Oxidation of Chlorine(III) by Hypobromous Acid: Kinetics and Mechanism

Article abstract of DOI:10.1021/ic0354318

The kinetics and mechanism of the chlorine(III)-HOBr reaction were studied by the stopped-flow method under acidic conditions, pH 1.0-3.0, in 1.0 M NaClO₄ and at 25.0 °C. The overall redox process occurs in two consecutive steps via the formation of the BrClO₂ intermediate. The electron transfer reactions are coupled with bromine hydrolysis, the formation of the tribromide ion, and the protolytic equilibrium of chlorine(III). On the basis of simultaneous evaluation of the kinetic traces, the following rate constants were obtained for the redox steps: HClO₂ + HOBr ? BrClO₂ + H₂O, k₃ = (3.34 ± 0.02) × 10⁴ M^-1 s^-1, k^-3 = (3.5 ± 1.3) × 10³ s^-1; BrClO₂ + ClO₂^- ? 2ClO₂ + Br^-, k ₄ = (2.9 ± 1.0) × 10⁷ M^-1 s ^-1. The second step was practically irreversible under the conditions applied, and the value of k_-4 could not be determined. The equilibrium constant for the formation of BrClO₂, K₃ = 9.5 M^-1, was calculated from the kinetic results, and it was confirmed that this species is a very powerful oxidant. The redox potential was also estimated for the BrClO₂ + e^- = Br^- + ClO₂ reaction: ε₀o ～ 1.70 V.

Full text of DOI:10.1021/ic0354318

Inorg. Chem. 2004, 43, 2717−2723
Oxidation of Chlorine(III) by Hypobromous Acid: Kinetics and
Mechanism
Zsuzsanna To´th and Istva´n Fa´bia´n*
UniVersity of Debrecen, Department of Inorganic and Analytical Chemistry, Debrecen 10,
P.O. Box 21, Hungary H-4010
Received December 13, 2003
The kinetics and mechanism of the chlorine(III)−HOBr reaction were studied by the stopped-flow method under
acidic conditions, pH 1.0−3.0, in 1.0 M NaClO and at 25.0 °C. The overall redox process occurs in two consecutive
4
steps via the formation of the BrClO intermediate. The electron transfer reactions are coupled with bromine hydrolysis,
2
the formation of the tribromide ion, and the protolytic equilibrium of chlorine(III). On the basis of simultaneous
evaluation of the kinetic traces, the following rate constants were obtained for the redox steps: HClO + HOBr h
2
BrClO + H O, k3 ) (3.34 ± 0.02) × 104 M-1 s-1, k-3 ) (3.5 ± 1.3) × 103 s-1; BrClO + ClO - h 2ClO + Br-,
2
2
2
2
2
k4 ) (2.9 ± 1.0) × 107 M-1 s-1. The second step was practically irreversible under the conditions applied, and the
value of k-4 could not be determined. The equilibrium constant for the formation of BrClO , K ) 9.5 M-1, was
2
3
calculated from the kinetic results, and it was confirmed that this species is a very powerful oxidant. The redox
potential was also estimated for the BrClO + e- ) Br- + ClO reaction: ꢀ0 ∼ 1.70 V.
2
2
Introduction
prototype of these species, Cl2O2, was first postulated in the
chlorite ion-chlorine reaction by Taube and Dodgen in
1949.1 While the significance of such intermediates has been
corroborated in numerous studies, direct experimental evi-
dence was not reported for their existence in aqueous phase.
The only exception is the work by Valdes-Aguilera and co-
workers on the bromine-chlorine(III) reaction, in which
spectral changes were assigned to the formation of BrClO2.8
Noncomplementary redox reactions between halogen and
oxyhalogen species often exhibit complex kinetic patterns
which can be understood in terms of multistep kinetic
models. The corresponding mechanisms are centered on the
formation and subsequent reactions of reactive intermediates
such as X2O2 (X ) halogen) and related compounds.1-20 The
Recently, we developed a ten-step kinetic model for the
oxidation of chlorine(III) by bromine in aqueous solution
and concluded that the overall reaction proceeds via compet-
* Corresponding author. E-mail: ifabian@delfin.unideb.hu.
(1) Taube, H.; Dodgen, H. J. Am. Chem. Soc. 1949, 71, 3330-3336.
(2) Emmenegger, F.; Gordon, G. Inorg. Chem. 1967, 6, 633-635.
(3) Gordon, G.; Kieffer, R. G.; Rosenblatt, D. H. Prog. Inorg. Chem. 1972,
15, 201-286.
ing paths with Br2, HOBr, Br2 , and Br as oxidants.16
-
(4) Grant, J. L.; De Kepper, P.; Epstein, I. R.; Kustin, K.; Orba´n, M. Inorg.
Chem. 1982, 21, 2192-2196.
Hypobromous acid is in fast hydrolytic equilibrium with
bromine, and the last two species are formed as intermediates
in the reaction. The formation of BrClO2 was also postulated
in the model, but in disagreement with the results by Valdes-
Aguilera et al., we could not find appropriate experimental
conditions for detecting this intermediate.
(5) Tang, T.; Gordon, G. EnViron. Sci. Technol. 1984, 18, 212-216.
(6) Epstein, I. R.; Kustin, K. J. Phys. Chem. 1985, 89, 2275-2282.
