Complex kinetics of a landolt-type reaction: The later phase of the thiosulfate-iodate reaction

Article abstract of DOI:10.1021/jp101458e

The thiosulfate-iodate reaction has been studied spectrophotometrically in slightly acidic medium at 25.0 ± 0.1 °C in acetate/acetic acid buffer by monitoring the absorbance at 468 nm at the isosbestic point of iodine-triiodide ion system. The formation of iodine after the Landolt time follows a rather complex kinetic behavior depending on the pH and on the concentration of the reactants as well. It is shown that the key intermediate of the reaction is I₂O₂, its equilibrium formation from the well-known Dushman reaction along with their further reactions followed by subsequent reactions of HOI, HIO₂, S₂O₃OH ^-, and S₂O₃I^- adequately accounts for all the experimentally measured characteristics of the kinetic curves. A 19-step kinetic model is proposed and discussed with 13 fitted and 7 fixed parameters in detail.

Full text of DOI:10.1021/jp101458e

5752
J. Phys. Chem. A 2010, 114, 5752–5758
Complex Kinetics of a Landolt-Type Reaction: The Later Phase of the Thiosulfate-Iodate
Reaction
De´nes Varga,†,‡ Istva´n Nagypa´l,†,¶ and Attila K. Horva´th*,†
Department of Chemistry, UniVersity of Pe´cs, Ifju´sa´g u´tja 6., H-7624 Pe´cs, Hungary
ReceiVed: February 17, 2010; ReVised Manuscript ReceiVed: March 31, 2010
The thiosulfate-iodate reaction has been studied spectrophotometrically in slightly acidic medium at 25.0 (
0.1 °C in acetate/acetic acid buffer by monitoring the absorbance at 468 nm at the isosbestic point of
iodine-triiodide ion system. The formation of iodine after the Landolt time follows a rather complex kinetic
behavior depending on the pH and on the concentration of the reactants as well. It is shown that the key
intermediate of the reaction is I2O2, its equilibrium formation from the well-known Dushman reaction along
with their further reactions followed by subsequent reactions of HOI, HIO2, S2O3OH-, and S2O3I- adequately
accounts for all the experimentally measured characteristics of the kinetic curves. A 19-step kinetic model is
proposed and discussed with 13 fitted and 7 fixed parameters in detail.
Introduction
perturbed by the noninert tetrathionate ion, may result in a
completely different kinetic behavior.
The sulfite-iodate reaction has long been known as a classical
type of clock reaction since Landolt’s original discovery.1 The
qualitative picture of the reaction has also been well-accepted,
iodate relatively slowly oxidizes sulfite into sulfate accompanied
by the formation of iodide as a result of the reduction of iodate.
Formation of iodide, however, opens up the route to the
appearance of the Dushman reaction2 in which the amount of
iodine formed is quickly3 removed as long as sulfite is present
in the reaction system. Once the reducing agent sulfite is
completely used up, iodine starts to accumulate, indicating the
end of the so-called Landolt time. The concentration dependence
of the Landolt time has been studied intensively in the past4-6
but resulted in different relationships with regard to the
concentration of the reactants. Recent studies,7,8 however, clearly
showed that these deviations arose only from the different
experimental conditions applied and a general complex formula
exists for the concentration dependence of the Landolt time.
In general, it is also expected if sulfite is replaced with a
different reducing agent that can react with iodate relatively
slowly but rapidly reduces iodine, then the system in question
behaves as a Landolt-type reaction as well. Eggert and Scharnow
have already reported that among the possible simple inorganic
oxyanions only thiosulfate fulfills this criterion.9 In the case of
Fe(CN)64- and AsO33- their oxidation by iodine may be slower
than their reactions with iodate in certain experimental condi-
tions; therefore, the Landolt effect (sudden appearance of the
The Landolt reaction has been brought into the focus of
interest by searching new chemical oscillators in the mid-1980s.
