Letters
J. Phys. Chem. A, Vol. 101, No. 15, 1997 2745
smoothing of the plot, due to the competition of this reaction
with the formation of ETA. For curve a (Figure 4) we replaced
glyoxylic acid by mesoxalic acid. The stoichiometry of
4
mesoxalic acid is known to be 4, which means a higher overall
stoichiometry of the aerobic pathway. Consequently, we see
that the plot starts with the expected value of 5. For curve d,
the production of oxygen during the decay of the peroxymalonyl
radical was excluded. It can be seen that the turning point shifts
significantly to lower values of [MA]initial, accounting for the
decreased availability of oxygen (cf. Figure 3). This finding
strongly supports the proposed oxygen release during the peroxy
radical decay. Finally, we included an additional decay
mechanism for the malonyl radical: the direct decarboxylation
of the malonyl radicals into acetic acid radicals forming succinic
13
acid by recombination. We found that this additional pathway,
however, introduces only small changes and would be of minor
importance for the realized stoichiometries (curve e).
Figure 3. Dependence of the consumption ratio f on the initial malonic
acid and oxygen concentrations. 100% oxygen equilibration is
estimated to be an effective oxygen concentration of 1 mM. Results
of the model calculations are based on the reactions R2-R5 (see text).
This report documents the following: For the Ce(IV) oxida-
tion of MA, the earlier reported range of consumption ratios
(5.9-6.6) around the textbook value of 6 is not primarily caused
by experimental errors but can be rather understood as the result
of a competition between anaerobic and aerobic reaction
pathways. The complete range of consumption ratios is found
to be between approximately 3.5 and 7 with a distinct
dependence on the initial concentrations of malonic acid and
oxygen, which can be quantitatively modeled on the basis of
only four main reactions. In a broader context, this study opens
a new avenue for the analysis of complex reaction mechanisms.
In particular, reactions with high stoichiometries have the
potential to show a significant dependence of consumption ratios
on initial parameters. The systematic measurement of this
dependence should allow, analogous to the presented case, the
extraction of the important information on branching reaction
pathways, which can be considered to be a fingerprint of the
mechanism.
Acknowledgment. This research was supported by the
Deutsche Forschungsgemeinschaft and Florida State University.
O.S. thanks the Fonds der Chemischen Industrie for a Liebig
Fellowship.
Figure 4. Numerical results obtained by modifying the original model
or the initial conditions. The solid circles represents the original model
(cf. Figure 1). (a) Exchange of glyoxylic acid to mesoxalic acid; (b)
and (c) rate constants of the formation of the peroxymalonyl radical
References and Notes
5
9
-1 -1
set to 1.7 × 10 and 1.7 × 10 M
s , respectively; (d) no oxygen
(1) Richardson, W. H. In Organic Chemistry; Blomquist, A. T., Ed.;
release during the decay of the peroxymalonyl radical; (e) implementa-
tion of an additional decay pathway for the malonyl radical.
Academic Press: New York and London, 1965; Vol. 5 (Wiberg, K. B.,
Ed.), Part A, Chapter IV, pp 244.
(
2) Harris, D. C. In QuantitatiVe Chemical Analysis, 4th ed.; Freeman,
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of the change in initial oxygen concentrations. The initial
consumption ratio of 4 is governed by the aerobic pathway,
whereas the straight line at f ) 7 represents the anaerobic
pathway. The turning points in the curves of different initial
oxygen concentrations define the condition at which oxygen is
consumed completely. Furthermore, we performed extensive
simulations to study the sensitivity of the model to variations
in rate constants, changes in product formation, and additional
pathways. The main results of these studies are summarized
in Figure 4. The model turns out to be quite robust against
changes in rate constants, usually over several orders of
magnitude. The solid circles describe the original model and
rate constants (R2-R5) (cf. Figure 2). We modified, for
example, the rate constant k4 for the formation of the peroxy-
(
(
(
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(
(
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9
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(12) Neumann, B.; Steinbock, O.; M u¨ ller, S. C.; Dalal, N. S. J. Phys.
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malonyl radical, up to 1.7 × 10 M
s
(curve c, Figure 4),
5
which introduces practically no change, and down to 1.7 × 10
(13) F o¨ rsterling, H.-D.; Pachl, R.; Schreiber, H. Z. Naturforsch. 1987,
-
1
-1
M
s
(curve b), where we observed the first significant
42a, 963.