Effect of chloride ion on the kinetics and mechanism of the reaction between chlorite ion and hypochlorous acid

Article abstract of DOI:10.1021/ic8006684

The effect of chloride ion on the chlorine dioxide formation in the ClO₂^--HOCl reaction was studied by following ?ClO₂ concentration spectrophotometrically at pH 5-6 in 0.5 M sodium acetate. On the basis of the earlier experimental data collected without initially added chloride and on new experiments, the earlier kinetic model was modified and extended to interpret the two series of experiments together. It was found that the chloride ion significantly increases the initial rate of ?ClO₂ formation. At the same time, the ?ClO₂ yield is increased in HOCl but decreased in ClO₂^- excess by the increase of the chloride ion concentration. The two-step hydrolysis of dissolved chlorine through Cl₂ + H₂O ? Cl ₂OH^- + H⁺ and Cl₂OH^- ? HOCl + Cl^- and the increased reactivity of Cl ₂OH^- compared to HOCl are proposed to explain these phenomena. It is reinforced that the hydrolysis of the transient Cl ₂O₂ takes place through a HOCl-catalyzed step instead of the spontaneous hydrolysis. A seven-step kinetic model with six rate parameters (constants and/or ratio of constants) is proposed on the basis of the rigorous least-squares fitting of the parameters simultaneously to 129 absorbance versus time curves measured up to ～90% conversion. The advantage of this method of evaluation is briefly outlined.

Full text of DOI:10.1021/ic8006684

Inorg. Chem. 2008, 47, 7914-7920
Effect of Chloride Ion on the Kinetics and Mechanism of the Reaction
between Chlorite Ion and Hypochlorous Acid
Bal a´ zs Korm a´ nyos, Istv a´ n Nagyp a´ l,* G a´ bor Peintler, and Attila K. Horv a´ th
Department of Physical Chemistry, UniVersity of Szeged, Szeged, Hungary
Received April 15, 2008
-
The effect of chloride ion on the chlorine dioxide formation in the ClO
2
-HOCl reaction was studied by following
·
ClO concentration spectrophotometrically at pH 5-6 in 0.5 M sodium acetate. On the basis of the earlier
2
experimental data collected without initially added chloride and on new experiments, the earlier kinetic model was
modified and extended to interpret the two series of experiments together. It was found that the chloride ion
2 2
significantly increases the initial rate of ·ClO formation. At the same time, the ·ClO yield is increased in HOCl
-
but decreased in ClO
chlorine through Cl
compared to HOCl are proposed to explain these phenomena. It is reinforced that the hydrolysis of the transient
Cl takes place through a HOCl-catalyzed step instead of the spontaneous hydrolysis. A seven-step kinetic
2
excess by the increase of the chloride ion concentration. The two-step hydrolysis of dissolved
-
+
-
-
-
2
+ H
2
O H Cl
2
OH + H and Cl
2
OH H HOCl + Cl and the increased reactivity of Cl
2
OH
2 2
O
model with six rate parameters (constants and/or ratio of constants) is proposed on the basis of the rigorous
least-squares fitting of the parameters simultaneously to 129 absorbance versus time curves measured up to
∼
90% conversion. The advantage of this method of evaluation is briefly outlined.
Introduction
Hypochlorous acid is one of the intermediates formed from
chlorite ion. Therefore the products of the reaction between
chlorite and hypochlorous acid (i.e., chlorine dioxide
and chlorate ion) always appear in the redox reactions of
chlorite ion in slightly acidic solution. The chlorate is usually
a final product, but the fate of chlorine dioxide depends on
the stoichiometric ratio of the reactants. It is usually a final
product in chlorite excess and an intermediate in excess of
the reducer because chlorine dioxide is also a strong
oxidizing agent. Because of its high absorbance at 360 nm
The reaction of chlorite ion with hypochlorous acid and
(at lower pH) with dissolved chlorine has important practical
1
applications in water and wastewater treatment and in pulp
2
bleaching. Beside the practical aspects, the kinetics and
mechanism of the reaction is important from theoretical point
of view; it has central role in the dynamics of the systemati-
cally designed chlorite-driven chemical oscillators.
3
–5
The
-
stoichiometry, kinetics, and mechanism of the ClO
2
-HOCl
reaction have therefore been the focus of interest for
compared to other oxyhalogen species, measuring the ·ClO
2
6
–10
decades.
concentration may therefore be regarded as a convenient tool
for kinetic study of the redox reactions of chlorite ion. The
kinetics and mehanism of the decomposition of chlorous
*
To whom correspondence should be addressed. E-mail: nagypal@chem.u-
szeged.hu.
11
acid and the supercatalytic tetrathionate-chlorite reaction
(
1) Clapper, T. W.; Gale, W. A. In Encyclopedia of Chemical Technology,
2
nd ed.; Kirk, R. E., Othmer, D. F., Eds.; New York. 1964; Vol. 5.
have recently been studied and interpreted in our laboratory,
1
2,13
pp 27-61.
using the principle outlined.
