Compatible Mechanism for a Simultaneous Description of the Roebuck, Dushman, and Iodate-Arsenous Acid Reactions in an Acidic Medium

Article abstract of DOI:10.1021/acs.inorgchem.5b02513

The iodine-arsenous acid (Roebuck), iodide-iodate (Dushman), and iodate-arsenous acid reactions have been studied simultaneously by a stopped-flow technique by monitoring the absorbance-time profiles at the isosbestic point of the I₂/I₃^- system (468 nm). Using the well-accepted rate coefficients of iodine hydrolysis, we have proven that iodine is the kinetically active species of the iodine-arsenous acid reaction. Strong iodide inhibition of this system is explained by a rapidly established equilibrium between iodine and arsenous acid to produce an iodide ion, a hydrogen ion, and a short-lived intermediate H₂AsO₃I, which is shifted far to the left. Taking into consideration the generally accepted kinetic model of the Dushman reaction where I₂O₂ plays a key role to account for all of the most important observations in this subsystem and a sequence of simple formal oxygen-transfer reactions between arsenous acid and iodic acid as well as iodous acid and hypoiodous acid, we propose a 13-step comprehensive kinetic model, including seven rapidly established equilibria with only six fitted parameters, that is able to explain all of the most important characteristics of the kinetic curves of all of the title systems both individually and simultaneously.

Full text of DOI:10.1021/acs.inorgchem.5b02513

Article
pubs.acs.org/IC
Compatible Mechanism for a Simultaneous Description of the
Roebuck, Dushman, and Iodate−Arsenous Acid Reactions in an
Acidic Medium
́ ́ ́
Laszlo Valkai and Attila K. Horvath*
́ ́
́ ́ ́
Department of Inorganic Chemistry, University of Pecs, Ifjusag utja 6, H-7624 Pecs, Hungary
ABSTRACT: The iodine−arsenous acid (Roebuck), iodide−
iodate (Dushman), and iodate−arsenous acid reactions have
been studied simultaneously by a stopped-flow technique by
monitoring the absorbance−time profiles at the isosbestic point
−
of the I /I system (468 nm). Using the well-accepted rate
2
3
coefficients of iodine hydrolysis, we have proven that iodine is
the kinetically active species of the iodine−arsenous acid
reaction. Strong iodide inhibition of this system is explained
by a rapidly established equilibrium between iodine and
arsenous acid to produce an iodide ion, a hydrogen ion, and a
short-lived intermediate H AsO I, which is shifted far to the left.
2
3
Taking into consideration the generally accepted kinetic model
of the Dushman reaction where I O plays a key role to account
2
2
for all of the most important observations in this subsystem and
a sequence of simple formal oxygen-transfer reactions between arsenous acid and iodic acid as well as iodous acid and
hypoiodous acid, we propose a 13-step comprehensive kinetic model, including seven rapidly established equilibria with only six
fitted parameters, that is able to explain all of the most important characteristics of the kinetic curves of all of the title systems
both individually and simultaneously.
12,13
9
INTRODUCTION
ion.
Our very recent study has just provided experimental
■
evidence that, although stock iodate solutions are usually not
free from iodide contamination, mainly the direct process is
responsible for initiation of the reaction, in agreement with an
The iodate−arsenous acid reaction has been frequently used as
1
,2
a tool to study buoyancy-driven convection, Marangoni
3
4
instability, convective dynamics in a modulated gravity field,
and other spatiotemporal phenomena connected to its clock
feature and front propagation.
because it starts with a slow direct overall reaction between the
reactants to produce an iodide ion
1
4
earlier study by Eggert and Scharnow. Furthermore,
11
5
−8
Roebuck, in his pioneering work on the kinetics of the
iodine−arsenous acid reaction, proposed that the reactive
species in the aqueous iodine solution is HOI. This assumption
The kinetic model is simple
9
was strongly challenged by Liebhafsky, who interpreted his
−
−
3
H AsO + IO → 3H AsO + I
(1)
15,16
3
3
3
3
4
results in terms of the hydrates of iodine.
Later Pendlebury
17
and Smith found that indeed iodine is the kinetically active
followed by the iodide−iodate process often referred to as the
Dushman reaction.
10
species that attacks arsenous acid, and this was later confirmed
18
by Patil and Rewatkar. It is generally well-known that an
equilibrium between iodine and hypoiodous acid is established
relatively rapidly; therefore, it is not straightforward at all which
of these species is kinetically more active to react with arsenous
acid. In principle, both possibilities are kinetically conceivable.
Therefore, the kinetics of iodine hydrolysis appears to be a
crucial process in comprehensively describing the temporal
behavior of the title systems. The hydrolysis constant of iodine
has been thoroughly studied by several independent research
groups for more than a century and was established to be (2−
I− + IO + 6H → 3I + 3H O
−
+
5
(2)
3
2
2
Iodine produced in this way is, however, removed by the
1
1
iodine−arsenous acid reaction, as discovered by Roebuck, to
reestablish an iodide ion that eventually closes the autocatalytic
cycle.
−
+
H AsO + I + H O → H AsO + 2I + 2H
(3)
3
3
2
2
3
4
Even though this kinetic model seems to be relatively simple
and all of these individual reactions are long known, it is
interesting to note that the quantitative pictures of the
component reactions are still in dispute. For example, up to
now, it was a general belief that there is no direct reaction
between iodate and arsenous acid, and the reaction is
supposedly initiated by the iodide impurity of an iodate
6
) × 10− M .
