Reinvestigation of the kinetics of reduction of bromite by hexacyanoferrate(II) in slightly basic solution

Article abstract of DOI:10.1039/b308878b

The reaction BrO₂^- + 4 Fe(CN)₆^4- + 2H₂O → Br^- + 4Fe(CN)₆^3- + 4OH^- has been studied by spectrophotometry at 30, 40 and 50°C and both with equivalent amounts of reactants and with an excess of bromite. It follows the kinetic expression dξ/dt = k_obs[BrO₂^-] [Fe(CN)₆^4-]² with k_obs = 8.2 M^-2 s^-1 at 25°C, ΔH^≠ = 66 kJ mol^-1 and ΔS^≠ = -121.7 J K^-1 mol^-1. The proposed mechanism is a two-stage process, the first, rate-determining stage being reduction of bromite to hypobromous acid, the second further reduction to bromide. Either stage consists of two bimolecular reactions. The major contribution to the energy barriers comes from electrostatic repulsion between negative ions.

Full text of DOI:10.1039/b308878b

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Reinvestigation of the kinetics of reduction of bromite by
hexacyanoferrate(II) in slightly basic solution
Hans E. Lundager Madsen
Kemisk Institut, KVL, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark.
E-mail: helm@kvl.dk
Received 28th July 2003, Accepted 13th October 2003
First published as an Advance Article on the web 23rd October 2003
The reaction
BrO2Ϫ ϩ 4Fe(CN)64Ϫ ϩ 2H2O
BrϪ ϩ 4Fe(CN)63Ϫ ϩ 4OHϪ
has been studied by spectrophotometry at 30, 40 and 50 ЊC and both with equivalent amounts of reactants and with
an excess of bromite. It follows the kinetic expression
with kobs = 8.2 MϪ2 sϪ1 at 25 ЊC, ∆H≠ = 66 kJ molϪ1 and ∆S≠ = Ϫ121.7 J KϪ1 molϪ1. The proposed mechanism is a two-
stage process, the first, rate-determining stage being reduction of bromite to hypobromous acid, the second further
reduction to bromide. Either stage consists of two bimolecular reactions. The major contribution to the energy
barriers comes from electrostatic repulsion between negative ions.
in ice-cooled 0.3 M NaOH. A fresh solution was prepared daily,
stored at 0 ЊC and standardized by adding an excess of arsen-
ic() oxide solution and titrating the excess with a solution of
Introduction
Ϫ
Many years ago we studied the reduction of BrO2 by
4Ϫ
1
Fe(CN)6
:
iodine in potassium iodide. Potassium hexacyanoferrate()
stock solution, 0.01 M, also contained 0.2 g of sodium
carbonate LϪ1 and was stored in a dark bottle. The solutions for
the kinetic experiments were prepared at 0 ЊC and contained
0.225 mol of NaHCO3 LϪ1 as well as a small amount of acetic
acid to adjust the pH to 8.9. The total volume of solution for
each experiment was 200 mL.
Since at that time, a recording spectrophotometer with
thermostatted cell compartment was not available, we had to
take samples from the reaction mixture at selected time inter-
vals for absorbance measurements. The flask with solution was
placed in the thermostat immediately after mixing, and each
sample was cooled in ice to slow down the reaction and then
measured as soon as possible.
BrO2Ϫ ϩ 4Fe(CN)64Ϫ ϩ 2H2O
BrϪ ϩ 4Fe(CN)63Ϫ ϩ 4OHϪ
with the aim of finding a reliable method for the separate
determination of hypobromite and bromite in solutions of elec-
tron- and gamma-irradiated solid bromates.2 It was demon-
strated that the reduction of the former is sufficiently fast to
permit its use in a potentiometric titration, whereas the latter
reacts so slowly that it will not interfere under normal con-
ditions. Of the reacting species Fe(CN)63Ϫ is more strongly col-
oured than the others, so spectrophotometry is a convenient
method for measuring the rate of reaction. It was stated in the
paper on the analytical method that the reaction with bromite is
first order in either reactant and thus second order overall.
However, a recent detailed analysis of the data showed this to
be incorrect. The results of the renewed investigation are
presented in the present paper.
