Pitfall of an initial rate study: On the kinetics and mechanism of the reaction of periodate with iodide ions in a slightly acidic medium

Article abstract of DOI:10.1021/jp067277r

The kinetics of the periodate-iodide reaction has a contradictory history dating back to almost a century. This reaction has been reinvestigated spectrophotometrically in the pH range 3.13-5.55 in both buffered (acetic acid/acetate) and unbuffered solution at T = 25.0 ± 0.1 °C with an I = 0.5 M ionic strength. The spectra between 290 and 500 nm were recorded and the reaction was followed until at least 95% of one of the reactants was consumed. The stoichiometry has been found to be strongly dependent on pH, but the rate of the initial step is independent of pH within the pH range studied. An eight-step kinetic model is proposed with four fitted kinetic parameters to take all the important characteristics of the experimental curves into account. On the basis of the model, a perfect reconciliation of the previous contradictory results is presented. It is shown that the kinetic parameters obtained from the initial rate of formation of a product unavoidably leads to misinterpretation of the results in the case of a branching mechanism (and stoichiometry).

Full text of DOI:10.1021/jp067277r

890
J. Phys. Chem. A 2007, 111, 890-896
Pitfall of an Initial Rate Study: On the Kinetics and Mechanism of the Reaction of
Periodate with Iodide Ions in a Slightly Acidic Medium
Attila K. Horv a´ th†
Department of Physical Chemistry, UniVersity of Szeged, P.O. Box 105, Szeged H-6701, Hungary
ReceiVed: NoVember 5, 2006; In Final Form: December 6, 2006
The kinetics of the periodate-iodide reaction has a contradictory history dating back to almost a century.
This reaction has been reinvestigated spectrophotometrically in the pH range 3.13-5.55 in both buffered
(acetic acid/acetate) and unbuffered solution at T ) 25.0 ( 0.1 °C with an I ) 0.5 M ionic strength. The
spectra between 290 and 500 nm were recorded and the reaction was followed until at least 95% of one of
the reactants was consumed. The stoichiometry has been found to be strongly dependent on pH, but the rate
of the initial step is independent of pH within the pH range studied. An eight-step kinetic model is proposed
with four fitted kinetic parameters to take all the important characteristics of the experimental curves into
account. On the basis of the model, a perfect reconciliation of the previous contradictory results is presented.
It is shown that the kinetic parameters obtained from the initial rate of formation of a product unavoidably
leads to misinterpretation of the results in the case of a branching mechanism (and stoichiometry).
Introduction
determined from the absorbance measured at 468 nm, the
-
corresponding isosbestic point of the system I2-I3 . They have
There is considerable disagreement in the literature regarding
the pH dependence of the periodate-iodide reaction. This
reaction occurs in both acidic and neutral media, and this feature
provides the analytical distinction between iodate and periodate
ions.1 The first kinetic study of this reaction has been carried
found again that the rate equation has both pH-independent and
+
[
H ]-dependent terms, in agreement with their previous study.
This long and contradictory story has provided us a challenge
to solve the mystery of the pH dependence of the rate of the
periodate-iodide reaction. In addition, the title reaction may
also play a significant role in the oscillatory behavior of the
,2
3
out by Abel and F u¨ rth almost a century ago. No pH dependence
has been found in neutral and slightly acidic media adjusted by
acetate buffer. In more acidic medium applying sulfuric acid,
however, Abel and Siebenschein have estimated that the rate
equation also contains a term that depends on [H ] besides
the pH-independent part. Later, Indelli and his co-workers have
6
thiosulfate-periodate reaction. To date, neither systematic
investigation on the stoichiometry nor a complete mechanism
is available for the title reaction.
+
2
4
Experimental Section
found that the rate equation contains a term that linearly depends
+
on [H ] besides the pH-independent path in a slightly acidic
Materials. All the commercially available reagents (potas-
sium periodate, potassium iodide, sodium acetate, acetic acid,
perchloric acid), except for sodium perchlorate, were of the
highest purity and were used without further purification. The
commercially available sodium perchlorate (Sigma-Aldrich) has
been purified by recrystallization. Four times distilled water was
used to prepare all the stock solutions. The periodate stock
solution was protected from light during the storage.