The kinetic model and the
(
(
(
2) Howard, W.; Strumila, G. B. In The Bleaching of Pulp, 3rd ed.; Singh,
R. P., Ed.; Tappi Press: Atlanta, GA, 1979; pp 113-157.
3) De Kepper, P.; Kustin, K.; Epstein, I. R. J. Am. Chem. Soc. 1981,
appropriate rate constants for the chlorite-hypochlorous acid
14
reaction published by Peintler et al. were used as auxiliary
1
03, 2133.
4) Epstein, I. R.; Orb a´ n, M. In Oscillations and TraVeling WaVes in
Chemical Systems; Field, R., Burger, M., Eds.; Wiley: New York,
(9) Tang, T. F.; Gordon, G. EnViron. Sci. Technol. 1984, 18, 212.
(10) Gordon, G.; Kieffer, R. G.; Rosenblatt, D. H. In Prog. Inorg. Chem.,
Lippard, S. J. Ed.; Wiley-Interscience: New York. 1972; Vol. 15, pp
201-286.
(11) Horv a´ th, A. K.; Nagyp a´ l, I.; Peintler, G.; Epstein, I. R.; Kustin, K. J.
Phys. Chem. A 2003, 107, 6966.
1
985.
(
(
(
(
5) Citri, O.; Epstein, I. R. J. Phys. Chem. 1987, 91, 6034. 1988, 92, 1865.
6) Taube, H.; Dodgen, H. J. Am. Chem. Soc. 1949, 71, 3330.
7) Emmenegger, F.; Gordon, G. Inorg. Chem. 1967, 6, 633.
8) Aieta, E. M.; Roberts, P. X. EnViron. Sci. Technol. 1986, 20, 50.
7914 Inorganic Chemistry, Vol. 47, No. 17, 2008
10.1021/ic8006684 CCC: $40.75  2008 American Chemical Society
Published on Web 07/31/2008

Reaction between Chlorite Ion and Hypochlorous Acid
-
data in these studies. The model suggested previously has
six steps with four independent constants:
2
ClO -HOCl reaction. These new results make the reinves-
tigation of the system necessary to modify and to extend
the basic core of the kinetic model proposed 20 years ago.
We shall mainly focus on five important issues: the inter-
pretation of the third order process (eq 3), the formation
of chlorate from Cl
the effect of chloride ion, and the further reaction of ·ClO
with hypochlorite ion.
The second order dependence of the rate on [HOCl] in eq
3 was originally explained by assuming a weak hydrogen-
bonded association between ClO
its reaction with HOCl. Beach and Margerum, however,
have determined the equilibrium as well as the forward rate
constant of the formation of Cl
HOCl.
-
2
+
ClO + HOCl + H f Cl O + H O;
2
2
2
k ) 1.12 × 10 M s-1 (1)
6
-2
17
1
18
19
2
O
2
, the unusually high yield of ·ClO
2
,
-
2
-
20
Cl O + ClO f 2 · ClO + Cl ; k2 : see below (2)
2
2
2
2
2
1
-
-
2
HOCl + ClO f ClO + Cl + H O;
2 3 2 2
3
-2 -1
k ) 2.1 × 10 M s (3)
3
-
2
and HOCl, followed by
-
2
-
ClO + Cl f Cl O + Cl ; k4 : see below
(4)
22
2
2
2
-
3
-
+
-1
Cl O + H O f ClO + Cl + 2H ; k5 > 10 s
(
fixed
)
2
2
2
2
O in aqueous solution of
HOCl h Cl O + H O (7)
2 2
(5)
-
+
Cl + H O h HOCl + Cl + H
2
2
2
[
Cl-][H+
]
(6)
V6 ) kf6
[
Cl2
]
) kb6
[
HOCl
]
The equilibrium constant, the forward rate constants for
the uncatalyzed, and acetic acid catalyzed pathways are 1.15
The forward and reverse rate constants for eq 6 (kf6 ) 11
s- and kb6 ) 1.8 × 10 M s ) were taken from the work
1
4
-2 -1
-2
-1
-1 -1
-2 -1
× 10 M , 0.12 M s , and 280 M s , respectively.
1
5
17
of Eigen and Kustin.
F a´ bi a´ n and Gordon proposed an alternative interpretation
Cl O
2 2
and Cl
2
are reactive intermediates, and both are
of the second order dependence of [HOCl] in eq 3 by
involved in two different further reactions. Therefore, the
ratio of these rate constants of the two pathways could only
2
assuming that the reactive intermediate is Cl O instead of a
hydrogen-bonded association. Their interpretation seems to
be more plausible than ours, but it has no effect on the fitting
because eq 7 is in fact a fast preequilibrium through the acetic
be calculated. Using the above kinetic model, k
2
/k
/kf6 ) 3.7 × 10 M were calculated beside
by rigorous fitting of the parameters to the 87
5
) 5.4 ×
4
-1
3
-1
1
0 M and k
and k
4
k
1
3
acid catalyzed pathway. In other words, k
by k′ ) k
× 0.0115 if eq 3 is replaced by the reaction of
chlorite with dichlorine oxide.