Whereas the chemical properties of the hexacyanoferrates
are well known, not much information on the behaviour of
bromite ion in aqueous solution is found in the literature, and
statements concerning its stability relative to other oxoanions
are often unreliable. Recently, a few studies on the reactivity of
bromite have been published by Margerum and coworkers.3,4 In
the former paper they also give a procedure for preparation of
barium bromite and a salt mixture containing sodium bromite,
but no hypobromite. The latter is removed by reduction with
sulfite, which reacts orders of magnitude faster with hypobro-
mite5 than with bromite.6 An earlier method is reduction with
ammonia,7,8 but this substance also reacts fairly quickly with
bromite, thus reducing the yield.1
The measurements were carried out at 423 nm, the absorb-
ance maximum of Fe(CN)63Ϫ, on a Beckman DU spectro-
photometer model G4700. A 1.00 mM solution of K4Fe(CN)6
3Ϫ
was used as reference, and a standard curve of Fe(CN)6 had
previously been recorded, yielding A423 = 1000 MϪ1 cmϪ1
.
Results
Experiments with equivalent concentrations of bromite and
hexacyanoferrate() were carried out at 30, 40 and 50 ЊC, and
one experiment with a 10-fold excess of bromite was carried
out at 50 ЊC. The first sample was taken 10 min after start and
subsequent samples at intervals of 10 min up to 1 h, then
at intervals of 15 min up to 2 h. The experiment with excess
bromite was terminated after 50 min.
As already stated above, the assumption of second-order
kinetics turned out to be wrong, because the two experiments at
50 ЊC do not yield the same rate constant; the discrepancy
is significantly larger than expected from experimental
uncertainty. Instead, we try the rate expression
Experimental
The experimental parameters are given in Table 1. Sodium
bromite stock solution was prepared by dissolving crystals of
NaBrO2ؒ3H2O, obtained as a gift from the Société d’Etudes
Chimiques pour l’Industrie et l’Agriculture, Paris (SECPIA),9
(1)
T h i s j o u r n a l i s © T h e R o y a l S o c i e t y o f C h e m i s t r y 2 0 0 3
D a l t o n T r a n s . , 2 0 0 3 , 4 6 5 1 – 4 6 5 3
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Table 1 Experimental parameters and results
T/ЊC
[Fe(CN)6
25
30
1.00
0.25
13.5 0.4
13.0
40
1.00
0.25
28.3 0.7
30.8
50
1.00
0.25
71.1 0.8
69.5
50
1.00
2.50
71
69.5
4Ϫ
]t = 0/mM
Ϫ
[BrO2
]
t = 0/mM
kobs/MϪ2 sϪ1
kfit/MϪ2 sϪ1
4
8.2 0.6
The standard deviation of kfit is 7%.
where ξ is the usual degree of advancement. In the case of
equivalent concentrations we have
sampling and measurement. It took some time to cool the
samples, and they were partly reheated when placed in the
spectrophotometer, resulting in a small progress of the reaction.
The relative error arising from this is more important in the
early stage of an experiment, where reactant concentrations are
highest, and it increases with decreasing temperature as seen
from both Fig. 1 and the standard deviations (on a relative
scale) of kobs (Table 1).
(2)
which may be integrated to yield
Discussion
(3)
We propose the following mechanism:
Fe(CN)64Ϫ ϩ BrO2
[Fe(CN)6ؒBrO2]5Ϫ
(I)
Ϫ
a being the initial concentration of hexacyanoferrate(). With
nonequivalent concentrations we have [Fe(CN)64Ϫ] = a Ϫ 4ξ and
[BrO2Ϫ] = b Ϫ ξ, and thus
[Fe(CN)6ؒBrO2]5Ϫ ϩ Fe(CN)64Ϫ ϩ 2H2O
2Fe(CN)63Ϫ ϩ HBrO ϩ 3OHϪ (II)
(4)
Fe(CN)64Ϫ ϩ HBrO
[Fe(CN)6ؒHBrO]4Ϫ
(III)
4Ϫ
[Fe(CN)6ؒHBrO]4Ϫ ϩ Fe(CN)6
On integration this yields
2Fe(CN)63Ϫ ϩ BrϪ ϩ OHϪ (IV)
(5)
Both the hexacyanoferrate() ion and the bromite ion are
very weak bases and are not protonated to any appreciable
extent at pH 8.9. On the other hand, hypobromous acid is a
very weak acid with pKa = 8.8 at an ionic strength of 0.5,5 so
a substantial fraction is protonated at pH 8.9 at the present
ionic strength of about 0.25, where pKa is higher. It is therefore
reasonable to take the undissociated acid as reactant in reaction
(III).
