformed into a 0
e x,y e 1 “box” and that the square-sum of the perpendicular
deviation in this box is minimized. The best fits were found to
be 0.0159 and 0.0106 in the case of relative and orthogonal
fittings, respectively. The agreement of the rate coefficients
calculated by the three different minimization methods does not
differ significantly, but the difference is out of the range of the
standard errors. Therefore, the realistic values and standard
errors given in the last column of Table 4 were calculated from
the average of the three types of fitting.
References and Notes
(1) Ra´bai, Gy.; Orba´n, M. J. Phys. Chem. 1993, 97, 5935.
(2) Orba´n, M.; De Kepper, P.; Epstein, I. R. J. Phys. Chem. 1982, 86,
431.
(3) Nagypa´l, I.; Bazsa, Gy.; Epstein, I. R. J. Am. Chem. Soc. 1986,
108, 3635.
(4) Nagypa´l, I.; Epstein, I. R. J. Phys. Chem. 1986, 90, 6285.
(5) Peintler, G.; Horva´th, A. K.; Nagy, A.; Nagypa´l, I. J. Phys. Chem.
1998. Submitted for publication.
(6) Peintler, G. ZiTa, Version 4.2, a ComprehensiVe Program Package
for Fitting Parameters of Chemical Reaction Mechanism. Attila Jo´zsef
University: Szeged, Hungary, 1989.
(7) Peintler, G.; Nagypa´l, I.; Epstein, I. R. J. Phys. Chem. 1990, 94,
2954.
(8) Peintler, G.; Nagypa´l, I.; Epstein, I. R. In proceedings of the
International Conference on Dynamics of Exotic Phenomena in Chemistry;
Hajdu´szoboszlo´, Hungary, August 22-25, 1989; Abstract 237.
(9) Ainsworth, S. J. Phys. Chem. 1961, 65, 1968.
(10) Wallace, R. M.; Katz, S. M. J. Phys. Chem. 1964, 68, 3890.
(11) Katakis, D. Anal. Chem. 1965, 37, 876.
(12) Hugus, Z. Z.; El-Awady, A. A. J. Phys. Chem. 1971, 75, 2954.
(13) Peintler, G.; Nagypa´l, I.; Jancso´, A.; Kustin K.; Epstein, I. R. J.
Phys. Chem. A 1997, 101, 8013.
(14) Dogliotti, L.; Hayon, E. J. Phys. Chem. 1968, 72, 1800.
(15) Scho¨nesho¨fer, M. Int. J. Radiat. Phys. Chem. 1973, 5, 375.
(16) Hug, G. L. Optical Spectra of Nonmetallic Inorganic Transient
Species in Aqueous Solution, National Bureau of Standards, U.S. Department
of Commerce: Washington, DC, 1981.
(17) Ra´bai, Gy.; Bazsa, Gy.; Beck, M. T. J. Am. Chem. Soc. 1979, 101,
6746.
Summary
The fast reaction between thiosulfate and chloride dioxide
in slightly alkaline medium was studied by using the following
three methods elaborated recently: (1) A multipurpose kinetic
(18) Nagy, A.; Peintler, G.; Nagypa´l, I. Unpublished results.