The Kinetics and Mechanism of the Chlorine Dioxide - Iodide Ion Reaction

Article abstract of DOI:10.1021/ic961279g

The oxidation of iodide ion by chlorine dioxide has been studied by stopped-flow techniques at I = 1.0 M (NaClO₄). The following two-term rate law was confirmed for the reaction: -d[ClO₂]/dt = k_I[ClO₂][I^-

Full text of DOI:10.1021/ic961279g

2494
Inorg. Chem. 1997, 36, 2494-2497
Ar ticles
The Kinetics and Mechanism of the Chlorine Dioxide-Iodide Ion Reaction
Istva´n Fa´bia´n*,† and Gilbert Gordon‡
Department of Inorganic and Analytical Chemistry, Kossuth L. University, Debrecen P.O.B. 21,
H-4010 Hungary, and Department of Chemistry, Miami University, Oxford, Ohio 45056
ReceiVed October 24, 1996X
The oxidation of iodide ion by chlorine dioxide has been studied by stopped-flow techniques at I ) 1.0 M (NaClO4).
The following two-term rate law was confirmed for the reaction: -d[ClO2]/dt ) kI[ClO2][I-] + kII[ClO2][I-]2.
The rate constants at 298 K and the activation parameters are kI ) (1.87 ( 0.02) × 103 M-1 s-1, ∆HIq ) 35.4
q
( 0.7 kJ/mol, ∆SIq ) -63.5 ( 2.3 J/(mol K), kII ) (1.25 ( 0.04) × 104 M-2 s-1, ∆HII ) 36.7 ( 1.3 kJ/mol,
q
∆SII ) -43.2 ( 4.6 J/(mol K). Both the second- and third-order paths are interpreted in terms of an outer-
sphere electron-transfer mechanism. The calculations based on the Marcus theory yield kI ) 1358 M-1 s-1 for
the second-order path.
tometrically by using the characteristic absorbance band9 of ClO2 in
Introduction
the near-UV-visible region (λmax) 358.5 nm; ꢀmax ) 1250 M-1cm-1).
The redox reaction between chlorine dioxide and iodide ion
NaClO4 was prepared from Na2CO3 and HClO4 and purified as detailed
has been the subject of intense studies for decades.1-4 This
reaction serves as a basis for the iodometric determination of
ClO2.5 It is also an important subset in a series of oxychlorine-
based exotic reactive systems.4,6,7
elsewhere.10 Other reagents, i.e., NaI, CH3COONa, and CH3COOH,
were analytical grade and used without further purification. All
experiments were carried out in 0.04 M acetic acid/acetate buffer and
at 1.0 M ionic strength set by adding appropriate amounts of NaClO4.
Methods. Stopped-flow traces were recorded on an Applied
Photophysics SX-17MV unit. Pseudo-first-order conditions were
applied by using at least a 10-fold excess of iodide ion over chlorine
dioxide ([ClO2] ) (2.0-8.0) × 10-4 M; [I-] ) 0.006-0.3 M). The
reaction was monitored by following the formation of I3- in the 350-
470 nm region. First-order rate constants were obtained by fitting the
average of at least five replicate runs by using a nonlinear least squares
routine provided with the stopped-flow instrument. In test experiments,
the rate constants obtained at various wavelengths agreed within (2%.
Thus, most of the measurements were made at a single wavelength
(400 or 410 nm). The temperature dependence of the rate constants
was studied from 3 to 46 °C.
Earlier it was suggested2 that the oxidation of iodide ion by
ClO2 proceeds via the fast formation and subsequent slower
decomposition of a transient species, ClO2I-. Recently a more
simple kinetic behavior was reported by Lengyel et al.4 The
reaction was found to be first order with respect to both
reactants. It was assumed that the rate-determining step in the
overall process is a simple electron-transfer reaction between
the reactants. The details of the mechanism were not discussed
in that paper, and kinetic data are not available to evaluate
whether the electron transfer occurs by means of an inner- or
outer-sphere process. Therefore, we have designed a temper-
ature dependent study in order to explore the intimate nature
of this reaction. Preliminary results indicated a somewhat
unexpected kinetic behavior, which is discussed in the present
paper in detail.