13
2
19−23
The kinetics of iodine hydrolysis was
investigated by two independent research groups by means of
Received: October 31, 2015
Published: February 3, 2016
©
2016 American Chemical Society
1595
DOI: 10.1021/acs.inorgchem.5b02513
Inorg. Chem. 2016, 55, 1595−1603

Inorganic Chemistry
Article
2
4,25
26
temperature-jump studies.
Later Furrow established the
case, the ionic strength was controlled by the addition of sodium
perchlorate.
+
9
−
rate law d[I ]/dt = 0.0018[I ]/[H ] − 3.6 × 10 [HOI][I ],
which was confirmed indirectly by Schmitz. All of these
studies clearly support the equilibrium constant of iodine
hydrolysis to be 5.4 × 10
completeness, it should also be mentioned that some earlier
works reported a significantly higher, but seemingly unreliable,
2
2
27
Instrumentation. Spectrophotometric measurements were carried
out by a Zeiss S600 diode-array spectrophotometer equipped with a
thermostated cell holder. The kinetic curves were recorded by a SX20
diode-array stopped-flow spectrophotometer manufactured by Applied
Photophysics. As we shall see later, the kinetic runs last for several
seconds, so a dead-time correction (found to be less than 1.0 ms) did
not need to be applied.
−
13
2
M , but for the sake of
2
8,29
value.
We shall see that, of course, the value of the
equilibrium constant of iodine has a substantial impact whether
iodine or hypoiodous acid is the kinetically active species in the
more complicated iodate−arsenous acid reaction as well. Our
aim here is to establish a comprehensive kinetic model to be
able to describe quantitatively the measured absorbance−time
profiles of the iodine−arsenous acid, iodide−iodate, and
iodate−arsenous acid reactions simultaneously.
Data Treatment. The absorbance−time profiles were evaluated
30
simultaneously by the program package ZiTa/Chemmech. The
orthogonal fitting procedure was applied meaning that all of the kinetic
curves were transformed into a 0 ≤ x, y ≤ 1 box and the sum of the
perpendicular deviation between the measured and calculated
absorbances was minimized by kinetic parameter optimization. Our
criterion was that the average deviation approaches 1.5%, which is the
experimentally achievable limit of error under our experimental
conditions.
EXPERIMENTAL SECTION
■
(
(
(
RESULTS AND DISCUSSION
Kinetics of the Roebuck Reaction and Iodine
Hydrolysis. The stoichiometry of the iodine−arsenous acid
Roebuck) reaction has long been accepted, as indicated by
Methods and Materials. All of the reagentsarsenic(III) oxide
■
Reanal), anhydrous sodium sulfate (Reanal), perchloric acid
Germed), iodine (Reanal), sodium iodide (Reanal), sodium iodate
Reanal), sodium hydrogen carbonate (Reanal), methyl red (Reanal),
11
(
and absolute ethanol (Merck)were of the highest purity available
commercially and were used without further purification. Stock
solutions were made by dissolving the necessary amount of the target
compound (except for an arsenous acid stock solution detailed below).
Water was twice ion-exchanged and then distilled twice to remove
ionic exchange resin residues and dissolved gases. All of the solutions
were deoxygenated by bubbling oxygen-free argon for at least 10 min.
All of the experiments were performed at temperature-controlled
conditions (25.0 ± 0.1 °C) and at a constant ionic strength set to 0.68
M using sodium sulfate, sodium perchlorate, or both. The initial
iodine, hydrogen ion, arsenous acid, and iodide concentrations were
eq 3. Despite the simplicity of this equation, the identity of the
kinetically active iodine-containing species is still in question.
Moreover, our very recent study has just revealed that the rate
equation of this reaction (see eq 5) is rather complex, and a
factor (u) was introduced that may easily be interpreted as the
iodide impurity of the stock iodate solution.
9
r = k [[
H AsO ][I ]
H ]([I ] + u)
3 3 2
+
−
(5)
−4
varied in the ranges of (1−5) × 10 , 0.1−0.6, 0.0050−0.07, and 0−
To clarify, we have reinvestigated the reaction by a stopped-
flow technique. Figure 1 depicts the effect of the arsenous acid
concentration on the decay of the total amount of iodine. As is
seen, these kinetic curves were measured in a high excess of
arsenous acid, therefore one may expect that the absorbance−
time profiles can easily be calculated by a single-exponential fit
0.05 M, respectively. The concentration of a perchloric acid stock
solution was determined by a standard titration method by applying
sodium hydrogen carbonate and a methyl red indicator. All of the
iodine solutions were prepared by dissolving excess iodine in a
solution containing the necessary amount of perchloric acid and
sodium sulfate and stirred at least for 1 night. These solutions were
kept in the dark to avoid any photocatalyzed reaction. In the case of
the iodide−iodate reaction, the initial concentrations of iodide, iodate,
and hydrogen ion were varied in the ranges of 16−87.5 μM, 0.5−2.0
mM, and 0.05−0.5 M, respectively. The ionic strength was adjusted by
the necessary amount of sodium perchlorate.
