A three-variable model for the explanation of the supercatalytic effect of hydrogen ion in the chlorite-tetrathionate reaction

Article abstract of DOI:10.1021/jp0508857

It has been shown that not only the slow direct but also the indirect (HOCl-catalyzed) reaction between chlorite and tetrathionate ions is second order with respect to hydrogen ion. Since the direct reaction was found to be orders of magnitude slower than the parallel HOCl-catalyzed pathway, a three-variable model is derived from the previously published five-step model taking into account the experimentally determined H+ concentration dependence of its rate coefficients by neglecting the direct reaction. The new three-variable model indicates that the supercatalytic effect of the hydrogen ion in the HOCl-catalyzed pathway arises from the pH dependence of the individual reactions of the five-step model. The new three-variable model also accounts for the continuous change of the stoichiometric ratio of the reactants and provides a simple kinetic law for involving it in the partial differential equation systems widely used in the study of spatiotemporal behavior of the chlorite-tetrathionate reaction.

Full text of DOI:10.1021/jp0508857

5124
J. Phys. Chem. A 2005, 109, 5124-5128
A Three-Variable Model for the Explanation of the “Supercatalytic” Effect of Hydrogen
Ion in the Chlorite-Tetrathionate Reaction
Attila K. Horva´th
UniVersity of Szeged, Department of Physical Chemistry, Szeged, P. O. Box 105, H-6701, Hungary
ReceiVed: February 21, 2005; In Final Form: April 20, 2005
It has been shown that not only the slow direct but also the indirect (HOCl-catalyzed) reaction between
chlorite and tetrathionate ions is second order with respect to hydrogen ion. Since the direct reaction was
found to be orders of magnitude slower than the parallel HOCl-catalyzed pathway, a three-variable model is
derived from the previously published five-step model taking into account the experimentally determined H+
concentration dependence of its rate coefficients by neglecting the direct reaction. The new three-variable
model indicates that the “supercatalytic” effect of the hydrogen ion in the HOCl-catalyzed pathway arises
from the pH dependence of the individual reactions of the five-step model. The new three-variable model
also accounts for the continuous change of the stoichiometric ratio of the reactants and provides a simple
kinetic law for involving it in the partial differential equation systems widely used in the study of spatiotemporal
behavior of the chlorite-tetrathionate reaction.
S4O62- + ClO2- + H2O + H+ f 2S2O3OH- + HOCl (3)
Introduction
It is well-known1 that the initial rate of the chlorite-
ClO2- + S2O3OH- + H2O f 2HSO3- + HOCl (4)
tetrathionate reaction is second-order with respect to [H+], that
is, the reaction is “supercatalytic”. Diffusion-driven instabilities,2
cellular acidity fronts,3 spatial bistability,4,5 and lateral instabil-
ity6,7 studies have brought the chlorite-tetrathionate reaction
into the focus of interest by this supercatalytic effect of H+.
Although a complete mechanism of this reaction is still missing,
preliminary investigation1 suggested the following stoichiometry
ClO2- + HSO3- f SO42- + HOCl
ClO2- + HOCl + H+ f Cl2O2 + H2O
ClO2- + Cl2O2 f 2‚ClO2 + Cl-
(5)
(6)
(7)
(8)
(9)
2S4O62- + 7ClO2- + 6H2O f 7Cl- + 8SO42- + 12H+ (1)
S4O62- + HOCl f S2O3OH- + S2O3Cl-
HSO3- + HOCl f SO42- + Cl- + 2H+
with the appropriate rate law
V ) 109[S4O62-][ClO2 ][H+]2
(2)
-
S2O3Cl- + ClO2- + 2H2O f
2HSO3- + HOCl + H+ + Cl- (10)
that is extensively used in recent spatiotemporal behavior
studies.2,4,5,7 These investigations have revealed that eq 1 with
its simple rate equation provides good qualitative agreement
with the experiments as long as the stoichiometric ratio of the
reactants is kept constant at 1:4. This evidently complex
stoichiometry along with its rate equation was also used to
investigate the velocity of the propagation in reaction-diffusion
fronts.8 This study, however, has provided experimental evi-
dence that the model does not work properly at higher relative
chlorite excess, and the rate coefficient of eq 1 appeared to be
much lower than it was predicted to be earlier. Moreover, the
velocity of the propagation fronts was found to show a
maximum as a function of chlorite concentration, and this feature
could not be interpreted by eq 1 along with its simple rate
equation (eq 2).
