Kinetic modeling of pyruvic acid ozonation in aqueous solutions catalyzed by Mn(II) and Mn(IV) ions

Article abstract of DOI:10.1016/S0043-1354(00)00237-2

The ozonation of pyruvic acid (2-ketopropionic acid) in aqueous solutions, catalyzed by Mn(II) and Mn(IV) ions, has been studied at three different pH values (pH=1.1, 2.0 and 3.0). A mathematical model of the unsteady operation of the experimental reactor has been developed, which takes into account the reactions occurring in the liquid phase and the ozone mass transfer from the gas bubbles. Those reactions have been described with two alternative kinetic models, both made out of four elementary steps. The two kinetic models correlate the experimental data with a fair accuracy, respectively at the lowest and at the highest pH examined. In particular, at pH=3.0, the ozonation results are inhibited by the acetate ions produced by the reaction itself. This effect has been correctly described in the terms of a complex formed with the low oxidation-state manganese, which successively reacts with the dissolved ozone. Copyright (C) 2000 Elsevier Science Ltd. The ozonation of pyruvic acid (2-ketopropionic acid) in aqueous solutions, catalyzed by Mn(II) and Mn(IV) ions, has been studied at three different pH values (pH = 1.1, 2.0 and 3.0). A mathematical model of the unsteady operation of the experimental reactor has been developed, which takes into account the reactions occurring in the liquid phase and the ozone mass transfer from the gas bubbles. Those reactions have been described with two alternative kinetic models, both made out of four elementary steps. The two kinetic models correlate the experimental data with a fair accuracy, respectively at the lowest and at the highest pH examined. In particular, at pH = 3.0, the ozonation results are inhibited by the acetate ions produced by the reaction itself. This effect has been correctly described in the terms of a complex formed with the low oxidation-state manganese, which successively reacts with the dissolved ozone.

Full text of DOI:10.1016/S0043-1354(00)00237-2

Wat. Res. Vol. 35, No. 1, pp. 109±120, 2001
7 2000 Elsevier Science Ltd. All rights reserved
Printed in Great Britain
PII: S0043-1354(00)00237-2
0043-1354/00/$ - see front matter
www.elsevier.com/locate/watres
KINETIC MODELING OF PYRUVIC ACID OZONATION IN
AQUEOUS SOLUTIONS CATALYZED BY Mn(II) AND
Mn(IV) IONS
R. ANDREOZZI1*M, V. CAPRIO1, R. MAROTTA1 and V. TUFANO2
1Universita degli Studi di Napoli ``Federico II'', Facolta di Ingegneria, Dipartimento di Ingegneria
Chimica, p.le V. Tecchio, 80-80125, Napoli, Italy and 2Universita della Basilicata, Dipartimento di
Ingegneria e Fisica dell'Ambiente, c/da Macchiaromana, 85100, Potenza, Italy
(First received 11 June 1999; accepted in revised form 20 April 2000)
AbstractÐThe ozonation of pyruvic acid (2-ketopropionic acid) in aqueous solutions, catalyzed by
Mn(II) and Mn(IV) ions, has been studied at three di€erent pH values (pH=1.1, 2.0 and 3.0). A
mathematical model of the unsteady operation of the experimental reactor has been developed, which
takes into account the reactions occurring in the liquid phase and the ozone mass transfer from the gas
bubbles. Those reactions have been described with two alternative kinetic models, both made out of
four elementary steps. The two kinetic models correlate the experimental data with a fair accuracy,
respectively at the lowest and at the highest pH examined. In particular, at pH=3.0, the ozonation
results are inhibited by the acetate ions produced by the reaction itself. This e€ect has been correctly
described in the terms of a complex formed with the low oxidation-state manganese, which successively
reacts with the dissolved ozone. 7 2000 Elsevier Science Ltd. All rights reserved
Key wordsÐpyruvic acid, catalytic ozonation, manganese, chemical kinetics, kinetic modeling
NOMENCLATURE
measured concentration, mM
degrees of freedom=number of experimental points
minus the number of identi®ed parameters
rate constant
INTRODUCTION
C
F
The use of homogeneous and heterogeneous cata-
lysts to improve the ozone capability for the abate-
ment of refractory organic pollutants is
continuously attracting the attention of an increas-
ing number of researchers. So far, TiO2, MnO2, Mn
ions (Al-Hayek et al., 1989; Allemane et al., 1993;
Andreozzi et al., 1992a; Jun Ma and Graham, 1999;
Gracia et al., 1998; Paillard et al., 1991) have been
used as ozonation catalysts for removing substances
such as short-chain carboxylic acids, which are nor-
mally produced during the ozonation of aromatics
and which weakly react with ozone itself.
k
K
R
Y
f
s
equilibrium constant
reaction rate, mM min
1
computed concentration, mM
Sjss ꢀCjs Yjs† ˆSjfj objective function mM2
2
p
f=F standard deviation mM
Subscripts
A pyruvic acid
av average
F
L
i
ozone in the exit stream
ozone in the liquid phase
reaction
component
rate constant
permanganate ion
initial
In our previous papers, both experimental and
modeling work demonstrated that manganese ions
and manganese dioxide can strongly improve the
ozonation eciency of several organic pollutants
such as oxalic acid (Andreozzi et al., 1997) and
pyruvic acid (Andreozzi et al., 1998).
j
k
M
0
s
experiment
total
t
Since pyruvic acid (PA) showed a more complex
reaction mechanism, as compared to oxalic acid, in
a previous paper (Andreozzi et al., 1998) the atten-
tion was focused on the homogeneous catalysis
from Mn(IV) ions, and a ®rst attempt at the kinetic
modeling of this system was proposed. Notwith-
standing the limited experimental evidence avail-
able, few main points were explained, in particular,
the roles of Mn(IV) and Mn(VII) in the oxidation
*Author to whom all correspondence should be addressed.
Tel.: +39-81-7682251; fax: +39-81-5936936; e-mail:
andreo@hp3.irc.na.cnr.it
109

