Three autocatalysts and self-inhibition in a single reaction: A detailed mechanism of the chlorite-tetrathionate reaction

Article abstract of DOI:10.1021/ic061332t

The chlorite-tetrathionate reaction has been studied spectrophotometrically in the pH range of 4.65-5.35 at T = 25.0 ± 0.2°C with an ionic strength of 0.5 M, adjusted with sodium acetate as a buffer component. The reaction is unique in that it demonstrates autocatalysis with respect to the hydrogen and chloride ion products and the key intermediate, HOCl. The thermodynamically most-favorable stoichiometry, 2S₄O₆ ^2- + 7ClO₂^- + 6H₂O → 8SO ₄^2- + 7Cl^- + 12H⁺, is not found. Under our experimental conditions, chlorine dioxide, the chlorate ion, or both are detected in appreciable amounts among the products. Initial rate studies reveal that the formation of chlorine dioxide varies in an unusual way, with the chlorite ion acting as a self-inhibitor. The reaction is supercatalytic (i.e., second order with respect to autocatalyst H⁺). The autocatalytic behavior with respect to Cl^- comes from chloride catalysis of the chlorite-hypochlorous acid and hypochlorous acid-tetrathionate subsystems. A detailed kinetic study and a model that explains this unusual kinetic behavior are presented.

Full text of DOI:10.1021/ic061332t

Inorg. Chem. 2006, 45, 9877−9883
Three Autocatalysts and Self-Inhibition in a Single Reaction: A Detailed
Mechanism of the Chlorite Tetrathionate Reaction
−
Attila K. Horva´th,*,† Istva´n Nagypa´l,† and Irving R. Epstein*,‡
Department of Physical Chemistry, UniVersity of Szeged, P.O.Box 105, Szeged H-6701, Hungary,
and Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis
UniVersity, Waltham, Massachusetts 02454-9110
Received July 18, 2006
The chlorite
25.0 0.2
is unique in that it demonstrates autocatalysis with respect to the hydrogen and chloride ion products and the key
−
tetrathionate reaction has been studied spectrophotometrically in the pH range of 4.65
−5.35 at T )
±
°C with an ionic strength of 0.5 M, adjusted with sodium acetate as a buffer component. The reaction
-
2-
2-
intermediate, HOCl. The thermodynamically most-favorable stoichiometry, 2S4O6
+
7ClO2
+
6H2O
f
8SO4
+
7Cl- 12H+, is not found. Under our experimental conditions, chlorine dioxide, the chlorate ion, or both are
+
detected in appreciable amounts among the products. Initial rate studies reveal that the formation of chlorine
dioxide varies in an unusual way, with the chlorite ion acting as a self-inhibitor. The reaction is supercatalytic (i.e.,
second order with respect to autocatalyst H+). The autocatalytic behavior with respect to Cl- comes from chloride
catalysis of the chlorite
−hypochlorous acid and hypochlorous acid−tetrathionate subsystems. A detailed kinetic
study and a model that explains this unusual kinetic behavior are presented.
Introduction
chlorine dioxide9 and the decomposition of chlorous acid,10
have been elucidated. Recently, a five-step model was
proposed11 for interpreting the unusual kinetic behavior of
the chlorite-tetrathionate reaction, in which HSO-3 plays a
crucial role in regulating the concentration of the autocatalyst
HOCl. It has also been shown12 that the reaction proceeds
via parallel pathways: a direct reaction and an indirect HOCl-
catalyzed path. This simplified model, however, accurately
describes only the early stages of the reaction but fails to
predict the behavior of the system on a longer time scale
and does not explain the chloride catalysis. Here, we present
a more detailed kinetic study and propose an extended kinetic
model that is able to explain the formation of chlorine dioxide
up to 50-100% of the total conversion.
The chlorite-thiosulfate reaction displays a remarkable
range of “exotic” kinetic phenomena, including complex
periodic and aperiodic oscillation1,2 and chaos3 in a flow
reactor and extreme sensitivity to stirring rate effects and
fluctuations4 under batch conditions. To date, no attempt has
been made to unravel the kinetics and mechanism of the full
reaction system because of its complexity. Three long-lived
intermediates and end-products, tetrathionate, hypochlorous
acid, and chlorine dioxide, have been been shown to react
further not only with the reactants but also with each other,
making the mechanism particularly complicated. During the
past two decades, the kinetics and mechanisms of several
subsystems of the parent reaction, including hypochlorous
acid-chlorite,5 thiosulfate-chlorine dioxide,6 tetrathionate-
hypochlorous acid,7 tetrathionate-chlorine dioxide,8 sulfite-
Experimental Section
Materials. Commercially available NaClO2 (Sigma-Aldrich) was
purified as described previously.5 The purity of NaClO2 was
* To whom correspondence should be addressed. E-mail: epstein@
brandeis. edu (I.R.E.); horvatha@chem.u-szeged.hu (A.K.H.)