by making the simplifying assumption that reactions 4 and 10
and the well-known10 fast reaction 7 occur essentially instan-
taneously, allowing us to eliminate the intermediates S2O3OH-,
Cl2O2, and S2O3Cl-. The five-step model therefore consists of
the following reactions
A + 3B + H ) 4X + 3Y r1 ) k1[A][B]
B + X ) Y r2 ) k2[B][X]
(I)
(II)
2B + Y + H ) 2P r3 ) k3[B][Y]
(III)
A + 2B + Y ) 4X + 2Y + H r4 ) k4[A][Y] (IV)
X + Y ) 2H r5 ) k5[X][Y]
(V)
-
A five-step model taking the coupled autocatalytic and self-
inhibitory effects into account in the chlorite-tetrathionate
reaction9 at constant pH was published recently. It was derived
from the following mechanism
where A, B, H, X, Y, and P denote S4O62-, ClO2-, H+, HSO3
,
HOCl, and ‚ClO2, respectively. Only one product (‚ClO2) is
indicated in the five-step model, since its concentration was
followed experimentally. Note, moreover, that H was not
10.1021/jp0508857 CCC: $30.25 © 2005 American Chemical Society
Published on Web 05/18/2005

Supercatalytic Effect of H+ in Chlorite-Tetrathionate Reaction
J. Phys. Chem. A, Vol. 109, No. 23, 2005 5125
) -k2BX - 2k3BY - 2k4AY )
involved in the previous five-step model, as the experiments
were carried out at constant pH, but it has to be taken into
account for the interpretation of the supercatalytic effect in
unbuffered solution. The reported model properly takes into
account the apparently independent kinetic characteristics of the
reaction, that is, the high formal kinetic order of the tetrathionate
ion and the self-inhibitory effect of the chlorite ion for the
formation of chlorine dioxide at a given pH. It was also pointed
out9 that in buffered solutions the key species of the model is
the autocatalyst HOCl.
dB
dt
k2k4 5RG - 1
k2k3 5RG - 1
k5 3RG + 1
5RG - 1
3RG + 1
-
+ 2‚
AB - 2
‚
B2
(
)
k5
2RG
(16)
dH
dt
) k4AY + 2k5XY - k3BY )
(5RG - 1)2
2RG(3RG + 1)
k2k4 5RG - 1
k5 3RG + 1
k2k3 5RG - 1
‚B2
+ 2
AB -
‚
(
)
k5 3RG + 1
The aim of this work was to investigate whether the five-
step model is able to provide an explanation for the supercata-
lytic effect of the hydrogen ion and to derive a simplified three-
variable model involving the effect of hydrogen ion for the
kinetics of the chlorite-tetrathionate reaction based on the five-
step model reported previously. A more precise description for
the kinetics adopted into the partial differential equation system
describing the spatiotemporal behavior of the chlorite-
tetrathionate reaction may pave the way not only for the
explanation of the systematic deviation between the prediction
of the old model and the experiments in propagating reaction
front studies but also for a better understanding of the inherent
feature of the reaction and even to the discovery of the
possibility of new spatiotemporal structures.
(17)
Since RG > 0.2, the following inequalities must hold
5RG - 1
3RG + 1
5
3
5RG - 1
2RG
5
2
0 <
<
0 <
<
(18)
Finally, applying the R ≈ A0/B0 ) R0 approximation in eq 18,
where A0 and B0 are the initial concentrations of the reactants
and making some rearrangements, we arrive at the following
differential equation system
k2k4 5R0G - 1
k5 3R0G + 1
dA
dt
) -
‚
‚AB
Model Reduction
k2k4 (5R0G - 1)(7R0G + 1)
dB
dt
) -
‚
‚AB -
k5
(3R0G + 1)(2R0G)
As a first step for reducing the five-step model further to
contain only three variables (A, B, and H), it is assumed that X
and Y are steady-state intermediates, that is
k2k3 5R0G - 1
2‚
‚
‚B2 (19)
k5 3R0G + 1
dX
dt
k2k4 (5R0G - 1)(6R0G - 1)
k2k3 5R0G - 1
k5 3R0G + 1
dH
dt
‚B2
) 4k1AB - k2BX + 4k4AY - k5XY = 0
(11)
)
‚
‚AB -
‚
k5
(3R0G + 1)(R0G)
dY
dt
) 3k1AB + k2BX - k3BY + k4AY - k5XY = 0 (12)
It is easily seen that two constant combinations are important
in the reduced model, namely, k2k3/k5 and k2k4/k5. The super-
catalytic effect of the hydrogen ion is evidently hidden in the
pH dependence of these rate-constant combinations. Therefore,
we carried out our experiments at four different pH values of
4.25, 4.55, 4.85, and 5.07.