(7) Aieta, E. M.; Roberts, P. V. EnViron. Sci. Technol. 1986, 20, 50-55.
(8) Valdes-Aguilera, O.; Boyd, D. W.; Epstein, I. R.; Kustin, K. J. Phys.
Chem. 1986, 90, 6696-6702.
(9) Ra´bai, Gy.; Beck, M. T. Inorg. Chem. 1987, 26, 1195-1199.
(10) Peintler, G.; Nagypa´l, I.; Epstein, I. R. J. Phys. Chem. 1990, 94, 2954-
2958.
In order to validate the kinetic model and to explore further
details of the mechanism, a series of new experiments were
designed to evaluate independently the rate law for some of
(11) Gordon, G.; Tachiyashiki, S. EnViron. Sci. Technol. 1991, 25, 468-
474.
(12) Fa´bia´n, I.; Gordon, G. Inorg. Chem. 1992, 31, 2144-2150.
(13) Ra´bai, Gy.; Orba´n, M. J. Phys. Chem. 1993, 97, 5935-5939.
(14) Furman, C. S.; Margerum, D. W. Inorg. Chem. 1998, 37, 4321-4327.
(15) Xie, Y.; McDonald, M.; Margerum, D. W. Inorg. Chem. 1999, 38,
3938-3940.
(16) To´th, Zs.; Fa´bia´n, I. Inorg. Chem. 2000, 39, 4608-4704.
(17) Csorda´s, V.; Bubnis, B.; Fa´bia´n, I.; Gordon, G. Inorg. Chem., 2001,
40, 1833-1836.
(18) Wang, L.; Margerum, D. W. Inorg. Chem. 2002, 41, 6099-6105.
(19) Nicoson, J. S.; Perrone, T. F.; Hartz, K. E. H.; Wang, L.; Margerum,
D. W. Inorg. Chem. 2003, 42, 5818-5824.
(20) Horva´th, A. K.; Nagypa´l, I.; Peintler, G.; Epstein, I. R.; Kustin, K. J.
Phys. Chem. A 2003, 107, 6966-6973.
10.1021/ic0354318 CCC: $27.50 © 2004 American Chemical Society
Published on Web 03/16/2004
Inorganic Chemistry, Vol. 43, No. 8, 2004 2717

To´th and Fa´bia´n
The HOBr solutions were always freshly prepared and used within
a few hours. The pH was set by using acetic acid/acetate buffer
(pKa ) 4.61) in the hydrolytic experiments. Reagent solutions were
prepared with doubly deionized and ultrafiltered water obtained
from a Milli-Q RG, Millipore system. The pH ()-log[H+]) was
either measured with a Metrohm 6.0202.000 combined glass
elctrode connected to a Radiometer PHM85 Precision pH-meter
or calculated from the total concentrations of the reactants by using
the appropriate equilibrium constants for the pH-dependent equi-
librium steps. The electrode was calibrated for two buffers in
accordance with IUPAC recommendations,24 and the pH readings
were converted to -log[H+] using a correction coefficient deter-
mined by measuring the pH of standardized perchloric acid in 1.0
M NaClO4.25
Methods. Hypobromous acid stock solutions were standardized
by using two independent analytical methods. First, NaI was added
to a portion of the stock solution under acidic conditions, and the
product I2 was titrated with standardized Na2S2O3 solution using a
Metrohm 721 NET Titrino potentiometric titrating system equipped
with a Metrohm 6.0420.100 combined Pt wire electrode. This
method overestimates the HOBr concentration when bromate ion
is present as impurity. In another set of experiments, aliquots of
the stock solution were made alkaline (pH > 10), and their spectra
were recorded on a Unicam Helios Alpha spectrophotometer. The
concentration was determined at the 332 nm absorbance maximum
of OBr- (ꢀ ) 316.7 M-1 cm-1). The HOBr stock solutions were
considered to be of acceptable quality when the two analytical
results agreed within the experimental error. The free acid
concentration of the stock solution was determined potentiometri-
cally by acid-base titration.
Bromine hydrolysis was studied by spectrophotometry with an
HP-8453 diode-array spectrophotometer. The sample is exposed
to a high-intensity continuous light source in such an instrument,
and photochemical decomposition of the reactant(s) should always
be a major concern during the measurements.26,27 Our test experi-
ments confirmed that this photometer is unfit for kinetic studies
on the HOBr-Cl(III) reaction because repeated irradiation of the
same sample led to significant photodecay of hypobromous acid
and chlorine dioxide during time-resolved spectral scans. Neverthe-
less, photochemical reactions did not interfere with our equilibrium
studies because the exposure of each sample to the photometer light
lasted only for the duration of one scan, 0.5 s.