A plot of the left side of eqns. (3) or (5) vs. time should thus
yield a straight line with slope kobs. Fig. 1 shows the results.
We already know that reactions (III) and (IV) are fast,1
whence reactions (I) and (II) are likely to be rate-determining.
The overall reaction rate is the rate of disappearance of
bromite, which equals the rate of formation of hypobromous
acid by reaction (II):
(6)
where A and B are short-hand notations for hexacyano-
ferrate() and bromite, respectively. We further have for the
ion-pair hexacyanoferrate()–bromite
Fig. 1 Plots of third-order kinetics. The ordinate, indicated f(ξ), is .the
left-hand side of eqn. (3) in the experiments with equivalent
concentrations and the left-hand side of eqn. (5) in the experiment with
excess of bromite.
(7)
We may conclude that the reduction of bromite by hexa-
cyanoferrate() is a third-order reaction, being first order with
respect to the former and second order with respect to the latter.
The Arrhenius plot yields the activation energy Ea = 68 4 kJ
Using the stationary-state approximation for AB yields
molϪ1 and the frequency factor A = 7.8 × 1012
M
Ϫ2 sϪ1, whereas
(8)
the transition state formalism, plotting ln(kobs/T) against 1/T,
yields ∆H≠ = 66 4 kJ molϪ1 and ∆S≠ = Ϫ121.7 0.6 J KϪ1
molϪ1
Table 1 gives the values of kobs and the fitted values kfit from
these plots.
which, when inserted in eqn. (6), results in
A close inspection of Fig. 1 reveals that the regression lines
for the experiments at 30 and 40 ЊC do not pass precisely
through the origin. This is a consequence of the method of
(9)
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This is identical with the observed kinetics, provided that
ϪI ӷ kII[A], and we have kobs = kIkII/kϪI.
However, a reaction between two negative ions, of which at
least one has a high charge, does not seem very probable,
whence a theoretical estimate of the kinetic parameters should
be attempted. The necessary expressions of rate constants,
based on theories of Debye10 and Fuoss,11 are found in a clas-
sical paper by Eigen.12 For the rate constant of a diffusion-
controlled bimolecular reaction between two ions A and B in
solution, represented by kI and kII, we have
When we insert these values in eqns. (10)–(13) together with
k
the relative permittivity of water at 25 ЊC, Kr = 78.54, we find
EaЈ(I) = 13.2 kJ molϪ1, kI = 2.06 × 108 MϪ1 sϪ1 and EaЈ(II) =
51.4 kJ molϪ1, kII = 149.2 MϪ1 sϪ1
There is no significant electrostatic contribution to the
activation energy related to kϪI, because the exponential in
the denominator of eqn. (12) is Ӷ 1. We have from eqn. (12)
k
ϪI = 1.077 × 1011 sϪ1
The sum of the two activation energies is 64.6 kJ molϪ1, to
which we should add a contribution from the dependence of
diffusion coefficients on temperature. This may be estimated
from the temperature dependence of ionic conductivities of
(10)
4Ϫ 13
D
Fe(CN)6
,
which yields Ea = 13.8 kJ molϪ1; it enters only
where
once, because two of the factors DA ϩ DB cancel as seen from
eqns. (10) and (12). We note that the condition kϪI ӷ kII[A] for
third-order kinetics (eqn. (9)) is fulfilled.
(11)
The resulting estimated activation energy and rate constant
are thus Ea = 78.4 kJ molϪ1 and kcalc = 0.285 MϪ2 sϪ1
Each z denotes the charge in units of the electronic charge,
each D the diffusion coefficient and each r the radius of the ion,
and Kr is the relative dielectric constant of the solution (Eigen
uses c.g.s. units, whence his expression of Z is slightly different).
Similarly, the rate constant kϪI is given by
The former value is significantly higher and the latter signifi-
cantly lower than the experimental values. However, the theor-
etical values are highly sensitive to the choice of ionic radii. For
instance, by increasing the radii of the hexacyanoferrate() ion
and the hexacyanoferrate()-bromite ion pair by as little as
15%, perfect agreement between theory and experiment is
obtained.