+
2
medium and that may even be supplemented with a [H ] term
in more acidic medium. The essence of their method was to
5
add a slight amount of thiosulfate in the reacting solution to
consume all the iodine produced in the system and the time of
reappearance of iodine was registered. This procedure was
repeated several times during each experiment. The method
applied by these authors has raised an important question. If
thiosulfate reacts with species present in the reacting system
other than iodine with a commensurable rate, then the time of
reappearance of iodine is no longer connected uniquely to the
periodate-iodide reaction. This situation may happen easily
In series 1, acetic acid-acetate buffer was used to maintain
the pH between 4.55 and 5.55. The acetate concentration was
kept constant at 0.3 M and the desired amount of acetic acid
was added to adjust the pH taking the pKa of acetic acid as
4.55. The ionic strength was adjusted to 0.5 M with 0.2 M
sodium perchlorate solution. In series 2, we have checked the
possibility of general acid catalysis, keeping the acetate-acetic
acid concentration ratio constant at 2.5 (pH ) 4.95) and varying
because both iodate and periodate are well-known to react with
thiosulfate.6-8 This possible artifact was also noticed by Marques
9
and Hasty, and they have reinvestigated the periodate-iodide
reaction by applying an iodide selective electrode and have
found no pH dependence on the rate in the pH range 3.51-
-2
3
the acetate concentration from 1.667 × 10 to 0.4 M. The ionic
strength was also adjusted to 0.5 M in these experiments by
adding the necessary amount of sodium perchlorate. Finally, in
series 3, the initial pH was adjusted by perchloric acid and the
ionic strength was kept constant at 0.5 M adjusted by sodium
perchlorate.
5
.31 using acetate buffer, in agreement with Abel and F u¨ rth.
In a response to their study Ferranti and Indelli have remea-
sured10 the kinetics of the periodate-iodide reaction by spec-
+
-4
trophotometry at [H ]0 ) (1.0-10.0) × 10 M. The apparent
+
rate coefficients at different H concentrations were estimated
-
from the initial rate of formation of total iodine ([I2] + [I3 ])
Methods. The kinetic measurements were carried out in a
standard 1 cm quartz cuvette equipped with a Teflon cap and a
†
E-mail: horvatha@chem.u-szeged.hu.
1
0.1021/jp067277r CCC: $37.00 © 2007 American Chemical Society
Published on Web 01/12/2007

Reaction of Periodate with Iodide Ions
J. Phys. Chem. A, Vol. 111, No. 5, 2007 891
magnetic stirrer. The cuvette was carefully sealed with Parafilm
at the Teflon cap to minimize the loss of iodine. The reaction
was followed with a Zeiss Specord S10 diode array spectro-
photometer within the 290-500 nm wavelength range. Separate
experiments have shown that the light source of spectropho-
tometer does not have significant influence on either the
periodate or the iodine solutions within the acquisition time for
following the reaction.
After the reaction was complete, the final spectra of the
solutions were analyzed for the composition to establish the
stoichiometry of the reaction by taking the molar absorbances
of the iodine-containing species into account.
TABLE 1: Molar Absorbances of the Absorbing Species at
the Wavelengths Selected for Evaluation of the
Stoichiometric and Kinetic Measurementsa
λ (nm)
90
320
ꢀ(IO
4
-)
ꢀ(IO
3
-)
ꢀ(I
2
)
ꢀ(I
3
-)
2
224.6
37.7
2.97
0
0
1.76
302.1
72.47
36.9
754.2
605.0
38431
14157
26035
747.1
323.0
0
0
0
0
3
4
4
50
68
90
a
The molar absorbances are given in M-1 cm-1
.
