Citric acid oxidation by vanadium(V) in sulfuric acid medium: Kinetic and mechanistic study

Article abstract of DOI:10.1002/1097-4601(2000)32:9<566::AID-KIN6>3.0.CO;2-Q

The citric acid oxidation by vanadium(V) in sulfuric acid medium at 303 K is reported. The reaction rate was determined spectrophotometrically by monitoring the formation of vanadium(IV) at 760 nm. The oxidation showed a first-order dependence with respect to vanadium(V) concentration and fractional order with respect to citric acid concentrations, with no control and with constant ionic strength. The reaction is also first order with respect to sulfuric acid concentration with no control and of fractional order at constant ionic strength. The reaction rate is enhanced by an increase of ionic strength and increased by a decrease of the dielectric constant. The activation parameters were calculated based on the rate constants determined in the 293 to 313 K interval. The proposed oxidation mechanisms and the derived rate laws are consistent with the experimental rate laws.

Full text of DOI:10.1002/1097-4601(2000)32:9<566::AID-KIN6>3.0.CO;2-Q

Citric Acid Oxidation by
Vanadium(V) in Sulfuric
Acid Medium: Kinetic and
Mechanistic Study
´
CRISTIANO RAMINELLI, WAGNER JOSE BARRETO, AND KEIKO TAKASHIMA
Departamento de Quı´mica, Universidade Estadual de Londrina, caixa postal 6001, 86051-990, Londrina, PR, Brazil
Received 27 September 1999; accepted 26 April 2000
ABSTRACT: The citric acid oxidation by vanadium(V) in sulfuric acid medium at 303 K is re-
ported. The reaction rate was determined spectrophotometrically by monitoring the formation
of vanadium(IV) at 760 nm. The oxidation showed a first-order dependence with respect to
vanadium(V) concentration and fractional order with respect to citric acid concentrations, with
no control and with constant ionic strength. The reaction is also first order with respect to
sulfuric acid concentration with no control and of fractional order at constant ionic strength.
The reaction rate is enhanced by an increase of ionic strength and increased by a decrease of
the dielectric constant. The activation parameters were calculated based on the rate constants
determined in the 293 to 313 K interval. The proposed oxidation mechanisms and the derived
rate laws are consistent with the experimental rate laws. ᭧ 2000 John Wiley & Sons, Inc. Int J Chem
Kinet 32: 566–572, 2000
INTRODUCTION
are operative in sulfuric acid and/or perchloric acid
media. For example, the oxidation of malic acid was
carried out in both media [5,7] and displays a faster
rate in sulfuric acid with ionic strength control. The
reaction rate in this medium showed first-order behav-
ior with respect to oxidant, substrate, and hydrogen
ion concentrations with or without control of the ionic
strength [5]. However, when this oxidation was per-
formed in perchloric acid, the rate law was the same
regardless of the ionic strength variation displaying
first-order behavior with respect to the oxidant and
malic acid concentrations and fractional order with re-
spect to the hydrogen ion concentration. Therefore, a
similar mechanism appears to be in effect with or with-
out control of ionic strength [7]. Meanwhile, the tar-
taric acid oxidation in sulfuric acid medium presented
a first-order dependence with respect to vanadium(V)
and fractional orders with respect to tartaric acid and
sulfuric acid concentrations, with no control and with
constant ionic strength. In this case, a faster rate is
The kinetics and mechanism of the oxidation of or-
ganic ligands by aquavanadium(V) ions has been pre-
viously reviewed [1]. However, relatively few studies
have addressed the question of the nature of the oxi-
dizing species in these systems [2,3] because, appar-
ently, the kinetic behavior of hydroxyacids oxidations
are considered well established.
We have observed in our investigations [4–7] that
the mechanism route depends on several factors, such
as the structure of the substrates, the nature and the
oxidizing capacity of the oxidant, the reaction condi-
tions, and the actual products isolated. The participa-
tion of some active species of vanadium(V) in these
oxidations [4–7] showed that different mechanisms
Correspondence to: K. Takashima (keiko@uel.br)
᭧ 2000 John Wiley & Sons, Inc.