3
may be replaced
experimental curves simultaneously. It should be mentioned
that the third order eq 1 may be replaced by
3
3
1
8
Gordon and Takiyashiki studied the reaction in 0.1 M
phosphate buffer at pH 6-10, where the main product is
chlorate. They proposed fast preequilibrium instead of the
irreversible eq 1, and the step
HClO + HOCl f Cl O + H O
2
2
2
2
V ) k′
HClO2
HOCl ;
[
]
1
1
[
]
H+ ClO
-
[
][
]
′
2
-
3
+
k ) K × k ;
K )
d
1
d
1
Cl O + HOCl f ClO + Cl + H
(8)
2
2
2
[
HClO
]
2
In other words, it is hypothetically assumed that the reactive
instead of the spontaneous, first-order hydrolysis of Cl
(eq 5).
Jia et al. investigated the process in phosphate buffer at
2 2
O
species is in fact chlorous acid instead of the chlorite ion.
To our best knowledge, it was the first attempt of the rigorous,
simultaneous fitting of all experimental curves to calculate rate
1
9
pH 5.5-7.5 and in 1:1 acetate/acetic acid buffer at 1.0 M
constants of a complex kinetic system. The general interest of
(NaClO
the pseudofirst order condition applies. According to them,
the reactive species is the chlorite ion and the Cl is formed
through a general acid-catalyzed pathway, as follows:
4
) ionic strength and at large chlorite excess, where
-
the ClO
2
-HOCl reaction and the slow spreading of the
rigorous, simultaneous evaluation of the kinetic experiments
explains that this publication has received more than 60
independent citations. The general approach of the evaluation
of the kinetic experiments is still the fitting of the individual
curves and to analyze the parameters calculated as a function
of the initial concentrations, in spite of the significant advances
in computing power. We have recently proved, however, that
the individual evaluation of the kinetic curves may lead to
2 2
O
-
2
-
HOCl + ClO h HOClOClO
(9)
-
-
HOClOClO + HA f Cl O + H O + A
(10)
2
2
2
2 2
They assumed that further reactions of Cl O are eq 2,
-
-
-
-
3
and the OH and A assisted formation of ClO and Cl
16
inherent pitfalls in complex kinetic systems.
(
16) Korm a´ nyos, B.; Horv a´ th, A. K.; Peintler, G.; Nagyp a´ l, I. J. Phys.
Chem. A 2007, 111, 8104.
The last two decades have witnessed the publication of
several new aspects on the kinetics and mechanism of the
(
(
17) F a´ bi a´ n, I.; Gordon, G. Inorg. Chem. 1992, 31, 2144.
18) Gordon, G.; Takiyashiki, S. EnViron. Sci. Technol. 1991, 25, 468.
(
(
12) Horv a´ th, A. K.; Nagyp a´ l, I.; Peintler, G.; Epstein, I. R. J. Am. Chem.
Soc. 2004, 126, 6246.
(19) Jia, Z.; Margerum, D. W.; Francisco, J. S. Inorg. Chem. 2000, 39,
2614.
13) Horv a´ th, A. K.; Nagyp a´ l, I.; Epstein, I. R. Inorg. Chem. 2006, 45,
(20) Nicoson, J. S.; Margerum, D. W. Inorg. Chem. 2002, 41, 342.
(21) Csord a´ s, V.; Bubnis, B.; F a´ bi a´ n, I.; Gordon, G. Inorg. Chem. 2001,
40, 1833.
9
877.
(14) Peintler, G.; Nagyp a´ l, I.; Epstein, I. R. J. Phys. Chem. 1990, 94, 2954.
15) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84, 1355.
(
(22) Beach, M. W.; Margerum, D. W. Inorg. Chem. 1990, 29, 1225.
Inorganic Chemistry, Vol. 47, No. 17, 2008 7915

Korm a´ nyos et al.
instead of the spontaneous hydrolysis (eq 5). Moreover, they
found that acetate ion accelerates the formation of · ClO
enormously. It was interpreted by a steady-state formation
and further reactions of acetyl hypochlorite. They found
moreover, that in some cases, when HOCl was the limiting
M initial chloride concentration increases the initial rate by
a factor of 2. Another important finding of the authors is
that no chlorine dioxide is formed in 4.5 M sulfuric acid in
2
2
5
the absence of added chloride ion.
In the light of new results, we were prompted to carry out
new experiments on the system in presence of chloride ion
and re-evaluate the earlier and new experiments together.
reagent, greater than 100% of ·ClO
2
was formed even if the
-
2
+
-
HOCl + 2ClO + H f 2 · ClO + H O + Cl
(11)
2
2
Our aim is to check the newly proposed steps and to reveal
-
the effect of chloride ion on the ClO
2
-HOCl reaction not
stoichiometry was assumed. This finding was interpreted by
-
only under pseudofirst order condition or at fixed initial
concentration ratio of the reactant but also in a wide ratio of
the reagent concentrations. At the same time, the whole set
of kinetic curves are evaluated simultaneously, instead of
the usual simplified calculation.
partial transformation of the excess ClO
cording to the step
2
into HOCl ac-
-
2
-
3
Cl O + ClO + H O f 2HOCl + ClO
(12)
2
2
2
Later on, we have also found it to be a crucial step in the
1
1
kinetic model of the decomposition of chlorous acid.