110
R. Andreozzi et al.
saturated with solid MnO2 and ®ltered with cellulose acet-
ate ®lters, pore diameter 0.45 mm.
The experiments were performed at T = 258C, for 1.0 <
[PA]0 < 4.0 mM, 12.0 < [Mn(II)]0 < 24.0 mM, and
pH=1.1, 2.0 and 3.0.
process and the inhibiting e€ect of acetic acid
(HAc), which is present in the solution in the form
of acetate ions (Ac ).
Successively, the experimental campaign was
extended to solutions containing Mn(II) ions, to
di€erent initial concentrations of PA and manga-
nese ions, and to three di€erent pH values. The
availability of a wider set of experimental data
allowed substantial improvement in the kinetic
modeling of the PA±Mn±O3 system, as discussed in
the present paper.
KINETIC MODELS
The simpli®ed kinetic model previously pro-
posedÐkinetic model A (Andreozzi et al., 1998)Ðis
shown in Fig. 1(A). In this model, most of the PA
oxidation was attributed to the catalytic e€ect of
Mn(IV) (reaction no. 1: R1=k1[Mn(IV)][PA]). The
oxidation of Mn(IV) to Mn(VII) (reaction no. 2:
R2=k2[Mn(IV)][O3L]) produces the completion of
reaction no. 1 by subtracting the catalyst, so that
the residual (small) oxidation rate experimentally
observed must be attributed to the permanganate
ion (reaction no. 3: R3=k3[Mn(VII)][PA]).
Finally, reaction no. 4 (R4=k4[Mn(IV)][HAc])
was included in the kinetic model in order to
account for the inhibiting e€ect of the acetate ions,
experimentally observed at di€erent pHs when add-
ing acetic acid to the reacting solutions. In e€ect,
under the experimental conditions used to test this
kinetic model (pH=2.0, [Mn(IV)]0=5.0 mM,
[PA]0=2.5 mM, no HAc added to the reacting sol-
ution), the expected e€ect of HAc, which is also a
product of PA oxidation, was, in fact, very small.
Two new kinetic models were developed and
tested in the present work. Both the kinetic models
B (Fig. 1(B)) and C (Fig. 1(C)) include a more
detailed description of reaction no. 1, also based on
the new experimental evidence available. Moreover,
the inhibiting e€ect of Ac is neglected in the
model B and explained in the model C on the basis
of a manganese±acetic acid complex.
EXPERIMENTAL
The experimental apparatus and procedures have been
widely discussed in a previous paper (Andreozzi et al.,
1992b). The experiments were performed in a cylindrical
glass tank (V = 1.090 dm3, internal diameter=8.5 cm)
provided with a mechanical Te¯on stirrer and gas sparger
(sintered glass disk). The reaction was started by bubbling
a 36 l/h ozonized oxygen stream whose ozone content was
3.0% by volume. The ozone concentration in the gaseous
stream leaving the reactor was monitored continuously by
an UV spectrophotometer. Samples withdrawn from the
reactor at di€erent ozonation times were analyzed for
pyruvic acid by means of a Hewlett-Packard 1090L HPLC
equipped with a spherisorb S5C6 reverse-phase column
¯owed with 1.0 ml/min aqueous bu€ered acidic solution.
Great care was taken to quench the reaction by rapidly
degassing the analytical samples. Permanganate and ozone
concentrations in the liquid bulk were evaluated by means
of spectrophotometric measurements at l=522 nm and
l=254 nm, respectively. Typical percent standard devi-
ations found were 1.74% for pyruvic acid and 2.52% for
permanganate. MnSO4 (98% purity) was used as a cata-
lyst and perchloric acid as a pH's regulator. Mn(IV) cata-
lyzed ozonation runs were conducted in aqueous solutions
In the new experimental campaign, the use of
Mn(II) instead of Mn(IV) allowed us to demon-
strate the equivalence of the two ions as oxidation
catalysts. As an example, Fig. 2 shows the concen-
tration±time data measured at pH=3.0 and
[PA]0=2.0 mM.
On the basis of this result, the catalytic reaction
no. 1 was modeled with a chain mechanism made
out of two elementary reactions:
1a: MnꢀII† ‡ O3L 4MnꢀIV† R1a ˆ k1a‰MnꢀII†Š Á ‰O3L
Š
1b: MnꢀIV† ‡ PA4MnꢀII† ‡ HAc
R1b ˆ k1b‰MnꢀIV†Š Á ‰PAŠ
The overall stoichiometric ratio O3L/PA was ®xed
to one on the basis of the experimental results.
Since the other reactions involving Mn(II) and
Mn(IV) are much slower than reactions 1a and 1b,
the steady-state hypothesis for those ions gives:
k1a‰MnꢀII†Š Á ‰O3LŠ ˆ k1b‰MnꢀIV†Š Á ‰PAŠ
ꢀ1†
Fig. 1. Kinetic models (schematic).