† University of Szeged.
‡ Brandeis University.
(7) Horva´th, A. K.; Nagypa´l, I. Int. J. Chem. Kinet. 2000, 32, 395.
(8) Horva´th, A. K.; Nagypa´l, I.; Epstein, I. R. J. Phys. Chem. A 2003,
107, 10063.
(1) Orba´n, M.; De Kepper, P.; Epstein, I. R. J. Phys. Chem. 1982, 86,
431.
(2) Orba´n, M.; Epstein, I. R. J. Phys. Chem. 1982, 86, 3907.
(3) Maselko, J.; Epstein, I. R. J. Chem. Phys. 1984, 80, 3175.
(4) Nagypa´l, I.; Epstein, I. R. J. Phys. Chem. 1986, 90, 6285.
(5) Peintler, G.; Nagypa´l, I.; Epstein, I. R. J. Phys. Chem. 1990, 94, 2954.
(6) Horva´th, A. K.; Nagypa´l, I. J. Phys. Chem. A 1998, 102, 7267.
(9) Horva´th, A. K.; Nagypa´l, J. Phys. Chem. A 2006, 110, 4753.
(10) Horva´th, A. K.; Nagypa´l, I.; Peintler, G.; Epstein, I. R.; Kustin, K. J.
Phys. Chem. A 2003, 107, 6966.
(11) Horva´th, A. K.; Nagypa´l, I.; Peintler, G.; Epstein, I. R. J. Am. Chem.
Soc. 2004, 126, 6246.
10.1021/ic061332t CCC: $33.50
Published on Web 10/26/2006
© 2006 American Chemical Society
Inorganic Chemistry, Vol. 45, No. 24, 2006 9877

Horva´th et al.
Table 1. Initial Reactant Concentrationsa
in several kinetic runs, the final absorbance of chlorine dioxide
did not reach 0.1 absorbance units, relative fits of the kinetic curves
were also conducted (i.e., the deviation between the measured and
calculated data was normalized to the largest absorbance change
in the given experiment and the sum of squares of these was then
minimized). The final kinetic parameters of the proposed model
are taken as averages of values from the absolute and relative fits.
Our quantitative criterion for an acceptable fit was that the average
deviation for the absolute fit approach 0.004 absorbance unit, which
is close to the uncertainty of the spectrophotometer. In addition, a
satisfactory mechanism was required to qualitatively reproduce all
the important characteristics of the measured data such as depend-
ences on initial concentrations and pH.
no.
[ClO2-]0 (mM)
[S4O62-]0 (mM)
[Cl-]0 (mM)
1-16
0.5, 0.7, 1.0, 1.4 0.5
2.0, 3.0, 5.0, 7.0 0.5
0
0
0
0
0
0
0
0
17-32
33-44
10.0, 14.0, 17.0
0.5
45-56
20.0, 25.0, 30.0
0.5
57-72
5.0
5.0
5.0
5.0
5.0
5.0
0.1, 0.14, 0.2, 0.3
0.5, 0.7, 0.8, 0.9
1.0, 1.2, 1.4
2.0, 3.0, 5.0
0.3
73-88
89-100
101-112
113-132
133-152
0, 1.0, 3.0, 6.0, 10
0, 1.0, 3.0, 6.0, 10
0.14
a Each composition was studied at 4 different pHs.
checked by standard iodometric titration and found to be better
than 99.5%. No chloride impurities could be detected in the purified
NaClO2. All other chemicals (K2S4O6, acetic acid, sodium acetate,
and sodium chloride) were of the highest purity available (Sigma-
Aldrich and Fluka) and were used without further purification.
Acetic acid-acetate buffer was used to maintain the pH between
4.65 and 5.35. The ionic strength was adjusted to 0.5 M with sodium
acetate as a buffer component, and the desired amount of acetic
acid was added to adjust the pH, taking the pKa of acetic acid as
4.55. Table 1 shows the initial composition of the solutions studied
in the kinetic runs. Each composition was studied at 4 different
pHs: 4.65, 4.85, 5.07, and 5.35.
Methods. The kinetic measurements were carried out in a
standard 1 cm quartz cuvette equipped with a Teflon cap and a
magnetic stirrer. The cuvette was carefully sealed with Parafilm at
the Teflon cap to minimize the loss of chlorine dioxide. The reaction
was followed at 400 nm with a Zeiss Specord S10 diode array
spectrophotometer, excluding ultraviolet light to avoid the photo-
chemical decomposition of tetrathionate ion.13 This wavelength was
chosen instead of the absorption maximum of ClO2 at 359 nm to
minimize any contribution from the chlorite ion at higher chlorite
concentrations.