Often the original Landolt reaction perturbed by suitable
components such as ferrocyanide, thiosulfate resulted in oscil-
lations in a continuously fed stirred tank reactor (CSTR).10,11
Even the very rare large amplitude pH-oscillation phenomenon
has also been found in the thiosulfate perturbation of the Landolt
reaction in batch system.12 The skeleton mechanism of these
combined systems has been accepted13,14 and even a temperature
oscillation could be explained in case of the iodate-sulfite-
thiosulfate system.15 More recently, these systems are thoroughly
studied to produce different spatiotemporal structures and may
thus have potential applications in designing chemical waves,
Turing structures, and even pH responsive gels with rhythmical
motions.16-19 Therefore, to gain deeper insight into the intimate
details of the Landolt reaction perturbed by thiosulfate we
decided to investigate the later phase of thiosulfate-iodate
reaction. Although the detailed kinetics and the mechanism of
the thiosulfate-iodate reaction was already studied 80 years
ago by Rieder,20 recent studies have pointed out11,12,14 that the
reaction cannot exclusively produce tetrathionate, sulfite has to
be formed as well to explain adequately the batch pH oscillatory
behavior.
Experimental Section
-
I2 + I- h I3 equilibrium) may already be manifested in the
Materials and Buffers. All the chemicals (sodium thiosulfate,
potassium iodate, potassium iodide, acetic acid, sodium acetate)
were of the highest purity available commercially and used
without further purification. The stock solutions were freshly
prepared each day from double-distilled and twice ion-
exchanged water. The concentration of the thiosulfate was
determined prior to each run by standard iodometric titrations.
The pH of the solutions was regulated between 3.34 and 4.24
by acetic acid/acetate buffer taking the pKa of acetic acid as
4.55.21 The acetate concentration was always kept constant as
0.1 M, and the pH was adjusted by the necessary amount of
acetic acid. The temperature of the reaction vessel was
maintained at 25.0 ( 0.1 °C. The initial concentrations of the
presence of an appreciable fraction of the reducing agent.9
Though the thiosulfate and sulfite ions were classified in the
same group of Landolt-type reactions the formation of iodine
after the Landolt time has never been studied in detail. The fact
that in the sulfite-iodate reaction only the Dushman reaction
is reponsible for the formation of iodine after the Landolt time
but in the thiosulfate-iodate reaction the Dushman reaction is
* E-mail: horvatha@gamma.ttk.pte.hu.
† University of Pe´cs;
‡ This paper is dedicated to the memory of De´nes Varga, who passed
away after finishing the experimental work of this system.
¶ Permanent address: Department of Physical Chemistry and Materials
Science, University of Szeged, Rerrich B. te´r 1, H-6720, Szeged, Hungary.
10.1021/jp101458e  2010 American Chemical Society
Published on Web 04/16/2010

Complex Kinetics of a Landolt-Type Reaction
J. Phys. Chem. A, Vol. 114, No. 18, 2010 5753
TABLE 1: Fitted and Fixed Rate Coefficients of the Proposed Kinetic Modela
step
rate equation
parameter
kR1[I2][I-]
(R1)
5.7 × 109 M-1 s-1
-
(-R1)
(R2)
(R3)
(R4)
(R5)
8.5 × 106 s-1
k-R1[I3 ]
kR2[S2O32-][IO3 ]
kR3[S2O32-][HIO2]
kR4[S2O32-][HOI]
kR5[S2O32-][HOI]
-
(2.84 ( 0.17) × 10-1 M-1 s-1
kR3/kR10 ) 6.65 ( 1.20
kR4/kR9 ) 8.76 ( 0.48
kR5/kR9 ) 2.55 ( 0.16
KR6 ) kR6/k-R6 ) 100 M-3
-
kR6[IO3 ][I-][H+]2
(R6)
(-R6)
k-R6[I2O2]
kR7[S2O32-][I2O2]
kR8[I-][I2O2]
kR9[I-][HOI]
kR10[S2O32-][I2]
(kR11 + kR′ 11[H+])[S2O32-][S2O3OH-]
kR12[S2O3OH-][I2]
(R7)
KR6kR7 ) (5.74 ( 0.06) × 109 M-4 s-1
KR6kR8 ) (4.26 ( 0.02) × 108 M-4 s-1
3.67 × 109 M-1 s-1
(R8)
(R9)
(R10)
(R11)
(R12)
(R13)
(R14)
(R15)
(R16)
(-R16)
(R17)
(R18)
(R19)
e2 × 107 M-1 s-1
kR11 ) 50 M-1 s-1; kR′ 11 ) 2.5 × 109 M-2 s-1
(1.94 ( 0.06) × 10-2 M-1 s-1
71.8 ( 1.2 M-2 s-1
3.58 ( 0.12 M-1 s-1
7.96 ( 0.56 M-2 s-1
-
kR13[S2O3OH-][IO3 ][H+]
-
kR14[S2O3I-][IO3 ]
kR15[S2O3I-]2[I-]
kR16[S4O62-][I2]
k-R16[S4O6I-][I-]
kR17[S4O6I-]
(8.41 ( 0.12) × 10-2 M-1 s-1
KR16 ) kR16/k-R16 ) 1.92 × 10-7
kR17/k-R16 ) (4.9 ( 0.1) × 10-3
3.1 × 109 M-1 s-1
M
-
kR18[HSO3 ][I2]
-
kR19/kR18 ) 6.32 ( 0.35
kR19[HSO3 ][HIO2]
a No error indicates that the value in question was fixed during the fitting procedure.
