Kinetics and mechanism of the initial phase of the bromine - chlorite ion reaction in aqueous solution

Article abstract of DOI:10.1021/ic990329p

The kinetics and mechanism of the chlorine(III)-bromine reaction are studied by the stopped-flow method under acidic conditions in 1.0 M NaClO₄ and at 25.0 °C. There are two kinetically well-separated phases in this reaction. A detailed mechanism is proposed for the first phase of the reaction, in which Br₂ oxidizes ClO₂^- to chlorine dioxide. It is confirmed that the oxidation occurs via competing parallel reaction steps. The autoinhibition observed in the reaction is attributed to a backward shift in the reversible initial step as the oxidation proceeds. On the basis of simultaneous evaluations of the kinetic traces, the following forward rate constants are obtained for the kinetically significant reaction steps: Br₂ + ClO₂^- = ClO₂ + Br₂^-, k₁ = (1.3 ± 0.2) x 10³ M^-1 s^-1 (k_-1 = 1.1 x 10⁹ M^-1 s^-1); Br₂^- + ClO₂^- = ClO₂ + 2Br^-, k₂ = (4.0 ± 0.1) x 10⁶ M^-1 s ^-1; Br + ClO₂^- = ClO₂ + Br^-, k₈ = (2.3 ± 0.7) x 10⁸ M^-1 s^-1; HOBr + HClO₂ = BrClO₂ + H₂0 (BrClO₂ + ClO₂^- = Br^- + 2ClO₂, very fast), k₉ = (1.9 ± 0.1) x 10⁵ M^-1 s^-1. The possible kinetic role of the reactive BrClO₂ intermediate is discussed in detail.

Full text of DOI:10.1021/ic990329p

4608
Inorg. Chem. 2000, 39, 4608-4614
Kinetics and Mechanism of the Initial Phase of the Bromine-Chlorite Ion Reaction in
Aqueous Solution
Zsuzsanna To´th and Istva´n Fa´bia´n*
Department of Inorganic and Analytical Chemistry, University of Debrecen, P.O.B. 21,
Debrecen H-4010 Hungary
ReceiVed March 23, 1999
The kinetics and mechanism of the chlorine(III)-bromine reaction are studied by the stopped-flow method under
acidic conditions in 1.0 M NaClO4 and at 25.0 °C. There are two kinetically well-separated phases in this reaction.
-
A detailed mechanism is proposed for the first phase of the reaction, in which Br2 oxidizes ClO2 to chlorine
dioxide. It is confirmed that the oxidation occurs via competing parallel reaction steps. The autoinhibition observed
in the reaction is attributed to a backward shift in the reversible initial step as the oxidation proceeds. On the
basis of simultaneous evaluations of the kinetic traces, the following forward rate constants are obtained for the
kinetically significant reaction steps: Br2 + ClO2- h ClO2 + Br2-, k1 ) (1.3 ( 0.2) × 103 M-1 s-1 (k-1 ) 1.1
× 109 M-1 s-1); Br2 + ClO2 ) ClO2 + 2Br-, k2 ) (4.0 ( 0.1) × 106 M-1 s-1; Br + ClO2 ) ClO2 + Br-,
-
-
-
-
k8 ) (2.3 ( 0.7) × 108 M-1 s-1; HOBr + HClO2 ) BrClO2 + H2O (BrClO2 + ClO2 ) Br- + 2ClO2, very
fast), k9 ) (1.9 ( 0.1) × 105 M-1 s-1. The possible kinetic role of the reactive BrClO2 intermediate is discussed
in detail.
Introduction
detected in polycrystalline ice and gas phases, and theoretical
discussions of their structures and reactivities were presented.16-23
The kinetics and mechanisms of chlorine dioxide formation
in the bromine-chlorite ion system were previously studied by
Valdes-Aguilera and co-workers.1 The reaction was character-
ized with a strictly 1:2 final stoichiometry:
However, direct experimental evidence to prove the existence
of such species in aqueous solutions has not, until now, been
found. The primary objective of our present study was to obtain
evidence for the formation of BrClO2 and, if possible, to observe
its properties in selected reactions. Because BrClO2 can be
considered as a prototype of the X2O2 intermediates, the results
were also expected to lead to a better understanding of the
significance of these species in the redox chemistry of oxy-
halogen compounds.
Br2 + 2ClO2- ) 2Br- + 2ClO2
(1)
According to these authors, simple first-order kinetic traces were
observed whenever the chlorite ion was used in excess over
Br2. The appropriate rate law was deduced on the basis of the
concentration dependencies of the pseudo-first-order rate con-
stants.
The reactions of the chlorite ion are notorious for their
complexities, and the relatively simple stoichiometric and kinetic
features reported for this system are somewhat unexpected. The
most interesting result from the cited paper is the direct
observation of the BrClO2 intermediate. The first X2O2-type
transient species (X ) halogen atom) was postulated in 1948
by Taube and Dodgen2 in their study of the reactions of the
chlorite ion with Cl2 and HOCl. Since then, the formation and
subsequent reactions of these reactive intermediates have been
in the cores of the mechanisms postulated for aqueous reactions
of oxyhalogen species.3-15 Some of the X2O2 species were
Our preliminary experiments were not fully consistent with
the results reported by Valdes-Aguilera and co-workers.1 We
found no direct experimental evidence for the formation of
BrClO2, and most of our kinetic traces showed significant
(9) Ra´bai, G.; 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.
(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, G.; 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) Mu¨ller, H. S. P.; Willner, H. Ber. Bunsen-Ges. Phys. Chem. 1992,
96, 427-431.
* Corresponding author. E-mail: ifabian@delfin.klte.hu.