Experimental Section
It was found that the—in principle sluggish—chloride ion
is also an active species in many steps of the redox reactions
Reagents. Commercially available (Sigma-Aldrich) sodium
1
1–13
of the chlorite ion.
Nicoson and Margerum have also
14
chlorite was purified and recrystallized as described previously.
studied the kinetics and mechanism of the reaction of chlorine
with chlorite ion in presence of chloride ion and in acetic
The chlorite content of the purified compound was checked by
standard iodometric titration and found to be 99.5%. No chloride
impurities could be detected in the purified sodium chlorite. The
hypochlorous acid solution was freshly prepared by dissolving
chlorine gas in a slurry of yellow HgO in distilled water and
distilling the solution from the HgO. All other chemicals (sodium
chloride, sodium acetate, acetic acid) were of the highest purity
commercially available. The stock solutions were freshly prepared
for each series of experiments.
2
0
acid/acetate buffer. The background chloride ion concen-
tration was—in general—1 M, but it was replaced by acetate
ion in some experiments up to 0.5 M. The chloride ion did
not appear on the reagent side of the proposed mechanism.
Its effect was interpreted through the
-
-
3
Cl + Cl h Cl
(13)
2
and eq 6 equilibrium.
Csord a´ s et al. investigated the interaction between
Methods
2
1
All kinetic runs were carried out in 0.5 M sodium acetate,
chlorine dioxide and hypochlorite ion at pH 6.5-10.5 and
at 1.0 M (NaClO ) ionic strength. Their interesting result is
4
that hypochlorite reacts with chlorine dioxide at lower pH
according to the
with the pH of solutions regulated between 5 and 6 by adding
HAc
the necessary amount of acetic acid (pK
d
) 4.55). The
temperature was adjusted to 25.0 ( 0.1 °C. Solutions for
the kinetic runs were prepared in a 10 mm quartz cuvette
equipped with Teflon stopper and a magnetic stirrer. The
last component (HOCl stock solution in 0.5 M NaAC) was
introduced from a fast delivery pipet just before the cuvette
-
-
3
-
+
ClO + 2 · ClO f 2ClO + Cl + 2H
(14)
2
stoichiometry, and catalyzes the decomposition of · ClO
2
-
3
-
2
+
3
was closed. The total volume of the solution was 3.2 cm to
2
· ClO + H O ) ClO + ClO + 2H
(15)
2
2
minimize the air above the solution. By this setup, less than
-
above pH 9. Finally, in a longer period, ClO
2
reacts with
0
.5% of the · ClO
2
evolved could escape from the solution.
-
-
-
OCl , producing Cl and ClO
3
, that is, eventually the
The reaction was followed by Zeiss S10 diode-array
stoichiometry given in eq 14 will be established at high pH,
too.
UV-vis spectrophotometer at the visible range. Absorbance
measured at 360 nm was used to evaluate the kinetic traces,
where chlorine dioxide has a strong absorption maximum
Yin and Ni have thoroughly studied many practical aspects
2
3–25
of · ClO
2
generation.
They found that the initial rate
-1
-1
(ε·ClO2 ) 1250 M cm ), but weak absorbances of hy-
significantly increases if chloride is added to the initial
-1
-1
-
pochlorous acid (εHOCl ) 7.0 M cm ) and chlorite (εClO2
-
solution. At 2:1 [ClO
2
]
0
/[HOCl]
0
concentration ratio the
-
1
-1
)
2.0 M cm ) were also taken into consideration during
initial rate is given by the equation
the calculation process. Twenty-one experimental curves
-
d
[
·ClO2
dt
]
were recorded at [ClO
2
] ) 4.74 mM and [HOCl] ) 0.15
)
(
k1 + k′1[Cl-
]
)[
ClO-2
]
[
HOCl
]
[
H+
]
(16)
mM, at three pH values (5.25, 5.55, 5.95), and at each pH
at seven different chloride concentrations in the range of
.0-10.00 mM. In an other series of experiments, the pH
6
-2
) 1.1 × 10 M s-1
9
-3
with k
1
) 1.2 × 10 M s-1 and k′
1
0
at 25 °C, I ) 0.2 M NaAc. According to these data, 0.001
values and the chloride concentrations were the same but
-
HOCl was in excess, that is, [ClO
2
] ) 0.568 mM, [HOCl]
(
23) Yin, G. Fundamental Aspects of Reactions During Chloride Dioxide
Generation and Use, PhD Thesis, The University of New Brunswick,
) 3.00 mM.
1
999.
(
24) Yin, G.; Ni, Y. Can. J. Chem. Eng. 1998, 76, 921. Interpolated to 25
C and taking pK )1.74.
(25) Ni, J.; Yin, G. Ind. Eng. Chem. Res. 1998, 37, 2367.