reactants for all the 108 kinetic runs are collected in Table 1 of
the Supporting Information.
points from the 108 kinetic series were used for the simultaneous
evaluation. Our quantitative criterion for an acceptable fit was
that the average deviation for the absolute fit approach 0.008
(in case of relative average deviation it corresponds to ap-
proximately 2.5%), which is close to the experimentally
achievable limit of error taking the complexity of the kinetic
curves into account (see later).
Methods and Instrumentation. The reaction was followed
by a Zeiss S10 diode array spectrophotometer in the visible
range without using the deuterium lamp to prevent the photo-
chemical decomposition of tetrathionate at a longer time scale.22
The reaction has been carried out in a standard quartz cuvette
equipped with magnetic stirrer and Teflon cap having 1 cm
optical path. The buffer components were delivered from a pipet
first followed by the addition of thiosulfate and iodide (if nec-
essary) solutions. The stirring rate was then controlled at 750
rpm to provide sufficiently fast (within 1 s) mixing of the
reactants before injecting the iodate solution from a fast delivery
pipet. The spectra of the reacting solution at the wavelength
range of 400-700 nm was acquired up to 15 000-50 000 s.
Data Treatment. MRA studies have shown23 that the only
absorbing species in the visible range are iodine and triiodide
ion. Therefore, the simultaneous evaluation of the kinetic curves
Results
Preliminary Observations. The most important character-
istics of the kinetic curves can be summarized as follows:
• Figure 1 shows the effect of the initial concentration of
thiosulfate on the length of the Landolt time as well as on
formation of total amount of iodine ([I2] + [I3-]) at the later
phase of the reaction. First, the insert indicates that the induction
period decreases with increasing thiosulfate concentration within
the range studied. Second, as thiosulfate disappears from the
reacting solution the concentration of iodine starts to increase.
At low initial thiosulfate concentrations, however, the monoto-
nous formation of the total amount of iodine goes through an
inflection point. At higher thiosulfate concentrations the total
amount of iodine reaches a maximum followed by a decrease
in its concentration.
• Figure 2 indicates the effect of the iodate concentration on
the formation of iodine. It is easily seen that the Landolt time
significantly decreases by an increase of the initial iodate
concentration. The shape of the absorbance-time curves also
varies; at low iodate concentration the formation of the total
amount of iodine shows a saturation-like kinetic curves, but at
-
was carried out at the isosbestic point of I2-I3 system at 468
nm by the program package ZiTa.24 The molar absorbance of
both species was found to be 750 M-1 cm-1 at this wavelength.
Originally, each kinetic run contained more than 400 absor-
bance-time data pairs; therefore, it was necessary to reduce
the number of time points (50-60) to avoid unnecessary time-
consuming calculations. The essence of this method has already
been described elsewhere.25 To obtain the kinetic model and
the rate coefficients, an absolute fitting procedure has been
chosen to minimize the average deviation between the measured
and calculated absorbance. Altogether almost 5800 experimental

5754 J. Phys. Chem. A, Vol. 114, No. 18, 2010
Varga et al.