Results and Discussion
In excess iodide ion, ClO2 is reduced to Cl-. However, in
slightly acidic to neutral solutions the reaction occurs in two,
well-separated phases. In the first, fast step, chlorine dioxide
is reduced to ClO2-. Further redox reaction between chlorite
ion and iodide ion is slower by several orders of magnitude
and does not interfere with the first process. Under the applied
conditions, the observed kinetic traces correspond to the
following overall redox reaction:
Experimental Section
Chemicals. Chlorine dioxide solutions were prepared by mixing
aqueous solutions of K2S2O8 and NaClO2 as described earlier.8 The
concentration of the ClO2 stock solutions was determined spectropho-
† Kossuth L. University.
‡ Miami University.
2ClO2 + 2I- ) 2ClO2- + I2
(1)
X Abstract published in AdVance ACS Abstracts, May 1, 1997.
(1) Bray, W. C. Z. Phys. Chem. 1906, 54, 575.
(2) Fukutomi, H.; Gordon, G. J. Am. Chem. Soc. 1967, 89, 1362.
(3) Huie, R. E.; Neta, P. J. Phys. Chem. 1986, 90, 1362.
(4) Lengyel, I.; Ra´bai, Gy.; Epstein, I. R. J. Am. Chem. Soc. 1990, 112,
9104.
In agreement with recent results,4 simple first-order kinetic
traces were obtained, indicating that the reaction is first order
with respect to ClO2. Our observations also confirmed that the
reaction rate is independent of pH. The pseudo-first-order rate
constants (kobs) are statistically identical in the pH 4.09-5.04
region (Figure 1). However, Figure 1 also indicates an
(5) Gordon, G.; Cooper, W. J.; Rice, R. G.; Pacey, G. E. Disinfectant
Residual Measurement Methods; AWWA Research Report: Denver,
CO, 1987 and references therein.
(6) Noszticius, Z.; Quyang, Q.; McCormick, W. D.; Swinney, H. L. J.
Am. Chem. Soc. 1992, 114, 4290.
(7) Ra´bai, Gy. J. Phys. Chem. 1994, 98, 5920.
(8) Rosenblatt, D. H.; Hayes, A. J. J. Org. Chem. 1963, 28, 2790.
(9) Kieffer, R. G.; Gordon, G. Inorg. Chem. 1968, 7, 235.
(10) Fa´bia´n, I.; Gordon, G. Inorg. Chem. 1991, 30, 3785.
S0020-1669(96)01279-7 CCC: $14.00 © 1997 American Chemical Society

Chlorine Dioxide-Iodide Ion Reaction
Inorganic Chemistry, Vol. 36, No. 12, 1997 2495
Figure 1. The pseudo-first-order rate constant as a function of iodide
concentration at various pH values (25.0 °C, I ) 1.0 M NaClO4).
Figure 3. LFER for the second-order path of oxidation reactions of
3+
I-. The oxidants are as follows: Fe(phen)33+, Fe(5,6-(CH3)2-phen)3
,
Fe(4,7-(CH3)2-phen)33+, Fe(3,4,7,8-(CH3)4-phen)33+, Fe(bpy)33+, Fe(4,4′-
(CH3)2-bpy)33+, IrCl62-, IrBr62-, Mo(CN)82-, Os(bpy)33+, Os(phen)3
3+
(b); ClO2 (9); NpO22+, PuO2 (O). The data were used as given or
2+
cited in refs 13-15.
Table 1. Kinetic Results for the Oxidation of I- by Chlorine
Dioxide
parameter
kI (M-1 s-1) at 298 K
∆HIq (kJ/mol)
(1.87 ( 0.02) × 103
35.4 ( 0.7
∆SIq (J/(mol K))
kII (M-2 s-1) at 298 K
∆HIIq (kJ/mol)
-63.5 ( 2.3
(1.25 ( 0.04) × 104
36.7 ( 1.3
Figure 2. The plot of the data at various temperatures according to
eq 4 (pH ) 4.57, I ) 1.0 M NaClO4).
∆SIIq (J/(mol K))
-43.2 ( 4.6
third-order term, i.e., the second term in eq 2, led to a higher
rate constant in the earlier paper.