A negative activation entropy is typical of second- or higher-
order reactions between ions which are not strongly hydrated.
The value found in the present study is in line with values for
other reactions between negative ions in aqueous solution.14
(12)
For two positive or two negative ions the exponential in the
denominator of eqn. (10) is ӷ 1, and so the contribution from
electrostatic interactions to the activation energy is
Conclusion
The reduction of bromite by hexacyanoferrate() is a third-
order reaction in two stages, of which the first, being rate-
determining, is the reduction of bromite to hypobromous acid,
and the second and much faster, is the further reduction to
bromide. The first stage involves two bimolecular reactions,
either one between two negative ions, which means that electro-
static repulsion is the main contribution to energy barriers. This
also explains the much faster reduction of hypobromite: Due to
the low dissociation constant of hypobromous acid, the electro-
static energy barrier is absent in the first elementary process,
and in the second it is reduced by 20%. This alone would cause
an increase in reaction rate by more than a factor of 104 com-
pared to the reduction of bromite, provided that the mechanism
proposed above is correct.
(13)
The diffusion coefficients may be obtained from the ionic
conductivities, using the Nernst–Einstein equation
(14)
For Fe(CN)64Ϫ we have13 λ = 0.0444 S m2 molϪ1, which yields
D = 0.739 × 10Ϫ9 m2 sϪ1. The value of λ for the bromite ion is
unknown, but a reasonable guess on the basis of the values for
the oxoions of Cl and for BrO3Ϫ is λ = 0.0045 S m2 molϪ1, which
gives D = 1.198 × 10Ϫ9 m2 sϪ1
.
For the ionic radii we have several choices, but to avoid the
complication of using different values in different expressions,
we shall use the hydrodynamic radii calculated from the Stokes–
Einstein equation
References
1 T. Andersen and H. E. Lundager Madsen, Anal. Chem., 1965, 37,
49.
2 T. Andersen, H. E. Lundager Madsen and K. Olesen, Trans.
Faraday Soc., 1966, 62, 2409.
3 L. Wang, J. S. Nicoson, K. E. Huff Hartz, J. S. Francisco and
D. W. Margerum, Inorg. Chem., 2002, 41, 108.
(15)
4 J. S. Nicoson, L. Wang, R. H. Becker, K. E. Huff Hartz, C. E.
Muller and D. W. Margerum, Inorg. Chem., 2002, 41, 2975.
5 R. C. Troy and D. W. Margerum, Inorg. Chem., 1991, 30, 3538.
6 C. L. Lee and M. W. Lister, Can. J. Chem., 1979, 57, 1524.
7 J. Clarens, C. R. Acad. Sci, 1913, 156, 1998.
8 M. H. Hashmi and A. A. Ayaz, Anal. Chem., 1963, 35, 908.
9 I. Meybeck, I. Leclerc and R. Kircher, Ger. Pat., 1,069,123 1959
(to SECPIA).
10 P. Debye, Trans. Electrochem. Soc., 1942, 82, 265.
11 R. M. Fuoss, J. Am. Chem. Soc., 1958, 80, 5059.
12 M. Eigen, Z. Elektrochem., 1960, 64, 115.
13 Landolt-Börnstein, Zahlenwerte und Funktionen, 6. Aufl., II. Band,
7. Teil, Springer, Berlin, 1960, pp. 259, 261.
where η, the dynamic viscosity of water at 25 ЊC, equals
0.8903 mPa s. This yields
Fe(CN)64Ϫ: r = 3.32 × 10Ϫ10 m
BrO2Ϫ: r = 2.05 × 10Ϫ10 m
We also need the radius and the diffusion coefficient of the
ion pair of hexacyanoferrate() and bromite. We assume that
the two ions are spherical and then add the volumes calculated
from the above radii. If we further assume that the ion pair is
also spherical, we find its radius r = 3.56 × 10Ϫ10 m. Finally, we
calculate its diffusion coefficient from eqn. (15): D = 0.689 ×
14 A. A. Frost and R. G. Pearson, Kinetics and Mechanism, Wiley,
New York, 2nd edn., 1961, p. 144.
10Ϫ9 m2 sϪ1
.
D a l t o n T r a n s . , 2 0 0 3 , 4 6 5 1 – 4 6 5 3
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