Figure 1. Measured (dots) and calculated (solid lines) absorbance-time curves at pH ) 3.64 and [IO3-]0 ) 0.004 M in the absence of initially
added iodide ion. [S2O32-]0/mM ) 2.0 (black), 3.0 (blue), 4.0 (green), 5.0 (cyan), 6.0 (red), 7.4 (magenta), 8.4 (yellow), and 10.0 (brown). The inset
shows the initial phase of the reaction.
Figure 2. Measured (symbols) and calculated (solid lines) absorbance-time curves at pH ) 3.94 and [S2O32-]0 ) 0.0057 M in the the absence
of initially added iodide ion. [IO3-]0/mM ) 2.0 (b), 3.0 (0), 4.0 (2), 6.0 ()), 8.0 (9), 10.0 (O), 12.0 (().
higher iodate concentration the increase of [I2] + [I3-] goes
through an inflection point.
participate in the reaction mechanism. This group consists
of the reactants thiosulfate and iodate, the products sulfate,
iodide, and tetrathionate, and finally the intermediates such
as hydrogen sulfite, iodous acid, hypoiodous acid, I2O2,
S2O3OH-, S4O6I-, and S2O3I- and the species H+, OH-, and
H2O that are always present in an aqueous medium. After
that, all the possible mono- and bimolecular steps of these
species were considered along with their H+-catalyzed
pathways. During the fitting procedure, the steps, the rate
coefficients of which became insensitive on the average
deviation, were omitted step by step. This method has been
applied successfully in several cases of our previous work.25-28
After long but straightforward systematic reduction, the
following model has emerged.
• Figure 3 depicts the pH dependence of the formation of
the total amount of iodine. As seen, the Landolt time
decreases with decreasing pH. At higher pHs the iodine
formedaftertheLandolttimelevelsoffat2:1thiosulfate-iodate
initial ratio. With a decrease of pH the amount of iodine
formed increases and the absorbance-time curves first go
through an inflection point. A further decrease in pH changes
the shape of the measured kinetic traces and results in a
maximum of the concentration of total amount of iodine as
a function of time.
• Figure 4 shows the effect of the initially added iodide ion on
the Landolt time as well as on the shape of the kinetic traces. As
easily seen, the Landolt time decreases and the amount of iodine
formed significantly increases with increasing iodide concentration.
Proposed Kinetic Model. To build up the kinetic model,
we have chosen the following set of species that most likely
CH3COOH h H+ + CH3COO-
(E1)

Complex Kinetics of a Landolt-Type Reaction
J. Phys. Chem. A, Vol. 114, No. 18, 2010 5755
-
I2 + I- h I3
(R1)
(R2)
parameters used in the simultaneous evaluation of the kinetic
curves. The average deviation was found to be 0.008 absorbance
unit (AU). The Supporting Information containing all the
measured and calculated kinetic curves indicates a sound
description of the measured curves by the proposed model.
2-
-
S2O3 + IO3 + 2H+ f S2O3OH- + HIO2
S2O3 + HIO2 + H+ f S2O3OH- + HOI (R3)
2-
Discussion
Step R1 is the rapid equilibrium formation of triiodide ion
investigated by several authors.29,30 The rate coefficients of the
2-
S2O3 + HOI f S2O3OH- + I-
(R4)
(R5)
(R6)
forward and reverse reactions were set to kR1 ) 5.7 × 109 M-1
s-1 and k-R1 ) 8.5 × 106 s-1, respectively, to give log ꢀI
)
-
3
2.83, where ꢀ is the formation constant of triiodide ion.21
2-
S2O3 + HOI + H+ f S2O3I- + H2O
I3
-
Step R2 is a second-order rate-determining process respon-
sible for the initiation of the reaction that may proceed via a
simple oxygen transfer from the iodate molecule to the
thiosulfate ion. The surprising result of our calculation is that
this reaction turned out to be pH-independent despite the fact
that the overall thiosulfate-iodate reaction strongly depends on
pH, as found in earlier works.14,20 As we shall see later, our
result is not contradictory with the previous ones, because step
R2 is not the only rate-determining process of the kinetic model
proposed. Namely, as the reaction proceeds, more and more iodate
is reduced to iodide ion that results in an increase of the
concentration of the steady-state intermediate I2O2, which also
converts thiosulfate eventually into sulfate and tetrathionate ions.