The two-term rate equation obtained here is quite common
in the noncomplementary redox chemistry of iodide ion.12-16
Equation 2 seems to be consistent with the following mecha-
nism:
unexpected kinetic feature in this system. According to previous
literature the reaction is first order with respect to iodide ion.
This would predict a simple linear concentration dependence
of kobs on [I-]. However, the systematic deviation from linear
behavior at higher iodide ion concentrations clearly indicates a
more complex kinetic pattern. The problem was investigated
in an extended concentration range of iodide ion at various
temperatures.
ClO2 + I- h ClO2I-
ClO2I- f ClO2- + I•
Ka, fast pre-equilibrium (6)
The concentration dependence of the rate constants was
consistent with the following rate law:
k1
(7)
(8)
-
I• + I- ) I2
fast
-d[ClO2]/dt ) kI[ClO2][I-] + kII[ClO2][I-]2
It follows that
(2)
(3)
(4)
-
ClO2I- + I- f ClO2- + I2
k2
fast
(9)
ClO2 + I2- ) ClO2- + I2
(10)
(11)
kobs ) kI[I-] + kII[I-]2
-
I2 + I- ) I3
fast
and eq 3 can be rearranged into the following form:
In this mechanism ClO2I- is either an outer-sphere complex
or a weakly bonded species characterized by stability constant
k
obs/[I-] ) kI + kII[I-]
-
Ka. Provided that I• and I2 are at steady state, standard
The plot of the experimental data according to eq 4 is shown
at three different temperatures in Figure 2. The excellent
linearity of these plots confirms the above rate law.
The activation parameters of rate constants kI and kII were
calculated by fitting kobs data on the basis of eq 5, by using
the nonlinear least squares routine of the program SCIENTIST
2.0.11 Experimental and calculated rate constants are given
in the Supporting Information. The results are listed in
Table 1.
derivation yields kI ) 2k1Ka and kII ) 2k2Ka. In principle
reaction 7 is reversible. However, reaction 8 is close to diffusion
controlled,17 and under the applied conditions the reverse
step of reaction 7 is negligible compared to the fast formation
-
of I2
.
On the basis of a somewhat limited data set Stanbury and
co-workers15 showed excellent LFER for the kI path. The
correlation remains valid when additional data are included
(Figure 3). The data for the ClO2-I- reaction is also in
q
q
q
q
kT
h
kT
h
kobs
)
e∆S /Re-∆H /(RT)[I-] + e∆S /Re-∆H /(RT)[I-]2 (5)
I
I
II
II
(12) Cooper, J.; Reents, W. D., Jr.; Woods, M.; Sjoblom, R.; Sullivan, J.
C. Inorg. Chem. 1977, 16, 1030.
(13) Nord, G.; Pedersen, B.; Farver, O. Inorg. Chem. 1978, 17, 2233.
(14) Adedinsewo, C. O.; Adegite, A. Inorg. Chem. 1979, 18, 3597.
(15) Stanbury, D. M.; Wilmarth, W. K.; Khalaf, S.; Po, H. N.; Byrd, J. E.
Inorg. Chem. 1980, 19, 2715.
(16) Nord, G. Comments Inorg. Chem. 1992, 13, 221.
(17) Baxendale, J. H.; Bevan, P. L. T.; Stott, D. A. Trans. Faraday. Soc.
1968, 64, 2389.
The value of kI is about 3 times smaller than the rate constant
reported by Lengyel and co-workers;4 however, the source of
the discrepancy is not apparent. Perhaps the omission of the
(11) SCIENTIST 2.0, MicroMath Software, 1995.