Pyruvic acid ozonation in aqueous solutions catalyzed by Mn(II) and Mn(IV) ions
111
and allows us to explicitate the (not measured) con- which correspond to reactions no. 2 and no. 3 of
centrations [Mn(II)] and [Mn(IV)], as a function of the kinetic model A. Since this model does not take
the overall concentration of the low oxidation-state into account the role played by the acetic acid, reac-
manganese, Mnlow
:
tion no. 4 is disregarded.
The kinetic model C includes reaction no. 3 and
a modi®ed reaction no. 2 which accounts for the
e€ect of Ac . On the basis of the experimental evi-
dence that the ®nal amounts of Mn(VII) strictly
corresponded to the manganese added to the react-
ing solution, it was hypothesized that the observed
inhibition of PA oxidation (observed at pH=3.0)
can be ascribed to the conversion of Mnlow to
Mn(VII) favoured by its complexation with Ac
ions. Thus, the oxidation of Mnlow to permanganate
was modeled as a two-step process which involves a
complex between Mnlow and acetate ions.
‰MnlowŠ ˆ ‰MnꢀII†Š ‡ ‰MnꢀIV†Š
ꢀ2†
which is indirectly evaluable from the measurements
of [Mn(VII)] and from the mass conservation for
manganese. It results as:
k1b‰MnlowŠ‰PAŠ
‰MnꢀII†Š ˆ
ꢀ3†
k1a‰O3LŠ ‡ k1b‰PAŠ
k1a‰MnlowŠ‰O3L
Š
‰MnꢀIV†Š ˆ
ꢀ4†
k1a‰O3LŠ ‡ k1b‰PAŠ
Manganese-acetate complexes are widely docu-
mented in the literature (Gmelin, 1980) but the
available quantitative informations only refer to the
dissociation constants of complexes {Mn(II)±Ac2}
and {Mn(II)±Ac}+, Kd=1.58 Â 102 mM and
Kd=3.98 Â 102 mM, respectively. Thus, the lack of
measurements of Mn(II) and Mn(IV) concen-
trations and of a priori informations forced us to
represent those complexes by the simplest possible
form, i.e. Com={Mnlow±Ac }, whose concen-
tration may be expressed as:
The kinetic model B is completed by reactions no. 2
and no. 3:
2: MnꢀIV† ‡ 1:5O3L 4MnꢀVII†
R2 ˆ k2‰MnꢀIV†Š Á ‰O3L
Š
3: MnꢀVII† ‡ 1:5PA4MnꢀIV† ‡ 1:5HAc
R3 ˆ k3‰MnꢀVII†Š Á ‰PAŠ
Fig. 2. Concentration±time data measured at T = 258C, pH=3.0 and [PA]0=2.0 mM. Hollow symbols:
[Mn(IV)]0=11 mM, full symbols: [Mn(II)]0=12 mM. q, Q=[PA] (mM); r, R=[Mn(VII)] Â 100 (mM);
w, *=[O3]liq (mM).