(1) Valdes-Aguilera, O.; Boyd, D. W.; Epstein, I. R.; Kustin, K. J. Phys.
Chem. 1986, 90, 6696-6702.
(2) Taube, H.; Dodgen, H. J. Am. Chem. Soc. 1949, 71, 3330-3336.
(3) Emmenegger, F.; Gordon, G. Inorg. Chem. 1967, 6, 633-635.
(4) Gordon, G.; Kieffer, R. G.; Rosenblatt, D. H. Prog. Inorg. Chem. 1972,
15, 201-286.
(5) Grant, J. L.; De Kepper, P.; Epstein, I. R.; Kustin, K.; Orba´n, M. Inorg.
Chem. 1982, 21, 2192-2196.
(6) Tang, T.; Gordon, G. EnViron. Sci. Technol. 1984, 18, 212-216.
(7) Epstein, I. R.; Kustin, K. J. Phys. Chem. 1985, 89, 2275-2282.
(8) Aieta, E. M.; Roberts, P. V. EnViron. Sci. Technol. 1986, 20, 50-55.
(17) Mu¨ller, H. S. P.; Willner, H. Inorg. Chem. 1992, 31, 2527-2534.
(18) Jacobs, J.; Kronberg, M.; Mu¨ller, H. S. P.; Willner, H. J. Am. Chem.
Soc. 1994, 116, 1106-1114.
(19) Francisco, J. S.; Sander, S. P. J. Am. Chem. Soc. 1995, 117, 9917-
9918.
(20) Johnson, K.; Engdahl, A.; Ko¨lm, J.; Nieminen, J.; Nelander, B. J.
Phys. Chem. 1995, 99, 3902-3904.
(21) Pursell, C. J.; Conyers, J.; Denison, C. J. Phys. Chem. 1996, 100,
15450-15453.
(22) Guha, S.; Francisco, J. S. J. Phys. Chem. A 1997, 101, 5347-5359.
(23) Misra, A.; Marshall, P. J. Chem. Soc., Faraday Trans. 1997, 93, 3301-
3304.
10.1021/ic990329p CCC: $19.00 © 2000 American Chemical Society
Published on Web 09/15/2000

Initial Phase of the Bromine-Chlorite Ion Reaction
Inorganic Chemistry, Vol. 39, No. 20, 2000 4609
deviations from pseudo-first-order behavior. In the present study,
the kinetics of the oxidation of the chlorite ion by bromine is
reinvestigated. On the basis of a new set of experimental data,
we propose an improved mechanism which seems to be
consistent with our observations. While this work was in
-
progress, a thorough kinetic study of the related HOBr-ClO2
reaction under slightly acidic-neutral conditions was published
by Furman and Margerum.14 The results reported by these
authors and those obtained here are complementary and are used
-
to provide a detailed interpretation of the Br2/HOBr-ClO2
HClO2 reaction over an extended pH range.
/
Experimental Section
Chemicals. Commercially available NaClO2 (Fluka, 80% purity) was
purified as described earlier.24 Bromine stock solutions were prepared
by distilling Br2 (Ferak) into 0.01 M HClO4 (Carlo Erba) solution.25
The ionic strength was adjusted to 1.00 M with NaClO4 prepared from
perchloric acid (Carlo Erba) and Na2CO3 (Reanal). All other reagents
were of analytical grade and were used without further purification.
The reagent solutions were prepared in doubly deionized and ultra-
filtered water obtained from a Milli-Q RG (Millipore) water purification
system. pHs were calculated from the total concentrations of the
components by using the appropriate equilibrium constants for the pH-
dependent equilibrium steps. pH corresponds to -log [H+] throughout
this paper. With a few exceptions, all experiments were carried out by
using a large excess of the chlorite ion over bromine.
Figure 1. Time-resolved spectral changes in the bromine-chlorite ion
reaction in the absence of added bromide ion. [ClO2-]0 ) 0.01 M; [Br2]0
) 5.0 × 10-4 M; pH ) 1.50. In the order of increasing absorbance at
360 nm, the spectra were recorded at 0.34, 2.34, 65.9, 237, 457, 599,
786, 901, 1033, and 1185 s. Inset: Stopped-flow trace under the same
conditions at 280 nm.
equilibrium constant obtained, K ) 19.3 ( 1.2 M-1, was in excellent
agreement with previous literature data.29-31
Results and Discussions
Instrumentation and Methods. Bromine stock solutions were stored
in and dispensed from a home-built, electronic version of the “shrinking
bottle” described by Silverman and Gordon.26 With this device, bromine
solutions could be stored with less than 1% concentration loss per day
and the error of each dispensed volume was (0.5%. The concentrations
of Br2 were determined by the standard iodometric method using a
Metrohm 721 NET Titrino potentiometric titrator equipped with a
Metrohm combined platinum wire electrode.
Preliminary Observations. Typical time-resolved UV-vis
spectra recorded in the absence of added bromide ion indicate
-
composite kinetic features in the Br2-ClO2 system (Figure
1). In the near-UV-visible region, the main absorbing species
is ClO2 (λmax ) 360 nm, ꢀ ) 1250 M-1 cm-1),32 while, below
300 nm, the absorbance is due to chlorite ion/chlorous acid,33
ClO2, Br2, and Br3-. A very intense absorbance band is
characteristic for Br3- (λmax ) 266 nm, ꢀ ) 40 900 M-1 cm-1),29
which suppresses any spectral effect when the tribromide ion
and the other absorbing species are present in comparable
concentrations. It should be kept in mind that the contribution
of Br3- to the spectra can be significant even when it is formed
at relatively low concentration levels.