7916 Inorganic Chemistry, Vol. 47, No. 17, 2008

Reaction between Chlorite Ion and Hypochlorous Acid
Figure 1. Measured (symbols) and calculated (solid lines) absorbances as
a function of the initial chloride concentration in HOCl excess. [HOCl]0 )
Figure 3. Measured (symbols) and calculated (solid lines) absorbances at
-
different pH in HOCl excess. [HOCl] 0 )3.00 mM, [ClO2 ]0 ) 0.568 mM,
-
-
-
3
.00 mM, [ClO2 ]0 ) 0.568 mM, pH 5.55; [Cl ]0 (mM) ) 0 (•), 1.0 (0),
[Cl ]0 ) 4.0 mM, pH 5.95 (2), 5.55 (0), 5.25 (•).
2
.0 (2), 4.0 ([), 8.0 (9). To see the trends better, the inset shows the
measured and calculated absorbances at the beginning of the reaction.
Figure 4. Measured (symbols) and calculated (solid lines) absorbances at
-
-
different pH in ClO2 excess. [HOCl]0 ) 0.15 mM, [ClO2 ]0 ) 4.74 mM,
-
Figure 2. Measured (symbols) and calculated (solid lines) absorbances at
[Cl ] 0 ) 4.0 mM, pH 5.95 (2), 5.55 (0), 5.25 (•).
-
different initial chloride concentrations in ClO2 excess. [HOCl]0 ) 0.15
-
-
mM, [ClO2 ]0 ) 4.74 mM, pH 5.25; [Cl ]0 (mM) ) 0 (•), 1.0 (0), 2.0 (2),
4
.0 ([), 10.0 (9).
significant increasing effect of the initial chloride concentra-
tion on the rate of the · ClO
that, contrary to Figure 1, the · ClO
with increasing initial chloride concentration. Note that the
maximum absorbance under the given concentration would
2
formation. It is seen moreover
yield slightly decreases
Results
The new experimental results are illustrated in Figures 1–4.
It is seen in Figure 1 that the increasing initial chloride
concentration significantly increases the rate and the yield
2
be 0.384, and the experimental curves are approaching this
of ·ClO
2
formation in HOCl excess. Note, that after reaching
-
value at [Cl ]
0
) 0 M only. Figures 3–4 show that the
2
the maximum, [ · ClO ] slightly decreases. The maximum
absorbance, assuming
increase of pH shifts the reaction in the direction of formation
-
of ClO
3
2
instead of · ClO .
-
2
+
-
Building up the Kinetic Model. The experimental data
HOCl + 2ClO + H f 2 · ClO + Cl + H O (17)
2
2
2
6
were evaluated by the program package ZiTa. The earliest
version of this program was also used to evaluate those 87
experimental curves that were used to set up the model given
stoichiometry, would be 0.73 at 360 nm, and the actual
maximum is only 70% of that. Figure 2 illustrates again the
Inorganic Chemistry, Vol. 47, No. 17, 2008 7917

Korm a´ nyos et al.
by eqs 1-6 in the Introduction. That model was in perfect
harmony with the experimental findings, including the initial
practically the same average deviation, which was calculated
by the earliest version of ZiTa.
rates, the changing stoichiometry, and reaction order with
As a next step of the evaluation, we included those
experiments from the present work in which no chloride was
added to the initial solutions. The average deviation slightly
decreased, which justifies the possibility of simultaneous
evaluation of the earlier and present experiments. Then, we
systematically checked the role of the steps suggested since
the publication of the model eqs 1–6.
-
the change of the [HOCl]
0
/[ClO
2
]
0
concentration ratio and
pH (Figures 1-4 in ref 14). The earliest version of the
program package was not able to take into account the slight
pH change in buffered solution. Besides, it could fit only
2
concentrations and it was assumed that ·ClO is the only
absorbing species at 360 nm. The newest version of the
program is able to evaluate practically all types of kinetic
experiments, taking into account the possible fast equilibria
and preequilibria, the stoichiometric constraint, and any
measured experimental data that can be calculated from the
concentrations, without any constraint on the number of
experiments and experimental points.
As a first step, the earlier data were evaluated by fitting
the relative deviation of the measured and calculated absor-
bances, taking into account the weak absorbance of the
reactants at 360 nm and the following fast equilibria:
It turned out that the eq 1 is not reversible. More
specifically, the rate in reverse direction is much slower than
the further transformation of Cl O . However, the replace-
2
2
ment of the spontaneous hydrolysis of Cl O (eq 5) by eq 8
2
2
significantly improved the fitting. Note that eq 8 along with
eq 6 is in fact a HOCl-catalyzed hydrolytic disproportionation
of Cl O because the fast hydrolysis of Cl produces HOCl
2
2
2
back. Including
-
-
3
-
+
2
· ClO + OCl + H O f 2ClO + Cl + 2H (24)
2
2
+
-
HAc
stoichiometry with a rate equation to be first order with
respect of both chlorine dioxide and hypochlorite ion,
according to Csord a´ s et al., is also justified by the
improvement of the fitting.