Kinetic runs were made with an Applied Photophysics DX-17
MV sequential stopped flow instrument in the single wavelength
detection mode at 370 nm. This wavelength was selected in order
to use the same conditions as in our related study on the bromine-
chlorine(III) reaction.16 Each kinetic trace was obtained as an
average of 5 replicate runs. The initial rates were obtained at t )
0 using the first derivative of an appropriate polynomial function
fitted to the experimental traces with the program package
the component reactions. The results of a recent laser flash
-
photolytic study on the reverse step of the Br2 + ClO2
h
Br2- + ClO2 reaction were fully consistent with our earlier
conclusions and lent strong support to the model proposed.21
Hypobromous acid was shown to contribute to the initial
part of the Br2-Cl(III) reaction in the absence of added
bromide ion.16 The concentration of HOBr sharply decreased,
and the corresponding reaction path vanished at longer
reaction times when the hydrolysis of bromine was sup-
pressed by Br- formed in the reaction. In general, the
contribution of the HOBr-path to the overall redox process
was apparent but not large enough to establish the corre-
sponding rate law, and certain approximations had to be
introduced for the evaluation of the experimental data. Our
early attempts to eliminate the uncertainties associated with
the HOBr-path were unsuccessful because the kinetic traces
obtained with different HOBr stock solutions were not
reproducible. Apparently, literature procedures were not
suitable to prepare HOBr stock solutions of appropriate
quality. The solutions contained halogenide ions and in some
cases presumably BrO3- as impurities, and these species had
profound effects on the kinetics under acidic conditions.
Eventually, this problem could be circumvented by using a
somewhat modified procedure for the preparation of hy-
pobomous acid stock solutions, as will be discussed in this
paper.
Now we report a thorough kinetic study on the HOBr-
Cl(III) reaction in the pH < 3.0 region. The results presented
here complement a related study by Furman and Margerum
-
on the HOBr-ClO2 system in the pH 5.0-9.0 range.14
According to those authors, the oxidation of the base form
of Cl(III) is general-acid-catalyzed and first-order in each
reactant. However, they did not test the validity of the rate
law under acidic conditions where the overall redox process
becomes faster by orders of magnitude. Calculations on the
basis of these literature data predicted reaction rates con-
siderably slower than experimentally observed at low pH in
preliminary studies. In this paper, we confirm that an
alternative reaction path needs to be considered for proper
interpretation of the experimental data in acidic solution. The
combination of our results with those of Furman and
Margerum provides a coherent description of the hypobro-
mous acid-chlorine(III) reaction in the 1.0-9.0 pH range.
A quantitative description of the redox properties of the
BrClO2 intermediate in aqueous solution is also given.
SCIENTIST;28 V0 ) -d[HOBr]0/dt ) (dA370 nm/dt)/ꢀClO /2, ꢀClO
)
Experimental Section
2
2
962 M-1 cm-1 (the molar absorbance of ClO2 at 370 nm).16 This
expression implies that the contribution of the reactants and
intermediate(s) to the measured absorbance change is negligible
Chemicals. Sodium chlorite (Fluka, 80% purity) and Br2 (Ferak)
were purified as described earlier.22,23 All measurements were made
at 25 ( 0.1 °C and 1.00 M ionic strength set by sodium perchlorate
prepared from perchloric acid (Carlo Erba) and Na2CO3 (Reanal).
Other reagents were of the highest available quality and were used
without further purification. The preparation of halogenide-free
acidic HOBr stock solution will be discussed in the next chapter.
(24) Covington, A. K.; Bates, R. G.; Durst, R. A. Pure Appl. Chem. 1983,
55, 1467-1476.
(25) Irving, H. M. L.; Miles, M. G.; Pettit, L. P. Anal. Chim. Acta 1967,
38, 475-488.
(26) Stanbury, D. M.; Figlar, J. N. Coord. Chem. ReV. 1999, 187, 223-
232.
(21) To´th, Zs.; Fa´bia´n, I.; Bakac, A. Inorg. React. Mech. 2001, 3, 147-
152.
(22) Fa´bia´n, I.; Gordon, G. Inorg. Chem. 1991, 30, 3785-3787.
(23) Gauw, R. D. Ph.D. Thesis, Miami University, Oxford, OH, 1999.
(27) Ko¨rtve´lyesi, Z. Thesis, University of Debrecen, Debrecen, Hungary,
2000.
(28) SCIENTIST, version 2.0; Micromath Software: Salt Lake City, UT,
1995.
2718 Inorganic Chemistry, Vol. 43, No. 8, 2004

Oxidation of Chlorine(III) by Hypobromous Acid
and the spectral effects are exclusively due to the formation of
chlorine dioxide at this wavelength. These assumptions are cor-
roborated by the results presented in this paper. Comprehensive
evaluation of the data was made with the program package ZITA.29
presence of bromate ion in that iodometry always yielded
considerably higher OBr- concentration than spectropho-
tometry.
In order to prepare HOBr solution of acceptable quality,
the previous procedure was modified by eliminating the use
of Ag2O. A known amount of Br2 was dissolved in NaOH,
and the pH was set between 7.5 and 7.8 by adding
appropriate amounts of HClO4. The Br- content was removed
with an equivalent amount of AgClO4. Strict control of the
pH of the solution is a crucial element of the procedure. The
precipitation of the catalytically active Ag2O is unavoidable
at pH > 7.8, and experimental complications arise from the
formation of colloidal AgBr at pH < 7.5. In the final step,
AgBr was filtered off, and the stock solution was made
slightly acidic by adding a known amount of HClO4. The
noted reproducibility problems were not observed with these
solutions, and the analytical results obtained by iodometry
and spectrophotometry agreed within 1%.
Results and Discussions
Preparation of Halogenide-Free HOBr Solution. Several
methods were reported for the preparation of hypobromous
acid in the literature. The procedure described by Orlando
and Burkholder is similar to the preparation of high purity
HOCl.30 In this case, bromine is oxidized with yellow HgO,
and the product Br2O is flushed into an alkaline solution
with a steady stream of nitrogen gas. While Cl2 can
completely be eliminated from the HOCl solution, the final
HOBr solution is always contaminated with relatively large
quantities of unoxidized Br2. This renders these stock
solutions useless for kinetic studies under acidic conditions.