obs
−k t
(
A = A0e
) to obtain pseudo-first-order apparent rate
coefficients at each condition individually if the formal kinetic
An arsenous acid stock solution was prepared by dissolving an
excess of arsenic(III) oxide in boiling water by continuous stirring. The
solution was then left to cool under persistent stirring. This procedure
was repeated one more time. After the solution reached room
temperature, the residues of undissolved arsenic(III) oxide were
removed by filtration. An arsenous acid stock solution obtained in this
way was completely free from carbonate impurities. The concentration
of the stock solution was checked by spectrophotometry. In an excess
of sodium iodate and perchloric acid, arsenous acid was delivered into
a quartz cuvette having a Teflon stopper and was left to stand for at
least 20 min. The absorption spectrum was recorded by UV−vis
spectrophotometer, and according to the equation
−
+
2
IO3 + 5H AsO + 2H → I + 5H AsO + H O
(4)
3
3
2
3
4
2
Figure 1. Individual fits in the iodine−arsenous acid (Roebuck)
reaction at different arsenous acid concentrations in the absence of an
the concentration of an arsenous acid stock solution could be
0
initially added iodide ion. Conditions are as follows: T = 0.5 mM;
−
I
2
calculated. (An absorbance at 468 nm was used, where ε = ε = 747
I2
I3
−
1
−1
TSO42− = 0.2 M; [HClO ] = 0.4 M. [H AsO ] /mM = 7.5 (black), 10.0
4 3 3 0
M
cm .) The reproducibility of the method was found to be better
than 1%. The stock solution prepared was stable at room temperature;
no crystal formation or any decomposition was visible, and the
concentration was constant for over 1 month. In the case of the
iodate−arsenous acid reaction, the initial concentrations of iodate,
arsenous acid, and hydrogen perchlorate were varied in the ranges of
(blue), 20.0 (green), 40.0 (cyan), and 60.0 (red). Color dots
correspond to experimental values. Dashed lines indicate the result
of an individual single-exponential curve fit in each case. Solid lines
represent the result of the individual curve fit by eq 3 with a specific
second-order rate coefficient (k ) along with taking into account the
r
1.65−13 mM, 0.285−4.7 mM, and 0.14−1.0 M, respectively. In this
rapid equilibrium formation of a triiodide ion.
1
596
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Inorganic Chemistry
Article
order of iodine is 1. The results are illustrated in Figure 1 by
dashed lines: Although the average deviation of these curves
was found to be 2.8%, evidently systematic deviations may be
found between the experimental and calculated absorbance. At
the initial stage of each curve, experiments indicate a much
faster drop of the absorbance than that of the calculated one,
while at the final stages, this trend is reversed. As a result, we
concluded that, although arsenous acid is applied in a high
excess, the kinetic curves cannot be described by a single-
exponential fit. A conceivable explanation of this fact is that the
iodide ion produced during the course of the reaction
continuously transforms iodine into the kinetically less reactive
triiodide ion. Therefore, as a next step, we tried to describe our
kinetic data by considering eq 3 having law-of-mass-action
of the initially added iodide ion cannot be taken into
consideration simply by supposing the formation of a triiodide
ion. One thing is, however, straightforward; the reaction is
autoinhibitory with respect to the iodide ion because formation
of the product iodide inhibits the initial rate of consumption of
iodine.
Because this observation is very reminiscent of what we have
recently reported in the case of the polythionate−iodine
31
reactions, as a next step, we considered the following kinetic
model to provide a reasonable description of the kinetic runs.
Below this point, the term “fitting” refers to the simultaneous
evaluation of the kinetic curves.
HSO4 ⇌ SO42− + H+
−
(E1)
(R1)
(R2)
(R3)
(R4)
(R5)
kinetics (r = k [H AsO ][I ]) along with the well-known rapid
3
r
3
3
2
kR1, k
−R1
−
−
−
−
equilibrium formation of a triiodide ion (I + I ⇌ I ) by
I + I HoooooooI I
2
3
2
3
fitting only rate coefficient k . These fitting procedures were
r
kR2, kR2′, k , k
′
−R2 −R2
−
+
also carried out individually experiment by experiment. The
results can also be seen in Figure 1 and represented by solid
lines. As is visualized, a slight improvement is achievedthe
average deviation decreased to 2.14%but inspection of the
results still indicates notable systematic deviations, from which
we concluded that the iodide ion has a significantly more
complex contribution to the kinetics of the reaction than just
the simple triiodide formation. This result contradicts the main
I + H O HoooooooooooooooooooI HOI + I + H
2
2
kR3, k
−R3
+
+
H OI HoooooooI HOI + H
2
k
R4
−
+
H AsO + HOI ⎯ →⎯ H AsO + I + H
3
3
3
4
k
+
R5
−
+
H AsO + H OI ⎯ →⎯ H AsO + I + 2H
3
3
2
3
4
18
message reported by Patil and Rewatkar, who showed that the
kinetics of the Roebuck reaction can be described by a specific
second-order rate coefficient that depends on the pH but not
on the concentration of the iodide ion. To further prove
experimentally that the reaction is more complex and cannot be
described by a single specific rate coefficient, we present below
the results of the initial rate studies. Figure 2 shows the log−log
Step E1 is an auxiliary process, only necessary to take the
slight pH change correctly into account during the course of
the reaction. The rate coefficients of the forward and reverse
8
−1
reactions were set to the fixed values of k = 5.75 × 10 s and
E1
k−E1 = 1010
M
−1
s
−1
to give the pK of HSO4 as 1.24. The
−
32
a
rate coefficients of the forward and backward reactions of step
9
R1 were also fixed as determined previously (k = 5.6 × 10
R1
−1
−1
6
−1 33,34
M
s
and k−R1 = 8.5 × 10 s ).
The mechanism of iodine hydrolysis was proposed to
proceed via multiple equilibrium steps involving species like
H OI and I OH , but later it was shown that the role of
I OH can be neglected at a strongly acidic solution; hence,
24
+
−
2
2
−
35
2
the rate equation of step R2 can be established as
rR2 = kR2 [
I ]
H ]
− k−R2[HOI][I−]
2
+
[
(6)
where kR2 = 1.98 × 10− M s−1 and k−R2 = 3.67 × 10 M s ,
3
9
−1 −1
−13
which give us an equilibrium constant of iodine of 5.4 × 10
2
26,35
+
M .