TABLE 2: Determination of the Stoichiometric Ratio (SR)
in an Excess of Iodidea
Data Treatment
-
-]
-]
-
[
I ]
0
[IO
4
0
pH
[I
3
∞
[I ]
∞
SR
Stoichiometry. In excess periodate, according to the laws
of mass and oxidation number balance applied for the iodine
containing species, the following equation may be derived to
calculate the stoichiometric ratio (SR) of the consumed iodide
and periodate ions
3
1
1
.0
.0
.4
0.4
5.55
5.55
5.55
5.03
5.03
5.03
4.55
4.55
4.55
4.48
4.30
4.18
4.08
4.00
3.93
3.88
3.78
3.70
3.63
3.57
3.52
3.48
3.13
0.2262
0.0427
0.1046
0.0607
0.1038
0.1615
0.0346
0.0556
0.1706
0.0946
0.2911
0.2329
0.2900
0.2353
0.0687
0.1497
0.3054
0.9551
0.9542
0.9508
0.9460
0.9486
0.9449
0.9399
0.9419
0.9327
0.9343
0.9282
0.9248
0.9201
0.8871
1.96
2.00
1.89
1.83
1.90
2.02
2.09
1.93
2.05
2.28
2.32
2.53
2.78
2.62
2.83
3.13
2.97
3.49
3.38
3.71
3.87
4.13
5.72
0.14
0.4
0.3
0.4
0.4
0.1
0.2
0.4
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
0.01667
1.0
1
2
1
.4
.0
.0
-
[
I ]
1.0
.4
1.0
0
SR )
(1)
1
0.0977
-
3
[I ] - 5[I ]
0 2 ∞
0.006829
0.007033
0.007017
0.007561
0.007780
0.007864
0.007787
0.008515
0.009025
0.009289
0.009964
0.01055
0.01097
0.01756
1
1
1
1
1
1.0
1.0
1
1
1
1
1
.0
.0
.0
.0
.0
if iodate, iodine and periodate are the only iodine-containing
species that can be detected after the reaction was complete.
With an excess of iodide the concentration of iodine and
triiodide were determined from the spectra of the solutions at
the end of the reaction. Having known the stability constant of
the triiodide ion the equilibrium concentration of the iodide ion
can easily be calculated, from which SR is given as
.0
.0
.0
.0
.0
-
-
-
[
I ] - [I ] - [I ]
0
∞
3
∞
SR )
(2)
1.0
-
[
IO ]
4
0
a
The concentrations are given in mM.
Kinetics. The experimental curves were analyzed with the
program package ZiTa.11 Five different wavelengths have been
TABLE 3: Determination of the Stoichiometric Ratio (SR)
in an Excess of Periodatea
chosen for the evaluation procedure: 290, 320, 350, 468, 490
nm. The selection contains the two characteristic absorption
maxima of triiodide (290, 350 nm), the isosbestic point of the
triiodide-iodine system (468 nm). Only the absorbance up to
[I
2
]
∞
(mM)
SR
pH
-
-]
[
I ]
.1
.2
0
[IO
4
0
pH
1
pH
2
pH
3
pH
1
2
pH
3
0
0
0.3
0.4
0.4
0.4
0.4
0.4
0.4
0.4
1.0
1.4
2.0
0.0448 0.0439 0.0396 1.32 1.24 0.98
0.0928 0.0895 0.0848 1.47 1.31 1.14
0.1399 0.1313 0.1343 1.50 1.43 1.31
0.1892 0.1864 0.1799 1.58 1.49 1.33
0.2388 0.2341 0.2269 1.63 1.52 1.37
0.3452 0.3411 0.3407 1.87 1.77 1.76
0.4811 0.4803 0.4681 1.68 1.67 1.52
0.4819 0.4792 0.4649 1.69 1.66 1.48
0.4792 0.4772 0.4640 1.66 1.63 1.47
1
.0 has been used for evaluation because above this value the
relative error of absorbance measurement increases significantly.
Altogether almost 15000 experimental points from 355 absor-
bance-time series (71 different compositions at 5 different
wavelengths) were used for simultaneous fitting that contained
both the buffered and the nonbuffered experiments. The sum
of squares of the deviations between the measured and calculated
absorbances was selected as the parameter to be minimized.
Our quantitative criterion for an acceptable fit was that the
average deviation for the absolute fit approach 0.004 absorbance
unit, which is close to the uncertainty of the spectrophotometer.
0
0
1
1
1
.5
.7
.0
.0
.0
a
1 2 3
The concentrations are given in mM. pH , pH and pH stand for
5
.55, 5.03 and 4.55, respectively.