Spectrophotometric measurements were performed with an HP-8453
spectrophotometer, and kinetic measurements were obtained with an
Applied Photophysics DX-17 MV sequential stopped-flow apparatus
either in the single-wavelength detection mode or by using an Applied
Photophysics PDA 1 diode array detector. At longer reaction times,
time-resolved spectra were recorded on the HP-8453 spectrophotometer
equipped with an RX2000 Rapid Kinetics Spectrometer Accessory
(Applied Photophysics). The optical path was 10 mm, and all
measurements were made at 25.0 ( 0.1 °C. The kinetic runs were
triggered by mixing acidic bromine and neutral chlorite ion solutions
in 1:1 ratios. In the corresponding experiments, Br- was added to the
bromine solution. The individual stopped-flow traces were fitted with
the program package SCIENTIST.27 For simultaneous evaluations
of more than one kinetic curve, the program package ZITA was
used.28
As shown, the intensity of the characteristic 360 nm band of
ClO2 steadily increased in the absence of added bromide ion.
At the same time, a very small opposite change was observed
in the 260-290 nm region. However, in a few cases, stopped-
flow measurements at 280 nm revealed a small absorbance
increase at the very beginning of the reaction (Figure 1, inset).
These observations can be interpreted as follows. Chlorine
dioxide is generated by the oxidation of the chlorite ion, as
shown in eq 1. This reaction also produces the bromide ion,
Equilibrium Constant for the Br2 + Br- h Br3- Reaction. This
equilibrium constant was redetermined spectrophotometrically for the
conditions applied here. The individual samples were prepared by
adding excess NaBr to NaBrO3 solutions in increasing concentrations
at pH 1.00.29 Prior to spectral acquisitions at 25.0 °C, the samples were
incubated at 50 °C in sealed vials for 3 h. Under these conditions, the
bromate ion was completely converted to Br2. The equilibrium constant
-
which shifts the Br2-Br3 equilibrium toward tribromide ion
formation. On the basis of a rough estimate, the small initial
absorbance increase at 280 nm corresponds to the conversion
of less than 1% of bromine into Br3-. At longer reaction times
(not shown in Figure 1), the absorbance slightly increases again
in the UV region. This indicates the formation of Br2/Br3- in a
subsequent slow reaction between the excess chlorite ion and
Br-.34
-
and the molar absorbancies of Br2 and Br3 at several wavelengths
were calculated by using a nonlinear least-squares fitting routine. The
(24) Fa´bia´n, I.; Gordon, G. Inorg. Chem. 1991, 30, 3785-3787.
(25) Gauw, R. D. Ph.D. Thesis, Miami University, Oxford, OH, 1999.
(26) Silverman, R. A.; Gordon, G. Anal. Chem. 1974, 46, 178.
(27) SCIENTIST 2.0; Micromath Software: Salt Lake City, UT, 1995.
(28) Peintler, G. ZITA: A ComprehensiVe Program Package for Fitting
Parameters of Chemical Reaction Mechanisms; Attila Jo´zsef Univer-
sity: Szeged, Hungary, 1997.
(30) Scaife, D. B.; Tyrrell, H. J. V. J. Chem. Soc. 1958, 386-392.
(31) Irving, H.; Wilson, P. D. J. Inorg. Nucl. Chem. 1964, 26, 2235.
(32) Kieffer, R. G.; Gordon, G. Inorg. Chem. 1968, 7, 235-239.
(33) In aqueous solutions, the protolytic equilibria between HClO2 and
-
ClO2 are fast and the concentration ratios of the two species are
determined by the pH. Unless it has particular significance, we do
not distinguish the two species and refer to chlorine(III) as the chlorite
ion thorough this paper.
(29) Wang, T. X.; Kelley, M. D.; Cooper, J. N.; Beckwith, R. C.; Margerum,
D. W. Inorg. Chem. 1994, 33, 5872-5878.

4610 Inorganic Chemistry, Vol. 39, No. 20, 2000
To´th and Fa´bia´n
In the presence of added Br-, the results provided further
evidence that there are two kinetically well-separated phases
in this reaction. In this case, the [Br2]/[Br3-] ratio was practically
constant during the reaction. In the first phase, the fast
absorbance change was consistent with the consumption of
bromine and the formation of chlorine dioxide. At longer
-
reaction times, the intensiy of the characteristic Br3 band
-
increased because of the formation of Br2 in the Br--ClO2
reaction. The latter process was relatively slow and kinetically
coupled with acid-catalyzed decomposition of the chlorite ion.
In separate experiments, a similarly slow formation of Br3- in
-
the Br--ClO2 reaction confirmed this interpretation.
Our attempt to establish a uniform final stoichiometry for
the overall process failed. This is not very surprising because
Br2 is not only consumed but also generated in the reaction
and ClO2 is produced by both the oxidation and the acid-
catalyzed decomposition of chlorite ion. The actual ratios of
the reactants consumed and products formed are determined by
the interplay of these reactions and are strongly dependent on
the experimental conditions applied. However, in the first phase,
when the oxidation of Br- by ClO2- was negligible, the spectral
changes were consistent with the stoichiometry given in eq 1.
In the remainder of this paper, kinetic results are presented only
for the initial phase of the bromine-chlorite ion reaction.