The acidic dissociation constant of H OI was
2
35
determined to be 2 M under our experimental conditions;
Figure 2. Initial rate studies to determine the formal kinetic orders of
the reactants in the iodine−arsenous acid (Roebuck) reaction.
9
−1
9
−1 −1
therefore, we set kR3 = 2 × 10 s and k−R3 = 10 M s .
Because these values appeared to be well-established,
0
Conditions are as follows: (black) [H AsO ] = 10 mM, T = 0.54
3
3
0
I
2
consequently the only parameters that remained to be fitted
−
mM, [HClO4]0 = 0.4 M, and c0 corresponds to [I ] ; (blue)
+
0
were kR4 and/or kR5 if both hypoiodous acid and H OI are
2
0
−
[
H AsO ] = 10 mM, TI2 = 0.65 mM, [I ]0 = 0 mM, and c0
3 3 0
kinetically active species.
corresponds to [HClO ]; (green) [H AsO ] = 10 mM, [HClO ] =
The result of the fit was found to be completely
unacceptable, having an average deviation of 91%, with values
of kR4 and kR5 being orders of magnitude higher than the
diffusion control limit for second-order processes in aqueous
solution! From this result, we concluded that indeed the direct
reaction between arsenous acid and iodine has to be taken into
4
3
3
0
4
−
0
0
0
.4 M, [I ] = 0 mM, and c corresponds to T ; (red) T = 0.4 mM,
0 0 I I
2
2
−
[
I ] = 0 mM, [HClO ] = 0.4 M, and c corresponds to [H AsO ].
0
4
0
3
3
2−
TSO4 = 0.2 M was kept constant in all of these experiments.
plots indicating that the formal kinetic orders of both arsenous
−
consideration, which agrees well with the main message of the
acid and iodine (where T id defined as [I ] + [I ]) are strictly
I2
2
3
17,18
most recent reports;
i.e., the kinetically active species is
1
, while that of the hydrogen ion is −1. However, the logarithm
iodine. As a result, steps E1 and R1−R5 were supplemented by
two new processes to describe our kinetic data as follows:
of the initial rate against the logarithm of the initial iodide
concentration is clearly not linear, suggesting the fact that
iodide dependence of the rate should be considered as a
complex issue. It also indirectly supports that fact that the effect
k
R6, k−R6
−
+
H AsO + I HoooooooI H AsO I + I + H
(R6)
3
3
2
2
3
1
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k
R7
+
−
H AsO I + H O ⎯ →⎯ H AsO + H + I
(R7)
2
3
2
3
4
We first fixed kR4 = kR5 = 10 M s−1 to enlarge the role of a
hypoiodous acid driven route as much as possible compared to
the iodine-driven pathway. Because the rate coefficients kR6,
k−R6, and kR7 cannot be determined individually because of a
strong correlation between the kinetic parameters (this
observation will be discussed later in the Validation of the
Kinetic Model and Rate Coefficients section), we set k = 1 ×
9
−1
−R6
9
−2 −1
1
0 M
any value higher than 10 M
average deviation; therefore, we chose the lower limit of k−R6
s
and fitted kR6 and k . It should be emphasized that
R7
−2 −1
9
s
would lead to the same
.
The final result indicated a perfect description of the kinetic
Figure 4. Measured (dots) and calculated (solid lines) absorbance−
data of an average deviation of 0.92% when the values of 9040
100 M−1
−1
−1
time curves in the absence of an initially added iodide ion in the case
±
s
and 8980 ± 80 s were obtained for kR6 and
of the iodine−arsenous acid (Roebuck) reaction. The initial conditions
kR7, respectively. It should, however, be noted that the values of
2−
4
are as follows: [H AsO ] = 10 mM; T
= 0.2 M; [HClO ] = 0.4
3
3
0
SO
4 0
kR7 and k−R6 were found to be in total correlation with each
0
M; T /mM = 0.088 (black), 0.19 (blue), 0.23 (green), 0.28 (cyan), 0.4
I
2
other, meaning that we could actually determine k /k
=
R7 −R6
.98 × 10−6 M . In addition to that, a strong (correlation
2
(red), and 0.52 (magenta).
8
coefficient of 0.96), but not total, correlation was also observed
between kR6 and k , from which we concluded that we actually
R7
= 0.081 ± 0.002 M s− from our
1
could determine k k /k
R6 R7 −R6
measurements, which is consistent with the value determined
indirectly from our previous measurements. Furthermore, the
9
final result was completely insensitive for the highest possible
values of kR4 and k , from which we concluded that the role of
R5
the hypoiodous acid route is negligible in the case of the
Roebuck reaction. As a result, the astonishingly perfect fit
illustrated in Figures 3−6 may also be obtained by setting kR4
Figure 5. Measured (dots) and calculated (solid lines) absorbance−
time curves in the absence of an initially added iodide ion in the case
of the iodine−arsenous acid (Roebuck) reaction. [H AsO ] = 10 mM
3
3 0
0
I
2
2
−
and TSO4 = 0.2 M for all of the curves. [HClO ] = 0.1 M and T /
4
0
0
mM = 0.41 (black); [HClO ] = 0.2 M and T /mM = 0.50 (blue);
4
0
I
2
0
[
HClO ] = 0.6 M and T /mM = 0.62 (green); [HClO ] = 0.8 M
2
4 0 I 4 0
0
0
I
2
and T /mM = 0.64 (cyan); [HClO ] = 1.0 M and T /mM = 0.74
I
2
4
0
(red).