stability constant and the molar absorbances of the absorbing
species agree well with the data found in the literature.1
Stoichiometric Considerations. The results of the stoichio-
metric studies are collected in Tables 2 and 3. Several authors
3,14
Results
Equilibrium Study. The evaluation of the stoichiometric and
kinetic measurements requires precise stability constant of
triiodide ion and molar absorbances of both iodine and triiodide
ion in the 290-500 nm wavelength range at the given
experimental conditions. Table 1 contains the molar absorbances
3
,5,9
have found,
without providing primary data in determining
the stoichiometry, that iodine and iodate are the first product
of the reaction according to the following equation:
IO4- + 2I + 2H f IO + I + H O
-
+
-
(3)
1
2
of iodine and triiodide ion calculated by PSEQUAD at the
wavelengths selected for the kinetic evaluation. The stability
3
2
2
-
1
constant of triiodide ion was calculated to be 666 ( 19 M
with an average deviation of 0.0025 absorbance unit. The fitted
It is clearly seen from Table 2 that, with excess iodide and above
pH ) 4.55 within the experimental error, SR is 2.00, in

892 J. Phys. Chem. A, Vol. 111, No. 5, 2007
Horv a´ th
-]
Figure 2. Effect of buffer concentration on the rate of the periodate-
iodide reaction at I ) 0.5 M ionic strength adjusted by sodium
Figure 1. Kinetic orders of the reactants at different pHs. [IO
4
0
)
-
0
.4 mM and [I ]
symbols, respectively. pH ) 5.55 and J ) 0 for (b) and (O), pH )
.03 and J ) 0.1 for (9) and (0), pH ) 4.55 and J ) 0.2 for (]) and
[). Note that some of the curves are shifted along the Y-axis to see
0
) 1.0 mM were kept constant for the filled and empty
-
-
-
perchlorate. [IO
4
]
0
) 0.25 mM, [I ] ) 1.5 mM, [HAc]/[Ac ] ) 0.4.
0
5
(
the trends better.
agreement with the previous findings. If, however, the iodide
excess is high enough and the pH falls below 4.5, the following
equation
IO4- + 7I + 8H f 4I + 4H O
-
+
(4)
2
2
occurs parallel to eq 3 and SR starts to increase, as seen in the
lower part of Table 2. It is easily seen that, if these processes
alone determined the stoichiometry of the reaction, then SR
would definitely be higher than 2. Table 3, however, clearly
shows that in excess periodate SR is significantly lower than 2,
meaning that beside eqs 3 and 4 another process must be taken
into consideration. Later, we shall see that
Figure 3. Apparent dependence of the second-order rate coefficient
-
-
0
determined from the initial rate study on pH. [I ]
0
) 1.0 mM, [IO
4
]
)
0.01667 mM, I ) 0.5 M adjusted by sodium perchlorate.
I + 3IO4 f 4IO -
-
-
(5)
3
used in our experiments may lead to a relatively huge change
in pH during the course of the reaction, especially at low
perchloric acid concentrations, the rate coefficients have been
determined from initial rate studies in accordance with Ferranti
also plays a significant role in determining the stoichiometry
of the reaction. It should be mentioned that the effect of this
process has already been tentatively realized by Abel and F u¨ rth,
but later it somehow escaped the investigators’ attention.
Kinetics in Acetate Buffer. The initial rate study has revealed
that the reaction of periodate with iodide is perfectly first order
3
1
0
and Indelli. Our results are illustrated in Figure 3 and are in
perfect harmony with Ferranti and Indelli’s findings. The fit
-
1 -1
has yielded a 4.82 ( 0.13 M
s
value for the pH-independent
-
2 -1
with respect to both species, independently of pH (see Figure
part of the periodate-iodide reaction and 6680 ( 420 M
s
-5
1
) as was found in previous works.3 The second-order rate
value for the pH-dependent term of the rate equation. Although
the slope is somewhat greater than it was previously found to
coefficients determined from the individual fit of the absor-
bance-time curves at 468 nm (isosbestic point of triiodide-
iodine system) with the strict 2:1 stoichiometry shown in eq 3
were found to be 12.17 ( 0.91, 12.13 ( 0.71 and 12.05 (
-
2 -1
be, 1420 ( 40 and 2730 ( 240 M
s
by the above-mentioned
5
,10
authors, the intercept is surprisingly good compared to 4.72
-1 -1
( 0.03 and 4.78 ( 0.06 M s , even though the experimental
circumstances were quite different in these studies. Nevertheless,
it also means that there is an apparent contradiction between
the results obtained from the presence and absence of acetate
buffer, because on the one hand the reaction is independent of
both the pH and the buffer concentration in the presence of the
acetate/acetic acid buffer and on the other hand its rate law
contains a [H ]-dependent path besides the [H ]-independent
term in the absence of buffer! Later, we shall see that this
apparent contradiction can entirely be resolved by an ap-
propriately suggested mechanism in which the rate determining
step is pH-independent but the stoichiometry of the reaction
strongly depends on pH.