Figure 2. pH dependence of the initial rate of the bromine-chlorite
ion reaction. Key: initial rates estimated on the basis of the experimental
kinetic traces (b) and predicted by model C in Table 1 (dashed line);
fit of the data to eq 6 (solid line). Vi,25ms ) dA370nm/dt at 25 ms, in s-1
;
[ClO2-]0 ) 5.0 × 10-3 M; [Br2]0 ) 5.0 × 10-4 M; [Br-] ) 0.05 M.
about a factor of 4. Despite the limitations, it could be shown
that the initial reaction was roughly first order with respect to
-
both [ClO2
as
]tot and [Br2]tot. The corresponding rate law is given
-
Because of the very intense Br3 absorbance band at 266 nm,
meaningful data could not be collected from the entire UV
region in the presence of added bromide ion. Thus, only kinetic
traces from the 340-390 nm wavelength region were used for
quantitative evaluation of the system.
-
d[Br2]
d[ClO2 ]
1
2
-
-
) -
) k [Br ] [ClO ] (2)
(
)
(
)
i
2 tot
2
tot
dt
i
dt
i
Reaction Orders in the Absence of Added Bromide Ion.
Because of the hydrolysis of bromine and the protolytic
equilibrium of chlorine(III), this simple rate law represents the
combined effect of the parallel reactions of Br2 and HOBr with
HClO2 and ClO2-. At pH 1.50, the estimated value for ki is
-
Although a large excess of ClO2 over Br2 was applied, the
stopped-flow traces could not be fitted with a single-exponential
function in most cases. Because the complexity of the reaction
prevented the use of a well-defined, uniform rate law, the
reaction orders for the reactants were estimated by using the
initial-rate method. This technique is not suitable for exploring
the details of a complex reactive system, but it can be efficiently
used to establish the basic kinetic features of the reaction. The
kinetic traces were fitted to a combination of exponential
functions or an appropriately selected polynomial function, and
the first derivatives of the fitted curves were calculated at t )
0. The initial absorbance change is almost exclusively due to
the formation of ClO2, and the first derivative is proportional
to the initial rate. It should be emphasized that the mathematical
functions used in these calculations were not derived on the
basis of any specific kinetic model and the parameters obtained
from this fitting procedure cannot be assigned to any part of
the mechanism.
The rate, defined as V ) dA/dt, was very sensitive to the
conditions applied at t ) 0, and it decreased significantly in
the first 50-100 ms of the reaction. Because the reactant
concentrations changed only slightly within this time frame, the
observations strongly suggest the contribution of more than one
step to the overall redox process. These features of the reaction
resulted in relatively large uncertainties in the estimated values
of the initial rates (Vi). Therefore, whenever it was feasible, the
better defined derivatives of the kinetic traces at 25 ms were
used as Vi.
∼2700 M-1 s-1
.
Effect of pH. In the pH 1.00-8.00 region, the initial rate
shows a maximum as a function of pH. For the interpretation
of the results, the following fast preequilibria need to be
considered:
Br2 + H2O h HOBr + Br- + H+
(3)
BrO- + H+ h HOBr
ClO2- + H+ h HClO2
(4)
(5)
In the slightly acidic-neutral pH range, chlorine(III) is present
as ClO2-, while bromine undergoes hydrolysis and is converted
to BrO- when the pH is increased. The hypobromite ion is
practically inert in the redox process, and the decreasing reaction
rate correlates well with the deprotonation of HOBr. These
findings confirm recent results reported by Furman and Mar-
gerum.14 Under acidic conditions (pH <3.0), reaction 4 is shifted
to the right, and the pH dependence of the initial rate may
-
indicate different reactivities between HClO2 and ClO2 and/
or between Br2 and HOBr.
In the presence of excess Br- and at pH <3.0, the hydrolysis
of Br2 is suppressed, Br3 is formed in significant amounts,
-
and the [Br2]/[Br3-] ratio is practically constant (∼1/1 when
[Br-] ) 0.05 M). Thus, any variation in the rate as a function
of pH corresponds to the acid dissociation of chlorous acid. As
indicated by Figure 2, only the ClO2- form of Cl(III) is reactive
in the redox process and the initial rate should reach a limiting
value when the deprotonation of HClO2 is completed by
increasing the pH. On the basis of the above considerations,
At constant pH, the initial rate was proportional to either
[ClO2-] or [Br2] when the concentration of the other reactant
was kept constant. It should be added that the experimentally
accessible concentrations of bromine could be changed by only
(34) Valdes-Aguilera, O.; Boyd, D. W.; Epstein, I. R.; Kustin, K. J. Phys.
Chem. 1986, 90, 6702-6708.

Initial Phase of the Bromine-Chlorite Ion Reaction
Inorganic Chemistry, Vol. 39, No. 20, 2000 4611
Figure 3. Initial rate and bromine concentration as functions of [Br-].
Key: initial rates estimated on the basis of the experimental kinetic
traces (b) and predicted by model C in Table 1 (dashed line); Br2
concentration expressed as the mole fraction of total bromine (solid
line). Vi,25ms ) dA370nm/dt at 25 ms, in s-1; [ClO2-]0 ) 1.0 × 10-2 M;
[Br2]0 ) 5.0 × 10-4 M; pH ) 1.50.
Figure 4. Initial rate as a function of added chlorine dioxide
concentration. Key: initial rates estimated on the basis of the
experimental kinetic traces (b) and predicted by model C in Table 1
(O). Vi,25ms ) dA370nm/dt at 25 ms, in s-1; [ClO2-]0 ) 1.0 × 10-3 M;
[Br2]0 ) 5.0 × 10-4 M; [Br-] ) 0.05 M; pH ) 1.50.
the pH dependence of the initial rate can be expressed as
be assumed that the inhibition involves the reaction of ClO2
with a reactive intermediate which may regenerate the chlorite
ion. When [Br-] is low, this step is inferior to the reaction path
that leads to the completion of the overall process. According
to these considerations, Br- is not involved directly in the
inhibition. To account for the [Br-] dependence, we propose
that the bromide ion increases the kinetic weight of the inhibition
step by suppressing the competing reaction path.