Data Treatment. Only experimental data with values up to 1.0
absorbance unit were used for evaluation of the kinetic runs because
the relative error of the absorbance measurements is not acceptable
at higher absorbances. Since each kinetic curve contained 250-
300 data points, the number of points in each run was reduced to
70 to avoid unnecessary and time-consuming calculations. The
reduction was achieved by normalizing the data to fit in a square
of unit size and then deleting points to increase the shortest distance
between pairs of points at each step until the desired final number
of points was reached. The final data are then renormalized to the
original scale. This process results in kinetic curves with smooth
distributions of points that represent all portions of the curve
accurately.14 In the visible range, the only absorbing species found
was chlorine dioxide, so the evaluation procedures were executed
at only a single wavelength, 400 nm.
Results
Stoichiometric Considerations. Several analytical meth-
ods have confirmed that the sulfate ion is the only sulfur-
containing product after the reaction is complete. However,
the thermodynamically most favorable stoichiometry
2S4O62- + 7ClO2- + 6H2O f 8SO42- + 7Cl- + 12H+ (1)
is never found under our experimental conditions, since
chlorine dioxide is almost immediately detected after starting
the reaction, even in high excess of tetrathionate. In addition
to chlorine dioxide, the chlorate ion is also present among
the end-products. As we shall see later, in principle there
are two other limiting stoichiometries
S4O62- + 21ClO-2 + 8H+ f
4SO42- + 14‚ClO2 + 7Cl- + 4H2O (2)
S4O62- + 14ClO2- + 3H2O f
4SO42- + 7ClO-3 + 7Cl- + 6H+ (3)
but neither of these can be reached experimentally. The
complexity of the stoichiometry of the overall reaction
reflects that of the subsystems, such as hypochlorous acid-
chlorite, sulfite-chlorite, and chlorine dioxide-tetrathionate.
Initial Rate Studies. We have demonstrated earlier11 that
the formal kinetic orders of the reactants vary considerably
with the initial reactant concentrations. We analyzed the
dependence of the stabilized rate (i.e., the rate during the
period of constant ‚ClO2 production), rather than the initial
rates. The use of the stabilized rate was suggested by the
existence of two qualitatively different types of behavior in
the early phase of the kinetic curves. The first type, illustrated
by the upper curve in Figure 1, starts with a slow rise in
absorbance followed by a faster, nearly linear increase, while
the other, seen in the lower curve in Figure 1, begins with a
sudden rise in absorbance followed by a slower, linear
increase. The linear regime lasts at least several hundred
seconds in each kinetic curve and can thus be used to
characterize the stabilized rate. The duration of this interval
depends strongly on the initial concentrations of the reactants.
The measured stabilized rate shows a maximum as a
function of the initial chlorite concentration, as seen in Figure
The experimental curves were analyzed with the program
package ZiTa.15 Altogether, 10 640 experimental points from 152
absorbance-time series were used for simultaneous fitting. The sum
of squares of the deviations between the measured and calculated
absorbances was selected as the parameter to be minimized. Since,
(12) Horva´th, A. K. J. Phys. Chem. A 2005, 109, 5124.
(13) Horva´th, A. K.; Nagypa´l, I.; Epstein, I. R. J. Am. Chem. Soc. 2002,
124, 10956.
(14) Peintler, G. Manuscript in preparation.
(15) Peintler, G. ZiTa, A ComprehensiVe Program Package for Fitting
Parameters of Chemical Reaction Mechanisms, version 5.0; Attila
Jo´zsef University: Szeged, Hungary, 1989-1998. This package
can be downloaded from the following website: http://
www.staff.u-szeged.hu/∼peintler/enindex.htm.
-
2. At low [ClO2 ]0, the formal kinetic order of chlorite is
between 1 and 2 (the relationship is almost linear), but at
9878 Inorganic Chemistry, Vol. 45, No. 24, 2006

Mechanism of the Chlorite-Tetrathionate Reaction
-
Figure 1. Measured early phase kinetic curves. Initial conditions: [ClO2
]
0
Figure 3. Measured (symbols) and calculated (solid lines) stabilized rates
as a function of tetrathionate concentration at [ClO2-]0 ) 5.0 mM. pH )
4.65 (b), 4.85 (0), 5.07 (2), and 5.35 (]). [Cl-]0 ) 0 M.
) 3.0 mM, pH ) 4.65, [S4O62-]0 ) 0.5 mM (b); pH ) 4.85, [ClO2-]0 )
30.0 mM, [S4O62-]0 ) 0.5 mM (0). The upper curve (b) is shifted by J )
0.02 along the y axis to make the trends clearer. The absorbing species is
chlorine dioxide.
Figure 4. Measured (symbols) and calculated (solid lines) stabilized rates
2-
as a function of chloride concentration at [ClO2-]0 ) 5.0 mM, [S4O6
) 0.3 mM. pH ) 4.65 (b), 4.85 (0), 5.07 (2), and 5.35 (]).