The oxidation of Br- to bromate ion by ozone proceeds
via HOBr.31 This offers a possibility to prepare hypobromous
acid in adequate quality provided that the oxidation is
terminated at suitable conversion. A particular advantage of
this procedure would be that the presence of the byproduct
dioxygen does not affect the reactions of oxyhalogen species.
Our attempts failed to control the ozonation process quan-
titatively, and the method was abandoned.
Gazda and Margerum oxidized bromide ion quantitatively
to hypobromite ion with an equivalent amount of OCl- at
pH ∼ 9.0.32 Apparently, the product Cl- did not interfere
with their studies in the slightly acidic-neutral pH range.
However, the presence of chloride ion clearly affected the
kinetic traces at lower pH in our experiments. This phenom-
enon is presumably the consequence of the formation of BrCl
at low concentration levels which, in turn, can initiate
alternative reaction paths for the oxidation of Cl(III) or some
other unidentified side reactions. The problem was not
studied in any further detail, but the method was considered
to be inappropriate for our purposes.
Equilibrium Constant for the Hydrolysis of Bromine.
Literature values for the equilibrium constant of reaction 1
cover more than an order of magnitude range, (0.6-11) ×
36-45
10-9 M2.
Br2 + H2O h HOBr + Br- + H+
(1)
[HOBr][Br-][H+]
K1 )
[Br2]
The variation in the experimental conditions does not
explain this discrepancy, and a thorough review of the
relevant publications did not reveal the source of the
unusually large differences. It should be added that the
evaluation of the experimental data typically involved
approximations which could lead to biased results. Thus, the
hydrolysis constant of bromine was redetermined spectro-
photometrically for the conditions applied here.
Individual samples were prepared by mixing solutions of
HOBr and Br- in a stoppered spectrophotometric cell such
that the headspace was minimized. The hydrolytic equilib-
rium was shifted between 0 and 100% completion by varying
the pH and the concentrations of the reactants systematically.
The hydrolysis constant and the molar absorbtivities of Br2,
In the most promising procedure, Br2 is fully hydrolyzed
into OBr- and Br- by dissolving liquid bromine in alkaline
solution, and bromide ion is precipitated by adding freshly
prepared Ag2O to the solution in excess.33 However, kinetic
runs were highly irreproducible with samples prepared from
different batches of HOBr stock solutions. This problem was
attributed to Ag2O-catalyzed disproportionation of hypobro-
mite ion. Such a catalytic activity of various metal oxides
and hydroxides in the disproportionation of hypohalites was
reported in the earlier literature.34,35 The analysis of the
solutions prepared with Ag2O was consistent with the
-
Br3 , and HOBr were calculated by fitting the experimental
data at 80 wavelengths in the 255-450 nm wavelength range
with the program package PSEQUAD.46 The molar absorp-
tivities of OBr- were determined in separate experiments
(36) Bray, W. C.; Connolly, E. L. J. Am. Chem. Soc. 1911, 33, 1485-
1487.
(37) Jones, G.; Baeckstro¨m, S. J. Am. Chem. Soc. 1934, 56, 1517-1524.
(38) Liebhafsky, H. A. J. Am. Chem. Soc. 1939, 61, 3513-3519.
(39) Eigen, M.; Kustin, K. J. Am. Chem. Soc. 1962, 84, 1355-1361.
(40) Perlmutter-Hayman, B.; Weissman, Y. J. Am. Chem. Soc. 1969, 91,
668-672.
(29) Peintler, G. ZITA: A Comprehensive Program Package for Fitting
Parameters of Chemical Reaction Mechanisms; Attila Jo´zsef Univer-
sity: Szeged, Hungary, 1997.
(30) Orlando, J. J.; Burkholder, J. B. J. Phys. Chem. 1995, 99, 1143-
1150.
(41) Pink, J. M. Can. J. Chem. 1970, 48, 1169-1171.
(42) Pusenok, G. I.; Mischenko, K. P. J. Appl. Chem. (USSR) 1971, 44,
934-935.
(31) von Gunten, U. Water Res. 2003, 37, 1469-1487.
(32) Gazda, M.; Margerum, D. W. Inorg. Chem. 1994, 33, 118-123.
(33) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J. Phys. Chem. 1983,
87, 510-524.
(34) Lister, M. W. Can. J. Chem. 1956, 34, 479-488.
(35) Gray, E. T.; Taylor, R. W.; Margerum, D. W. Inorg. Chem. 1977, 16,
3047-3055.
(43) Kshirsagar, G.; Field, R. J. J. Phys. Chem. 1988, 92, 7074-7079.
(44) Fo¨rsterling, H.-D.; Mura´nyi, S.; Schreiber, H. Z. Naturforsch. 1989,
44a, 555-566.
(45) Beckwith, R. C.; Wang, T. X.; Margerum, D. W. Inorg. Chem. 1996,
35, 995-1000.
Inorganic Chemistry, Vol. 43, No. 8, 2004 2719

To´th and Fa´bia´n
Figure 1. Spectra of absorbing bromine species.