1
Vi ) Vi,lim
(6)
1 + Kp[H+]
where Vi, Vi,lim, and Kp are the initial rate, the limiting initial
-
rate characteristic for the ClO2 form of Cl(III), and the
protonation constant of the chlorite ion, respectively. The
protonation constant obtained by fitting the kinetic data, log Kp
) 1.80 ( 0.04, agrees reasonably well with our value reported
earlier,24 1.72. It should be noted that Vi,lim cannot be determined
experimentally because the hydrolysis of Br2 interferes with the
ClO2--Br2 reaction at higher pH, even in the excess of bromide
ion.
Detection of BrClO2. The formation of this intermediate was
deduced from single-wavelength stopped-flow measurements
by Valdes-Aguilera and co-workers.1 It was assumed that the
nonzero initial absorbance of the traces in the near UV-visible
region was due to BrClO2. The spectrum reported for this species
was very similar to that of ClO2. The maxima of the charac-
teristic spectral bands occurred at the same wavelengths, though
the transient species had a somewhat weaker absorbance.
Time-resolved spectra obtained in the present study are
consistent with steady formation of ClO2, and the extrapolated
small absorbance values at t ) 0 can be interpreted by taking
into account the colored bromine species. In the single-
wavelength stopped-flow measurements, the variation of the
initial absorbance as a function of [Br-] could also be interpreted
Bromide Ion Effect. The bromide ion has a significant
retarding effect on the reaction rate. To some extent, this is due
to the conversion of Br2 into the unreactive Br3-. The initial
rate is proportional to the free bromine concentration, [Br2], in
a large excess of the bromide ion. However, a comparison of
the reaction rate and the speciation as a function of [Br-] reveals
that the formation of the tribromide ion alone does not explain
the noted inhibition. As shown in Figure 3, the initial rate
decreases more sharply than [Br2] at low [Br-]. These observa-
tions strongly suggest that the bromide ion controls not only
the [Br2]/[Br3-] ratio but also the concentrations of HOBr and
-
in terms of the Br2-Br3 equilibrium. Thus, the experimental
data do not confirm the formation of any new absorbing species.
The spectrum of BrClO2 reported previously should be termed
an artifact probably due to the limitations of the equipment used
in that early study. As will be discussed in detail, these findings
do not exclude the possibility that BrClO2 is formed at low
concentration levels and plays an important kinetic role in this
system.
-
other reactive intermediates, such as Br2 and Br, which are
presumably significant in the redox process.
The effect of the bromide ion on the HOBr-chlorite ion
reaction was studied in separate experiments at pH 1.50. As
expected, the initial rate gradually decreased when Br- was
added to the samples in increasing concentrations.
Effect of Chlorine Dioxide. In most kinetic runs, the
absorbance changes became increasingly slower over the course
of the reaction. This autoinhibitive feature of the kinetic traces
was more pronounced when [Br-]0 was increased. The inhibition
is probably due to the formation of chlorine dioxide because
this species is able to efficiently reduce the initial rate in the
presence of excess Br- (Figure 4). It was also confirmed that
the apparent reaction order for [ClO2-] increased when chlorine
dioxide was initially added to the reaction mixture.
The Kinetic Model. The complex pH and concentration
dependencies of the reaction rate require the use of a multistep
kinetic model for the interpretation of the experimental data.
Several models were tested by comparing experimental and
simulated kinetic curves at 370 nm. In these calculations, the
traces were truncated such that the second phase of the overall
process, i.e., the relatively slow Br--ClO2- reaction, could be
omitted. In the absence and presence of added Br-, the traces
were used up to 90 and 60% conversion of Br2, respectively.
The kinetic model was represented by an appropriate differential
equation system which was solved with the GEAR algorithm.28
The absorbance-time profiles were calculated by using the
following molar absorbances (in M-1 cm-1): ClO2, 962; Br2,
133; Br3-, 545; HOBr, 12. These values were determined in
In related experiments, we found that the initial rate was
independent of [ClO2] in the absence of added bromide ion.
There is ample evidence in the literature that chlorine dioxide
and the bromide ion coexist in aqueous solution and direct
reaction does not occur between these species. Therefore, it must
-
separate experiments by recording the spectra of ClO2, ClO2

4612 Inorganic Chemistry, Vol. 39, No. 20, 2000
To´th and Fa´bia´n
Table 1. Kinetic Models for Br2 Oxidation of the Chlorite Ion
rate const valuesa
model B
rate
const
reaction
Br2 + ClO2- ) ClO2 + Br2
no.