]
0
Figure 2. Measured (symbols) and calculated (solid lines) stabilized rates
as a function of chlorite concentration at [S4O62-]0 ) 0.50 mM. pH ) 4.65
(b), 4.85 (0), 5.07 (2), and 5.35 (]). [Cl-]0 ) 0 M.
in a high formal kinetic order of tetrathionate. This behavior
also arises from the switch from the slow direct reaction to
the HOCl-catalyzed pathway. The experiments in which
[S4O62-]0 was varied were not extended to lower tetrathionate
concentrations, where only the slow direct reaction governs
the formation of chlorine dioxide, because the reaction would
have become painfully slow, as seen in Figure 3. One may
ask whether our data provide sufficient information about
the direct reaction. This information can be obtained from
those experiments in which more than a 40-fold molar excess
of chlorite is present (experiments 45-56 in Table 1), since
the inhibitory effect of chlorite then suppresses the HOCl-
catalyzed pathway almost completely.
An early preliminary study of this reaction4 has suggested
that the product chloride ion also increases the rate of reaction
(i.e., that the reaction is autocatalytic not only in H+ but
also in Cl-). Figure 4 clearly demonstrates this effect,
yielding a rough formal kinetic order of 0.3 for chloride.
This fractional order and the increase in the formal kinetic
order of chloride as a function of [Cl-]0 suggest that the
chloride ion plays a complex role through its effect on the
various subsystems of the parent reaction.
high chlorite concentration, the rate of formation of chlorine
dioxide starts to decrease, implying that chlorite has an
inhibitory effect. As shown previously,11 this behavior results
from a switch from the fast HOCl-catalyzed reaction to the
slow direct reaction. The stabilized rates calculated from the
proposed model (see below) show similar trends and also
suggest that at higher chlorite concentration (>0.1 M) the
stabilized rate starts to increase again. This complex behavior
was pointed out earlier11 and is explained by the increasing
importance of the slow direct reaction, which is first order
with respect to chlorite.
As shown in Figure 3, the measured stabilized rate
increases monotonically with the initial tetrathionate con-
centration. The formal kinetic order of tetrathionate ion varies
between 0 and 1 and decreases with acidity. Under the
experimental conditions employed here, we do not observe
the unusual high formal kinetic order of tetrathionate because
the excess of chlorite is not sufficient to suppress the HOCl-
catalyzed pathway. In our previous study,11 more than a 50-
fold excess of chlorite was employed. When we explored
the behavior of the extended kinetic model at lower initial
tetrathionate concentrations corresponding to larger excess
Proposed Kinetic Model. As a starting point to develop
a kinetic model that describes the formation of chlorine
dioxide over the time course of the reaction, we took the
-
of [ClO2 ]0, we found, as observed earlier,11 that the formal
kinetic order of tetrathionate varies sigmoidally, resulting
Inorganic Chemistry, Vol. 45, No. 24, 2006 9879

Horva´th et al.
eight-step mechanism12 for the initial phase of the reaction,
from which the reduced five-step model was derived. Since
tetrathionate can also be oxidized by chlorine dioxide under
our experimental conditions, we adopted a previously
proposed 14-step mechanism for the chlorine dioxide-
tetrathionate reaction,8 which we refer to as the CDT
mechanism, keeping all kinetic parameters unchanged. We
then considered all additional mono- and bimolecular reac-
tions of the species in the eight-step model and the CDT
mechanism, as well as their H+-, OH-- and Cl--catalyzed
pathways, a total of more than 600 steps, in our analysis.
Lengthy and time-consuming but straightforward systematic
reduction of this initial model led to the following set of
essential steps:
Table 2. Rate Equations and Rate Coefficients Obtained from the
Fitting Procedurea
rate equation
suggested params
R1
R2
R3
R4
k1[S4O62-][ClO2-][H+]2
(2.08 ( 0.16) × 105 M-3 s-1
k2[S2O3OH-][ClO2
k3[S2O3OH-][ClO2
]
]
g10 M-1 s-1
-
-
k3/k2 ) 0.59 ( 0.10
(k4 + k′[Cl-])[HOCl][ClO2-][H+] k4 ) 1.06 × 106 M-2 s-1
4
k′ ) (5.03 ( 0.13) × 108 M-3 s-1
4
5.31 ( 0.22 M-1 s-1
-
R5
R6
k5[HOCl][ClO2
(k6[H+] + k′[Cl-])[Cl2O2][ClO2
]
]
k6 ) (1.85 ( 0.62) × 106 M-2 s-1
-
6
k′ ) (4.80 ( 0.78) × 104 M-2 s-1
6
R7
(k7 + k′[Cl-])[S4O62-][HOCl][H+] k7 ) (1.82 ( 0.19) × 107 M-2 s-1
7
k′ ) (2.35 ( 0.58) × 109 M-3 s-1
7
R8
R9
R10
R11
R12
R13
k8[S2O3Cl-][ClO2-][H+]
k9[S2O3Cl-][ClO2-][Cl-]
g107 M-2 s-1
k9/k8 ) 1.32 ( 0.52
k
k
k
k
10[HSO3-][ClO2-][H+]
11[HSO3-][HOCl]
(8.20 ( 0.12) × 109 M-2 s-1
7.6 × 108 M-1 s-1 (ref 30)
(7.30 ( 0.39) × 107 M-2 s-1
12[HOCl][S2O3ClO2-][Cl-]
13[HOCl][S2O3ClO2-][Cl-][OH-] (3.36 ( 0.28) × 1016 M-3 s-1
S4O62- + ClO2- + H+ + H2O f 2S2O3OH- + HOCl (R1)
S2O3OH- + ClO2- + H2O f 2HSO3- + HOCl (R2)
S2O3OH- + ClO2- + H+ f S2O3ClO2- + H2O (R3)
a No error indicates that the value was fixed during the fitting procedure.