2496 Inorganic Chemistry, Vol. 36, No. 12, 1997
Fa´bia´n and Gordon
Table 2. Test of the Marcus Cross Relation for the Third-Order
agreement with previous results. The correlation was observed
regardless of the charge and type of the oxidants. The only
Patha,b
2+
exceptions are the data for the reactions of PuO22+ and NpO2
meas
calc
k22
k12
(M-1 s-1
k12
(M-1 s-1
)
oxidantc
ꢀ22 (V) (M-1 s-1
)
)
(open circles in Figure 3). In these cases the deviation is
supposedly due to the nonadiabaticity of the electron-transfer
reaction.15 The rest of the data indicates that probably the same
mechanism is operative in all reactions which have the same,
close to diffusion-controlled reverse rate constant. Earlier it
was suggested that these reactions proceed via an outer-sphere
mechanism.15,16 On this basis, the Marcus theory18 was tested
by using the following equations:
2-
IrBr6
V(III)
Os(phen)3
0.843 2.0 × 108 4.3 × 103 7.6 × 103
-0.255 1.0 × 10-2 1.8 × 10-14 5.1 × 10-14
0.840 3.1 × 108 1.7 × 104 8.8 × 103
0.837 1.8 × 108 9.2 × 103 6.3 × 103
0.97 3.3 × 108 1.6 × 106 1.5 × 105
0.87 3.3 × 108 1.3 × 106 1.8 × 104
0.81 3.3 × 108 5.4 × 104 4.6 × 103
0.88 3.3 × 108 2.6 × 104 2.2 × 104
0.934d 3.3 × 104 e 6.5 × 103 f 7.3 × 102
3+
3+
Os(bpy)3
Fe(5,6-(CH3)2-phen)3
Fe(4,7-(CH3)2-phen)3
Fe(3,4,7,8-(CH3)4-phen)3
Fe(4,4′-(CH3)2-bpy)3
3+
3+
3+
3+
ClO2
-
a For the 2I-/I2 couple: ꢀ11 ) 1.04 V, k11 ) 1.15 × 103 M-1 s-1
k12 ) (k11k22K12f)1/2
(12)
(13)
b
from ref 15. ꢀ22, k22, and k12 values were taken as cited in refs 13, 14,
and 15. c phen, 1,10-phenanthroline; bpy, 2,2′-bipyridine. d From ref
(log K12)2
log f )
20. e From ref 21. f This work.
4 log k11k22/Z2
on the Marcus theory. Without specifying the actual redox
couples, Adedinsewo and Adegite suggested that the values of
f and k11 (eqs 12 and 13) are the same for both the second- and
third-order terms.14 According to their suggestion, kI and kII
can be related to each other on the basis of thermodynamic
In eq 13, k12 () k1Ka) and K12 are the rate constant and
equilibrium constant for the cross reaction:
ClO2 + I- ) ClO2- + I•
(14)
considerations, and the kII/kI ratio should be around 300 M-1
.
For most of the available data the actual kII/kI ratio is within 1
order of magnitude of the expected value. Clearly, our results
for the ClO2-I- system do not comply with the expectations
(kII/kI ∼ 7 M-1).
Parameters k11, k22, and Z (∼1011 M-1 s-1) are the self-exchange
rate constants and the collision frequency, respectively. It
should be noted that one of the reactants is neutral in both redox
couples; therefore, work terms do not complicate the calculation
of the rate constant.
The main problem with the considerations of Adedinsewo
and Adegite is that the Marcus theory cannot be directly applied
for the overall third-order term. This problem was discussed
by Stanbury and co-workers in detail.15 The theory implies a
bimolecular electron exchange process (k11) between 2I- and
I2-, which was interpreted by postulating the highly hypothetical
I-,I- species.15,23 With this self-exchange process the Marcus
theory predicted the rate constants for a few selected reactions
reasonably well.15 In other cases, including the ClO2-I-
reaction, the agreement is less satisfactory (Table 2).24 In order
to justify the proposed self-exchange process the Franck-
Condon barrier was estimated for the I2-/I-,I- redox couple on
the basis of various models.23 Still, a quantitative interpretation
of the reorganizational energies and an exact description of the
self-exchange process could not be given.
Due to the protolytic equilibrium10 between chlorite ion and
chlorous acid (pKa ) 1.72) the redox potential for the ClO2/
-
ClO2 couple is pH dependent.19 However, in slightly acidic
-
to neutral (pH > 4.0) solutions the dominant species is ClO2
and the redox potential20 is invariably E° ) 0.936 V. The self-
exchange rate constant for the same couple was reported
recently,21 k11 ) (2.6-6.7) × 104 M-1 s-1 (average: 3.3 × 104
M-1 s-1).
The parameters for the I•/I- couple are more controversial.