Figure 3. The initial rate (b) and the initial hypobromous acid concentra-
tion (- - -) as a function of added bromide ion concentration at Cl(III)
excess: [HOBr]0 ) 2.0 × 10-4 M, [Cl(III)]0 ) 4.0 × 10-3 M, pH ) 1.50.
At HOBr excess (inset): [HOBr]0 ) 4.0 × 10-3 M, [Cl(III)]0 ) 3.0 ×
10-4 M, pH ) 1.50. T ) 25 °C, I ) 1.0 M.
period of time, and composite kinetic profiles were observed.
These observations are qualitatively consistent with the
assumption that the oxidation of Cl(III) by HOBr is relatively
fast. When chlorine(III) is the limiting reagent, it is pre-
dominantly oxidized by HOBr. This reaction swiftly removes
Cl(III), and other reactions have a marginal role in the overall
process. In excess chlorine(III), the reaction between HOBr
and the product Br- leads to the fast formation of Br2 which
reacts with Cl(III) relatively slowly. Acid-catalyzed decom-
position of unoxidized chlorine(III) also generates chlorine
dioxide in a side reaction on the same time scale.
Reaction Orders, pH-Dependence. According to the
initial rate method, the order of the reaction is one with
respect to HOBr and varies between 1 and 2 in chlorine-
(III). In contrast, first-order kinetics was reported with respect
to both reactants in the 5.0-9.0 pH range.14 These results
confirm that the kinetic behavior of the reaction is strongly
dependent on the conditions applied and different reaction
paths may become operative by varying the pH.
Figure 3 demonstrates the retarding effect of bromide ion
on the initial rate. Bromide ion shifts equlibrium 1 to the
left even at low concentration levels and efficiently converts
HOBr into the less reactive Br2. Hypobromous acid is fully
removed when its concentration is low, while the rate
decreases proportionally to the added amount of Br- at large
[HOBr] (cf. inset, Figure 3). There is an excellent correlation
between the concentration of HOBr and the initial rate in
both cases. This indicates again that the reaction is first-
order in HOBr.
Figure 2. Typical kinetic traces at HOBr excess: [HOBr]0 ) 1.0 × 10-3
M, [Cl(III)]0 ) 4.0 × 10-4 M, pH ) 1.50 (a). At Cl(III) excess: [HOBr]0
) 4.0 × 10-4 M, [Cl(III)]0 ) 2.0 × 10-3 M, pH ) 1.50 (b). T ) 25 °C,
I ) 1.0 M.
and used as fixed parameters in the calculations. The
equilibrium model also included the formation of tribromide
ion and the protonation of hypobromite ion using literature
-
values for the corresponding equilibrium constants: KBr
3
) 19.3 M-1,16 and log KOBr ) 8.59,47 respectively. This
-
data treatment is expected to provide the most accurate
estimate for the equilibrium constant of bromine hydrolysis
because it does not involve any simplifying assumption. The
calculations yielded K1 ) (7.17 ( 0.04) × 10-9 M2 in
reasonable agreement with some of the literature data. The
spectra of the absorbing species are shown in Figure 1.
Kinetic Observations. The kinetic traces exhibited distinct
features depending on the concentration ratios of the reactants
(Figure 2). In large excess of HOBr, the formation of ClO2
could be approximated by single exponential traces up to
70-80% conversion in most cases. The final amount of ClO2
formed was consistent with the following overall stoichi-
ometry:
Earlier, we proposed the following reaction sequence for
the oxidation of chlorine(III) by HOBr:16
HOBr + 2ClO2- + H+ ) Br- + 2ClO2 + H2O (2)
HClO2 + HOBr h BrClO2 + H2O k3, k!3
BrClO2 + ClO2- h 2ClO2 + Br- k4, k-4
(3)
(4)
When the concentration ratio of the reactants was reversed,
the formation of chlorine dioxide occurred for an extended
Provided that BrClO2 is in steady state and the reverse step
of eq 4 is negligible (or the reaction is irreversible), the
following equation can be derived for the initial rate of the
reaction:
(46) Ze´ka´ny, L.; Nagypa´l, I. In Computational Methods for the Determi-
nation of Formation Constants; Legett, D. J., Ed.; Plenum Press: New
York, 1985; p 291.
(47) Gerritsen, C. M.; Gazda, M.; Margerum, D. W. Inorg. Chem. 1993,
32, 5739-5748.
2720 Inorganic Chemistry, Vol. 43, No. 8, 2004

Oxidation of Chlorine(III) by Hypobromous Acid
-
k3k4[HOBr][HClO2][ClO2 ]
d[HOBr]
-
) V0 )
(5)
-
dt
k-3 + k4[ClO2 ]
-
Equation 5 predicts either a first-order (k-3 , k4[ClO2 ])
-
or a second-order (k-3 . k4[ClO2 ]) rate law with respect
to chlorine(III) in the two limiting cases. The fractional
reaction order (1 < n < 2) found for Cl(III) clearly indicates
that such approximations cannot be applied for the whole
concentration range; i.e., the conversion of BrClO2 back into
its precursors and its reaction with chlorite ion proceed at
comparable rates at low chlorine(III) concentrations. The
reaction becomes first-order in chlorine(III) only at relatively
high concentrations (Figure 4).