CITRIC ACID OXIDATION BY VANADIUM(V) IN SULFURIC ACID MEDIUM
567
observed at a fixed ionic strength [4]. When lactic acid
was oxidized in sulfuric acid medium, a faster rate was
also observed with ionic strength control, and the plot
of ln kobs vs. ln[Hϩ] displayed an inflection under both
conditions, indicating two different orders in the in-
vestigated hydrogen ion concentration range. The vari-
ation of the reaction order was more significant when
the ionic strength was not controlled, showing a be-
havior of approximately first and second orders, re-
spectively. We attributed these changes not only to the
nature of the vanadium(V) but also to the oxidizing
capacity promoted by the increase of the hydrogen ion
concentration [8]. In continuation with our studies, we
report herein the results of the oxidation of citric acid
by vanadium(V) in sulfuric acid medium under vari-
able and constant ionic strength conditions.
least 50-fold excess over vanadium(V), V(V), by mon-
itoring the appearance of vanadium(IV), V(IV), at
760 nm with a Varian spectrophotometer model DMS-
80 at 303.0 K (Ϯ0.1 K). Spectra of different vana-
3
dium(IV) solutions in the range from 5.0 ϫ 10Ϫ to
2
3
3.0 ϫ 10Ϫ mol dmϪ were recorded from 500 to
800 nm using a cell of 1-cm path length. At 760 nm,
the molar absorption coefficient has been found to be
3
1
(18.91 Ϯ 0.83) mol dmϪ cmϪ . The first-order rate
constants, kobs, were evaluated from the slopes of the
linear plots of ln[V(V)] against time and were repro-
ducible within Ϯ5%. The measurements were carried
out in duplicate and, when necessary, in triplicate.
The reaction mixture was allowed to stand for sev-
eral hours with recrystallized acrylamide (25% v/v)
under kinetic conditions. The formation of gel indi-
cates free-radical intervention in the oxidation. Con-
trol experiments in which either V(V) or HCi were
excluded demonstrated the absence of polymerization.
The other oxidation product was identified as ace-
tone after some reactions, such as with 2,4-dinitro-
phenylhydrazine, displayed positive result; the Tollens
reagent and chromotropic acid test both yielded neg-
ative [8]. The stoichiometry was determined as de-
scribed earlier [6]. A reaction mixture containing an
EXPERIMENTAL SECTION
Solutions of vanadium(V), V(V), (Merck) and citric
acid, HCi (Reagen), were prepared by dissolving ap-
propriate amounts in deionized water, with or without
control of the ionic strength, as described previously
[4–7]. NaHSO4 was used to maintain the ionic
strength. All the reagents were of analytical grade.
All kinetic measurements were performed under
pseudo-first-order rate conditions with citric acid in at
3
excess of V(V) of 0.15 M over HCi (2.0 ϫ 10Ϫ mol
3
3
dmϪ ) in acidic medium (2.50 mol dmϪ ) was ther-
mostated at 313 K. A yield of 3.0 (Ϯ0.3) moles of
CO2 for each mole of HCi was obtained in a Warburg
Table I Pseudo-First-Order Rate Constants for the Oxidation of Citric Acid by V(V) with No Control of Ionic
Strength (I) and at Constant Ionic Strength;* [H2SO4] ϭ 0.20 mol dmϪ3 and T ϭ 303 K
Ϫ
Ϫ3
Ϫ3
Ϫ
Ϫ1
I/mol dmϪ3
[V(V)]/10 2 mol dm
[HCi]/mol dm
kobs/10 3 s
a
a
a
a
a
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.50
1.50
2.00
2.50
0.50
1.50
2.00
2.50
0.50
0.75
1.00
1.25
1.50
0.50
0.75
1.00
1.25
1.50
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
4.11
4.84
5.71
6.19
6.97
6.35
7.91
9.40
10.57
12.13
6.10
5.38
5.08
4.87
10.37
7.65
6.93
6.23
1.00
1.00
1.00
1.00
1.00
a
a
a
a
1.00
1.00
1.00
1.00
a Initial ionic strength is 0.21 mol dmϪ3 but changes in the course of the reaction.