112
R. Andreozzi et al.
‰ComŠ ˆ Keq‰MnlowŠ‰Ac Š
METHOD OF DATA ANALYSIS
ˆ KeqKa10pH‰MnlowŠ‰HAcŠ
According to previous work (Andreozzi et al.,
1991), in order to obtain a complete mathematical
model of the unsteady operation of the experimen-
tal gas±liquid reactor, the multi-step reaction net-
work established in the liquid phase and described
by the di€erent kinetic models discussed in the pre-
vious section was coupled with the mathematical
description of the ozone mass transfer from the gas
bubbles.
ˆ b‰MnlowŠ‰HACŠ
ꢀ5†
where Ka is the dissociation constant of the acetic
2
acid
(Ka=1.85
Â
10
mM)
and
b=KeqÁKaÁ[H+]=KaÁ10pH/Kd. In e€ect, the values
of b are very small. As an example, assuming the
above reported literature value of Kd for the com-
plex {Mn(II)±Ac }+, one obtains b varying from
This model assumes a kinetic regime of absorp-
tion with reaction, i.e., that the reactions take place
only in the well mixed liquid bulk. This assumption
is veri®ed in the case under study, because the
values of the ®rst order equivalent rate constant for
7
1
5
5.84 Â 10
mM
at pH=1.1 to 4.64 Â 10
1
mM at pH=3.0. The same data also show that
the ratio {Mn(II)±Ac2}/{Mn(II)±Ac}+ is much
smaller than one, so that the assumption of lump-
ing all the complexes in one overall species is justi-
®ed.
ozone consumption, kc=k1a[Mn(II)], do not exceed
1
10 min
(at pH=1.1), and because the value
1
kLa=4.97 min is assumed for the gas±liquid mass
transfer coecient, on the basis of previous
measurements (Andreozzi et al., 1998), so that the
estimated values of the Damkholer number,
Da=kc/kLa, are smaller than 2.
If the manganese±acetate complex reacts with the
dissolved ozone, reaction no. 2 of model B can be
subsituted in model C by the reaction:
C2: Com ‡ aO3L 4MnꢀVII† ‡ Ac
Moreover, no enhancement factor was included,
because the Hatta number can be estimated to be
smaller than 0.35.
RC2 ˆ KC2‰MnlowŠ Á ‰HAcŠ Á ‰O3L
Š
where the rate constant kC2=k2 includes the factor
b de®ned above. The stoichiometric coecient a
should vary in the range 1.5±2.5, depending on the
ratio Mn(IV):Mn(II) in the complex, which is not
computable. Since in this range the results were
almost independent of a, the value a=1.5 was
adopted, because it is consistent with the stoichio-
metric coecients assumed for reactions no. 1 and
no. 3.
The Henry constants were independently
measured (Andreozzi et al., 1996). Di€erent values
were adopted (6045 atm at pH=1.1, 5550 atm at
pH=2.0, and 5130 atm at pH=3.0), because the
ionic strength of the solutions was varied on vary-
ing the pH.
The resulting set of ODEs was numerically inte-
grated and the values of the computed concen-
trations Yj ( j = PA, O3F, O3L, Mn(VII), Mnlow
,
The inclusion in the kinetic model of the manga-
nese±acetate complex modi®es the de®nition of the
low oxidation-state manganese:
HAc) and of the partial sensitivities @Yj=@ki at each
experimental time were used in an optimization pro-
cedure aimed at the identi®cation of the unknown
rate constants ki: Subsequently, the statistical analy-
sis of the residual errors allowed the comparison
among alternative kinetic models (Andreozzi et al.,
1991).
‰MnlowŠ ˆ ‰MnꢀII†Š ‡ ‰MNꢀIV†Š ‡ ‰ComŠ
ꢀ6†
so that new expressions are produced for [Mn(II)]
and [Mn(IV)]:
The unweighed least squares objective function
based on the measured components (PA, O3F, O3L
and Mn(VII)) was used in any case because no sig-
ni®cant improvement of the results was obtained
when using the weights derived from the experimen-
tally evaluated accuracies of the measurements.
Due to the complexity of the studied system it
was not possible to measure the concentration of all
the components. This fact hinders the use of too
complex kinetic models because, when the optimiz-
ation procedure is not adequately constrained by
the experimental data, in some cases it is not poss-
ible to obtain meaningful values of the rate con-
stants.
k1b‰MnlowŠ‰PAŠ
‰MnꢀII†Š ˆ
ꢀ7†
k1a‰O3LŠ ‡ k1b‰PAŠꢀ1 ‡ b‰HAcŠ†
k1a‰MnlowŠ‰O3L
Š
‰MnꢀIV†Š ˆ
ꢀ8†
k1a‰O3LŠ ‡ k1b‰PAŠꢀ1 ‡ b‰HAcŠ†
In e€ect, because of the very small value of b, the
product b [HAc] is in any case much smaller than 1
and can be disregarded, so that equations (7) and
(8) turn into equations (3) and (4), respectively.
Nevertheless, the manganese±acetic acid complex,
although negligible in the equtions of mass conser-
vation, strongly a€ects the kinetic dependence of
permanganate formation (reaction C2), which is
These diculties were (at least partially) over-
comed by the use of the MULTI computational
strongly di€erent from that included in the model B strategy (described hereafter) and, when necessary,
(reaction 2, to be interpreted as reaction B2). by the use of ``truncated'' and of ``reduced'' kinetic