The oxidation rate shows a very characteristic acid
concentration dependence (Figure 5). The dissociation of
HOBr is negligible under acidic conditions, and the observa-
tions need to be interpreted in terms of the protolytic reaction
of chlorine(III):
Figure 4. The normalized initial rate as a function of [Cl(III)] at constant
pH. Solid line (s): fitted curve on the basis of eq 8. [HOBr]0 ) (0.1-2.0)
× 10-3 M, pH ) 1.50. T ) 25 °C, I ) 1.0 M.
ClO2- + H+ h HClO2 Kp
(6)
According to earlier results, log Kp ) 1.72, and the
conjugate acid and base forms of chlorine(III) are always
present at comparable concentration levels in the 1.0-2.5
pH range.22 Thus, the pH dependence of the reaction rate is
expected to reflect the variation of the concentration ratio
of these two species as a function of pH. Equation 5 can be
converted into the following form by including reaction 6
as a diffusion controlled equilibrium step:
Figure 5. The normalized initial rate as a function of [H+] at constant
reactant concentrations. Solid line: fitted curve on the basis of eq 9. [HOBr]0
) 2.0 × 10-4 M, [Cl(III)]0 ) 4.0 × 10-3 M. T ) 25 °C, I ) 1.0 M.
V0 )
k3k4
k-3
k4
d ) -
e )
k3k4[C1(III)]20Kp[H+]
[HOBr] (7)
k-3
(k-3(1 + Kp[H+]) + k4[C1(III)]0)(1 + Kp[H+])
The equation predicts that the reaction rate should eventu-
ally decrease by increasing [H+], but experimental limitations
did not make it possible to work at sufficiently high acid
concentrations to demonstrate this effect (Figure 5). By fixing
log Kp at 1.72,22 the estimated values for c and d are (8.2 (
0.7) × 107 M-2 s-1 and (1.6 ( 0.2) × 103 M-1, respectively.
The combination of parameters a, b, and Kp as well as d
and e predicts that the value of k3 is somewhere around (3.5-
5.0) × 104 M-1 s-1.
At constant pH, the [Cl(III)] dependence of the initial rate
can be expressed as follows:
a[HOBr][C1(III)]02
V0 )
(8)
1 + b[C1(III)]0
where
Comprehensive Data Treatment. In order to overcome
the constraints of the initial rate method and to explore further
details of the reaction, the kinetic model was validated by
using a comprehensive data fitting method. This procedure
comprises numerical integration of a differential equation
system representing the kinetic model and fitting the
calculated kinetic traces to the experimental data by a
nonlinear least squares algorithm. The advantages of this
approach over classical data treatment in complex reactive
systems were demonstrated in some of our earlier stud-
ies.16,48-53 In the present study, 19 kinetic traces (ca. 5000
k3k4Kp[H+]
k-3(1 + Kp[H+])2
k4
a )
b )
k-3(1 + Kp[H+])
Fitting of the initial rates to eq 8 with a nonlinear least
squares routine yielded a ) (4.5 ( 0.4) × 107 M-2 s-1 and
b ) (1.3 ( 0.2) × 103 M-1 at pH ) 1.50 (Figure 4).
The effect of acid concentration on the reaction rate was
studied at constant reactant concentrations by using the
following form of eq 7:
d[HOBr][C1(III)]20Kp[H+]
(1 + Kp[H+] + e[C1(III)]0)(1 + Kp[H+])
(48) Lente, G.; Fa´bia´n, I. Inorg. Chem. 1998, 37, 4204-4209.
(49) Lente, G.; Magalha˜es, M. E. A.; Fa´bia´n, I. Inorg. Chem. 2000, 39,
V0 )
(9)
1950-1954.
(50) Nemes, A.; Fa´bia´n, I.; Gordon, G. Ozone: Sci. Eng. 2000, 22, 287-
where
304.
Inorganic Chemistry, Vol. 43, No. 8, 2004 2721

To´th and Fa´bia´n
Table 1. Kinetic Model for the Oxidation of Chlorine(III) by HOBr (I
) 1.0 M NaClO4, T ) 25.0 °C)
reaction
log K ref
rate constanta
ref
HOBr + HClO2 h BrClO2 + H2O
k3 (3.34 ( 0.02) × 104
k-3 (3.5 ( 1.3) × 103
k4 (2.9 ( 1.0) × 107
k-4 n.a.
b
b
b
c
39, f
d
54
d
e
d
BrClO2 + ClO2- h 2ClO2 + Br-
Br2 + H2O h HOBr + H+ + Br- -8.14
b
k5 110
k-5 1.5 × 1010
Br2 + Br- h Br3
1.28 16 k6 1.5 × 109
k-6 7.8 × 107
-
ClO2- + H+ h HClO2
1.72 22 k7 1.0 × 1010
k-7 1.9 × 108
a The units for the first-, second-, and third-order rate rate constants are
s-1, M-1 s-1, and M-2s-1, respectively. b This work. c Too small to be
determined. d k- ) k+/K. e Estimated value assuming diffusion control.f I
) 0.1 M, T ) 20.0 °C.