* Ionic strength was achieved by using NaHSO4 as added electrolyte.

568
RAMINELLI ET AL.
Table II Effect of the H2SO4 Concentration on the
Pseudo-First-Order Rate Constants at 303 K with No
Control of Ionic Strength (I) and at Constant Ionic
Strength;* [V(V)] ϭ 1.00 ϫ 10Ϫ2 mol dmϪ3 and [HCi] ϭ
respirometer (B. Braun, model V-85) at 313 K. The
overall reaction for citric acid oxidation may be rep-
resented by the following equation:
3
1.00 mol dmϪ
HOOCCH2(OH)C(COOH)CH2COOH ϩ 3V(V) !:
CH3COCH3 ϩ 3CO2 ϩ 3V(IV) ϩ 2H2O
Ϫ3
Ϫ3
Ϫ
Ϫ1
[H2SO4]/mol dm
I/mol dm
kobs/10 3 s
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.11
0.21
0.31
0.41
0.51
0.61
0.71
0.81
0.91
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.25
2.78
5.71
8.40
11.21
12.89
16.80
17.14
18.44
21.49
6.88
where V(V) and V(IV) represent the charged vana-
dium species in sulfuric acid medium with no control
ϩ
of ionic strength—V(OH)3HSO4ϩ and V(OH)2HSO4 ,
respectively.
RESULTS
9.40
11.54
13.52
15.72
17.61
18.86
22.52
23.14
4.94
5.38
5.85
6.76
7.34
Effect of Reactants Concentration
The citric acid concentration, [HCi], was varied in the
3
range from 0.50 to 1.50 mol dmϪ when the initial
concentrations of V(V), [V(V)]0 , and sulfuric acid,
[H2SO4]0 , were maintained constant at 303 K. The ox-
idation rate was more rapid when the ionic strength
was controlled and the rate constants, kobs, varied by
about 65% with no control of ionic strength and
ϳ90% at constant ionic strength as shown in Table I
4
(r Ն 0.9963 and s Յ 1.087 ϫ 10Ϫ ). Individual plots
of ln[V(V)] as a function of time for different initial
concentrations of citric acid, [HCi]0 , display satisfac-
7.84
8.22
10.59
4
tory linearity (r Ն 0.9988 and s Յ 3.580 ϫ 10Ϫ ) at
303 K, and the order with respect to [HCi] is around
a Constant ionic strength was achieved by using NaHSO4 as
added electrolyte.
2
0.5 (r Ն 0.9978 and s Յ 1.567 ϫ 10Ϫ ) in both media
with no control of ionic strength and at constant ionic
2
strength. The variation of [V(V)]0 from 0.50 ϫ 10Ϫ
to 2.50 ϫ 10Ϫ mol dmϪ decreased the rate constant
by about 20% (r ϭ Ϫ0.9943 and s ϭ 6.074 ϫ 10Ϫ )
2
3
Effect of Ionic Strength
5
The pseudo-first-order rate constant doubled when the
ionic strength was changed in the range of 0.30 to 1.25
in solutions with no control of ionic strength, and by
4
about 40% (r ϭ Ϫ0.9850 and s ϭ 3.435 ϫ 10Ϫ ) at
3
mol dmϪ by the addition of a concentrated solution
constant ionic strength as indicated also in Table I.
3
of sodium bisulfate (5.0 mol dmϪ ) in the reactant so-
lution (Table II). The plot of log kobs as a function of
the square root of the ionic strength at 303 K [9, 10]
gives a product of the ionic charges, zϩzϪ , of 0.60
Effect of Hydrogen Ion Concentration
2
(r ϭ 0.9959 and s ϭ 1.07 ϫ 10Ϫ ).