R1
log K comment
model A
model C
comment
(4.3 ( 0.4) × 103 (1.7 ( 0.4) × 103 (1.3 ( 0.2) × 103
c
d
c
d
-
-5.93
11.40
1.28
b
k1
k-1
k2
k-2
k3
k-3
k4
k-4
k5
k-5
k6
k-6
k7
k-7
k8
3.7 × 109
1.5 × 109
1.1 × 109
Br2- + ClO2- ) ClO2 + 2Br-
R2
R3
R4
R5
R6
R7
R8
b
(2.9 ( 0.1) × 106 (4.0 ( 0.1) × 106 (4.0 ( 0.1) × 106
1.2 × 10-5
1.5 × 109
7.8 × 107
1.0 × 1010
1.9 × 108
9.7 × 10
1.6 × 10-5
1.5 × 109
7.8 × 107
1.0 × 1010
1.9 × 108
9.7 × 10
1.6 × 10-5
-
Br2 + Br- ) Br3
c
1.5 × 109
ref 36
d
e
d
ref 35
ref 35
c
d
e
d
c
d
c,g
d
7.8 × 107
ClO2- + H+ ) HClO2
1.72
ref 24
1.0 × 1010
1.9 × 108
Br2 ) HOBr + Br- + H+
-8.22
5.04
ref 35
9.7 × 10
1.6 × 1010
1.6 × 1010
1.6 × 1010
1.0 × 1010
9.1 × 104
Br + Br- ) Br2
b
b
b
f
(1.3 ( 0.1) × 1010 1.0 × 1010
-
1.2 × 105
9.1 × 104
1.0 × 1010
4.5 × 10-18
Br + Br ) Br2
27.35
16.37
11.84
1.0 × 1010
1.0 × 1010
4.5 × 10-18
(2.3 ( 0.7) × 108
9.7 × 10-9
4.5 × 10-18
(5.4 ( 0.4) × 109
2.3 × 10-7
Br + ClO2- ) ClO2 + Br-
k-8
k9
k-9/K10
HOBr + HClO2 ) BrClO2 + H2O R9
BrClO2 + ClO2- ) 2ClO2 + Br-
R10
(2.4 ( 0.1) × 105 (1.9 ( 0.1) × 105
3.5 × 10-7
2.8 × 10-7
a The units for the first-, second-, and third-order rate constants are s-1, M-1 s-1, and M-2 s-1, respectively. b Calculated from the redox potentials
listed in Table 2. c This work. d k- ) k+/K. e Estimated value. f Overall equilibrium constant for R9 and R10. g On the basis of eq 10.
Table 2. Standard Redox Potentials of Redox Couples Formed in
the Br2-ClO2 Reaction
concentrations, its contribution to the spectral effects is always
negligible. The value of k3 was known from earlier studies,36
while the protolytic equilibrium between HClO2 and ClO2- was
assumed to be diffusion controlled (k4 ) 1.0 × 1010 M-1 s-1).
With these rate constants kept at fixed values, the calculations
gave k1 ) (1.4 ( 0.3) × 103 M-1 s-1 and k2 ) (4.1 ( 0.1) ×
-
reaction
E° (V) ref
reaction
E° (V) ref
ClO2 + e- h ClO2 +0.936 37 1/2Br2 + e- h Br- +1.098 38
-
Br2 + e- h Br2
+0.58 37 Br + e- h Br-
+1.92 37
-
Br2- + e- h 2 Br- +1.62 37
106 M-1 s-1
.
-
The simplified model does not account for the noted [Br-]
dependence of the reaction rate (Figure 3). Upon a decrease in
the bromide ion concentration, the hydrolysis of bromine, R5,
solutions, and a series of Br2/Br3 solutions in the stopped-
flow instrument. It was assumed that the absorbance was a linear
combination of the concentrations of the colored species, and
the speciation in the samples was calculated on the basis of the
equilibrium constants listed in Table 1. At 370 nm, only ClO2,
Br3-, and Br2 have measurable contributions to the absorbance.
The initial absorbance is determined by the two bromine species,
and the absorbance of chlorine dioxide becomes dominant at
longer reaction times.
-
is shifted toward HOBr formation, and the Br2 radical
dissociates into Br- and Br in a reversible step, R6.39,40 Both
HOBr and Br are strong oxidants, which may open new reaction
paths in the redox process. We included the corresponding steps
in the kinetic model and tested how separate reactions of the
chlorite ion with these oxidants would improve the overall fit
of the data.
The kinetic model postulates a series of reversible reaction
steps (Table 1). The equilibrium constants for these reactions
either were available from direct equilibrium studies,24,35 for
R4 and R5, or were calculated from the standard redox potentials
of the redox couples listed in Table 2. The value of KR3 was
determined in the present study (see the Experimental Section).
In the final calculations, the equilibrium constants were fixed
at their known values. The reverse reaction steps were included
by calculating their rate constants as the ratios of the corre-
sponding forward rate constants and equilibrium constants.
Kinetic traces obtained at various reactant concentrations and
pHs (ca. 3800 data points in 11 curves) were fitted simulta-
neously, and the forward rate constants were estimated using a
nonlinear least-squares algorithm.28
Model A (Table 1) implies that the R6, R8 sequence
efficiently competes with R2. Step R7 is a dead end with respect
to this path. However, Br is always present at very low
concentration levels, and this radical-radical type of recombi-
nation is always inferior compared to R8. The [Br-] dependence
of the overall rate can be explained by considering the
competition between the forward steps of R6 and R8. In the
absence of the bromide ion, Br may react exclusively with
ClO2-. When the concentration of Br- is increased, the
recombination of Br2-, R6, becomes faster and the steady-state
concentration of the Br radical decreases. Consequently, the
contribution of R8 to the oxidation process becomes negligible
by increasing [Br-].
In the presence of excess bromide ion, a limited kinetic model
using R1-R4 is sufficient to explain the observations. The initial
The agreement between experimental and calculated data was
substantially improved when the Br path was included in the
model. The results of the calculations are listed in Table 1. As
expected, the model predicts that the Br radical is involved in
extremely fast reactions. The value obtained for k6 is consistent
with the rough estimate, ∼1010 M-1 s-1, derived for the same
rate constant from pulse radiolytic experiments.39 The reactions
-
electron transfer between Br2 and ClO2 is not favored
thermodynamically, but the second step carries the reduction
of bromine to completion. On the basis of earlier reports, the
molar absorbance of Br2 is about 9500 M-1 cm-1 at 370
-
nm.39,40 Because this species is present at very low steady-state
(35) Beckwith, R. C.; Wang, T. X.; Margerum, D. W. Inorg. Chem. 1996,
35, 995-1000.