Figure 3. Measured (dots) and calculated (solid lines) absorbance−
time curves in the absence of an initially added iodide ion in the case
of the iodine−arsenous acid (Roebuck) reaction. The initial conditions
0
2
4
−
are as follows: T = 0.5 mM; T
= 0.2 M; [HClO ] = 0.4 M;
I
2
SO
4 0
[
H AsO ] /mM = 5.0 (black), 7.5 (blue), 10.0 (green), 20.0 (cyan),
3 3 0
4
0.0 (red), 60.0 (magenta), and 70.0 (brown).
and kR5 to be zero, but actually these figures were generated by
8
−1 −1
using kR4 = 0 and kR5 = 7.4 × 10 M s , which was
determined with the help of the kinetic curves measured in the
iodate−arsenous acid system (see later).
Kinetics of the Dushman Reaction. The kinetics of the
Figure 6. Measured (dots) and calculated (solid lines) absorbance−
time curves in the presence of an initially added iodide ion in the case
of the iodine−arsenous acid (Roebuck) reaction. The initial conditions
36,37
Dushman reaction has been well-established since 2000.
In
1
999, Schmitz correctly pointed out that in acidic conditions,
0
2−
pH < 3, one should consider the rapid protonation equilibrium
of iodate to form iodic acid by taking the different reactivities of
iodate ion and iodic acid into consideration. The acid
dissociation constant of iodic acid is accepted as 0.156 ±
are as follows: T = 0.54 mM; T
= 0.2 M; [HClO ] = 0.4 M;
I
2
SO
4
4 0
−
[H AsO ] /mM = 10.0. [I ] /mM = 0.05 (black), 0.15 (blue), 0.3
3
3
0
0
(green), 0.5 (cyan), 1.5 (red), 3.0 (magenta), and 5.0 (brown).
3
8
0
.002 M, determined independently by Ramette and Palmer
Taking into account that at I = 0.68 M, the activity coefficient
γ± ≈ 0.7 KR8 was set to 0.32 using sufficiently high values for
39
as well as by Strong and Pethybridge at zero ionic strength.
1
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Inorganic Chemistry
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kR8 and k−R8 to establish this protonation equilibrium
instantaneously.
Table 1. Fitted and Fixed Rate Coefficients of the Proposed
Kinetic Model
kR8, k
−R8
step
R1
rate equation
parameter value
refs
HIO HoooooooI IO + H+
−
3
3
(R8)
−
5.6 × 10 M s−1
9
−1
k [I ][I ]
28 and 29
R1
2
k−R1[I3−]
8.5 × 10 s
6
−1
28 and 29
−R1
It is also well-known that the Dushman reaction starts with the
following process to form the reactive intermediate I O in an
+
−1
R2
k [I ]/[H ]
0.00198 M s
39
39
39
39
31
31
R2
2
2
2
3
6,37,40
k−R2[HOI][I−]
3.67 × 10 M s−1
9
−1
−R2
equilibrium:
0.0552 s−
1
R2′
−R2′
R3
k ′[I ]
−R2′[HOI][H ][I ]
R2
2
kR9, k
+
−
1.023 × 10 M−2 s−1
11
−R9
−
+
k
I + HIO + H HoooooooI I O + H O
(R9)
3
2
2
2
+
9
−1
k [H OI ]
2 × 10 s
10 M s−1
R3
2
R3 k−R3[HOI][H+]
9
−1
−
This reaction is established rapidly but shifting far to the left to
provide a low concentration level of I O .
intermediate I O either then further reacts with an iodide ion
or hydrolyzes to give iodous and hypoiodous acid:
41,42
R4
k [H AsO ][HOI]
not
The steady-state
R4
3
3
a
2
2
necessary
2
2
+
(7.4 ± 0.3) × 10 M s−1 present work
8
−1
R5
R6
k [H AsO ][H OI ]
R5
3
3
2
−
1
−1
k [H AsO ][I ]
10830 ± 70 M
s
present work
R6
3
3
2
−
+
9
−2 −1
b
k
−R6 k−R6[H AsO I][I ][H ] 10 M
R7
s
fixed
−
+
R10
2
3
I + I O + H ⎯⎯ →⎯ I + HIO
(R10)
(R11)
−1
2
2
2
2
k [H AsO I]
7390 ± 50 s
present work
34 and 35
34 and 35
R7
2
3
8
−1
R8
k [HIO ]
10 s
R8
3
k
k−R8[H ][IO −]
+
3.125 × 10 M s−1
8
−1
R11
−R8
I O + H O ⎯⎯→ HIO + HOI
3
2
2
2
2
+
−
5
−2 −1
c
R9
k [H ][I ][HIO ]
≥10 M
s
fixed
R9
3
6
−1
c
Iodous acid then comproportionates with an iodide ion to give
hypoiodous acid in a rapid reaction:
−R9
R10
k
−R9[I
2
−
O
2
]
≥10 s
fixed
4
3
9
−1
k
R10[I ][I
O
]
2
(1.02 ± 0.01) × 10 M
present work
2
−
1
s
k
+
(3.2 ± 0.1) × 10 M s−1 present work
4
−1
−
+
R12
R11
R12
R13
kR11[H ][I O ]
2
2
HIO + I + H ⎯⎯ →⎯ 2HOI
(R12)
2
−
+
9
−2 −1
kR12[I ][[H ]HIO ]
≥10 M
s
39
2
0.33 ± 0.01 M s−1
−
3
present work
kR13[H AsO ][HIO ]
Along with steps R1 and R2, this mechanism gives us the
overall stoichiometry of the Dushman reaction, as shown in eq
. It is clear that, although hydrolysis of iodine is not necessary
to interpret the kinetics of the Roebuck reaction, its backward
reaction of hydrolysis is certainly obligatory to have the correct
stoichiometry to produce iodine from HOI and I in the case of
3
3
3
+
2
[
H ]
≥10 M s−1
6
−1
fixed
b
R14
a
kR14[H AsO ][HIO ]
3
3
2
2
Either step R4 or R5 is necessary to describe the experiments. The
description by step R4 is slightly worse (1.15%) compared to that by
b
c
−
step R5. Just a lower limit could be determined. KR9 = 0.1 was
chosen arbitrarily, and only KR9kR10 and KR9kR11 can be calculated.
the Dushman reaction.
