Autocatalysis and self-inhibition: Coupled kinetic phenomena in the chlorite-tetrathionate reaction

Article abstract of DOI:10.1021/ja048982l

The initial rate of formation of chlorine dioxide in the chlorite-tetrathionate reaction changes in an unusual fashion. The formal kinetic order of both reactants varies over a very wide range. Moreover, chlorite ion behaves not just as a simple reactant, but also as a self-inhibitor. A five-step scheme, derived from an eight-step mechanism, is proposed in which the autocatalytic formation of HOCl plays a central role in accounting for this kinetic behavior. Copyright

Full text of DOI:10.1021/ja048982l

Published on Web 05/01/2004
Autocatalysis and Self-Inhibition: Coupled Kinetic Phenomena in the
Chlorite-Tetrathionate Reaction
Attila K. Horv a´ th, Istv a´ n Nagyp a´ l,* G a´ bor Peintler, and Irving R. Epstein*
†
,†
†
,‡
Department of Phsyical Chemistry, UniVersity of Szeged, Szeged P.O. Box 105, H-6701, Hungary, and
Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis UniVersity,
Waltham, Massachusetts, 02454-9110
Received February 23, 2004; E-mail: nagypal@chem.u-szeged.hu; epstein@brandeis.edu
The chlorite-thiosulfate reaction displays a remarkable range
of “exotic” phenomena, including complex periodic and aperiodic
through two extrema as a function of initial chlorite concentration
(Figure 1). Chlorite ion thus behaves not just as a simple reactant
but also as a self-inhibitor, with a formal kinetic order, calculated
1
2
oscillation in a flow reactor, autocatalysis and stochastic reaction
3
time distributions under batch conditions, and propagation of
reaction fronts in unstirred mixtures. Ultimately, one would hope
0
as d(log(rate))/d(log([X] )), between +1.5 and -9.4! A similar
4
analysis to determine the order of tetrathionate ion shows that the
stabilized rate varies sigmoidally (Figure 2) as a function of initial
tetrathionate concentration, giving a formal kinetic order of
tetrathionate as high as 9!
Our aim here is to provide an explanation for this unusual kinetic
behavior. After examining many candidate mechanisms, we propose
the following scheme for the stabilized phase of the chlorite-
tetrathionate reaction:
to understand and describe quantitatively these and related phe-
nomena, a task that requires insight into the mechanism of the
reaction. As a part of the effort to elucidate the mechanism of the
chlorite-thiosulfate reaction, several subsystems of the parent
reaction have been investigated. The kinetics and mechanism of
the chlorite-hypochlorous acid, thiosulfate-chlorine dioxide,6
5
7
8
tetrathionate-hypochlorous acid, chlorine dioxide-hypochlorite,
9
and chlorine dioxide-tetrathionate reactions have been established.
We now report here the results of our investigation of the chlorite-
tetrathionate reaction. It is already known that the initial rate of
the reaction increases slightly with [Cl ] and is second order with
respect to [H ], i.e., the reaction is “supercatalytic”. This feature
A + 3B ) 4X + 3Y
B + X ) Y
r
) k
[A][B]
(1)
(2)
(3)
(4)
(5)
1
1
4
r ) k [B][X]
-
2
2
+
2B + Y ) 2P
r ) k [B][Y]
3 3
10
plays a key role in the diffusion-driven instabilities, cellular acidity
fronts, and lateral front instabilities observed in the ClO
11
12
-
A + 2B + Y ) 4X + 2Y r ) k [A][Y]
4 4
2
-
2-
S
4
O
6
system. The experiments presented here were conducted in
X + Y ) inert products
r ) k [X][Y]
5 5
acetic acid-acetate buffer (I ) 0.5 M adjusted with sodium acetate,
+
pK ) 4.55); thus, the “supercatalytic” effect of H was completely
2-, ClO
-, HSO
-
•
where A, B, X, Y, P denote S
respectively.
O
4 6
2
3 2
, HOCl, ClO ,
suppressed.
Equations 1-5 are derived from the following mechanism:
2
-
-
+
-
S4O6 + ClO2 + H O + H f 2S O OH + HOCl (6)
2
2
3
ClO2- + S O OH + H O f 2HSO + HOCl (7)
-
-
2
3
2
3
HSO3- + ClO2 f SO42- + HOCl
-
(8)
(9)
ClO2- + HOCl + H f Cl O + H O
+
2
2
2
ClO2- + Cl O f 2 ClO + Cl
•
-
(10)
(11)
(12)
2
2
2
2
-
-
-
S4O
6
+ HOCl f S O OH + S O Cl
2 3 2 3
Figure 1. Dependence of stabilized rate (symbols: measured, solid line:
-
2-
calculated) on [ClO2 ]0. [S4O6 ]0 ) 0.0005 M, pH ) 4.95. All other initial
HSO3- + HOCl f SO42- + Cl + 2H+
-
concentrations are zero in the simulation.
-
-
The surprising results of our investigations are illustrated in
Figures 1 and 2. The absorbance of the chlorite-tetrathionate
reaction mixtures at 400 nm, where chlorine dioxide is the only
S
2
O
3
Cl + ClO
2
+ 2H
2
O f
HSO3- + HOCl + H + Cl (13)
+
-
2
-1
-1
absorbing species (ꢀ ) 571.5 M cm ), was followed with a Zeiss
by making the simplifying assumption that reactions 7 and 13 and
the well-known fast reaction 10 occur essentially instantaneously,
S10 diode array spectrophotometer, excluding UV light to avoid
5
13
complications from UV irradiation of tetrathionate ion. After a
-
allowing us to eliminate the intermediates S
2 3
O
OH , Cl
2 2
O , and
•
brief (<40 s) induction period, the rate of ClO
2
formation becomes
-
S
2
O
3
Cl . The only product shown in the scheme is the absorbing
nearly constant for 5-30 min, depending on the initial concentra-
tions. This stabilized rate, calculated from the absorbances, goes
•
2
species, ClO .
) 11.5 M-1 s-1
were taken from the literature
Of the five rate constants in the scheme, two, k
3
8
-1 -1 5,14,15
and k
5
) 7.6 × 10 M
s
,
†
University of Szeged.
Brandeis University.
‡
and fixed during the fitting procedure. The others, k
1
) (8.4 (
6246
9
J. AM. CHEM. SOC. 2004, 126, 6246-6247
10.1021/ja048982l CCC: $27.50 © 2004 American Chemical Society