(38) Bratsch, S. G. J. Phys. Ref. Data 1989, 18, 1-21.
(39) Zehavi, D.; Rabani, J. J. Phys. Chem. 1972, 76, 312-319.
(40) Stevenson, K. L.; Knorr, D. W.; Horva´th, A. Inorg. Chem. 1996, 35,
835-839.
(36) Ruasse, M.; Aubard, J.; Galland, B.; Adenier, A. J. Phys. Chem. 1986,
90, 4382-4388.
(37) Stanbury, D. M. AdV. Inorg. Chem. 1989, 33, 69-138.

Initial Phase of the Bromine-Chlorite Ion Reaction
Inorganic Chemistry, Vol. 39, No. 20, 2000 4613
of simple neutral radicals are expected to be diffusion controlled,
and the value obtained for k8 seems to be acceptable also.
In model B, the bromide ion affects the reaction by controlling
the concentration of HOBr via R5. In a recent study, the
The calculations confirm that the inclusion of the HOBr (by
using eq 10) or the Br path leads to equivalent kinetic models.
This strongly suggests that the pH and [Br-] dependencies of
the corresponding reaction rates are very similar. However, it
is very likely that the oxidations of the chlorite ion by Br and
by HOBr occur simultaneously and that the alternative models
represent the limiting cases of the same mechanism. Therefore,
we combined models A and B and attempted to fit all relevant
kinetic data simultaneously. These calculations gave an unre-
alistically large value for k6, indicating that the experimental
data do not carry sufficient kinetic information for R6. When
this rate constant was fixed at 1010 M-1 s-1, k1, k2, k8, and k9
could be estimated with reasonable precision (model C, Table
1). The values of the fitted rate constants changed by 25% at
most (k1) when k6 was varied from 5 × 109 to 1.5 × 1010 M-1
s-1. This range was selected by considering an earlier estimate39
for k6. The calculations revealed that the oxidation of the chlorite
ion by HOBr was superior to the Br path, although the latter
process could not be completely neglected.
Available literature data for the individual reaction steps
support the results presented here. The reverse rate constant
obtained for R1 is in excellent agreement with the value reported
earlier,41 1.2 × 109 M-1 s-1. It follows that, in agreement with
our results, k1 needs to be on the order of 103 M-1 s-1. This
value is about 2 orders of magnitude larger than that predicted
by the Marcus theory. Such deviations from the outer-sphere
electron-transfer model were found in a few redox reactions
between simple main-group compounds. It was proposed that
some sort of overlap mechanism, which is very similar to the
inner-sphere mechanism in coordination chemistry, is operative
in these systems.42
-
oxidation of ClO2 by HOBr was found to be first order with
respect to both reactants.14 The proposed mechanism postulates
the formation of a weak adduct between the reactants,
HOBrOClO-, which is converted to BrClO2 in a subsequent
acid-catalyzed step. The reaction is completed by fast reactions
of the latter intermediate with ClO2- and OH-. This mechanism
is consistent with the experimental observations in the slightly
acidic-neutral pH region.14 When the ClO2--HOBr reaction
was incorporated into our model, the fit of the data did not
improve because this step is too slow to affect the overall rate
under the acidic conditions applied in the present study.
However, an additional reaction path may exist between HOBr
and the protonated form of chlorine(III). The corresponding
reaction steps are R9 and R10 in model B. These considerations
imply that the formation of BrClO2 is much faster from HClO2
than from ClO2-. It seems reasonable to assume that BrClO2 is
extremely reactive and is present at very low steady-state
concentrations. This would also explain why the formation of
this species could not be detected experimentally.
The properties of the BrClO2 intermediate are not known in
aqueous solution, and appropriate data are not available to
estimate even the approximate magnitudes of the equilibrium
and rate constants for R9 and R10. Only an overall equilibrium
constant, KR9,R10 ) 6.9 × 1011, can be calculated for the
combination of the two steps
HOBr + HClO2 + ClO2- ) Br- + 2ClO2 + H2O (7)
On the basis of pulse radiolytic experiments at pH 6.7, a
value, 2.0 × 107 M-1 s-1, ∼5 times larger than that obtained
here was reported for k2.43 Although the experimental details
are not given in that paper, it is very likely that a great part of
the noted deviation is due to the differences in the experimental
conditions and methods. The results are consistent in that the
rate of R2 is far below the diffusion-controlled limit. Electro-
static repulsion between the uniformly charged reactants may
somewhat retard this step, but other factors must have a more
significant effect on the reaction rate. For example, the dis-
To include steps R9 and R10 in the model, a rate equation was
derived for this sequence by using a steady-state approach for
BrClO2:
d[HOBr]
)
dt
-
-k9k10[HOBr][HClO2][ClO2 ] + k-9k-10[ClO2]2[Br-]
(8)
-
k-9 + k10[ClO2 ]
-
sociation of the Br-Br bond of Br2 may hinder the electron-
transfer process.
While the reverse path of the R9, R10 sequence is negligible,
the reverse step of R9 can be fast. The concentration depend-
encies of the rate law are determined by the relative rate of this
reaction compared to that of the forward step of R10. If R9 is
a fast preequilibrium compared to R10, i.e., k-9 . k10[ClO2-],
the forward and reverse rates for the combined reaction can be
given as
To test the validity of the proposed model, the concentration
dependencies of the initial rate were calculated for the conditions
shown in Figures 2-4. The model predicts the same trends as
observed experimentally though there are deviations between
the Vi values obtained from the experimental kinetic traces and
those calculated on the basis of the model. This reflects the
noted uncertainties associated with the estimation of Vi. Direct
comparison of the experimental and calculated kinetic curves
offers a better way to validate the model. In this case,
approximations are not involved and entire kinetic profiles are
compared. The reasonably good agreement between measured
and calculated traces (Figure 5) is a clear indication that the
proposed model gives a proper interpretation of the kinetic
features of the Br2-ClO2- reaction under the conditions studied.