-
1
-1
0
.62 M
s
at pH ) 5.55, 5.03 and 4.55, respectively,
indicating that no pH dependence could be observed, in
agreement with some earlier investigations.3,9 Furthermore, the
buffer concentration does not have any effect on the rate of the
reaction (see Figure 2) within the acetate concentration range
studied, indicating the lack of buffer assistance that frequently
accompanies the reactions1
5-17
of oxyhalogen species. This
+
+
result also agrees well with the previous work done by Abel
3
and F u¨ rth. It was considered to be important to strengthen this
early result because the lack of pH dependence found by
9
10
Marques and Hasty was argued by Ferranti and Indelli that
it is due to a possible unrecognized influence of undissociated
acetic acid.
Proposed Mechanism. As a starting point, to build up the
mechanism, we have chosen the following set of species that
are very likely to participate in the final kinetic model. This set
Kinetics without Acetate Buffer. Because the reaction
+
between periodate and iodide ion consumes H according to
-
-
-
eq 3 and application of no buffer at the concentration range
consists of the reactants I and IO4 , the products I2, I3 and

Reaction of Periodate with Iodide Ions
J. Phys. Chem. A, Vol. 111, No. 5, 2007 893
-
2-
5
-1 -1
IO3 , some intermediates such as HOI, HIO2, I2O4 and the
therefore fixed k3 ) 10 M
s
and calculated k2 to be (8.3 (
+
-
4
-1 -1
+
species H , H2O, OH that are always present in aqueous
medium. After that all the possible mono- and bimolecular steps
of these species were considered along with their H - and OH -
0.9) × 10 M s . At low H and high iodide concentration
the adduct formed in step R1 reacts almost exclusively with
iodide, yielding iodine and iodate in a 1:1 molar ratio, giving
back the stoichiometry indicated by eq 3. At low pH and iodide
concentrations, however, the reaction is shifted to the formation
of iodous acid.
Iodous acid, however, quickly reacts further with either iodide
or periodate in steps R4 and R5. Both reactions are fast, only
their ratio can be calculated from our experiment. Because k4
+
-
catalyzed pathways. This method has been successfully applied
in several cases of our previous work.1
8-20
After long but
straightforward systematic reduction, the following model has
emerged.
+
-
H + OH h H O
(P1)
2
9
-2 -1
)
10 M
s
was determined independently by Lengyel and
his co-workers, we have fixed it during the calculations. The
-
+
23
Ac + H h HAc
(P2)
(R1)
fitting procedure has yielded a reasonable value for k5 ) (1.23
-
-
2-
5
-1 -1
I + IO4 f I O4
( 0.34) × 10 M s . In excess periodate, step R5 drives the
reaction; thus the stoichiometry is shifted toward eq 5; however,
at low periodate concentration, step R4 yields hypoiodous acid
almost instantaneously. As one may notice, if step R4 dominates
(along with the iodine hydrolysis), then the stoichiometry of
the reaction is shifted toward eq 4, whereas prevalence of step
R5 leads to the stoichiometry indicated by eq 5. Several other
reactions of iodous acid were also considered, including the
well-known and easily conceivable disproportionation
2
2
-
+
-
I2O4 + H + H O f 2HIO + OH
(R2)
(R3)
(R4)
(R5)
(R6)
(R7)
(R8)
2
2
2
-
-
-
3
-
I2O4 + I + H O f I + IO + 2OH
2
2
-
+
HIO + I + H f 2HOI
2
HIO + IO4 f 2IO - + H
-
+
2
3
-
+
2
HIO f IO + HOI + H
(6)
2
3
-
+
I + H O h HOI + I + H
2
2
but none of them improved the quality of fit. The rate coefficient
-
-
3
2
3,24
I + I h I
of this process was determined
to be between 25 and 50
2
-
1
s-1, which is too slow to compete with either step R4 or
M
IO3- + 5I + 6H f 3I + 3H O
-
+
step R5 in our experimental circumstances.
Step R6 is the well-known hydrolysis of iodine studied by
2
2
2
5,26
Discussion
several authors.