C O MMU N I C A T I O N S
Figure 2. Dependence of the stabilized rate (symbols: measured, solid
line: calculated) on [S4O6 ]0. [ClO2 ]0 ) 0.04822 M, pH ) 4.95. All
other initial concentrations are zero in the simulation.
Figure 4. Calculated rates of eqs 1-5 at t ) 100 s plotted against initial
tetrathionate concentration. [ClO -] ) 0.04822 M, pH ) 4.95.
2
-
-
2
0
but that the autocatalytic pathway quickly comes to dominate as
2
-
[S
4
O
6
] is increased, resulting in the rapid rise in the rate seen in
2-
2-
Figure 2 for pS
the HSO
4
O
6
around 3. As we continue to increase S
4
O
6
,
-
3
produced in steps 1 and 4 begins to capture a significant
amount of the autocatalyst in step 5, which overtakes step 4 at about
2-
pS
behavior as [S
order with respect to S
4
O
6
) 2.7 (Figure 4), causing the rate to show saturation
2-
O
4 6
] is increased further. The high formal kinetic
2-
O
4 6
arises from the turning on and turning
off of the autocatalytic pathway as we sweep through a range of
initial tetrathionate concentrations.
We emphasize that only the formation of chlorine dioxide, not
the disappearance of tetrathionate and chlorite ion, becomes
2-
independent of [S
O
4 6
0
] . It should also be noted that the net rate
of chlorine dioxide formation may start to decrease at higher
tetrathionate concentrations because of the increasing importance
of the chlorine dioxide-tetrathionate reaction.9
Investigations are continuing in our laboratory to extend this
mechanism so as to describe accurately the kinetics and mechanism
of the chlorite-tetrathionate reaction over its entire time course.
Figure 3. Calculated rates of eqs 1-5 at t ) 100 s plotted against initial
2
-
chlorite concentration. [S4O6 ]0 ) 0.0005 M, pH ) 4.95.
-
6
) (1.0 ( 0.2) × 10 M s-1 and k
5
-1
1
(
.3) × 10 M-1 s-1, k
2
4
) 98
7 M s-1, were determined by nonlinear parameter estimation
-
1
1
6
with the multipurpose kinetic program package ZiTa. The two
data series (chlorite- and tetrathionate-dependence) were fitted
separately. The value obtained for k
found at very different pH and ionic strength in a study of the
4
is within a factor of 3 of that
Acknowledgment. This work was supported by Grant CHE-
0306262 from the U.S. National Science Foundation and OTKA
Grants T30446 and T029838 from the Hungarian Research Fund
as well as by the U.S.-Hungarian cooperative program. A.K.H is
grateful for the financial support of OTKA postdoctoral fellowship
Grant D38001.
7
2-
reaction of HOCl and S
1
4
O
6
2
. Our k differs by about a factor of
5 from that obtained in a study17 done in a large excess of sulfite
rather than chlorite. The calculated and measured rates are in
excellent agreement, as seen in Figures 1 and 2.
The unusual kinetic behavior of this system can be understood
by referring to eqs 1-5. The key species is the autocatalyst Y
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(
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-
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to pH 4.95, is 6300 M-
JA048982L
1
s
-1
.
When the initial tetrathionate concentration is varied as in Figures
2-
2
4 6
and 4, we find that steps 1 and 4 have similar rates at low [S O ]
J. AM. CHEM. SOC.
9
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