The oxidation rate increased with increasing hydrogen
ion concentration, [Hϩ], from 0.10 to 0.90 mol dmϪ
3
through the addition of sulfuric acid by about an eight-
fold with no control and approximately threefold with
control, maintaining the same initial reactant concen-
trations, [V(V)]0 and [HTA]0 . The pseudo-first-order
rate constants at 303 K are presented in Table II. The
reaction order for the reaction without ionic strength
control was first order (r ϭ 0.9977 and s ϭ 4.792 ϫ
Effect of Solvent
The oxidation rate enhanced with the increase of meth-
anol content for ϳ50% with no control of ionic
strength and ϳ30% with control (Table III), changing
the solvent composition by the addition of methanol
to aqueous medium (0–35% v/v). Plots of ln kobs vs.
the reciprocal of dielectric constant of the medium,
2
10Ϫ ); and with control, around 0.50 (r ϭ 0.9937 and
2
s ϭ 4.712 ϫ 10Ϫ ).

CITRIC ACID OXIDATION BY VANADIUM(V) IN SULFURIC ACID MEDIUM
569
Table III Pseudo-First-Order Rate Constants for the
0.5. Arrhenius plots were constructed from ln kЈ (the
apparent second-order rate constants, obtained from
Table IV) vs. the reciprocal absolute temperature. The
activation parameters were calculated from the slopes
and intercepts of Arrhenius plots (r Ն 0.9937 and
Oxidation of Citric Acid by V(V) in Binary Aqueous
Mixtures of Methanol with No Control of Ionic Strength
(I) and at Constant Ionic Strength;* [V(V)] ϭ 1.00 ϫ
2
10Ϫ mol dmϪ3, [HCi] ϭ 1.00 mol dmϪ3, [H2SO4] ϭ 0.20
mol dmϪ3 and T ϭ 303 K
2
s Յ 8.018 ϫ 10Ϫ ) and Eyring equation. The activa-
Ϫ3
Ϫ
Ϫ1
kobs/10 3 s
1
tion energies are 63.4 and 59.3 kJ molϪ ; the enthalpies
[MeOH]/%
I/mol dm
1
of activation, 60.9 and 56.8 kJ molϪ ; and the activa-
a
a
a
a
a
a
0
15
20
25
30
35
0
15
20
25
30
35
5.71
7.05
7.47
8.04
8.25
8.55
9.40
9.86
10.51
10.95
11.56
12.15
1
1
tion entropies, Ϫ93 and Ϫ101 J molϪ KϪ , with no
control and at constant ionic strength, respectively.
DISCUSSION
1.00
1.00
1.00
1.00
1.00
1.00
The first-order dependence of the rate on the vana-
dium(V) concentration, [V(V)], in sulfuric acid me-
dium, is evident from the linearity of the ln[V(V)] as
a function of time plots. Contrary to the oxidations
investigated earlier [4–7], a decrease was observed in
the rate constants when the concentrations were varied
* Ionic strength was achieved by using NaHSO4 as added elec-
trolyte
2
2
3
from 0.50 ϫ 10Ϫ to 2.50 ϫ 10Ϫ mol dmϪ without
or with control of ionic strength and maintaining all
the other experimental conditions (Table I). The in-
crease in the oxidation rate was attributed as a con-
sequence of the interaction between the hydrated form
V(OH)4ϩ and one or two bisulfate ions to produce the
a Initial ionic strength is 0.21 mol dmϪ3 but changes in the course
of the reaction.
1/␧ [11] resulted in straight lines (r Ն 0.9753, s Յ
2
3.65 ϫ 10Ϫ ). Control experiments showed a negligi-
ϩ
species V(OH)3HSO4 and V(OH)2(HSO4)2ϩ with no
ble oxidation of methanol by V(V).