Pyruvic acid ozonation in aqueous solutions catalyzed by Mn(II) and Mn(IV) ions
113
Table 1. Results at pH=3.0. Absolute [mM] and percent standard
Table 3. Results at pH=3.0, kinetic model C. Absolute [mM2] and
deviations (sj%=100 sj/Cjav
)
percent residuals (fj%=100 fj/ft)
Kinetic model B
Kinetic model C
Experimental
MULTI code
SINGLE code
st=87.2
st=42.6
ft=1.298
ft=0.635
sA=225=20.0%
sF=48.0=5.3%
sL=29.6=11.6%
sA=88.0=7.8%
sF=36.5=4.0%
sL=26.0=10.2%
sA=35.0
sF=20.0
sL=5.7
fA=0.670=51.6%
fF=0.552=42.6%
fL=0.076=5.8%
fA=0.150=23.6%
fF=0.419=66.0%
fL=0.066=10.4%
M=1.49 Â 10 4=0.02%
s
M=1.52=8.5%
s
M=1.14=6.4%
s
M=0.55
f
M=1.33 Â 10 4=0.01%
f
models. The truncated models were used at tive function to the single parameters and do not
pH=1.1 and were obtained by excluding reaction represent a performance index of the kinetic model.
no. 3, whereas the reduced models were obtained
by including the additional constraint k1b=k1a. In
this way, the ratio [Mn(IV)]:[Mn(II)] is ®xed at any
time at the value:
RESULTS AND DISCUSSION
The MULTI code and the kinetic models B and
C were used to correlate the experimental data
available at the three di€erent pH values examined.
At pH=3.0, the kinetic model C was able to
describe with a fair accuracy the experimental data,
whereas the kinetic model B was utilizable only in
the reduced version (k1b=k1a) and produced an
unsatisfactory correlation. Some interesting results
were also obtained when using the SINGLE code
and the kinetic model C.
In contrast, at pH=1.1 only the kinetic model B
produced a good correlation of the data. In these
conditions, the truncated models (k3=0) were used
because the ®rst reaction produced an almost com-
plete PA conversion.
‰MnꢀIV†Š
‰MnꢀII†Š
‰O3LŠ
ˆ
ꢀ9†
‰PAŠ
Of course, the use of a constant ratio k1b/k1a=d,
di€erent from unity, only produces di€erent com-
puted concentrations of the not measured species
Mn(II) and Mn(IV) and modi®es the values of kB2
which result in its multiplication by 2/(1+d ).
,
The computing code based on the MULTI strat-
egy uses in a single optimization run the results of
di€erent experimental runs performed at the same
pH and at di€erent initial concentration of PA and
manganese. This procedure imposes the same values
of the rate constants for all the experiments and
smooths out the errors deriving from the non com-
plete reproducibility of the data. In general, the
MULTI code produced results more signi®cant
than the SINGLE code, which elaborates one ex-
perimental run at a time thus producing a set of
rate constants for each experiment.
The values of the residual errors and of the stan-
dard deviations of the single components allowed
the comparison of the performance of alternative
kinetic models. The accuracy of the ®tting was eval-
uated from those data and from the comparison
with the experimental standard deviations, which
were obtained by repeating many times the same
measurement procedure.
At pH=2.0 the kinetic model B appeared to be
slightly better than the model C, although it was
more dicult to discriminate between the two kin-
etic models. All these results are discussed in more
detail in the following.
Results at pH=3.0
At pH=3.0, it was not possible to obtain a best
estimate value of the rate constants when using
model B in the entire version, since the code
increased without any limit of the rate constants k1b
and k2. This behaviour can be tentatively attributed
to the lack of experimental measurements of
Mn(IV), which is a reactant for both reactions. The
Table 4. Results at pH=1.1, truncated kinetic models. Best esti-
1
mate values of the rate constants (all measured in mM min
The best estimates of the rate constants were also
reported, together with the relevant standard devi-
ations sk. However, it should be pointed out that
the values of sk measure the sensitivity of the objec-
1
,
excluding kC2, measured in mM min 1), absolute [mM] and per-
2
cent standard deviations (sj%=100 sj/Cjav
)
Kinetic model B (truncated)
Kinetic model C (truncated)
Table 2. Results at pH=3.0. Best estimate values of the rate con-
Standard model
Reduced model
st=40.7
1
stants (all measured in mM min 1, excluding kC2, measured in
2
mM min
1
)
st=40.7
st=41.2
sA=90.0=9.9% sA=89.9=9.9%
sF=25.1=3.2% sF=25.2=3.3%
sL=41.6=24.8% sL=41.7=24.8%
M=0.89=4.4% M=0.55=2.7%
sA=92.8=10.2%
sF=24.3=3.1%
sL=41.6=24.8%
Kinetic model B
Kinetic model C
k1a=321216
k1b=k1a
kB2=67.325.6
k1a=503213
k1b=38.521.5
s
s
sM=9.16=45.5%
k1a=152.423.0
k1b=2752177
kB2=9.927.5
k1a=153.622.9
k1b=k1a
kB2=4.7620.70
k1a=152.123.9
k1b=95223
kC2=3.1520.17
103 k3=4.8720.60
103 k3=2.821.1
103 kC2=81240