On the basis of theoretical calculations, Woodruff and Marg-
erum22 estimated that E° ) +1.42 V. According to Stanbury
and co-workers15 this value would be consistent with a larger
than diffusion-controlled rate constant for the reverse step of
reaction 14. Their estimate for E° is +1.33 V. For the self-
exchange rate constant two markedly different values were
published. Adedinsewo and Adegite have reported14 k22 ) 7
× 107 M-1 s-1. However, on the basis of that paper, it is not
clear if this value is given for the I•/I- or the I•/I2- couple. The
considerably smaller than expected diffusion-controlled rate
constant was attributed to solvent reorganization in the activation
process. Stanbury and co-workers concluded 1.4 × 109 M-1
s-1 as a lower limit for the same rate constant.15 This value
seems to be more reasonable for redox couples involving a
radical species. The results presented here lend further support
to the conclusions of Stanbury and co-workers. When their data
was used, a satisfactory agreement was found between the
experimental and calculated rate constants for the cross reaction,
The third-order term requires the formation of a transition
species with a composition of ClO2I22-. By analogy with the
other path, eq 9 can be rewritten in the following form:
2-
ClO2I- + I- h ClO2I2
Ka2, fast pre-equilibrium
(9a)
ClO2I22- f {ClO2I2- + I•} f ClO2- + I- + I•
k2b
(9b1)
(9b2)
or
exp
calc
k12 ) 926 M-1 s-1 and k12 ) 679 M-1 s-1. With other
literature parameters, much larger deviations were obtained
between these values.
-
ClO2I22- f ClO2- + I2
k2b
In the case of related reactions of iodide ion, earlier attempts
for the interpretation of the third-order term in eq 2 were based
(23) Stanbury, D. M. Inorg. Chem. 1984, 23, 2914.
(24) In ref 15, k11 was defined for a third-order process which led to
incompatible dimensions in eqs 12 and 13. The problem was corrected
in ref 23 by introducing the ion-pair formation constant, KIP, for the
I-,I- species. While the new interpretation of the self-exchange
reaction between I2- and I-,I- resolves the problem of incompatibility,
it does not significantly modify the value of the calculated rate
constants for the cross reactions.
(18) Marcus, R. A.; Sutin, N. Inorg. Chem. 1975, 14, 213.
(19) Latimer, W. Oxidation Potentials, 2nd ed.; Englewood Cliffs: Prentice-
Hall Inc., N.J., 1952.
(20) Stanbury, D. M. AdV. Inorg. Chem. 1989, 33, 69.
(21) Awad, H. H.; Stanbury, D. M. J. Am. Chem. Soc. 1993, 115, 3636.
(22) Woodruff, W. H.; Margerum, D. W. Inorg. Chem. 1973, 12, 962.

Chlorine Dioxide-Iodide Ion Reaction
Inorganic Chemistry, Vol. 36, No. 12, 1997 2497
Table 3. Activation Parameters for the Oxidation of Iodide Ion
q
q
q 298
q
q
∆HIq
(kJ/mol)
∆SIq
(J/(mol K))
∆GIq 298
(kJ/mol)
∆HII
∆SII
∆GII
∆HII - ∆HIq
∆GII -∆GIq
oxidant
(kJ/mol)
(J/(mol K))
(kJ/mol)
(kJ/mol)
(kJ/mol)
3+ a
Os(bpy)3
72.9
57.4
33.1
35.4
-31.0
-16.7
-100.5
-63.5
82.1
62.4
63.1
54.3
38.1
31.4
17.7
36.7
-41.9
-54.4
-110.5
-43.2
50.6
47.6
50.6
49.6
-34.8
-26.0
-15.4
1.3
-31.5
-14.8
-12.5
-4.7
3+ a
Os(phen)3
2- b
IrBr6
c
ClO2
a Reference 13. b Reference 15. c This work.