The formation of I2O2, however, depends on the square of [H+],
meaning that the overall reaction strongly depends on pH as
expected.
Step R3 is the fast oxidation of thiosulfate ion by iodous acid
formed in the initiation process. Evidently, this reaction must
be much faster than step R2 because of the higher reactivity of
thiosulfate toward iodous acid. We found the rate coefficient
of this reaction to be in total correlation with that of step R10.
The reason for the correlation can be understood as follows.
Since iodine formed via a rapid reaction (step R9) and one of
the main source of hypoiodous acid is step R3 at the early phase
of the reaction, iodine has to be removed quickly so as not to
accumulate during the Landolt time. The ratio of kR3 and kR10
was found to be 6.65 ( 1.20 if kR10 is not higher than 2 × 107
M-1 s-1.
-
IO3 + I- + 2H+ h I2O2 + H2O
2-
S2O3 + I2O2 + H2O f S2O3OH- + I- + HIO2
(R7)
I- + H+ + H2O + I2O2 f 3HOI
I- + H+ + HOI f I2 + H2O
(R8)
(R9)
2-
S2O3 + I2 f S2O3I- + I-
(R10)
2-
2-
S2O3 + S2O3OH- + H+ f S4O6 + H2O
(R11)
-
S2O3OH- + I2 + 2H2O f 2HSO3 + 2I- + 3H+
(R12)
(R13)
-
-
S2O3OH- + IO3 + H2O f 2HSO3 + HIO2
-
-
S2O3I- + IO3 + 2H2O f 2HSO3 + 2HOI
Step R4 is a relatively fast formal oxygen transfer process to
oxidize thiosulfate with hypoiodous acid. The individual rate
coefficient of this reaction cannot be determined from our
experiments. The calculation showed that there is a total
correlation between the parameters kR4, kR5, and kR9; therefore,
only the ratio of kR4/kR9 and kR5/kR9 could be calculated.
Chemically it means that hypoiodous acid is a reactive
intermediate in the present system having relatively low steady-
state concentration. Since kR9 was determined independently31
as 3.67 × 109 M-1 s-1 and our calculation showed that kR4/kR9
is 8.76 ( 0.48, we could calculate a value of (3.2 ( 0.2) ×
1010 M-1 s-1 for kR4, indicating that this reaction is close to the
diffusion controlled limit as expected by the fact that iodine
also rapidly oxidizes thiosulfate.32
(R14)
(R15)
2-
-
2S2O3I- + I- f S4O6 + I3
2-
S4O6 + I2 h S4O6I- + I-
(R16)
S4O6I- + 2H2O f 2S2O3OH- + I- + 2H+
(R17)
(R18)
-
2-
HSO3 + I2 + H2O f 2I- + SO4 + 3H+
Step R5 is a competitive process with step R4 that leads to
the formation of S2O3I- instead of hypoiodous acid and
S2O3OH-. This process is a formal electrophilic I+ transfer
frequently occurring in different oxidation reactions of hypo-
halogenous acids.33,34 It may seem surprising that hypoiodous
acid can react with thiosulfate via an oxygen transfer (step R4)
and a I+ transfer (step R5) pathway simultaneously as well, but
this result is not a unique feature of the kinetic behavior of
hypohalogenous acid. Fogelman et al. have already reported33
that hypochlorous acid reacts with sulfite via parallel oxygen
-
2-
HSO3 + HIO2 f SO4 + H+ + HOI (R19)
The rapid de- and reprotonation process E1 was taken into
account with known equilibrium constant to follow the slight
change in pH during the reaction. This acid dissociation
equilibrium may be regarded as an auxiliary process necessary
for the detailed calculation, but it is not a central part of the
proposed model. Table 1 contains the fitted and fixed kinetic

5756 J. Phys. Chem. A, Vol. 114, No. 18, 2010
Varga et al.