HAc h H + Ac ; pKd ) 4.55
(18)
(19)
2
1
+
-
HOCl
HOCl h H + OCl ; pKd ) 7.40
and
The next step of building up the model was to include all
of the new experiments. The number of directly measured
data were reduced to have approximately the same number
of data from the new as from the earlier experiments. Then,
+
-
2
HClO2
HClO h H + ClO ; pKd
) 1.74
(20)
2
Besides, the earlier model was slightly modified by replacing
eq 1 with eq 20 and
-
we started a systematic search for the Cl -catalyzed steps.
As the presence of initial chloride increases the role of
chlorine, its possible further reactions were also systemati-
cally checked. It turned out that replacing eq 4 by
HClO + HOCl f Cl O + H O
(21)
2
2
2
2
Eq 3 was replaced by the preequilibrium
-
+
2
HOCl h Cl O + H O
(22)
Cl + HClO f Cl O + Cl + H
(25)
2
2
2
2
2
2
and by the reaction
significantly decreases the average deviation. If both pro-
cesses (eqs 4 and 25) are taken into account, then the further
improvement is less than 4%, that is, keeping eq 4 in the
model is not justified on computational basis. Two further
steps were found to be sufficient to describe all of the earlier
and present experiments, namely:
-
2
-
3
Cl O + ClO f Cl + ClO
(23)
2
2
The function to be minimized by fitting the rate constants
is defined as
N
pi
e
ij
c
ij
e
2
-
-
-
+
s )
[(
A - A
)
⁄ A
]
ClO + HOCl f ClO + Cl + H
∑
∑
i,max
2
3
i)1 j)1
ClO-2
Cl-
[ ]
V ) k
[
HOCl
]
[
]
where N is the number of experimental curves (87), p
i
)
the number of measured absorbance in the ith experimental
and
e
c
curve, Aij and Aij are the experimentally measured and the
calculated absorbances at the jth point of the ith experimental
HOCl + HClO f Cl O + H O
2
2
2
2
e
curve, and Ai, max is the maximum change of absorbance in
Cl-
V ) k
[
HOCl
]
[
HClO2
]
[
]
experiment i. The weighing of the curves by the reciprocal
of the maximum of the measured absorbance is important
because this value changed by more than 1 order of
magnitude. The weighing means that all of the curves have
similar influence on the average deviation, which may be
interpreted in this way as percentage. The model provided
The average deviation between the measured and calculated
absorbances at 1782 experimental points of 129 curves is 3.43%.
The proposed kinetic model contains the protonation equilibria
1
8-20 with the given data and the following steps:
fast
-
1
2
HOCl y z Cl O + H O; K ) 0.0115 M
(E1)
2
2
eq
(
26) Peintler, G. ZiTa, Version 5.0, A ComprehensiVe Program Package
for Fitting Parameters of Chemical Reaction Mechanism; Attila J o´ zsef
University: Szeged, Hungary, 1989-1998. The program package can
freely be downloaded from the following website: http://www.staff.u-
szeged.hu/∼ peintler.
-
+
-4
2
Cl + H O h HOCl + Cl + H ; K ) 6.1 × 10
M
2
2
eq
(E2)
7918 Inorganic Chemistry, Vol. 47, No. 17, 2008

Reaction between Chlorite Ion and Hypochlorous Acid
HOCl + HClO f Cl O + H O
2
leads to the same kr3/kr4 ratio. Cl is also a reactive
intermediate, taking place in E2 and R2 processes, which is
2
2
2
2
Cl-
(R1)
(R2)
V1 ) k
r1
[
HOCl
]
[
HClO2
]
+ k′r1
[
HOCl
]
[
HClO2
]
[
]
why the k /k ratio is given in the Table. k is responsible
r2 f6
r7
-
+
for the slight decrease of · ClO illustrated in Figure 1.
2
Cl + HClO f Cl O + Cl + H
2
2
2
2
2
Without kr7, the visible decrease of ·ClO in Figure 1 would
V2 ) kr2[Cl2][HClO2
]
be fitted by a horizontal line. The most interesting steps are
the chloride-catalyzed ones (k r′ 1 and kr6). Both are appearing
when HOCl is one of the reactant. For the interpretation of
the chloride catalysis, we should start from the plausible
assumption of Eigen and Kustin, that the hydrolysis of
chlorine in fact is a two-step process, namely:
-
2
-
Cl O + ClO f 2 · ClO + Cl
2
2
2
V3 ) kr3
[
Cl O2]
[
ClO-2
]
(R3)
(R4)
2
-
3
+
Cl O + HOCl f Cl + ClO + H
2
2
2
V4 ) kr4[Cl O2]
[
HOCl
]
-
+
2
Cl + H O h Cl OH + H
(R8)
(R9)
2
2
2
-
2
-
3
C1 O + ClO f C1 + C1O
-
-
2
2
Cl OH h HOCl + Cl
2
2
ClO-2
It is easy to realize that if kf6 ) kr8 )11 s , kb6 ) k-r9
)
-
1
V5 ) kr5[Cl O
]
[
]
(R5)
(R6)
(R7)
4
-1 -1
5
1
.8 × 10
M
s
and k-r8 ) kr9 > 10 then the result is
equivalent with process E2 from equilibrium and kinetic
-
2
-
-
+
ClO + HOCl f ClO + Cl + H
3
ClO-2
HOCl
Cl-
[
]
aspects too, but an intermediate with very low concentration
V6 ) kr6
[
]
[
]
-
appears in the system. Assuming Cl
2
OH to be the reacting
-
-
3
-
·
ClO + OCl f · Cl O
species, the third-order V′1 ) k′1 [HClO ][HOCl][Cl ]
2
2
2
R9
-
equation can be replaced by V′
1
1 2 2
) k′ Keq [HClO ][Cl OH ].