It was found and illustrated in our previous work that, if A0/
B0 J 0.02 is fulfilled, then the first term of the algebraic equation
is negligible (k1AB , k4AY).
Solving eqs 11 and 12 for X and Y without the k1AB term,
we obtain
Experimental Section
Materials. Commercially available Aldrich NaClO2 was
purified as described previously.10 The purity of NaClO2 was
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, and
sodium acetate) were of the highest purity available (Aldrich
and Fluka) and were used without further purification.
Acetic acid-acetate buffer was used to maintain the pH. 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 the acetic acid of
4.55. At each pH, 14 kinetic runs were carried out at constant
0.005 M chlorite concentrations by changing the tetrathionate
concentration between 0.0001 and 0.005 M, and 13 kinetic
curves were taken at constant 0.0005 M tetrathionate concentra-
tion by changing the chlorite concentrations between 0.0001
and 0.03 M.
k2 5RG - 1
k5 3RG + 1
Y ) B‚ ‚
(13)
and
k4 5RG - 1
X ) A‚ ‚
k5 2RG
(14)
where R ) A/B and G ) k4/k3. Since the steady-state concentra-
tions of X and Y can only be positive numbers, therefore the
inequality RG > 0.2 must also be fulfilled.
By the help of the steady-state concentrations of X and Y,
one can easily obtain the three-variable ordinary differential
equation system as follows
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 (beside the
k2k4 5RG - 1
k5 3RG + 1
dA
dt
) -k4AY ) -
‚
AB
(15)

5126 J. Phys. Chem. A, Vol. 109, No. 23, 2005
Horva´th
1010[H+], and k4 ) (1.08 ( 0.05) × 107[H+]. By comparing
these values with the corresponding ones found in the literature,
the following conclusion may be drawn.
For the rate coefficient of eq 1, a preliminary study1 yielded
a value of 109 M-3 s-1, but later from a front reaction study,
7.28 × 104 M-3 s-1 was estimated.8 More recently in a spatial
bistability study, the value of 5 × 106 M-3 s-1 was adjusted5
to eq 1. Our 4.58 × 105 M-3 s-1 value for k1 lies just between
these results. The comparison, however, should rather be made
between the values of 109 M-3 s-1 and (5/3)k′ ) 3.17 × 108
2
M-3 s-1 (the derivation of k′ is discussed later in the text),
2
since the direct reaction (k1) is only needed in the kinetic
-
experiments to produce trace amount of HSO3 from which
HOCl is formed to ignite the autocatalytic pathway. The factor
of 3 deviation is therefore believed to be more than satisfactory
compared to the value of 109 M-1 s-1 found by Nagypa´l and
Epstein.1
Figure 1. Dependence of the logarithm of rate coefficients k1(b), k2-
(0), and k4(2) on pH. The log ka values were shifted along the y-axis
by J ) 6, -3.5, and 0 units in the case of log(k1), log(k2), and log(k4),
respectively, in order to see the trends better. Fitted slopes were found
to be 2.02 ( 0.12, 1.19 ( 0.05, and 1.06 ( 0.03 for log(k1), log(k2),
and log(k4), respectively.
-
The pH-dependent rate coefficient of the oxidation of HSO3
by chlorite ion was determined by Huff Hartz18 and Frerichs19
and their co-workers. Huff Hartz et al. conducted their research
in huge excess of S(IV) in order to maintain pseudo-first-order
conditions. In this way, they established the value of 5.01 ×
108 M-2 s-1; meanwhile, Frerichs et al. obtained 2.19 × 108
M-2 s-1 by simulating of the oscillatory behavior of the
chlorite-sulfite reaction in the continuously stirred tank reactor
(CSTR) system. The former value was calculated from taking
pKa(SO2) ) 1.90. However, by taking the uncertainty of pKa-
(SO2) and the different experimental circumstances into con-
sideration, the 20-fold difference from our value of 1.34 × 1010
M-2 s-1 may be regarded acceptable.