agreement with the values found in the literature.12,20
Steps R2 and R3 are the only reactions of S2O3OH- that
need to be included for an adequate fit. The role of this
species in the reaction of tetrathionate has been documented
elsewhere.21,22 Both steps are fast, and their rate coefficients
cannot be calculated individually; only their ratio can be
determined. We therefore fixed k2 ) 100 M-1 s-1 and
determined k3/k2. Since any value of k2 higher than 10 M-1
s-1 leads to the same final result at fixed k3/k2, we simply
chose a reasonable, but arbitrary value for k2. The existence
of the parallel steps R2 and R3 is supported by the following
indirect evidence. First, eliminating either step not only
increases significantly the average deviation, from 0.0041
to 0.0081 and 0.0070 absorbance unit for dropping R2 and
R3, respectively, but also leads to systematic deviations
between the measured and calculated values, especially at
higher tetrathionate concentrations. As [S4O62-] increases,
the chlorine dioxide-tetrathionate reaction becomes more
HOCl + ClO2- + H+ f Cl2O2 + H2O
(R4)
(R5)
(R6)
(R7)
HOCl + ClO2- f H+ + Cl- + ClO3
-
Cl2O2 + ClO2- f 2‚ClO2 + Cl-
S4O62- + HOCl f S2O3OH- + S2O3Cl-
S2O3Cl- + ClO2- + H+ + H2O f S2O3OH- + 2HOCl (R8)
S2O3Cl- + ClO2- + 2H2O f
2HSO3- + HOCl + Cl- + H+ (R9)
HSO3- + ClO2- f SO42- + HOCl
(R10)
(R11)
HSO3- + HOCl f SO42- + Cl- + 2H+
S2O3ClO2- + HOCl + 2H2O f
-
significant, and the S2O3ClO2 formed in step R3 provides
2HSO3- + ClO2- + Cl- + 3H+ (R12)
another link to the chlorine dioxide-tetrathionate subsystem
in addition to chlorine dioxide itself. We attempted to replace
step R2 with the plausible reaction
S2O3ClO2- + HOCl f S2O3OH- + Cl2O2 (R13)
S4O62- + ‚ClO2 f CDT mechanism (14 steps)
(R14)
S2O3ClO2- + 2H2O f 2HSO3- + HOCl + H+ (4)
The corresponding rate equations and the suggested values
of the parameters are summarized in Table 2.
with no success. Several other efforts to eliminate either step
R2 or R3 also failed, leading us to conclude that both of
these reactions are required to quantitatively describe the
formation of chlorine dioxide.
Discussion
It is well-established that the rate of initiation of the
reaction, step R1, depends on [H+]2 (i.e., the reaction is
supercatalytic, that is, autocatalytic with an order greater than
one, with respect to H+). This feature of the reaction has
been extensively exploited to study the evolution of spa-
tiotemporal structures both experimentally and theoret-
ically.16-19 Our suggested rate constant is in reasonable
Step R4 is the well-known hypochlorous acid-chlorite
reaction that has been studied by several authors,5,23-26 who
give values of k4 ranging from 1.06 × 106 M-2 s-1 to 5.7 ×
106 M-1 s-1. The disagreement among these results likely
stems from unrecognized general acid catalysis of this
process. Since our experimental conditions were almost the
same as those used in the study performed by Peintler et
(16) Horva´th, D.; To´th, AÄ . J. Chem. Phys. 1998, 108, 1447.
(17) Stier, D. E.; Boissonade, J. Phys. ReV. E 2004, 70, 016210.
(18) Boissonade, J.; Dulos, E.; Gauffre, F.; Kuperman, M. N.; De Kepper,
P. Faraday Discuss. 2001, 120, 353.
(20) To´th, AÄ .; Horva´th, D.; Siska, A. J. Chem. Soc., Faraday Trans. 1997,
93, 73.
(21) Kurin-Cso¨rgei, K.; Orba´n, M.; Ra´bai, G.; Epstein, I. R. J. Chem. Soc.,
Faraday Trans. 1996, 92, 2851.