Figure 3. Measured (symbols) and calculated (solid lines) absorbance-time curves at [IO3-]0 ) 0.004 M and at [S2O32-]0 ) 0.008 M in the
absence of initially added iodide ion. pH ) 4.24 (b), 4.09 (0), 3.94 (2), 3.79 ()), 3.64 (9), 3.49 (O), 3.34 (().
Figure 4. Measured (symbols) and calculated (solid lines) absorbance-time curves at [IO3-]0 ) 0.004 M [S2O32-]0 ) 0.0077 M and pH ) 4.24
in the presence of initially added iodide ion. [I-]0/mM ) 0.2 (b), 0.3 (0), 0.5 (2), 0.7 ()), 0.9 (9), 1.2 (O), 1.5 (().
transfer and Cl+ transfer to produce sulfate and chloride eventually.
On the basis of this analogy, one may expect that hypoiodous acid
may behave in the same way in the title reaction. Our calculation
indicated that kR5/kR9 is 2.55 ( 0.16, which means that one can
calculate (9.4 ( 0.6) × 109 M-1 s-1 for kR5.
only determine the value of 5.74 × 109 M-4 s-1 for KR6kR7. It
is also interesting to note that this is one of the parameters that
could be determined the most precisely. The underlying
chemistry seems to be clear, though at the early stages of the
reaction the role of this route is negligible, the increase in the
concentration of the product iodide ion increases the importance
of this pathway during the reaction and gradually takes over
the role of step R1. Chemically, it means that step R7 is
responsible for the pH dependence of the Landolt time.
Step R8 is the other important reaction of the intermediate
I2O2 that has a dual role in determining the kinetics of the
reaction. Iodide ion competes with thiosulfate to react with I2O2
and therefore not only partly affects the length of the Landolt
time but also has a significant contribution to the later phase of
the reaction to produce iodine via hypoiodous acid. One may
also notice that combining step R8 with steps R9 and R12 results
in an autocatalytic production of iodine. This feature is only
partly manifested in some experimental curves, where the
maximum amount of iodine is reached via an absorbance-time
curve having an inflection point. Our calculation showed that
Step R6 is the well-known equilibrium suggested by several
researchers35 to interpret many experimentally found aspects of
the Dushman reaction. We found that neither the rate coefficient
of the forward nor that of the reverse reaction could be
determined independently from our measurements. This process
is rapidly equilibrated and provides I2O2 as a steady-state
intermediate. We set an arbitrary KR6 ) kR6/k-R6 ) 100 M-3
value that is able to maintain the concentration of I2O2 in a
sufficiently low level under our experimental conditions.
Step R7 is the other rate-determining step of the kinetic model
and also responsible for the effect of pH on the Landolt time.
Evidently, this route is opened up when the concentration of
iodide reaches a certain level (at pH ) 4.0 the rate of step R7
is equal to that of step R1 at [I-] ≈ 0.0013 M) and gradually
overtakes the governing role as the reaction proceeds. We can

Complex Kinetics of a Landolt-Type Reaction
J. Phys. Chem. A, Vol. 114, No. 18, 2010 5757
only KR6kR8 can be determined from our experiments which was
reasonable agreement with our calculated kR15 ) 7960 ( 560
M-2 s-1 value. The triiodide inhibition suggested by Awtrey
and Connick, however, has not been found. It should also be
noted that changing the kR5[S2O3I-]2[I- ] rate equation by the
kR15[S2O3I-][I-] would lead to a slightly higher average devia-
tion (0.0095 AU). However, we noticed systematic deviations
between the experimental and the calculated kinetic curves
especially at larger initial thiosulfate concentrations and lower
pHs. We concluded that our results support the rate equation
indicated in Table 1 for step R15 rather than any other one.
Step R16 is the well-known initiating equilibrium process of
the tetrathionate-iodine reaction in which formal I+ transfer
occurs.28,40 Our calculations have provided for kR16 a value of
(8.41 ( 0.12) × 10-2 M-1 s-1. Since we found total correlation
between the parameters k-R16 and kR17 and previously we
determined28 this equilibrium constant to be 1.92 × 10-7, we
set k-R16 as 4.38 × 105 M-1 s-1 and calculated kR17 (see later).