114
R. Andreozzi et al.
The values of st show that kinetic model C corre-
results obtained with a reduced model B and with
model C are presented in Tables 1 and 2, respect- lates the data with an average error which is about
ively in terms of standard deviations and of rate one half of the value obtained with the kinetic
constants. The percent of standard deviations were model B. When the standard deviations of the
obtained by normalizing with respect to the average single measured components are considered, it
measured concentration Cjav
.
appears that model C allows us to obtain a very
Fig. 3. Concentration±time data measured at
T = 258C, pH=3.0, [PA]0=2.9 mM and
[Mn(II)]0=19.5 mM, compared to the curves computed with the MULTI strategy and the kinetic model
C. Upper box: q=[O3F], r=[O3L]. Lower box: q=102 [Mn(VII)], Q=[PA].

Pyruvic acid ozonation in aqueous solutions catalyzed by Mn(II) and Mn(IV) ions
115
marked improvement on PA, whose standard devi- tration which are about two orders of magnitude
ation (sA) is reduced approximatively by a factor of smaller than the other concentrations. This result is
three. It should be observed also that a compara- also con®rmed by the data reported in Table 3, to
tively good correlation is obtained in both cases for be discussed in the following.
Mn(VII), notwithstanding its values of concen-
Finally, the comparison with the experimentally
Fig. 4. Concentration±time data measured at
T = 258C, pH=3.0, [PA]0=2.9 mM and
[Mn(II)]0=19.5 mM, compared to the curves computed with the SINGLE strategy and the kinetic
model C. Upper box: q=[O3F], r=[O3L]. Lower box: q=102 [Mn(VII)], Q=[PA].

116
R. Andreozzi et al.
Fig. 5. Results at pH=3.0. Experimental and computed values of the PA conversion at t = 60 min,
X60, against the initial PA concentration, [PA]0, mM. q=experimental data; Q=kinetic model C,
SINGLE strategy; r=kinetic model C, MULTI strategy. The curves were obtained with the average
initial manganese concentration, respectively with the kinetic models B (dashed line) and C (solid line).
determined accuracy of the measurements (third kC2 and kB2 have di€erent meanings. An order of
column) indicates the presence of some systematic magnitude agreement is observed for k3.
residual error, in particular for PA. In fact, for this
component the computed standard deviation is lated also with the SINGLE code and the kinetic
much larger than the experimental value. model C. Table 3 shows the comparison between
The experimental data at pH=3.0 were corre-
The main rate constants are estimated with a the absolute and the percent residuals (normalized
good accuracy with both kinetic models (Table 2). with respect to ft) of each measured component. It
This result con®rms that the comparison between appears that the SINGLE strategy allows to
alternative models cannot be based on the values of increase markedly the accuracy of the ®tting, since
sk. The fair estimate of k3, which is much smaller the total residuals are reduced to slightly less than
than the other rate constants, depends on the avail- 50% of the value obtained with the MULTI code.
ability of accurate measurements of [Mn(VII)]. This result con®rms that the MULTI code produces
No direct comparison is possible among the systematic residual errors.
values of the corresponding rate constants obtained
Most of the observed improvement is attributable
with the two kinetic models, because k1a in model B to the PA data, whose residuals are reduced to
is biased by the ``reduced'' hypothesis and because about one quarter of the value obtained with the
Table 6. Results at pH=2.0. Best estimate values of the rate con-
1
stants (all measured in mM min 1, excluding kC2, measured in
Table 5. Results at pH=2.0. Absolute [mM] and percent standard
2
mM min
1
)
deviations (sj%=100 sj/Cjav
)
Kinetic model B
Kinetic model C
Kinetic model B
Kinetic model C
k1a=260216
k1b=45211
kB2=6.021.7
k1a=9402117
k1b=10.7220.59
st=58.4
st=68.8
sA=118=12.0%
sF=46.4=5.3%
sL=32.1=15.4%
sA=138=14.0%
sF=56.9=6.5%
sL=30.7=14.7%
kC2=0.82520.095
103 k3=35.926.2
103 k3=26.823.3
s
M=1.73=12.2%
sM=3.51=24.8%