Figure 6. Experimental (O) and fitted (s) kinetic traces at pH ) 1.50:
[HOBr]0 ) 1.0 × 10-4 M, [Cl(III)]0 ) 2.0 × 10-3 M (a); [HOBr]0 ) 2.0
× 10-4 M, [Cl(III)]0 ) 3.0 × 10-3 M (b); [HOBr]0 ) 1.0 × 10-3 M,
[Cl(III)]0 ) 4.0 × 10-4 M (c); [HOBr]0 ) 4.0 × 10-3 M, [Cl(III)]0 ) 2.0
× 10-4 M (d); [HOBr]0 ) 6.0 × 10-4 M, [Cl(III)]0 ) 2.0 × 10-3 M (e);
[HOBr]0 ) 2.0 × 10-3 M, [Cl(III)]0 ) 8.0 × 10-4 M (f); T ) 25 °C, I )
1.0 M. For sake of simplicity, only a portion of the experimental data points
is shown in each experimental trace.
data points) obtained at various reactant concentrations and
recorded at 370 nm were evaluated simultaneously. Some
of the traces were truncated in order to avoid the interference
by the slow acid-catalyzed decomposition of Cl(III) at longer
reaction times. While only about the first half of the kinetic
curves were useful when the chlorine(III) concentration was
relatively high, considerably larger sections of the traces
could be used at HOBr excess.
sequences leading to this species are different. In the HOBr-
-
ClO2 reaction, the formation of HOBrOClO- was consid-
ered to be the first step which is transformed into BrClO2 in
general acid-catalyzed subsequent reactions:14
The kinetic model includes the actual redox steps, the
acid-base equilibrium of chlorine(III), as well as the
hydrolysis of Br2 and the formation of the tribromide ion
(Table 1). These latter reactions have minor but increasing
role as the oxidation proceeds due to the formation of Br-
in increasing amounts. The forward rate constants for these
steps are available from the literature, and the reverse rate
constants were calculated on the basis of k- ) k+/K using
the appropriate equilibrium constants. Rate constants k3, k-3,
and k4 were fitted, and all other kinetic parameters were
included with fixed values in the calculations. We also made
several attempts to fit k-4 by assuming that reaction 4 is an
equilibrium step. However, these trials failed, indicating that
the oxidation of chlorite ion by BrClO2 is completely shifted
to the right.
The fitted value for k3 is in excellent agreement with those
obtained from the initial rate method. In addition, estimates
for the other two fitted parameters were also calculated. A
comparison of experimental and fitted kinetic traces (Figure
6) confirms that the model provides excellent interpretation
of the experimental observations. Nevertheless, there is an
about 30% error in k-3 and k4 due to the fact that the
contributions of the corresponding competing steps are very
similar and always comparable. Experimental conditions
could not be found to resolve better the strong cross-
correlation between these parameters.
HOBr + ClO2- h HOBrOClO-
HOBrOClO- + HA ) BrClO2 + H2O + A- (11)
(10)
BrClO2 + ClO2- ) 2ClO2 + Br-
(12)
(13)
BrClO2 + H2O ) ClO3- + Br- + 2H+
Assuming that HOBrOClO- and BrClO2 are in steady
state, HClO2 acts as a general acid, and the reaction with
H+ is negligible in eq 11, the model predicts the same
concentration dependencies of the overall rate as shown in
eq 7. However, this is only a formal analogy because on the
basis of our data the forward rate constant for reaction 10
would be about 2 orders of magnitude larger than reported
earlier. It follows that an alternative path, i.e., reactions 3
and 4, needs to be operative in the formation of BrClO2 under
acidic conditions.
Despite great many efforts to explore the intimate nature
of the X2O2 intermediates in solution phase, very limited
quantitative information is available for these species in the
literature. To our knowledge, this is the first time that
thermodynamic and redox properties of a member of the
X2O2 family are quantified in aqueous solution. The k3/k-3
ratio yields K3 ) 9.5 M-1 for the equilibrium constant of
reaction 3 indicating that the formation of BrClO2 is slightly
favored from HOBr and HClO2.
The Kinetic Role of the BrClO2 Intermediate. There
are some similarities between the kinetic models postulated
here and proposed by Furman and Margerum at higher pH.14
In both cases, the reaction is assumed to proceed via the
formation of the BrClO2 intermediate, but the reaction
The relatively small equilibrium constant clearly explains
why direct detection of BrClO2 failed in previous studies.
Under typical experimental conditions, the reactants are used
at concentration levels on the order of 10-3 M or less. It
follows that the conversion of the reactants into BrClO2
would be marginal, i.e., less than 10%, even if other reactions
did not occur. Due to subsequent fast reactions, the steady
(51) Nemes, A.; Fa´bia´n, I.; van Eldik, R. J. Phys. Chem. A 2000, 104,
7995-8000.
(52) Lente, G.; Fa´bia´n, I. Inorg. Chem. 2002, 41, 1306-1314.
(53) Lente, G.; Fa´bia´n, I. J. Chem. Soc., Dalton Trans. 2002, 778-784.
2722 Inorganic Chemistry, Vol. 43, No. 8, 2004

Oxidation of Chlorine(III) by Hypobromous Acid
-
state concentration of this species is probably orders of
magnitude smaller than calculated on the basis of reaction
3. For example, the concentration of this species is estimated
to be less than 10-5 M even at the largest reactant concentra-
tions applied in our experiments. Consequently, the spectral
change associated with the formation of BrClO2 is expected
to be negligible.