Step R17 is the hydrolysis of S4O6I- formed in step R16.
Although Awtrey and Connick40 suggested the following
reaction for the hydrolysis of S4O6I-
found to be 4.26 × 108 M-4 s-1
.
Step R9 is responsible for the formation of iodine. The rate
coefficient of this reaction was established31 previously as 3.67
× 109 M-1 s-1; therefore, we used this value as a fixed parameter
during the calculation procedure.
Step R10 is the initiating process of the well-known fast
thiosulfate-iodine reaction.32 The absolute value of this rate
coefficient cannot be determined from our experiments, but total
correlation was found between kR3 and kR10 if the latter one is not
higher than 2 × 107 M-1 s-1. Actually, our calculations have pro-
vided a slight minimum in the standard deviation if kR10 is fixed at
106 M-1 s-1. It is interesting to note that the actual value of this
rate coefficient is only slightly lower than that found by Scheper
and Margerum for the rate determining step of thiosulfate-iodine
reaction.36 Since the decrease in the average deviation (less than
3%) cannot be decisive in determining the absolute value of kR10
,
we inclined to report only the ratio of kR3 and kR10
.
Step R11 is also a fast reaction to produce tetrathionate ion
from the intermediate S2O3OH-. From our experiments we were
unable to calculate the individual rate coefficient of this reaction.
Other researchers37-39 have, however, found that this reaction has
a pH-dependent term besides the pH-independent one, and even
both rate coefficients were determined.39 Therefore, we have fixed
these values kR11 and kR′ 11 as 50 M-1 s-1 and 2.5 × 109 M-2 s-1.
Step R12 is responsible for the slow removal of iodine by
S2O3OH- at the later kinetic phase of the reaction. It also means
that S2O3OH- has to be a relatively long-lived intermediate
under the present experimental conditions. Elimination of this
step from the final model would lead to a more than 50%
increase in the final average deviation (0.012 absorbance unit)
from which we concluded this step to be firmly established.
Our investigations in other related systems like the
tetrathionate-bromine26 and the tetrathionate-hypochlorous
acid27 ones showed that the role of S2O3OH- and S2O3X-, where
X can be either chlorine or bromine, is commutable in the kinetic
model suggested. We have also tried to seek evidence for this
fact in the thiosulfate-iodate system with no success. It is
therefore concluded that the long-lived intermediate in the
thiosulfate-iodate system is S2O3OH-.
S2O6I- + H2O f S2O3OH- + S2O3I- + H+
(2)
it was already pointed out in our previous work28 that eq 2 can
completely be substituted with step R17. The present experi-
ments, however, rather confirm step R17 than eq 2 for the
hydrolysis of S4O6I- since inclusion of the latter process would
lead to an unacceptably high average deviation (0.0189 AU) in
the present system.
Step R18 is the well-known fast reaction between hydrogen
sulfite and iodine. This reaction was thoroughly studied by Yiin
and Margerum3 and even the rate coefficient of this process
was determined to be 3.1 × 109 M-1 s-1. Therefore, we have
fixed kR18 at this value.
Step R19 is also fast reaction between hydrogen sulfite and
iodous acid producing HOI. We found that kR19 is in total
correlation with kR18; therefore, we could only calculate the kR19
/
kR18 ratio. The underlying chemistry is clear; the short-lived
intermediate HSO3- reacts quickly with iodine and iodous acid
to give the product iodide ion and HOI, respectively. As pointed
out earlier, HOI has a decisive role in producing iodine but it
Step R13 is the other route that removes the long-lived
intermediate S2O3OH- by iodate. Our calculations indicated that
the rate of this reaction also depends on pH. It follows from
the experimental fact that significantly more iodine forms with
decreasing pH in excess of iodate. It is easily understood by
the help of this pH-dependent reaction since iodous acid formed
has to be controlled as well by step R18. We found the kR19
/
kR18 ratio to be 6.32 ( 0.35, from which we could calculate
1.96 × 1010 M-1 s-1 for kR19, indicating that this reaction is
essentially diffusion controlled.