(19) Vasquez, D. A.; De Wit, A. J. Chem. Phys. 2004, 121, 935.
(22) Voslar, M.; Matejka, P.; Schreiber, I. Inorg. Chem. 2006, 45, 2824.
9880 Inorganic Chemistry, Vol. 45, No. 24, 2006

Mechanism of the Chlorite-Tetrathionate Reaction
al.,5 we fixed the value of k4 at their value, 1.06 × 106 M-1
noted that the otherwise sluggish chloride ion catalyzes this
reaction in another system. Here, we present further experi-
mental evidence to support those findings. Our values of k6
s-1. We also tried to fit this rate coefficient, but we
encountered strong correlation among the parameters k4, k′,
4
k5, k7, k′, k12, and k13. We therefore chose to use the value
and k′ are in reasonable agreement with our previous
7
6
of k4 found independently under the conditions that most
closely correspond to our experiments. It should also be noted
determinations under very different experimental condi-
tions.10
that the necessity of k′ in the fit suggests that the chloride
Step R7 is the initial step of the oxidation of tetrathionate
by hypochlorous acid. A second-order rate coefficient, 32
M-1 s-1, was determined for this step in alkaline medium.7
Our previous considerations12 and the experiments presented
here suggest that the rate of this reaction must depend on
the concentration of H+ as well. This fact is hidden in the
previously determined rate coefficient, since it was deter-
mined between pH 8.2 and 9.0, where the concentration of
HOCl is roughly proportional to [H+], since the pK of HOCl
is 7.40.29 We have found that this reaction is also catalyzed
by the chloride ion, and this observation can easily be
explained by the fast hydrolytic equilibrium of Cl2 (eq 5)
followed by
4
ion has a significant impact on the kinetics of the hypochlo-
rous acid-chlorite reaction. Nicoson and Margerum27 found
that chloride accelerates this reaction because of the well-
known fast equilibrium28
HOCl + Cl- + H+ h Cl2 + H2O
(5)
followed by the reaction between chlorine and the chlorite
ion, which is much faster than the corresponding hypochlo-
rous acid-chlorite reaction. They obtained a value of 5.7 ×
105 M-1 s-1 for the rate-determining step of the chlorite-
chlorine reaction. Our calculated result, k′ ) (5.03 ( 0.13)
4
× 108 M-3 s-1, gives a value of 3.1 × 105 M-1 s-1 for the
chlorite-chlorine reaction, in reasonable agreement with
Nicoson’s value,27 if one uses the widely accepted equilib-
rium constant K ) 1640 M-2 for eq 4 determined by Eigen
and Kustin.28 The agreement is even better if we use
Nicoson’s K ) 960 M-2 for the chlorine hydrolysis, which
yields 5.24 × 105 M-1 s-1 for the rate coefficient of the
chlorite-chlorine reaction.
S4O62- + Cl2 + H2O f S2O3OH- + S2O3Cl- + H+ + Cl-
(7)
Steps R8 and R9 are fast reactions, whose individual
values cannot be determined, since only their ratio affects
the final fit. Our calculations reveal that k8 has a lower limit
of 107 M-2 s-1. Fixing k8 at this value determines k9 as 1.32
× 107 M-2 s-1. These steps are crucial to the kinetic model.
They imply that chloride not only increases the rate of
consumption of chlorite by the intermediate S2O3Cl- but also
alters the stoichiometry. All attempts to unify the stoichi-
ometry by having parallel proton- and chloride-catalyzed
paths were unsuccessful. Using the stoichiometry of step R8
with H+- and Cl--catalyzed pathways increased the average
deviation to 0.0107 and introduced a systematic deviation
between the measured and calculated curves, especially
where the initial chloride concentration was varied. The
stoichiometry of step R9 with both catalyzed pathways gave
an acceptable average deviation of 0.0047, but at large
chlorite excess, the simulated curves failed to reproduce the
early phase of the kinetic curves in which the measured
absorbance rises suddenly followed by a slower, nearly linear
increase. These unsuccessful efforts were, however, helpful
in understanding why both steps R8 and R9 are needed. At
low chloride concentrations, step R8 converts S2O3Cl- and
chlorite to HOCl, transforming all the chlorine atoms
originating from the reactant chlorite into HOCl, which can
ignite the HOCl-catalyzed path to produce chlorine dioxide
sooner. If, however, the chloride concentration is sufficiently
high, then step R8 is no longer needed, and S2O3Cl- and
chlorite (in the presence of chloride) react according to step
R9, in which only half of the converted chlorine produces
HOCl (the rest is converted to chloride ion), preventing the
autocatalytic buildup of HOCl.