In the HOBr-ClO2 reaction, the formation of the
precursor HOBrOClO- intermediate (eq 10) implies direct
interaction between bromine and one of the oxygen atoms
of chlorite ion.14 In the subsequent general-acid-catalyzed
step, the BrClO2 species is formed by retaining the chainlike
connectivity. This reaction was explained in terms of a
H-bond formed between the proton of the acid and the OH
group of the precursor complex. However, it should be noted
that an alternative path leading to the formation of the
Y-shaped isomer cannot be excluded. In this case, the
precursor complex would involve direct halogen-halogen
interaction and be stabilized by a H-bond between the OH
group of hypobromous acid and a chlorite oxygen. Our
pressure dependent kinetic studies were consistent with the
The oxidation power of the kinetically significant inter-
mediates is an intriguing question of oxyhalogen chemistry.
The BrClO2 intermediate is assumed to be a relatively strong
oxidant which is capable of oxidizing chlorine(III) to chlorine
dioxide (eq 4). Now that the equilibrium constant is available
for reaction 3, the relevant redox potential can be estimated
by using log Kp ) 1.72 for the protonation constant of
chlorite ion,22 and ꢀ0 ) 1.341 V55 and 0.934 V56 for the
-
formation of such an intermediate in the BrO3 -I- system.61
-
HOBr/Br- and ClO2/ClO2 redox couples, respectively:
The formation of a chainlike species does not seem to be
appropriate in the HOBr-HClO2 reaction for the following
reasons. Protonation would clearly weaken the interaction
between HOBr and the chlorite oxygen and reduce the
stability of the corresponding precursor complex. In addition,
the partial negative charge of the OH oxygen would also be
smaller making the acid catalyzed step less favorable. As a
consequence, chlorous acid should react considerably slower
with HOBr than chlorite ion. The experimental results do
not support these expectations, and in fact, we observe the
opposite trend.
BrClO2 + e- ) Br- + ClO2 ꢀ0 ∼ 1.70 V
(14)
The calculations confirm that the redox potential of BrClO2
is comparable to or even higher than that of the strongest
inorganic oxidants such as permanganate ion, dichromate ion,
bromate ion, chlorine, etc. Consequently, reaction 4 is very
favorable and should be regarded as an irreversible step for
all practical purposes.
The formation of a halogen-halogen bonded adduct may
account for the kinetic effects of protonation better. The
higher electron deficiency of chlorine in HClO2 compared
The connectivity of the X2O2 intermediates has been
discussed extensively in recent years. In their pioneering
work, Taube and Dodgen concluded that the two halogen
atoms are not equivalent in Cl2O2.1 These results were widely
adopted in subsequent studies and also extended to other
members of the X2O2 family by assuming a Y-shape
geometry for these intermediates. However, recently Furman
and Margerum have presented arguments that, after all, the
X-O-X-O type structure cannot be ruled out,14 and later
studies from that group postulated a series of chainlike
intermediates in the reactions between various oxychlorine
and oxybromine species.18,19 Gas phase studies confirmed
the existence of both isomers,57-59 but according to a
functional density study, the Y-shaped geometry of BrClO2
is somewhat more stable than the other form.60 However,
the relevance of these results in aqueous solution is dubious
because solvation effects can significantly alter the stability
order of these species.
-
to ClO2 may strengthen the X-X bond and stabilize the
precursor complex. Furthermore, there are two possibilities
for the formation of the H-bond via the OH group of either
HOBr or HClO2. This makes the formation of the adduct
statistically more favorable. These considerations lend sup-
port to our earlier assumption that the BrClO2 intermediate
is formed via a cyclic hydrogen bonded precursor complex
and has a Y geometry.16 Having said that, we also have to
emphasize that direct experimental evidence is not available
to distinguish between the alternative isomers of BrClO2 in
solution phase. Thus, any conclusion regarding the geom-
etries of this and related intermediates is vague and should
be the subject of scrutiny.
In conclusion, the results presented here clarify mechanistic
aspects of the HOBr-HClO2 reaction under acidic conditions
and provide coherent interpretation of the kinetic data
obtained at different reactant concentrations and concentra-
tion ratios. Despite the noted ambiguity in its geometry, the
importance of the BrClO2 intermediate is well established,
and for the first time, its redox properties are quantified.
(54) Ruasse, M.; Aubard, J.; Galland, B.; Adenier, A. J. Phys. Chem. 1986,
90, 4382-4388.
(55) Mussini, T.; Longhi, P. In Standard Potentials in Aqueous Solution;
Bard, A. J., Parson, R., Jordan, J., Eds.; Marcel Dekker Inc.: New
York, 1985; p 79.
(56) Klaning, U.K.; Sehested, K.; Holcman, J. J. Phys. Chem. 1985, 89,
760-763.
Acknowledgment. This research was supported by the
Hungarian Funding Agency OTKA under Grants T 042755
and M 028244.
(57) Muller, H. S. P.; Willner, H. Inorg. Chem. 1992, 31, 2527-2534.
(58) Jacobs, J.; Kronberg, M.; Muller, H. S. P.; Willner, H. J. Am. Chem.
Soc. 1994, 116, 1106-1114.
(59) Johnsson, K.; Engdahl, A.; Kolm, J.; Nieminen, J.; Nelander, B. J.
Phys. Chem. 1995, 99, 3902-3904.
(60) Guha, S.; Francisco, J. S. J. Phys. Chem. A 1997, 101, 5347-5359.
IC0354318
(61) Fa´bia´n, I.; van Eldik, R. Int. J. Chem. Kinet. 1995, 27, 491-498.
Inorganic Chemistry, Vol. 43, No. 8, 2004 2723