-
in this process will react with HSO3 to give HOI (see: step
Finally, we shall point out how the seemingly complicated
absorbance-time curves, which reflect the concentration of the
total amount iodine formed via the reaction, can easily be
explained by the kinetic model proposed. We shall see that
iodide ion plays a crucial role to drive the reaction. As long as
thiosulfate is not consumed, the concentration of iodide ion
increases monotonously because all the iodine is removed by
the well-known fast thiosulfate-iodine reaction. Once thiosul-
fate is completely removed from the reacting solution the
concentration of iodine starts to build up as a result of steps R8
and R9, and simultaneously the concentration of iodide ion starts
to decrease. These processes are responsible for the relatively
fast increase of the total amount of iodine after the Landolt
period. It is well-known that at higher iodide concentrations
the tetrathionate-iodine reaction is strongly inhibited by iodide
ions.28,40 The decrease in the iodide concentration therefore
opens up this slow reaction that would decrease the concentra-
tion of iodine and simultaneously produce iodide ion, but as
R19 later), which then produces iodine via step R9.
Step R14 has a dual role in the kinetic model because on the
one hand it prevents the buildup of S2O3I- and on the other
hand in iodate excess it provides hypoiodous acid that produces
iodine by its reaction with iodide ion. The rate coefficient of
this reaction was found to be 3.58 ( 0.12 M-1 s-1
.
Step R15 was already proposed by Awtrey and Connick in
the thiosulfate-iodine reaction, although they suggested the
following rather complicated rate law for this reaction:32
[S2O3I-]2[I-]2
r ) k
(1)
-
[I3 ]
where k was found to be 5000 M-2 min-1. In the case of [I2] )
10-4 M bearing in mind that the stability constant of triiodide
ion is 660 M-1, we could calculate 1200 M-2 s-1, which is in

5758 J. Phys. Chem. A, Vol. 114, No. 18, 2010
Varga et al.
long as enough iodate is present in the reaction mixture, it
supplies the necessary amount of I2O2 via step R8 at a low
steady-state concentration level from which iodine can still form
at a much slower rate. During this stage of the reaction the main
components, iodate and tetrathionate ions, are slowly removed.
These changes, therefore, result in a much slower increase of
the total amount of iodine compared to the period right after
the end of the Landolt time. The shape of the absorbance-time
curves at the final stage of the reaction depends on the
concentration of tetrathionate and iodate. If tetrathionate is in
excess, i.e., the initial thiosulfate-iodate concentration ratio is
high, then iodate slowly disappears from the reacting mixture,
preventing the formation of iodine via I2O2. It means that
tetrathionate eventually consumes all the iodine responsible for
decrease of the absorbance at the final stage. It should be noted
that in the case of the initial thiosulfate-iodate concentration
ratio being larger than 6, no iodine is formed if one takes the
following overall equation into account:
Supporting Information Available: Table containing the
condition of each kinetic run and figures containing the
measured and fitted absorbances. This material is available free
of charge via the Internet at http://pubs.acs.org.
References and Notes
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Conclusion
This paper elucidates the kinetics and mechanism of the later
phase of the thiosulfate-iodate reaction that shows unexpectedly
complex kinetic behavior after the Landolt period, where iodine
starts to form in appropriate concentration ranges of the
reactants. The complexity of the measured kinetic curves clearly
suggests that no simplified evaluation (individual exponential
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the only way to unravel its kinetics and mechanism.
An important remark should, however, be emphasized. As
seen, the proposed kinetic model, almost perfectly describes the
measured kinetic curves at a relatively wide concentration range
of the reactants but in some cases it is not able to predict
properly the length of the Landolt period. (See some kinetic
curves in the Supporting Information, e.g., Figures S3A, S5B,
and S5C.) This inaccuracy emerges from the fact that at large
initial thiosulfate concentrations the measured absorbance signal
is too small compared to all the other cases (evidently, with a
huge excess of thiosulfate no iodine forms at all). It means that
further experiments are required to explore the thiosulfate-iodate
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Acknowledgment. This work was supported by the Hungar-
ian Research Fund (OTKA) Grant No. K68172. A.K.H is
grateful for the financial support of the Ja´nos Bolyai Research
Scholarship of the Hungarian Academy of Sciences.
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