TABLE 1: Determination of Second-Order Rate Coefficients
at Different pHs
parameter/pH
5.07
4.85
4.55
4.25
k1 × 105 (M-1 s-1
k4 × 10-1 (M-1 s-1
)
3.12 ( 0.15 7.76 ( 0.46 26.8 ( 3.40 148 ( 13.8
8.17 ( 0.10 13.2 ( 0.19 44.1 ( 0.08 74.4 ( 1.5
8.42 ( 0.07 14.1 ( 0.2 30.6 ( 0.4 61.0 ( 0.9
k2 × 10-4 (M-1 s-1
)
)
Teflon cap) with Parafilm to minimize the loss of chlorine
dioxide. The reaction was followed at 400 nm by a Zeiss
Specord S10 diode array spectrophotometer with exclusion of
the UV light in order to avoid the photochemical decomposition
of the tetrathionate ion.11
In the visible range, no other absorbing species was found
beside the chlorine dioxide; therefore, the evaluation procedure
was executed only at the single 400 nm wavelength. The
experimental curves were analyzed with the program package
ZiTa,12 developed recently for fitting kinetic data.
The rate coefficient of the tetrathionate-hypochlorous acid
reaction was found to be 32 M-1 s-1 at pH ) 8.2-9.0.20 At
this pH range, the rate of reaction was shown to have a linear
dependence on [H+]. If this trend is valid throughout a long
extrapolation to pH ) 4.2, the validity of the 1.08 × 107 M-1
s-1 value can also be accepted. To check the reality of the latter
rate constant, further investigations are needed on the tetra-
thionate-hypochlorous acid reaction in slightly acidic medium.
Discussion
Results
Having the rate coefficients (k1, k2, k3, k4, k5) in hand, we
first focus on the simplifying assumptions that have been applied
in the way of the derivation of the three-variable model.
Condition, where the first assumption is valid, must fulfill the
following inequality
We have analyzed the stabilized rate of chlorine dioxide
formation in the initial phase of the reaction as before.9 Step V
of the model corresponds to the well-known fast reaction
between HSO3- and HOCl studied thoroughly by Fogelman et
al.13 The rate coefficient was found to be 7.6 × 108 M-1 s-1
,
so this value was directly taken to our calculation as a fixed
number. Step III corresponds to the rate-determining step of
the chlorite-hypochlorous acid reaction. This reaction was
studied by several authors.10,14-17 The rate coefficient of the
forward reaction (VIII ) kIII[HOCl][ClO2-][H+]) was found to
be between 1.12 × 106 M-2 s-1 and 5.7 × 106 M-2 s-1. The
disagreement between these results apparently is due to the
unrecognized general acid catalysis. Since the experimental
circumstances here (ionic strength, buffer components, temper-
ature) were the same as those used in Peintler et al.’s study,10
the 1.12 × 106 M-2 s-1 value was taken to our calculation.
The values of k1, k2, and k4 were fitted as second-order rate
coefficients at each pH. The results can be seen in Table 1. A
plot of the logarithm of rate coefficients against the log([H+])
revealed that k2 and k4 linearly depend on [H+], but k1 is
proportional to [H+]2 within the pH range used in our experi-
ments! (see Figure 1). From these data, one can easily calculate
that k1 ) (4.58 ( 0.78) × 105[H+]2, k2 ) (1.34 ( 0.11) ×
4.58 × 105[H+]2
k
Y . B‚ 1 ) B‚
) 4.24 × 10-2‚[H+]‚B
1.08 × 107[H+]
k4
(20)
Taking pH ) 4.5, where the chlorite-tetrathionate reaction is
already rapid enough to be completed within hundreds of
seconds, and B ) 0.01 M, used in the study of investigating
the propagation of reaction-diffusion fronts and our kinetic
experiments, means that Y (concentration of HOCl) must be
higher than 10-8 M. This trace amount can easily be fulfilled,
since a high initial concentration of chlorite may itself contain
such a small amount of HOCl; so, our calculation supports the
validity of our first assumption. The chemical meaning of this
inequality is that the starting reaction is only needed to produce
a trace amount of X (HSO3-); from that point, the reaction is
governed by steps II-V, so step I is no longer needed. This
feature of the model was already illustrated in our previous

Supercatalytic Effect of H+ in Chlorite-Tetrathionate Reaction
J. Phys. Chem. A, Vol. 109, No. 23, 2005 5127
paper,9 where the rates of steps I-V were plotted against the
initial concentrations of the reactants at a given point in time,
indicating that the rate of step I is orders of magnitude slower
than that of step IV. In other words, it means that the direct
reaction between the tetrathionate ion and the chlorite ion is
orders of magnitude slower than the net disappearance of the
reactants caused by their individual reactions with HOCl
produced in a trace amount in the direct reaction.