Step R9 is a rapidly established equilibrium, and its
equilibrium constant was set to 0.1 M to provide a sufficiently
k ′
R10
−
+
−2
I + I O + H + H O ⎯⎯ ⎯→ 3HOI
(R10a)
2
2
2
low concentration level of I O . What this means is that the
2
2
Our choice, however, remains step R10, in agreement with
overall rate coefficient of the Dushman reaction can be
37
40
36
Schmitz and Agreda et al.
obtained by KR9kR10 and KR9kR11 (see later). Schmitz also
pointed out that the rate coefficients of both steps R10 and R11
depend on the buffer concentrations and on the nature of the
medium applied. Evidently, this means that both of the rate
coefficients (kR10 and kR11) are subject to being fitted during the
course of the reaction. One may also realize that in the case of
Figures 7−9 demonstrate that steps R1−R3 along with steps
R8−R12 are working properly to soundly describe the
absorbance−time profiles measured in the iodide−iodate
reaction.
Kinetics of the Arsenous Acid−Iodate Reaction. So far
we considered the mechanism of the subsystems of the
arsenous acid−iodate reaction. Certainly, in themselves, they
+
step R11 [H ] is also involved in the rate equation (see Table
1
). To support its role, we carried out an additional fitting
procedure with elimination of the pH dependence from the rate
law of step R11. This fitting procedure resulted in a 1.8%
average deviation, which is almost twice as high as that in the
original case. From this indirect support, we decided to keep
+
[
H ] in the rate equation of step R11. Step R12 is, however, a
rapid reaction under the condition studied; therefore, its rate
43
coefficient can be fixed to a sufficiently high value. Actually,
9
−2 −1
any value higher than 10 M
s
would give the same final
9
−2 −1
result; therefore, we set kR12 = 10 M s . This lower value is
in complete agreement with the one proposed by Lengyel et
4
3
26
al., but it should also be mentioned that Furrow used
a
9
−1 −1
+
significantly higher value (5 × 10 M s ) with no [H ]
dependence on the rate equation to explain the most important
kinetic feature of the iodate−hydrogen peroxide reaction.
Furthermore, it should also be emphasized that step R10 can
be completely substituted with the following reaction, and no
unambiguous decision can be made about which pathway is
more preferable to explain the second-order iodide dependence
of the Dushman reaction:
Figure 7. Measured (dots) and calculated (solid lines) absorbance−
time curves in the case of the iodide−iodate (Dushman) reaction. The
ionic strength is adjusted to 1.0 M by sodium perchlorate. The initial
−
conditions are as follows: [I ]
= 57 μM; [HClO
]
0
= 0.2 M. TIO
−]/
0
4
3
mM = 0.5 (black), 1.0 (blue), and 2.0 (green).
1
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Article
experimental curves containing 10300 experimental points can
be described by 1.0% average deviation by means of the
orthogonal fitting method, which indicates a perfect description
of the kinetic curves. While kR13 and kR5 can evidently be
determined from the absorbance−time traces of the iodate−
arsenous acid reaction, k and k are sensitive enough to
R10
R11
describe the kinetics feature of the Dushman reaction as well as
that of the iodate−arsenous acid reaction. Evidently, step R5 is
necessary to provide an iodide ion if the iodate−arsenous acid
reaction is studied; therefore, this value can be obtained from
the absorbance−time series of this system. A similar argument
can also be made about the values of k and k : they are
R6
R7
sensitive enough to determine the absorbance−time profiles of
both the iodine−arsenous acid and iodate−arsenous acid
reactions. The only difference is that if these parameters are
determined simply from the Roebuck reaction, then a strong
correlation is experienced between them. This correlation,
however, decreases when the kinetic curves of both systems are
evaluated simultaneously; hence, the individual rate coefficients
can be obtained. It is likely to stem from the fact that, at the
induction period of the iodate−arsenous acid reaction, the
concentration of the iodide ion is so low that inhibition is not
effective; hence, kR6 may be determined. It follows from the
point that the denominator of eq 9 (see later) may be simplified
as r = k [H AsO ][I ]. If this value is well-determined, then
Figure 8. Measured (dots) and calculated (solid lines) absorbance−
time curves in the case of the iodide−iodate (Dushman) reaction. The
ionic strength is adjusted to 1.0 M by sodium perchlorate. The initial
−
−
conditions are as follows: TIO3 = 0.66 mM; [HClO ] = 0.2 M. [I ] /
4
0
0
μM = 16 (black), 30 (blue), 57 (green), and 87.5 (cyan).
R6
3
3
2
from the later stages of the reaction, k /k
can also be
R7 −R6
obtained, so fixing k−R6 enables us to calculate kR7 as well. In the
case of the iodine−arsenous acid reaction, however, hydrolysis
of iodine easily produces an iodide ion to such an extent where
iodide inhibition appears in the very beginning stage of the
reaction; hence, there is no direct information to obtain kR6.