All the rate coefficients, including the
hydroxide-driven hydrolysis of iodine determined previously,
were implanted in our final model without any change. This
process together with their rate coefficients provides a suf-
The fast protonation and deprotonation processes (equilibria
P1 and P2) were taken into consideration with the well-known
equilibrium constants to adjust the pH in buffered solution and
to follow the pH change during the course of the reaction in
unbuffered solution. They are regarded as auxiliary processes,
necessary for the calculations, but they are not part of the
proposed model.
-
5
ficiently low level of hypoiodous acid (<10 M) that does not
have significant absorbance contribution in the wavelength range
used in our experiments. Moreover, it also implies that the well-
known back-reaction of step R4 cannot have a significant effect
2
3,27,28
-1 -1
with a rate coefficient being
between 5 and 22 M s ;
Step R1 is the initial elementary reaction of our model in
therefore it is not included in the proposed model. It should
also be mentioned that the following
2-
which the adduct I2O4 is formed. As we shall see, this is the
rate-limiting step and the second-order rate coefficient was found
-
1
-1
to be 12.3 ( 0.3 M
s
at I ) 0.5 M ionic strength. From
HOI + IO4- f HIO + IO
-
(7)
9
-1 -1
Marques and Hasty’s data one can estimate a 12.6 M
s
2
3
value at I ) 0.5 M, which perfectly agrees with the value
determined from this work. Nevertheless, Abel and F u¨ rth have
reaction was also considered but it turned out to be unnecessary
for describing the kinetics of the title reaction.
3
-1 -1
estimated a 11.8 M
s
value at an ionic strength of I ) 0.4
M adjusted by sodium acetate that also indicates perfect
agreement with our work. It has to be mentioned for the sake
Step R7 is the well-known fast formation of triiodide ion.
8
-1 -1
6
-1
For the values of k7 and k-7 6.66 × 10 M
s
and 10 s
-
1
-1
of correctness that in his early paper a 707 M
s
value was
have been used, respectively, which gives the formation constant
of triiodide to be 666 M determined independently from
equilibrium studies.
-
1
given, but it seems likely that it is a typographical error and
-
1
-1
the unit of this value is properly M min , which can be
-
1
-1
converted to 11.8 M s . It should also be noted that four
species are present in the aqueous periodate solution, H5IO6,
H4IO6 , IO4 and H3IO6 . Those are, however, rapidly
equilibrated with each other and the periodate is mainly in
univalent form (either H4IO6 or IO4 ) in the pH range studied.
Because there is a rapid pH-independent equilibrium between
H4IO6 and IO4 and the ratio of [IO4 ]/[H4IO6 ] is 29.5, it
looks reasonable to suppose that the reactive species is IO4
Step R8 is the well-known Dushman reaction that starts to
21
29
rise only at lower pH. From his early paper one can estimate
-
-
2-
8
-4 -1
a value of 8.0 × 10 M
s
for k8 at an ionic strength between
0.0015 and 0.003 M. Our fitted value k8 ) (2.35 ( 0.71) ×
-
-
9
-4 -1
10 M
s
at I ) 0.5 M is therefore in reasonable agreement
22
with his measurements. To show that this reaction plays only a
minor role, additional fitting has been carried out with three
fitted kinetic parameters (k1, k2/k3 and k5 without k8) on those
experimental curves where the pH was higher than 3.6. This
fitting procedure has led to a bit lower average deviation (0.0035
absorbance unit), meanwhile the values of the three fitted
parameters remained basically the same within their standard
deviation given in Table 4.
-
-
-
-
-
despite the fact that our measurements do not provide solid basis
to establish the kinetically active form of periodate.
Steps R2 and R3 are further reactions of I2O42-. The
individual rate coefficients k2 and k3 cannot be determined
independently; they are in total correlation with each other. We

894 J. Phys. Chem. A, Vol. 111, No. 5, 2007
Horv a´ th
TABLE 4: Fitted and Fixed Rate Coefficients Used in the
a
Fitting Procedure
step
rate equation
parameter
ref
-
-]
12.3 ( 0.3 M-1 s-1
(
R1)
R2)
R3)
R4)
R5)
R6)
k
k
k
k
k
k
k
k
k
k
k
k
1
2
3
4
5
6
[I ][IO
4
this work
2
2
-
-
+
(
(
(
(
(
[I
[I
2
O
O
4
][H ]
][I ]
-
2
4
k
2
/k
3
) 0.83 ( 0.09
this work
22
-
+
9
-2 -1
[HIO
[HIO
2
][I ][H ]
10 M
s
-
4
][IO ]
(1.23 ( 0.34) × 10 M s-1 this work
5
-1
2
-
1
[I
2
]
0.0552 s
22
22
22
22
-6[HOI][I ][H ] 1.023 × 10 M-2 s-1
-
+
11
+
-3
-1
6
′[I
2
]/[H ]
1.98 × 10 M s
-
3.67 × 10 M s-1
9
-1
-6′[HOI][I ]
[I ][I ]
7 2
-
(
R7)
-
/k-7 ) 666 M-1
-7[I
3
]
k
7
14
-
][I ] [H ] (2.35 ( 0.71) × 10 M s-1 this work
-
2
+
2
9
-4
(
R8)
[IO
8 3
a
No error indicates that the value in question was fixed during the
5
/k , k /k .