50R0 - 1
30R0 + 1
dA
dt
) -
‚k′‚ABH2
2
(50R0 - 1)(70R0 + 1)
(30R0 + 1)20R0
dB
dt
) -
‚k′‚ABH2 -
2
50R0 - 1
2‚
30R0 + 1
‚k′‚B2H2 (25)
1
Analyzing our second condition essentially means that
(50R0 - 1)(60R0 - 1)
(30R0 + 1)10R0
50R0 - 1
30R0 + 1
dH
dt
1.12 × 106[H+]
)
‚k′‚ABH2 -
‚k′‚B2H2
k3
2
1
A
B
1
R )
>
)
)
≈ 0.02
(21)
5 × 1.08 × 107[H+]
5G 5k4
This set of differential equations clearly indicates the fol-
lowing:
(i) Within the range 0.02 < R0 j 0.2, the following two-step
chemical model is operating properly
This inequality must easily be fulfilled by adjusting the initial
concentrations of the reactants. It also indicates that application
of a high excess of chlorite (more than 50-fold) prevents the
usage of the simplified model. The chemical background of this
feature is that a high excess of chlorite ion traps the autocatalyst
HOCl throughout step III, resulting in cessation of the domina-
tion of the autocatalytic step IV. In this case, not only the second
assumption but also the first one is violated, resulting in a
collapse of the model. Maintaining the initial concentration ratio
of the reactants in the proper range, however, allows everyone
to use the simplified three-variable model providing a useful
tool for studying the spatiotemporal behavior in this system.
70R0 + 1
20R0
60R0 - 1
10R0
A +
B f
H
VP ) kPABH2
2B + H f products VR ) kRB2H2
(26)
(27)
where
k2k4 50R0 - 1
k5 30R0 + 1
k2k3 50R0 - 1
kP )
‚
and kR )
‚
.
Our suggested final simplification, where R0 ) A0/B0 was
used instead of R ) A/B in eq 18, means a good average value
for terms (5RG - 1)/(3RG + 1) and (5RG - 1)/2RG that vary
within a narrow range as a function of the concentrations of
the reactants, allowing us further simplification in the kinetic
model. Taking G ) k4/k3 ≈ 10, the terms of eq 18 will be
reduced to
k5 30R0 + 1
(ii) Using the ratio of the initial concentrations of the reactants
within the range 0.2 j R0 j 2, however, allows anyone to use
a more simple two-step kinetic model with fixed stoichiometric
numbers
kP
2A + 7B f 12H VP ) ABH2
50R0 - 1
3RG + 1 30R0 + 1
50R0 - 1
20R0
5RG - 1
5RG - 1
2RG
2
≈
and
≈
(22)
2B + H f products VR ) kRB2H2
(28)
We must also bring up the question regarding how the cubic
autocatalysis can be interpreted by the new three-variable model,
as a necessary condition of lateral instability. To do this, we
have to focus on the terms k2k3/k5 and k2k4/k5 of the model.
The value of the rate coefficient k5 hits almost the limit of
diffusion control, so no essential pH dependence of it can be
expected. Therefore, substituting the values determined above
yields
(iii) Further increase in R0 (i.e., the usage of high excess of
tetrathionate) means that step III of the five-step model becomes
insignificant, resulting in a case where VP alone is capable of a
good description of the kinetics of the chlorite-tetrathionate
reaction in studies of spatiotemporal behavior, so eq 1 along
with its rate equation, eq 2, is suitable for the proper kinetic
part of the partial differential equation system.
Finally, in an earlier study, it was found8 that the velocity of
propagation of reaction-diffusion fronts in the chlorite-
tetrathionate reaction shows a maximum as a function of initial
chlorite concentration. The simple kinetic model, based on eqs
9-10, however, predicts a continuous increase in the velocity
versus chlorite concentration (see Figure 6 of the original paper).
It also suggests a much higher value (Figure 5 of the original
paper) for the velocity at lower tetrathionate concentration. This
deviation stems from a shift in the chemical mechanism claimed
by the authors. The ordinary differential equation system of our
new model contains a negative term that depends on the square
of the chlorite concentration that is responsible for explaining
the inhibitory effect of the chlorite ion in the kinetic curves
and may also be suitable for supporting the experimental results
of the front velocity study.