Typical measured and calculated curves in the arsenous acid−
iodate reactions are indicated in Figures 10−12. At the same
Figure 9. Measured (dots) and calculated (solid lines) absorbance−
time curves in the case of the iodide−iodate (Dushman) reaction. The
ionic strength is adjusted to 1.0 M by sodium perchlorate. The initial
−
−
conditions are as follows: [I ] = 57 μM; T = 0.66 mM. [HClO ] /
0
IO
3
4 0
mM = 0.05 (black), 0.1 (blue), 0.2 (green), 0.35 (cyan), and 0.5 (red).
are able to describe the kinetics of all of the subsystems
separately, meaning that they can conveniently be assembled to
describe the kinetics of the overall arsenous acid−iodate
reaction; meanwhile, the mechanisms of the subsystems
preserve their most important original characteristics. In
order to complete the mechanism of the title reaction, we
have to consider formal oxygen-transfer reactions between iodic
acid and arsenous acid as well as between iodous acid and
arsenous acid. The necessity of the pH dependence of step R13
9
was thoroughly discussed recently; therefore, we directly
adopted this rate equation (see Table 1).
Figure 10. Measured (dots) and calculated (solid lines) absorbance−
time curves in the case of the arsenous acid−iodate reaction. The
initial conditions are as follows: T0
= 10.0 mM; [HClO
−
IO
3
]
= 0.4 M;
k
4
0
R13
H AsO + HIO ⎯⎯ →⎯ H AsO + HIO
(R13)
(R14)
3
3
3
3
4
2
[
H AsO ] /mM = 0.29 (black), 0.48 (blue), 0.67 (green), 0.95 (cyan),
3
3 0
1
.9 (red), 2.9 (magenta), 3.8 (yellow), and 4.7 (brown).
k
R14
H AsO + HIO ⎯⎯ →⎯ H AsO + HOI
3
3
2
3
4
Therefore, combining these equations with steps R1−R12
should give the overall mechanism of the arsenous acid−iodate
reaction. To determine the rate coefficients of the kinetic model
mentioned above, we have fitted all of the experimental curves
of the arsenous acid−iodine, iodide−iodate, and arsenous
acid−iodate reactions simultaneously. With the help of six fitted
rate coefficients along with the fixed rate coefficients (among
them, eq 10 was directly taken from the literature, and in the
case of the remaining fixed parameters, only a lower limit could
be determined) indicated in Table 1, all of the measured 117
time, Figures 3−6 and 7−9 indicate the capability of the kinetic
model in describing the kinetic curves in the case of the
iodine−arsenous acid and iodide−iodate reactions, respectively.
Validation of the Kinetic Model and Rate Coefficients.
Arsenous Acid−Iodine (Roebuck) Reaction. Steps R6 and R7
constitute the mechanism of the arsenous acid−iodine
(Roebuck) reaction. At this point, reactions R1−R3 were not
considered to obtain eq 9. A steady-state approximation may be
applied for the short-lived H AsO I intermediate, from which
2
3
one can easily obtain the following expression:
1
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Inorganic Chemistry
Article
meaning that there is no direct connection between parameter
u and the iodide impurity.
It is also worth mentioning why the hypoiodous acid (or
+
H OI ) route of the Roebuck reaction is negligible compared to
2
the pathway driven through iodine. Applying a steady-state
approximation for species HOI, one can obtain
kR2
+
+
k ′ [I ]
(
+
R2
)
2
[
H ]
[
HOI] = (
−
k
+ k ′[H ])[I ] + k [H AsO ]
(10)
−
R2
−R2
R4
3
3
In this case, consumption of arsenous acid can be written as
follows:
Figure 11. Measured (dots) and calculated (solid lines) absorbance−
time curves in the case of the arsenous acid−iodate reaction. The
initial conditions are as follows: [H AsO ] = 3.8 mM; [HClO ] = 0.4
d[H AsO ]
dT2
I
3
3
−
= − dt = k [H AsO ][HOI]
R4
3
3
dt
(11)
3
3
0
4 0
M; T0
/mM = 1.65 (black), 2.1 (blue), 3.5 (green), 5.0 (cyan), 7.0
−
Substituting eq 10 into eq 11 followed by some algebraic
manipulation, we arrive at
IO
3
(red), 9.0 (magenta), 10.0 (brown), and 13.0 (yellow).
d[H AsO ]
dTI2
3
3
−
= − dt
dt
kR2 + kR2 ′ [H+]
+
kR4[H3AsO3][I2]
+ k−R2 ′ [H ]
k
−R2
=
+
−
kR4[H3AsO3]
[
H ] [I ] +
+
(
)
k
+ k−R2 ′ [H ]
−
R2
[
H AsO][I ]
3
2
=
kobs
+
−
[H ]([I ] + u)
(12)
A comparison of eq 12 by eq 9 reveals a similar expression
for the disappearance of iodine. However, substituting the well-
known rate coefficients of iodine hydrolysis and the upper limit
+
of k (or k in the case of H OI ), we shall obtain k = 4 ×
R4
−4
R5
2
obs
Figure 12. Measured (dots) and calculated (solid lines) absorbance−
−1
1
0
M s . This value is at least 200 times lower than the one
time curves in the case of the arsenous acid−iodate reaction. The
0
determined directly from the measured absorbance−time
series. Therefore, this route has no effective contribution to
the overall kinetics of the Roebuck reaction as long as the well-
known rate coefficients of iodine hydrolysis (see Table 1) are
held to provide the hydrolysis constant of iodine to be about
initial conditions are as follows: [H AsO ] = 3.8 mM; T
−
= 10.0
3
3
0
IO3
mM; [HClO ] /M = 0.14 (black), 0.2 (blue), 0.4 (green), 0.6 (cyan),
4
0
0
.8 (red), and 1.0 (magenta).
k [H AsO ][I ]
R6
3
3
2
−13
2
19,23,24
[
H AsO I] =
(2−6) × 10 M at room temperature.