Figure 5. Measured (symbols) and calculated (solid lines) kinetic
fitting procedure. Note that the actual calculations yielded k
2
3
4
-
-
0
curves at pH ) 5.55 and [I ]
mM) ) 0.1 (b), 0.14 (0), 0.2 (2), 0.3 (]), 0.4 (+), 0.5 (O), 0.7 (9),
.0 (4), 1.4 ([), 2.0 (3).
0
) 1.0 mM in acetate buffer. [IO
4
]
(
1
Figure 4. Measured (symbols) and calculated (solid lines) kinetic
-
-
0
curves at pH ) 5.55 and [IO
4
]
0
) 0.4 mM in acetate buffer. [I ]
Figure 6. Measured (symbols) and calculated (solid lines) kinetic
(
mM) ) 0.1 (b), 0.2 (0), 0.3 (2), 0.4 (]), 0.5 (+), 0.7 (O), 1.0 (9),
-
-
0
curves at pH ) 5.03 and [IO
mM) ) 0.1 (b), 0.2 (0), 0.3 (2), 0.4 (]), 0.5 (+), 0.7 (O), 1.0 (9),
.4 (4), 2.0 ([), 3.0 (3).
4
]
0
) 0.4 mM in acetate buffer. [I ]
1
.4 (4), 2.0 ([), 3.0 (3).
(
1
It should also be mentioned that any trial to include the easily
conceivable direct reaction between iodine and periodate
-
-
I2 + IO4 + H O f 2HOI + IO3
(8)
2
was unsuccessful; therefore we concluded that this reaction is
not necessary for describing the kinetics and mechanism of the
iodide-periodate reaction.
Table 4 summarizes the fixed and fitted rate coefficients in
the fitting procedure. Figures 4-9 demonstrate that the model
is capable of good description of the absorbance change during
the reaction in a wide concentration range of the reactants at
the selected wavelengths. The average deviation was found to
be 0.0037 absorbance unit, which is close to the experimentally
achievable limit of error of the spectrophotometer. The proposed
model perfectly fits all the experimental data because, besides
the low average deviation, all the most important characteristics
of the experimental kinetic curves are reflected in the fitted
curves. Among them, four important characteristics have to be
emphasized:
Figure 7. Measured (symbols) and calculated (solid lines) kinetic
-
-
0
curves at [I ]
buffer. pH ) 4.48 (b), 4.18 (0), 4.08 (9), 3.78 (+), 3.70 ([), 3.57
×), 3.52 (1), 3.13 (]).
0
) 1.0 mM and [IO
4
] ) 0.016667 mM without acetate
(
and more iodine (triiodide) is formed than could be expected
from eq 3 even at those pHs where the Dushman reaction29 is
extremely slow. It clearly indicates the continuously growing
effect of eq 4 on the stoichiometry of the reaction.
•
Figures 4-6 clearly demonstrate that at high pH and high
iodide concentration eq 3 rules the stoichiometry of the reaction.
If, however, periodate is in molar excess over the iodide ion,
then less iodine is formed that can be expected from eq 3,
meaning that the stoichiometry is slightly shifted toward eq 5.
•Figure 8 shows that there is no difference in the early stage
of the kinetic curves as a function of pH in buffered solution in
the pH range 4.55-5.55, meaning no pH dependence in the
•
Figure 7 clearly indicates that the reaction cannot be
interpreted by a single stoichiometry. As the pH decreases, more

Reaction of Periodate with Iodide Ions
J. Phys. Chem. A, Vol. 111, No. 5, 2007 895
found in unbuffered medium, which is slightly higher than the
-
1 -1
value of 12.1 ( 0.7 M
s
in the case of the buffered solutions.