Pyruvic acid ozonation in aqueous solutions catalyzed by Mn(II) and Mn(IV) ions
117
2
Fig. 6. Results at pH=3.0. Rate constant kC2, mM min 1, obtained with the SINGLE strategy and
the kinetic model C, against the initial PA concentration, [PA]0, mM.
MULTI code, and, to a lesser extent, to the ozone the initial manganese concentration. The point out-
in the exit stream. The non random nature of the side correlation at [PA]0=2.9 mM has been
residual errors produced by the use of the MULTI obtained with a much smaller manganese concen-
strategy clearly appears from the comparison tration ([Mn(II)]0=11.6 mM.
among the concentration±time experimental data
and the relevant computed curves. As an example, the corresponding curve computed with the kinetic
Figs and show the data measured at model B, which, however, fails in describing the ex-
[PA]0=2.9 mM and the curves computed with the perimentally observed behaviour.
For the sake of comparison, the ®gure also shows
3
4
MULTI and with the SINGLE codes, respectively.
The improvement of the correlation obtained
The MULTI code, which is forced to use the same when using the SINGLE code derives from the
values of the rate constants for all the experiments, possibility of adjusting the rate constants for each
is unable to describe exactly the quasi-asymptotic single experiment. Thus, when the rate constants
behaviour shown by the PA data in the latest stages produced with the SINGLE strategy are plotted
of the reaction.
against [PA]0, it should be possible to ascertain
Those errors may be measured synthetically by whether their di€erent values are produced by some
the PA conversion at the last experimental time (t random variation of the operating conditions or by
= 60 min), which is indicated as X60. The exper- a systematic disagreement between the experimental
imental and the computed values of X60 are plotted data and the kinetic model.
as a function of the initial PA concentration in
As an example, such a plot is shown in Fig. 6 for
Fig. 5. The hollow squares represent the experimen- the rate constant kC2. When the accuracy of the
tal data, which almost overlap with the values com- estimates, shown by the error bars, are accounted
puted with the SINGLE code (full squares). The for, most of the variation appears to be attributable
hollow triangles represent the data computed with to random errors.
the MULTI code and the kinetic model C, which
The residual slight decrease of kC2 on increasing
agree to a lesser extent with the experimental data. [PA]0 (if any) could be easily introduced in the kin-
Finally, the continuous line C shows the fair corre- etic model as an empiric correction. It appears
lation obtained with the MULTI code when assum- more dicult to account for this slight variation
ing the average value ([Mn(II)]0=20.34 mM), for through a di€erent reaction mechanism. In e€ect,

118
R. Andreozzi et al.
Fig. 7. Results at pH=2.0. Experimental and computed values of the PA conversion at t = 60 min,
X60, against the initial PA concentration, [PA]0, mM. q=experimental data; Q=model B; r=model
C. The curves were obtained with the average initial manganese concentration, respectively with the
kinetic models B (dashed line) and C (solid line).
the proposed kinetic models certainly include an good for both the versions. However, the inclusion
oversimpli®ed description of the reactivity of the of the additional constraint k1b=k1a (reduced
manganese ions, but, as discussed previously in this model B) allowed us to estimate more accurately
paper, the quantity and quality of the available the rate constants because of the decreased degrees
measurements hinder the inclusion of a larger num- of freedom. It should be observed that the value of
ber of components and/or of reactions into a more k2 depends on the version employed, because the
complex kinetic model. On the other hand, alterna- two kinetic models make use of di€erent values of
tive kinetic models which hypothesize the formation k1b and, correspondingly, compute di€erent values
of the complex with Mn(II) or with Mn(IV) and of [Mn(IV)]. In contrast, kinetic model C produced
which use di€erent orders of reaction for reaction an apparently good ®tting of the main reactants but
R1a were tested but did not produce signi®cant very marked errors on permanganate.
results.
Results at pH=1.1
Results at pH=2.0
The behaviour shown by the system at pH=1.1
At pH=2.0, it was more dicult to ascertain
was markedly di€erent from that shown at which kinetic model described more accurately the
pH=3.0. In fact, the ®rst reaction stage consumed experimental data. In these conditions, the exper-
almost completely the pyruvic acid so that it was iments appeared to be a€ected to a larger extent by
necessary to introduce the truncated kinetic models, small di€erences in the operating parameters (e.g.,
which were obtained by excluding reaction no. 3. It temperature or stirrer speed).
was also necessary to set at the value 1.3 the stoi-
The results, shown in Tables 5 and 6, indicate
chiometric coecient of ozone in reaction no.1 in that the kinetic model B should be preferred,
order to reconcile the experimentally determined because of the smaller value of the total standard
consumption rates of ozone and of PA.
deviation st and because of the better correlation
The results obtained with the di€erent kinetic obtained for the [Mn(VII)] data. However, the ob-
models tested are reported in Table 4. The ®tting servation of Fig. 7 indicates the rather poor corre-
obtained with the model B may be considered fairly lation obtained with both kinetics models.