∆GIq ) ∆G1q + ∆Ga + ln 2
This approach assumes that (i) the fast formation of a second
outer-sphere complex precedes the actual redox step and (ii)
the rate-determining step is the electron-transfer process within
the complex. Thus, the experimentally determined rate constant
can be given as follows: kII ) 2k2bKaKa2. As indicated, the
immediate products of the redox step are not well defined in
this case. Therefore, successful application of the Marcus
theory, which requires the exact knowledge of the self-exchange
electron-transfer steps, seems to be extremely difficult. In earlier
∆GIIq ) ∆G2bq + ∆Ga + ∆G2a + ln 2
∆GIIq - ∆GIq ) ∆G2bq - ∆G1q + ∆G2a
On the basis of these equations, and provided that K2a < 1.0
q
q
(∆G2a > 0) ∆G2b - ∆G1 < -4.7 kJ/mol (Table 3), i.e., the
energy barrier of the electron transfer is smaller through the kII
path. Only limited information is available for the activation
3+
3+
studies with Os(phen)3 and Os(bpy)3 as oxidants,13 it was
suggested that the ∆HIIq - ∆HIq difference is roughly equal to
the enthalpy of formation of the I2- radical (∆H° ) -23.4 kJ/
mol25 ). This led to a conclusion that the actual electron-transfer
step is associated with the same I--I• bond formation as the
formation of I2-. According to these considerations I2- would
form directly from the outer-sphere complex in reaction 9b2.
As shown in Table 3, in other systems the agreement between
2-
parameters of related reactions of I- (Table 3). For the IrBr6
-
I- system, ∆GIIq - ∆GIq is more negative than observed here.
Because of the similar charges of the reactants, K2a is also
expected to be much smaller than for the ClO2-I- reaction.
Thus, the results indicate an even more significant difference
between the energy barriers of the two pathways than in the
ClO2-I- reaction. For the reactions of the osmium complexes
∆G2a < 0 cannot be excluded. However, in order to predict a
more favorable second-order than third-order path, an unrealisti-
cally small value needs to be considered for ∆G2a. In other
words K2a should be larger than 390 M-1 (Os(phen)33+) or 3.3
× 105 M-1 (Os(bpy)33+).
q
∆HII - ∆HIq and ∆H° is not so convincing. The observed
deviations may indicate either that the reactions proceed via a
different path or that other factors also have significance in the
activation process.
It seems, regardless of the charge product of the reactants,
that the same mechanism is operative in all systems. In general,
a longer distance and weaker interactions are expected between
the redox centers in the third-order transition state as compared
to the second-order path. Still, the electron-transfer step within
the activated complex is always faster in the third-order process.
This finding, in spite of the very qualitative nature of the
considerations presented here, lend some support to the as-
sumption that the third-order process also occurs via an outer-
sphere mechanism.
Mechanistic details of the third-order path can be evaluated
by comparing kI and kII. The ratio of these rate constants is
given as follows: kII/kI ) (2k2bKaKa2)/(2k1Ka) ) (k2b/k1)Ka2. The
value of Ka in this expression can be estimated on the basis of
the Fuoss equation.26 According to literature data, the stability
constant of the outer-sphere complex between a charged and a
neutral species is around 0.3 M-1 in the absence of specific
interactions.27 The estimation of Ka2 is less straightforward;
however, on the basis of electrostatic and statistical consider-
ations, it is probably even smaller than Ka. Accordingly, by
using the data from Table 1, k2b/k1 > 7.0. This indicates that
the electron transfer within the precursor complex is more
favorable in the third-order process than in the second-order
path. We can reach the same conclusion on the basis of the
activation parameters. The experimentally determined free acti-
vation energies and their difference can be expressed as follows:
Acknowledgment. This work was supported by the U.S.-
Hungarian Scientific and Technology Joint Fund under JF No.
92b-263. Part of the instrumentation used in this study was a
generous gift from the Alexander von Humboldt Foundation.
Financial help from FO¨ NIX GAÄ Z Ltd. (Debrecen, Hungary) is
also appreciated.
Supporting Information Available: Table listing measured and
calculated rate constants for the oxidation of iodide ion by chlorine
dioxide and various temperatures (1 page). Ordering information is
given on any current masthead page.
(25) Baxendale, J. H.; Bevan, P. L. T. J. Chem. Soc. A 1969, 2240.
(26) Fuoss, R. M. J. Am. Chem. Soc. 1958, 80, 5059.
(27) Margerum, D. W.; Cayley, G. R.; Weatherburn, D. C.; Pagenkopf, G.
K. In Coordination Chemistry; Martell, A. E., Ed.; American Chemical
Society: Washington, DC, 1978; Vol. 2.
IC961279G