V7 ) kr7
[
·ClO2
]
[
OCl-
]
Similar transformation applies for kr6. It seems to be a
fast
reasonable assumption that these equilibria and the increased
-
3
-
+
-
3
·
ClO + · Cl O + H O 8 Cl + 2H + 2ClO
2
2
2
-
reactivity of Cl
2
OH are responsible for the appearance of
chloride catalysis in this and in many other redox reactions
of the oxychlorine species. As chloride ion is one of the
product of the reaction, it is in fact an autocatalyst. The
difference between the rate of the uncatalyzed and autocata-
lyzed path is not very high, thus the typical autocatalytic
feature of the product formation does not appear on the
experimental curves. Numerical calculations showed, how-
ever, that it may appear at higher (>0.1 M) initial concentra-
tions in stopped-flow time scale. It should be stressed again
that all the effects of the chloride ion are due to the shift of
The rate constants calculated are collected in Table 1. The
increase of the average deviation (column 2) if the given
step is omitted, and the others are fitted characterizes the
importance of the step in the model. Note, that if k
3
is zero
then this calculation becomes pointless, because no · ClO
2
is formed at all. Equilibrium E1 was taken to be fast, because
+
22
it is catalyzed by HAc and H .
Discussion
It is interesting that the model contains two different initial
steps (kr1 and kr5) between the species present in the reactant
solutions in absence of added chloride. In chlorite excess
k′r1 dominates and drives the reaction almost exclusively.
The presence of chloride opens three more initial steps
eq 6, which is decomposed to eqs R8 and R9 introducing
-
2
Cl OH .
Four comparable data is found in Table 1 from the
literature. Taking into account the basically different experi-
mental conditions, the agreements are satisfactory. Many
other thermodynamically and stoichiometrically conceivable
kinetic steps were checked. None of them decreased the
average deviation by more than 5% and seven of them
decreased it in between 1-5%. When all the seven reactions
were added to the model, the least-squares fit improved to
2.98%, and rate constants for the following three processes
could be calculated with acceptable standard error:
(k
r1, kr2, and kr6). k′r1 and kr2 are responsible for the increasing
initial rate and kr6 for the decreasing yield of ·ClO in chlorite
excess. Cl is a reactive intermediate; it is formed in three
2
2 2
O
and consumed in two steps. As usual, only the ratio of the
rate constants of the consuming steps can be calculated. kr4
4
-1 -1
but any value above 10 M s-1
3
-1
was fixed at 10 M
s
a
Table 1. Rate Constants of the Kinetic Model
+
-
average
Cl O + HClO f 2 · ClO + H + Cl ;
2 2 2 2
rate constant
deviation (%)
literature
9
-1 -1
kr10
)
(
1.5 ( 0.1 × 10 M s (R10)
)
kr1 ) (1.91 ( 0.01) × 10 M s-1
4
-1
22.8
2.3 × 10 (ref 24),
4
5
-
2
-
1
0 (ref 17)
ClO + Cl f Cl + Cl O ;
2
2
2
′
6
-2 -1
7
kr1 ) (7.8 ( 0.4) × 10 M
s
8.5
11.4
2.1 × 10 (ref 24)
4
-1
× 10 M s-1 (R11)
5
-1
kr2/kf6 ) (6.6 ( 0.2) × 10 M
kr11
)
(
1.3 ( 0.1
)
kr3/kr4 ) 41 ( 2
4
-1 -1
-
2
-
3
kr4 ) 10 M
s
(fixed)
5.0
7.9
5.3
4.2
ClO + Cl O + H O f 2HOCl + ClO ;
2
2
2
5
-1 -1
kr5 ) (1.4 ( 0.1) × 10 M
s
kr12
)
1.2 ( 0.2
× 10 M s-1 (R12)
4
-1
2
-2 -1
(
)
kr6 ) (1.8 ( 0.1) × 10 M
s
-
1
-1
kr7 ) 3.5 ( 0.3 M
s
0.91 (ref 21)
a
Note, however, that reactive intermediates (Cl
2
or Cl
2 2
O )
Note that the second column contains the average deviation in percent
if the given step is omitted from the model.
are involved in all the three steps, thus the data calculated
Inorganic Chemistry, Vol. 47, No. 17, 2008 7919

Korm a´ nyos et al.
