610 J. Phys. Chem. A, Vol. 102, No. 3, 1998
Chinake et al.
acid dissociation reaction of HClO2, the formation of the Cl2O2
intermediate (reactions M6 and M7), the hydrolysis reaction of
Cl2, (reaction M10), and the reaction which controls the
formation of ClO2 in high-pH environments (reaction M12).
Only three oxidizing agents were assumed to exist in the
-
reaction mixture: ClO2 , HOCl, and Cl2O2. There were also
only two reductants: HCHO and HCOOH. The remaining
seven possible reactions are M1, M6, M7 (formation of ClO2),
and M11-M13. These listed 13 reactions were exhaustive, as
there are no other reactions that are possible in the reaction
mixture.
Seven of the reactions listed, M1, M6, M7, M10, M11, M12,
and M13, are pure oxyhalogen reactions whose kinetics
parameters can be obtained from literature. Kinetics data for
18
M1 were taken from Chinake et al., and care was taken to
maintain the pKa of chlorous acid. Reaction M6 had been
studied by Peintler et al.15 as the composite M6 + M7 reaction.
19
M7 was taken from the work of Jones et al. Reaction M10
2
0
was studied by relaxation techniques by Eigen and Kustin,
and the kinetics parameters used were taken from this study.
Kinetics parameters for reactions M10 were derived from the
15
work of Peintler et al., and those of reaction M11 are from
2
1
Epstein et al. Reactions M12 and M13 are not simple single-
13
step elementary reactions.
They control the final ClO2
concentrations with respect to pH. They are the only reactions
in which ClO2 is consumed. At high pH, most of the ClO2
-
-
-
disproportionates to ClO3 , ClO2 , and Cl (see reaction M12),
hence the observed lower ClO2 absorbances at high pH (see
22-24
Figure 4).
Rapid autocatalytic formation of ClO2 is halted
1
5
-
by reaction M13. The Cl obtained from the reduction of
HOCl by the substrate species (reactions M4 and M5) halts the
uncontrolled buildup of ClO2 (reaction M13).
The derived 13 ordinary differential equations were numeri-
cally integrated by using a semiimplicit Runge-Kutta proce-
dure.25 The simulations were insensitive to the rate constants
used for reaction M1 as long as the acid dissociation constant
Figure 7. (a) Comparison of computer simulations with experimental
-
data for the ClO
2
-HCHO reaction. The simulations are generated from
-
2 0
]
the mechanism shown in Table 1. Conditions simulated are [ClO
) 0.001 33 M; [HCHO] ) 0.001 M; pH ) 3.7. (b) Other computer
simulations results predicting the concentration-time variations for
HCHO (dashed line), CO (dots and dashed line), and HCOOH (dotted
line). Conditions simulated are [ClO
M; pH ) 3.7.
17
0
(pKa ) 2.5) was maintained and the rate constants maintained
such that M1 was not rate-determining. Higher kinetics
parameters for M1 increased the stiffness of the integration but
did not change the simulations result. The forward rate constant
for reaction M2 was estimated from this study. Using reaction
R8 (a composite of M6 and M7 in the table), we observe that
in the initial stages of ClO2 production the rate of formation of
ClO2 is proportional to the rate of production of HOCl (assuming
R8 is fast).
2
-
2
]
0
) 0.006 M; [HCHO] ) 0.001
0
HCHO as well as the autocatalytic production of CO2(g).
HCOOH, as expected, shows a transient formation. The model
can be checked from the reaction’s material balance in which
the total concentration of the carbon-containing species is always
constant: [HCHO](t) + [HCOOH](t) + [CO2(g)](t) ) [HCHO]-
The rate constants for reactions M3, M4, and M5 initially
were estimated and then refined to give the best fit to the data.
The simulations were most sensitive to the value of the rate
constant for reactions M2 and M6 and insensitive to the values
given for M7 and M8. Increasing the rate constant for reaction
M2 rapidly built up the autocatalyst, HOCl, resulting in a much
more rapid buildup of ClO2. The major production of the
autocatalyst, HOCl, is through M6 but is initiated by reaction
M2.
(t)0) (initial HCHO concentration at time ) 0). No further
production of CO2 is expected as HCOOH concentration
vanishes since CO2 is only produced in reactions M3, M5, and
M9, all involving oxidation of HCOOH. Several initial condi-
tions were simulated which gave the same fit as the one in
Figure 7a: good fits at the beginning and at the end of the
reaction with a slight deviation some time into the reaction.
Figure 7a represents a typical simulations fit for conditions of
excess HCHO and Figure 7b is for excess chlorite, the only
conditions in which CO2 is produced as a product.
Using these 13 reactions, the simulations were quite simple
and gave a very close fit to the experimental data (see Figure
7
a,b). Our simulations easily predicted the rate of formation
Conclusion
of ClO2 (Figure 7a). The slightly lower concentrations predicted
for ClO2 are expected, as our simulations do not account for
the absorbance contributions at 360 nm from the intermediate
species. Figure 7b gives the model’s predictions for the
concentration variations of HCHO, HCOOH, and CO2(g).
There are no experimental data available for comparison, but
the model shows the expected autocatalytic consumption of
Our results prove that what looks like oligooscillatory
behavior in the production of ClO2 is not derived from an
oligooscillatory mechanism, but from a mechanical effect. The
reaction is still nonlinear, with an autocatalytic production of
ClO2 and an autocatalytic consumption of HCHO. The inertness
of ClO2 in the reaction solution can explain why the reaction