The 10% difference between these values can easily be
explained by the dissimilar characteristics of the background
salts of sodium acetate and sodium perchlorate.
Conclusions
It is clearly demonstrated in this paper that the rate of
periodate-iodide reaction is independent of pH in the pH range
9
3
.1-5.55, in agreement with Marques and Hasty’s study. The
stoichiometry of the reaction, however, is strongly affected by
pH. The lower the pH is, the higher the ratio of the formed
total iodine and consumed periodate is. A simple kinetic model
is suggested that is able to explain not only all the most
important characteristics of the kinetic curves but also the origin
of the completely different interpretation of pH dependence on
the rate of the title reaction. Four of the suggested eight kinetic
steps are well-known from the literature with well-determined
rate equations. Step R1 turned out to be the rate-limiting step,
the rate equation of which is independent of pH. The fate of
the adduct formed in this step, however, strongly depends on
the pH that results in branching stoichiometries. The higher the
acidity is, the more iodine can form in a time unit. The
increasing amount of iodine in a time unit as a function of pH,
however, might be defectively interpreted as if the rate coef-
ficient, obtained from initial rate study assuming a strict
stoichiometry, has an apparent pH dependence.
Figure 8. Measured (symbols) and calculated (solid lines) kinetic
-
-
0
curves at [I ]
0
4
) 0.7 mM and [IO ] ) 0.4 mM in acetate buffer. pH
)
5.55 (b), 5.03 (0), 4.55 (+).
This work, however, has a more serious consequence than
the refinement of the kinetics and stoichiometry of the title
reaction itself. The tool with which the information of the
experimental curves is extracted to draw the final conclusion
must be chosen with special circumspection. A badly chosen
evaluation method might unavoidably lead to a complete
misinterpretation of the results. Therefore even the seemingly
simple reactions can be handled with special care and be
evaluated by the recently available computational techniques
in chemical kinetics, because any simplification might carry in
itself the possibility of potential misinterpretation of the kinetic
data. The simultaneous fitting of all the measured kinetic curves
without any data transformation is therefore strongly recom-
mended if a feasible kinetic model is intended to be proposed.
Figure 9. Measured (symbols) and calculated (solid lines) kinetic
-
-
0
curves at pH ) 5.55 and [I ]
mM) ) 0.1 (b), 0.14 (0), 0.2 (2), 0.3 (]), 0.4 (+), 0.5 (O), 0.7 (9),
.0 (4), 1.4 ([), 2.0 (3).
0
) 1.0 mM in acetate buffer. [IO
4
]
(
1
rate-limiting step. Later a slight difference appears, indicating
a stoichiometric shift as the pH decreases.
•Figure 9 shows that in high periodate excess the total iodine
concentration gradually decreases after it reaches its maximum,
though the direct reaction between iodine and periodate is not
included in the proposed kinetic model. The decrease can also
be explained by the fact that the iodine hydrolysis is a
considerable iodide sourcesespecially at higher pHsthat can
serve as further breeding ground for the iodide-periodate
reaction.
Acknowledgment. This work was supported by the Hungar-
ian Research Fund (Grant No. T047031). A.K.H. is grateful for
the financial support of B e´ kesy Gy o¨ rgy (B12/2003) postdoctoral
fellowship. The author is also thankful to prof. Istv a´ n Nagyp a´ l
for his valuable advice after reading the manuscript.
Finally, we shall point out how the apparent contradiction
obtained from the two different approaches of the evaluation
should be resolved. The rate-determining step of the proposed
model is step R1, the rate equation of which is pH-independent.
The influence of pH, however, is that it shifts the stoichiometry
of the reaction from the strict 2:1 iodide-periodate ratio beyond
the stoichiometry that can be represented by the linear combina-
tion of eqs 3 and 4. It means that the ratio of the concentration
Supporting Information Available: File containing the
derivation of eq 1 and the measured and calculated absorbances
for all the kinetic curves (takes up 19 pages) are available free
of charge via the Internet at http://pubs.acs.org.
References and Notes
-
of the formed total iodine ([I2] + [I3 ]) and the consumed
(
(
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+
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(
6) R a´ bai, Gy.; Beck, M. T.; Kustin, K.; Epstein, I. R. J. Phys. Chem.
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1
-1
1
3.5 ( 1.2 M
s
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