Pyruvic acid ozonation in aqueous solutions catalyzed by Mn(II) and Mn(IV) ions
119
1
Fig. 8. Rate constant k1a (M
s
1) against pH. * present work, dashed line: data by Ghaieb et al.,
1991.
CONCLUSIONS
Comparing the rate constant values
In general, it is not very meaningful to compare
Some important results were obtained in the kin-
the best estimate values of the rate constants etic modeling of the pyruvic acid±manganese±ozone
obtained at di€erent pH values. In fact, the corre- system with two four-reaction kinetic models. In
particular, the inhibiting action of acetate ions on
PA oxidation was quantitatively explained in the
terms of a reactive complex formed with the low
oxidation-state manganese. This hypothesis was
con®rmed by the larger e€ectiveness of this action
observed on increasing pH.
It was possible to obtain a fair correlation of the
experimental data. The residual non random errors
observed can be tentatively attributed to the simpli-
®ed modeling of the very complex behaviour shown
by the manganese ions. However, it appears that
the development of a more detailed kinetic model-
ing is hindered by the lack of measurements of the
low oxidation-state manganese ions.
sponding parameters do not have exactly the same
meaning in di€erent kinetic models, because the use
of simpli®ed reaction mechanisms makes each rate
constant not completely independent form the
others.
However, it can be observed that the increase of
k1a (kinetic model B), computed on increasing pH,
corresponds to the observed increase of the overall
reactivity of the system. In Fig. 8 a comparison of
the results obtained in the present work with those
reported in the literature (Ghaieb et al., 1991) is
shown. The data are in good agreement when one
considers that the Ghaieb's data were obtained at
208C (instead of 258C).
The constant kC2 (kinetic model C) increases by
about a factor of four from pH=2.0 to pH=3.0.
This result agrees with the increasing importance of
the inhibition reaction, depending on the increasing
concentration of [Ac ]. The observed fourfold
increase cannot be directly compared to the theory,
which forecasts a one order of magnitude increase
for kC2, because the results suggest that, at
pH=2.0, most of the permanganate is formed via
the reaction B2.
REFERENCES
Al-Hayek N., Legube B. and Dore M. (1989) Catalytic
ozonationÐFe(III)/Al2O3 of phenol and its ozonation
by-products. Env. Techn. Letters 10, 415±426.
Allemane H., Delouane B., Paillard H. and Legube B.
(1993) Comparative eciency of three systems (O3, O3/
H2O2 and O3/TiO2) for the oxidation of natural organic
matter in water. Ozone Sci. & Engn. 15, 419.
Andreozzi R., Caprio V., D'Amore M. G., Insola A. and

120
R. Andreozzi et al.
Tufano V. (1991) Analysis of complex reaction networks Andreozzi R., Caprio V., Insola A., Marotta R. and
in gas-liquid systems: the ozonation of 2-hydroxypyri-
dine in aqueous solutions. Ind. Eng. Chem. Res. 30,
2098.
Tufano V. (1998) The ozonation of pyruvic acid in aqu-
eous solutions catalyzed by suspended and dissolved
manganese. Wat. Res. 32(5), 1492±1496.
Andreozzi R., Caprio V., Insola A. and D'Amore M. G.
(1992a) The kinetic of Mn(II) catalysed ozonation of
oxalic acid in aqueous solution. Wat. Res. 26(7), 917±
921.
Andreozzi R., Insola A., Caprio V. and D'Amore M. G.
(1992b) Quinoline ozonation in aqueous solutions. Wat.
Res. 26(5), 639±643.
Ghaieb J., Bes R. S. and Romdhane M. (1991) Mass
transfer studies of ozonation of manganese. Proc. 10th
Ozone World Congress, March 1991, Monaco.
Gmelin L. (1980) Gmelin Handbuch der Anorganischen
Chemie, Vol. D2. Mangan, Springer-Verlag, NY.
Gracia R., Aragues J. L. and Ovelleiro J. L. (1998)
Mn(II)-catalysed ozonation of raw Ebro river water and
its ozonation by-products. Wat. Res. 32(1), 57±62.
Andreozzi R., Caprio V., Ermellino I., Insola A. and
Tufano V. (1996) Ozone solubility in phosphate bu€ered Jun Ma and Graham J. D. (1999) Degradation of atrazine
aqueous solutions: the e€ect of temperature, t-butyl
alcohol, pH. Ind. Eng. Chem. Res. 35, 1467.
by manganese-catalysed ozonation: in¯uence of humic
substances. Wat. Res. 33(3), 785±793.
Andreozzi R., Caprio V., Insola A., Marotta R. and
Tufano V. (1997) Kinetics of oxalic acid ozonation pro-
moted by heterogeneous MnO2 catalysis. Ind. Eng.
Chem. Res. 36(11), 4774±4778.
Paillard H., Dore M. and Bourbigot M. M. (1991) Pro-
spects concerning applications of catalytic ozonation in
drinking water treatment. Proc. 10th Ozone World Con-
gress, Monaco, March 1991, Vol. 1 313±329.