1.34 × 1010[H+]‚1.12 × 106[H+]
k2k3
)
)
)
7.6 × 108
k5
1.97 × 107‚[H+]2 (23)
1.34 × 1010[H+]‚1.08 × 107[H+]
k2k4
k5
)
7.6 × 108
1.90 × 108‚[H+]2 (24)
where both terms depend on the power of 2 of the hydrogen
ion concentration, meaning that all the terms of the ordinary
differential equation system contain second-order dependence
on [H+]. By substituting eqs 22-24 into eq 19, denoted by k′
1
) 1.97 × 107 M-3 s-1 and k′ ) 1.90 × 108 M-3 s-1, we
The proposed two-step model may also be suitable for further
investigations of the decay of the autocatalyst with irreversible
binding21 in the present system by simply varying the initial
concentration ratio of the reactants.
1
finally arrive at the model believed to help in a more quantitative
investigation of spatiotemporal behavior of the chlorite-
tetrathionate reaction

5128 J. Phys. Chem. A, Vol. 109, No. 23, 2005
Horva´th
Another important remark has to be emphasized as well. The
extension of the pH studies to lower acidity may reveal that
even at a higher than cubic (second order with respect to [H+])
autocatalysis might occur in the chlorite-tetrathionate reaction.
There is indeed an allusion in the literature to this fact in an
earlier work1 at higher conversion in the chlorite-tetrathionate
reaction. Our new model may support this fact, because the H+
dependence of the model arises from the H+ dependence of the
combination of k2k3/k5 and k2k4/k5. The dependence of k2 on
the power of [H+] greater than 1 is easily conceivable chemi-
cally, since not only is the pKa of SO2 (or H2SO3) around 1.90
but also that of HClO2 is 1.86.22 The greater reactivity of
unsymmetrical protonated oxychlorine and oxysulfur species
toward each other is well-known. This realization has led to
the systematic design of the propagation of reaction fronts.23
of the initial concentration of the reactants (1:4) compared to
the old model.
It should also be mentioned, however, that the chemistry of
the chlorite-tetrathionate reaction still needs further refinements
in order to take into account, for example, the chlorate formation
and the chloride dependence on its rate. Further investigations
are continuing in our lab to unravel the kinetics and mechanism
of the chlorite-tetrathionate reaction. Despite the fact that the
mechanism of this reaction is still not explored entirely, the
model works remarkably well. It is also hoped that the present
refinement of the kinetic model may contribute to a deeper
understanding of the spatiotemporal behavior of the chlorite-
tetrathionate reaction.
Acknowledgment. The author is grateful for the financial
support of a Be´kesy Gyo¨rgy (B12/2003) postdoctoral fellowship
and the Hungarian Research Fund (OTKA T047031). Fruitful
discussions with Prof. Istva´n Nagypa´l are gratefully acknowl-
edged. The author is also thankful to Drs. AÄ gota To´th and Dezso˜
Horva´th for their helpful suggestions.
Conclusions
It was convincingly demonstrated in our previous paper9 that
the chlorite-tetrathionate reaction proceeds via two parallel
pathways: a direct reaction and an HOCl-catalyzed reaction.
In this paper, the result of a preliminary investigation1 was
confirmed in which the direct reaction is “supercatalytic” with
respect to the hydrogen ion, and it is clearly shown that the
HOCl-catalyzed route also has second-order dependence of [H+]
that may even grow further with increasing [H+]. It was pointed
out in our previous paper9 that apart from the very beginning
stage of the reaction the HOCl-catalyzed route governs the
reaction having a rate an order of magnitude greater than that
of the direct reaction. Therefore, a new simplified three-variable
model has been proposed for the kinetics of the chlorite-
tetrathionate reaction, which neglects the slow direct reaction,
to adapt it into investigations of the spatiotemporal behavior of
the chlorite-tetrathionate reaction. The new model was derived
from the five-step model that explains the most important
characteristics of the kinetic curves in this reaction, taking the
pH dependence of the reactions into consideration. It is,
however, quite remarkable that along with the simplifications
the unexpected maximum in chlorite dependence of the propa-
gation of reaction-diffusion fronts is still an inherent feature
of the three-variable model throughout its irreversible hydrogen
ion-consuming second step. It also indicates indirectly that the
HOCl-catalyzed pathway is probably responsible for the be-
havior of the system. It seems likely that the fortunate
coincidence of the second-order [H+] dependence of the direct
and indirect pathways makes it possible to use eqs 1 and 2 for
the proper kinetic parts of the reaction-diffusion models at the
strict A0/B0 ) 1:4 initial concentration ratio of the reactants with
the stoichiometry in eq 1. The new three-variable model also
offers a convenient tool for more quantitative investigations of
the lateral instabilities and other spatiotemporal behaviour in
this system, because it relieves the restriction of the fixed ratio
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