To clarify the
2
3
−
+
k
[I ][H ] + k
(7)
−
R6
R7
role of these pathways, however, reinvestigation of the kinetics
of iodine hydrolysis seems to be unavoidable because
surprisingly values of approximately 2 orders of magnitude
Because consumption of arsenous acid (as well as that of the
total amount of iodine according to eq 3) can be described by
higher (around 10− M ) have also been reported by
11
2
2
8,29
independent research groups.
This means that the
d[H AsO ]
dT
I
2
3
3
otherwise well-known iodine hydrolysis still leaves some
unresolved problems for future studies.
−
= − dt = k [H AsO I]
R7
2
3
dt
(8)
Dushman Reaction. It is easily seen that the rate of the
Dushman reaction is determined by steps R8−R12 along with
steps R1−R3. Applying a steady-state approximation for species
I O and after some algebraic manipulation along with some
Substitution of eq 7 into eq 8 gives the following equation:
d[H AsO ]
dT
I
2
3
3
2
2
−
= − dt
−
+
simplifications (k−R9 ≫ k [I ] and k
arrive at the following equation:
≫ kR11[H ]), one can
dt
R10
−R9
K k [H AsO ][I ]
R6 R7
3
3
2
=
−
+
kR7
⎛
k k [I ]
k k [H ]
⎞
⎠
+
−
R9 R10
R9 R11
+
−
[
H ] [I ] +
+
(
)
r = ⎜
+
⎟[H ][I ][HIO ]
k
[H ]
d
3
−
R6
⎝
k
k
−
R9
−R9
[
H AsO ][I ]
3
+
3
−
2
+
=
kobs
⎛
= ⎜
⎝
K k
K k [H ]⎞
R9 R10
KR8 + [H+]
−
R9 R11
+ 2
−
[
H ]([I ] + u)
(9)
[I ] +
⎟[H ] [I ]T
−
+
IO3
KR8 + [H ] ⎠
Substituting the rate coefficients indicated in Table 1, one can
(13)
−1
easily obtain KR6kR7 = 0.083 M s , which is in a good
Substitution of the corresponding rate coefficients and pH
−1
9
agreement with 0.094 M s determined in our previous work.
range used during the experiments leads to the overall rate
It straightforwardly means that parameter u introduced in the
8
−4 −1
−3
coefficients of (0.77−2.18) × 10 M
s
and 2230−2420 M
k
−1
R7
rate equation of the Roebuck reaction is equal to k
,
s
for the second-order and first-order pathways of the
+
[H ]
R6
−
1
601
DOI: 10.1021/acs.inorgchem.5b02513
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Inorganic Chemistry
Article
Dushman reaction with respect to the iodide ion, respectively.
These values are quite consistent with the ones reported by
Schmitz, giving therefore further support of the presented
mechanism.
iodine hydrolysis needs to be revised without a thorough
reinvestigation.
3
6
Although the story of the iodate−arsenous acid reaction
started more than a century ago by Roebuck’s and Bray’s
pioneering kinetic studies, it certainly does not end up here.
This work provides additional insight into how the application
of simultaneous evaluation in chemical kinetics is used to obtain
reliable models and mechanisms of an unknown or a well-
studied reaction. At the same time, it appears to establish a
strong warning flag that even a wide range of well-designed
kinetic experiments along with the recently available computa-
tional techniques may not be sufficient to establish
unambiguously the kinetically active species of a kinetic model.
Direct Iodate−Arsenous Acid Reaction. Our present study
provides here further support that the direct iodate−arsenous
acid reaction exists and starts the overall process. Again
considering no direct reaction at all between the reactants, the
iodide impurity of the stock iodate solution is insufficient to
describe simultaneously the measured absorbance−time series.
9
This is consistent with our very recent result. The obtained
rate coefficients for k , kR13, and kR14 are also in sound
R5
agreement with the fact that the reactivity of oxoacids of iodine
increases with the decreasing number of O atoms involved.
This result also means that the direct reaction (along with steps
R14 and R5) plays a significant role only during the induction
phase of the arsenous acid−iodate reaction, and the decisive
role is gradually shifted to the overall combined effect of the
Roebuck and Dushman reactions.
AUTHOR INFORMATION
Corresponding Author
*E-mail: horvatha@gamma.ttk.pte.hu.
■
Notes
The authors declare no competing financial interest.
A word is also in order here to mention that even a better
description of the kinetic curves of the arsenous acid−iodate
and arsenous acid−iodine reactions is possible if the rate
coefficient of the forward reaction of iodine is also fitted. This
fit (having an average deviation of 0.9%!) resulted a rate
ACKNOWLEDGMENTS
■
Financial support of the Hungarian Research Fund OTKA
Grant K116591 is gratefully acknowledged. The present
scientific contribution is dedicated to the 650th anniversary
−1
coefficient for kR2 of 1.54 ± 0.08 s ; meanwhile, k decreased
R6
of the foundation of the University of Pec
́
s, Hungary.
−
1 −1
by approximately 15% to 8730 ± 90 M
s
and kR7 increased
−1
to 9100 ± 90 s . The rest of the parameters did not change
significantly. This means that arsenous acid is capable of being
oxidized by both iodine and hypoiodous acid. This would,
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