Emmenegger and Gordon24 suggested that step R5 ac-
companies the formation of chlorine dioxide in the reaction
between hypochlorous acid and chlorite, giving chlorate in
a separate pathway. Later this simple nucleophilic displace-
ment was rejected by Peintler and co-workers5 because they
found that the ratio of chlorine dioxide to chlorate formed
decreases with pH. If step R5 is treated as a third-order
process with rate proportional to [H+], this ratio would be
independent of pH. The pH dependence of the [ClO2]/
-
[ClO3 ] ratio can be explained, however, if step R5 is a
simple second-order process and step R4 is a third-order
process whose rate is proportional to [H+]. Instead of the
simple nucleophilic displacement, Peintler et al. suggested
the third-order process
2HOCl + ClO2- f ClO3- + Cl2 + H2O
(6)
to explain their experimental findings. We tried to replace
step R5 with reaction 6 with no success, probably because
HOCl does not accumulate to a high enough level to allow
this third-order process to dominate. The proposed role of
R5 is also supported by the fact that its elimination from
the kinetic model destroys the fit, resulting in a nearly 7-fold
increase in the average deviation to 0.0282 absorbance units.
Step R6 is the well-known fast reaction that generates
chlorine dioxide from Cl2O2. In our previous work,10 we have
(23) Taube, H.; Dodgen, H. J. Am. Chem. Soc. 1949, 71, 3330.
(24) Emmenegger, F.; Gordon, G. Inorg. Chem. 1967, 6, 633.
(25) Aieta, E. M.; Roberts, P. X. EnViron. Sci. Technol. 1986, 20, 50.
(26) Tang, T.-F.; Gordon, G. EnViron. Sci. Technol. 1984, 18, 212.
(27) Nicoson, J. S.; Margerum, D. W. Inorg. Chem. 2002, 41, 342.
(28) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84, 1355.
Step R10 is the well-known oxidation of S(IV) by chlorite,
(29) IUPAC Stability Constant Database; Royal Society of Chemistry:
London, 1992-1997.
Inorganic Chemistry, Vol. 45, No. 24, 2006 9881

Horva´th et al.
Figure 5. Measured (symbols) and calculated (solid lines) absorbances
Figure 6. Measured (symbols) and calculated (solid lines) absorbances
2-
-
at pH ) 4.65 and [S4O6
]
0
) 0.5 mM in the absence of chloride ion.
at pH ) 5.07 and [ClO2
]
0
) 5.0 mM in the absence of chloride ion.
[ClO2-]0 (mM) ) 0.5 (b), 1.4 (]), 2.0 (+), 3.0 (O), 5.0 (9), 7.0 (4), 10.0
([), 14.0 (|), 17.0 (1), 20.0 (3), 25.0 (×), and 30.0 (-).
[S4O62-]0 (mM) ) 0.1 (b), 0.14 (0), 0.2 (2), 0.3 (]), 0.5 (+), 0.9 (4), 1.4
(1), 2.0 (3), 3.0 (×), and 5.0 (-).
which was studied previously by Huff Hartz,31 Frerichs,32
and their co-workers. Huff Hartz et al. conducted their
experiments with a large excess of S(IV) to maintain pseudo-
first-order conditions. Under their experimental conditions,
which are very different from ours, where chlorite is always
in huge excess over S(IV), k10 was found to be 5.01 × 108
M-2 s-1, taking pKa(SO2) ) 1.9029 into account. Frerichs et
al. obtained 2.19 × 108 M-2 s-1 for k10 by simulating the
oscillatory behavior of the chlorite-sulfite reaction in a
continuously stirred tank reactor. We have obtained a
somewhat higher value, (8.20 ( 0.12) × 109 M-2 s-1, which
agrees well with our earlier result.12 Taking into account the
uncertainty of pKa(SO2), the long extrapolation from pH )
4.0 from which this value was determined,31 and the different
experimental conditions, the 16-fold difference may be
regarded as acceptable.
Figure 7. Chloride dependence of the measured (symbols) and calculated
(solid lines) absorbances at pH ) 5.35, [ClO2-]0 ) 5.0 mM, [S4O62-]0 )
0.3 mM. [Cl-]0 (mM) ) 0.0 (b), 1.0 (0), 3.0 (2), 6.0 (]), and 10.0(9).
Step R11 is the fast oxidation of S(IV) by hypochlorous
acid. The rate coefficient k11 was found30 to be 7.6 × 108
M-1 s-1, which is close to the diffusion-controlled limit. We
fixed this parameter throughout the fitting procedure.
-
Steps R12 and R13 are the further reactions of S2O3ClO2
with hypochlorous acid. These processes suggest that the
reactive species (Cl2/HOCl/OCl-) can attack the proposed
intermediate at two different sites, resulting in alternative
products. Attempts to replace these reactions with other steps
met with no success. Eliminating either of them increased
the average deviation from 0.0041 to 0.0111 and 0.0112 for
k
12 and k13, respectively, and also altered the experimentally
measured trends in the presence of chloride ion.