Recently, some arguments regarding the aqueous-phase
structure of BrClO2 were presented by Furman and Margerum.14
-
ν+ ) k10K9[HOBr][HClO2][ClO2 ]
ν- ) k-10[ClO2]2[Br-] (9)
-
Alternatively, if k-9 , k10[ClO2
]
k-9 [ClO2]2[Br-]
ν+ ) k9[HOBr][HClO2]
ν- )
(10)
-
K10
[ClO2 ]
Both sets of rate expressions were used in the calculations by
fitting k1, k2, and k10K9 or k9. With eq 9, the fit was less
satisfactory, and this option was rejected in further calculations.
The results obtained with eq 10 are shown in Table 1 (model
B).
(41) Mialocq, J. C.; Barat, F.; Gilles, L.; Hickel, B.; Lesigne, B. J. Phys.
Chem. 1973, 77, 742-749.
(42) Stanbury, D. M.; Martinez, R.; Tseng, E.; Miller, C. E. Inorg. Chem.
1988, 27, 4277-4280.
(43) Huie, R. E.; Neta, P. J. Phys. Chem. 1986, 90, 1193-1198.

4614 Inorganic Chemistry, Vol. 39, No. 20, 2000
To´th and Fa´bia´n
Scheme 1
preequilibrium which precedes the rate-determining step. Ac-
cording to Scheme 1, BrClO2 most likely has a Y structure in
which the bromine and the two oxygen atoms are connected to
the central Cl atom. Nevertheless, other mechanisms leading
to other connectivities, for example, to Br-O-Cl-O, cannot
be excluded.
In summary, the results presented here confirm that, under
acidic conditions, the oxidation of the chlorite ion occurs in
competing parallel redox steps in the Br2-ClO2- reaction. The
concentration ratios of the oxidants, Br2-, Br, and HOBr, formed
after the initiation step, as well as the relative rates of the parallel
reactions, are controlled by the bromide ion concentration and
pH. The proposed model may lead to a better understanding of
the mechanistic details of complex reactive systems that contain
bromine and the chlorite ion.
Figure 5. Experimental (open circles) and fitted (solid lines) kinetic
traces for the bromine-chlorite ion reaction. The fitted traces were
calculated on the basis of model C in Table 1. a: [ClO2-]0 ) 3.0 ×
10-3 M, [Br2]0 ) 1.0 × 10-4 M, [Br-] ) 0.025 M, pH ) 1.50 (unit
time: 10 s). b: [ClO2-]0 ) 7.5 × 10-3 M, [Br2]0 ) 1.0 × 10-4 M, pH
) 1.50 (2 s). c: [ClO2-]0 ) 5.0 × 10-3 M, [Br2]0 ) 5.0 × 10-4 M,
[Br-] ) 0.05 M, pH ) 1.40 (2 s). d: [ClO2-]0 ) 5.0 × 10-3 M, [Br2]0
) 5.0 × 10-4 M, [Br-] ) 0.05 M, pH ) 1.80 (2 s).
We agree with these authors that to outline the exact connectivity
of the atoms is an elusive goal and that only indirect information
is available to deduce the properties of this species. Our
calculations confirmed that protonation of the chlorite ion
promotes the formation of BrClO2. However, this effect cannot
be explained by the concept of general-acid catalysis proposed
by Furman and Margerum.14 Their kinetic data were obtained
from the pH 4.5-9.5 region, where HClO2 is a minor species
and its reactions could be neglected. In that mechanism, the
acid-assisted step was necessary to explain how the precursor
complex of the reactants was transformed into BrClO2. How-
ever, a mechanistic changeover may occur in the reaction when
the pH is decreased. In acidic solution, chlorous acid is a major
species which can open a direct path to the formation of BrClO2.
We propose that HClO2 and HOBr form a precursor complex
that is stabilized by a hydrogen bond and a halogen-halogen
bond, as shown in Scheme 1. Thus, BrClO2 may form via fast
rearrangement of the adduct and subsequent elimination of a
water molecule. On the basis of pressure-dependent studies, the
formation of a very similar precursor complex was suggested
to occur in the initial phase of the BrO3--I- reaction.44 In the
Acknowledgment. We are indebted to Prof. Gilbert Gordon
for helpful discussions. This work was supported by NATO
Linkage Grant CRG.LG 973337 and by Grants OTKA T 029568
and M 028244 from the Hungarian National Research Founda-
tion.
Supporting Information Available: A textual description of
preliminary studies on the HOBr-chlorite ion reaction under acidic
conditions and figures showing time-resolved spectral changes in the
presence of added bromide ion, initial rate as a function of [ClO2-] in
the absence and presence of added ClO2 and Br-, pH dependence of
the initial rate in the pH 1.0-8.0 range, effect of the bromide ion on
the initial rate of the HOBr-chlorite ion reaction, time-resolved rapid-
scan spectra recorded in the first 130 ms of the reaction, and forward
and reverse rates of the redox steps proposed in model C as a function
of time in the absence and presence of added bromide ion. This material
is available free of charge via the Internet at http://pubs.acs.org.
-
model proposed here, the protonation of ClO2 is a fast
(44) Fa´bia´n, I.; van Eldik, R. Int. J. Chem. Kinet. 1995, 27, 491-498.
IC990329P