Scheme 1
then the rate equations of eq R1 may be transformed into a
kinetically equivalent steps as follows:
R13
eq
K
kr14
V ) V )
[
]
[ ]
HOCl HClO2 +
1
14
HClO2
Kd
R13
eq
K
k′r14
[
HOCl HClO2
][
]
[
Cl-
]
(R15)
HClO2
Kd
5
are in fact kr10/kr4 )1.5 × 10 ; kr12/kr4 ) 1.2 and kr11/kf6
)
4
-1
that is,
1
.2 × 10 M . As the inclusion of three further steps
decreases the average deviation by 13% only, and the
elimination of any of the remaining steps in the proposed
model increases it by at least 22% (R7, Table 1), the above
steps are not part of the proposed mechanism. They should
be regarded as tentative steps meaning that their effect cannot
be excluded, but they may play decisive role only under
basically different conditions. It should be mentioned that
eq R12 is responsible for the unusually high yield (>100%)
R13
eq
R13
eq
K
kr14
K
k′r14
k )
;
k′ )
r1
r1
HClO2
HClO2
Kd
Kd
It means that - on a computational basis - no unequivocal
-
answer can be given to the question whether HClO
2
or ClO
2
is the reactive species in the decisive initial steps. Taking
into account the plausible interpretation of the chloride
-
catalysis through Cl
2
OH and the well-known increased
2
of ·ClO . No direct experimental evidence is found in our
data for this phenomenon; however, the inclusion of step
R12 into the model decreases the average deviation from
reactivity of the protonated oxyhalogen species, we are
inclined to suggest that HClO reacts in the first, rate-
determining steps. Further work is in progress in our
laboratory to answer the yet open questions.
2
3
.43 to 3.30%. Furthermore, it should be noted that neither
-
the spontaneous nor the OH assisted hydrolysis of Cl
O
2 2
can be included into the model by least-squares fitting.
Scheme 1 provides a visual representation of the model
proposed that may help to comprehend it more easily.
The model presented does not contain any general acid
Conclusion
The practically and theoretically important, therefore
thoroughly studied ClO
to revise our earlier mechanism and supplement it with the
chloride ion concentration dependence of the · ClO forma-
-
2
-HOCl reaction was reinvestigated
catalyzed path. As the acetate concentration, therefore the
+
2
[
H ]/[HAc] concentration ratio was kept constant in all of
tion in the pH range 5-6 in a wide concentration range and
at an ionic strength of 0.5 M sodium acetate. An improved
version of our program package, which is able to take into
account the fast pre-equilibria and any measured parameter
that can be calculated from the concentrations without
restriction concerning the number of experiments and
experimental points was used in the rigorous least-squares
fitting of the kinetic parameters. A systematic search for the
best fitting model revealed that the presence of chloride ion
our experiments, they do not provide any basis to distinguish
between the specific and general acid catalysis. We will
continue our efforts to unravel the role of the general and
specific acid catalysis in as wide ratio of initial concentrations
as was used before and in this work.
It is assumed in the model that in all the processes of Cl
2 2
O
formation one of the reactive species is HClO . This
2
assumption is in accord with the general tendency that the
protonated oxyhalogen species are much more reactive than
the corresponding ions due to the decrease of the bond-order
of one of the halogen-oxygen bonds by protonation. This
principle was the basis of working out an algorithm to design
profoundly increases the initial rate and the yield of · ClO
in HOCl excess. It turned out, moreover that - in presence
2
of chloride, which increases the Cl
2
concentration - HClO
2
-
2
7
takes over the role of ClO in the reaction with chlorine.
2
2
4 new propagating acidity fronts. As it is mentioned in
19
-
All of these features are explained by taking into account
2
the Introduction, Jia et al. assumed ClO to be the reactive
that the hydrolysis of chlorine is in fact a two-step equilib-
species in the rate-determining step (eq 9). It should be noted
that our results do not exclude this possibility. If we assume
-
rium involving Cl
2
OH in low concentration.
-
The questions still open regarding the kinetic model of
the reaction are briefly outlined. It should be stressed again,
that the presented results are due to the practically unlimited
possibilities of our program ZiTa. Its use prevents us from
being trapped in the possible pitfalls, which may inherently
occur if the kinetic curves are analyzed individually.
that the transient OClOClOH reacts with an acid directly
and through a chloride catalyzed path
fast
-
2
-
ClO + HOCl y z OClOClOH
(R13)
(R14)
OClOClOH- + H f Cl O + H O
+
2
2
2
OClOClOH-
H+
Acknowledgment. This work was supported by the
Hungarian Research Fund (OTKA grant numbers T47031
and K68172). A.K.H. is grateful for the financial support of
the Bolyai Postdoctoral fellowship.
V14 ) kr14
[
]
[
[
]
+
k′r14
[ ]
OClOClOH-][H+][Cl-
(
27) Szirovicza, L.; Nagyp a´ l, I.; Boga, E. J. Am. Chem. Soc. 1989, 111,
842.
2
IC8006684
7920 Inorganic Chemistry, Vol. 47, No. 17, 2008