Table 2 summarizes the fixed and fitted rate coefficients
in the fitting procedure. Figures 5-9 demonstrate that the
kinetic model presented here gives a good description of the
formation of chlorine dioxide under our experimental condi-
tions. The average deviation was 0.0041 for the absolute fit
and 6.2% for the relative fit, which we believe to be close
to the experimentally achievable limit of error.
Figure 8. Chloride dependence of measured (symbols) and calculated
(solid lines) absorbances at pH ) 5.35, [ClO2-]0 ) 5.0 mM, [S4O62-]0 )
1.4 mM. [Cl-]0 (mM) ) 0.0 (b), 1.0 (0), 3.0 (2), 6.0 (]), and 10.0(9).
Finally, each of the three principal stoichiometries, eqs
1-3, is consistent with the proposed model. Equation 1 can
be generated as 2*(R1) + 4*(R2) + (R10) + 7*(R11), a
combination that assumes that hypochlorous acid never reacts
with chlorite to yield either chlorine dioxide or chlorate.
Equation 2 is obtained by combining (R1) + 2*(R2) + 7*-
(R4) + 7*(R6) + 4*(R10), which produces no chlorate from
the hypochlorous acid-chlorite reaction. Similarly, eq 3
(30) Fogelman, K. D.; Walker, D. M.; Margerum, D. W. Inorg. Chem.
1988, 27, 1672.
(31) Huff Hartz, K. E.; Nicoson, J. S.; Wang, L.; Margerum, D. W. Inorg.
Chem. 2003, 42, 78.
(32) Frerichs, G. A.; Mlnarik, T. M.; Grun, R. J.; Thompson, R. C. J. Phys.
Chem. A 2001, 105, 929.
9882 Inorganic Chemistry, Vol. 45, No. 24, 2006

Mechanism of the Chlorite-Tetrathionate Reaction
from the chloride dependence of the hypochlorous acid-
chlorite and hypochlorous acid-tetrathionate subsystems
rather than from chloride catalysis of the direct reaction. The
measured kinetic curves support our assertion that the slow
direct reaction is not the only rate-determining step and
confirm the essential role of the HOCl-catalyzed pathway.
Although the chloride catalysis in the experiments presented
here is relatively subtle (the formal kinetic order of chloride
is around 0.3), together with the HOCl-catalysis, it may play
a governing role in the spatiotemporal structures found
recently16-20 in the chlorite-tetrathionate system.
We hope that the results presented here will inspire
theoretical investigations of the proposed intermediates
-
S2O3OH- and S2O3ClO2 , which could test our assumption
Figure 9. pH dependence of measured (symbols) and calculated (solid
lines) absorbances in the initial absence of chloride ion at [ClO2-]0 ) 10.0
mM, [S4O62-]0 ) 0.5 mM. pH ) 4.65 (b), 4.85 (0), 5.07 (2), and 5.35
(]).
of the parallel pairs of steps R2 and R3, as well as R8 and
R9.
Finally we note that we have adopted without modification
the previously proposed kinetic model of the chlorine
dioxide-tetrathionate reaction. This was possible because
the kinetic parameters of the CDT reaction were determined
over wide concentration ranges of the reactants by simulta-
neous fitting of all measured kinetic curves without restriction
to pseudo-first-order conditions. We believe strongly that
complex reactions are best studied in this fashion, using data
acquired over a broad set of conditions and building on
studies of component subsystems.
comes about from (R1) + 2*(R2) + 7*(R5) + 4*R(10),
yielding no chlorine dioxide formation. As we have seen, it
is impossible to conform rigorously with any of these
restrictions experimentally, and it is therefore clear that eqs
1-3 can only be regarded as theoretical limiting stoichiom-
etries.
Conclusions
This study represents the first attempt to construct a kinetic
model for the chlorite-tetrathionate reaction applicable over
a wide range of initial reactant concentrations and in the
presence and absence of the autocatalyst chloride ion over
the entire time scale of the reaction. We demonstrated
earlier11 that the reaction proceeds via two parallel path-
ways: a direct reaction and a HOCl-catalyzed reaction. The
five step-model suggested there for interpreting the unusual
formal kinetic orders of the reactants is extended in this paper
to explain the formation of chlorine dioxide on a longer time
scale. We have also found that the chloride ion catalyzes
the formation of chlorine dioxide, but this catalysis arises
Acknowledgment. This work was supported by the
Hungarian Research Fund (Grant T047031) and the National
Science Foundation (CHE-0306262 and CHE-0615507).
A.K.H is grateful for the financial support of a Be´kesy
Gyo¨rgy (B12/2003) postdoctoral fellowship.
Supporting Information Available: Files containing the
measured and calculated absorbances for all the 152 kinetic curves.
This material is available free of charge via the Internet at
http://pubs.acs.org.
IC061332T
Inorganic Chemistry, Vol. 45, No. 24, 2006 9883