control and constant ionic strength, respectively:
Effect of Temperature
ϩ
Ϫ
V(OH)23 ϩ HSO4 ϭ V(OH)3HSOϩ4
The oxidation rate was measured by varying the tem-
perature from 293 to 313 K, keeping the other exper-
imental conditions constant. These results are given in
and
V(OH)23 ϩ Hϩ ϩ 2 HSO4
ϩ
Ϫ
4
Table IV (r Ն 0.9963 and s Յ 1.087 ϫ 10Ϫ ), and the
reaction order with respect to [HCi] remains around
ϭ V(OH)2(OH)2(HSO4)2ϩ
Table IV Effect of Temperature on the Citric Acid Oxidation with No Control of Ionic Strength (I) and at Constant
3
Ionic Strength;* [V(V)] ϭ 1.00 ϫ 10Ϫ2 mol dmϪ3, [HCi] ϭ 0.50–1.50 mol dmϪ3, [H2SO4] ϭ 0.20 mol dmϪ
Ϫ
Ϫ1
k
obs/10 3s
Ϫ
3
Ϫ3
I/mol dm
[HCi]/mol dm
T/K
293
298
303
308
313
a
a
a
a
a
0.50
0.75
1.00
1.25
1.50
0.50
0.75
1.00
1.25
1.50
1.30
1.60
1.83
2.22
2.56
2.13
2.60
3.34
3.89
4.54
2.32
2.68
3.17
3.70
4.11
4.20
5.23
6.29
7.04
8.38
4.11
4.48
5.71
6.19
6.87
6.16
8.07
9.40
10.57
12.13
5.47
6.54
7.50
8.84
9.98
8.72
9.85
11.90
13.75
14.77
13.61
16.10
19.06
22.91
25.89
1.00
1.00
1.00
1.00
1.00
9.10
10.45
12.65
14.51
16.39
* Ionic strength was achieved by using NaHSO4 as added electrolyte.
a Initial ionic strength is 0.21 mol dmϪ3 but changes in the course of the reaction.

570
RAMINELLI ET AL.
ϩ
On the other hand, the decrease in the rate-varying
[V(V)] in this interval of concentrations was around
25% with no control and about 66% at constant ionic
strength. This behavior indicates that the vanadium(V)
reacts in the coordinated form, and thus the three car-
boxyl groups of the citric acid are responsible for the
steric hindrance and a decrease in the rate. The more
concentrated the vanadium(V), the less the citric acid
solubility and consequently less reactivity. In all the
other substrate oxidations, such as tartaric, malic, and
lactic acids [4–6], the opened structures favored the
approximation of vanadium(V) enhancing gradually
the rate constants. As related previously, we assumed
that sulfuric acid behaves as a strong monobasic acid
for the purpose of hydrogen and/or bisulfate ions.
The oxidation of citric acid, HCi, by vanadium(V)
takes place more rapidly in comparison with lactic acid
[6], malic acid [5, 7], and tartaric acid [4], indicating
that electron-withdrawing substituents at the ␣-posi-
tion increase the oxidation rate. This was experimen-
tally verified through the use of a smaller concentra-
tion of sulfuric acid in the kinetic measurements. The
V(OH)2(HSO4)2 ϩ Hϩ
K1Ј
R
ϩ
ϩ HOOCCH2(OH)C(COOH)CH2COOH E
F Y*2
(1Ј)
It has been shown earlier that most reactions in-
volving V(V) proceed via a free-radical mechanism
[12]. In this investigation, the addition of acrylamide
to the reaction mixture has also been shown to yield
the formation of a polymeric product, indicating that
V(V) behaves as a one-equivalent oxidant. Thus, the
activated species, X*2 , interacts with Hϩ in a bimo-
lecular way, while Y*2 species decomposes unimo-
lecularly in the rate-determining step to give the first
ϩ
ϩ
CO2 through a C9C fission producing free radicals,
(HO) CϩCH C (OH)CH Cϩ(OH) and HOOCCH C
ؒ
ؒ
2
2
2
2
2
(OH)CH2Cϩ(OH)2 , without and with control of ionic
strength respectively, in the rate-determining step:
k2
9
X*2 ϩ Hϩ 9
: (HO) CϩCH C (OH)CH Cϩ(OH)
ϩ CO2 ϩ V(OH)2HSO4 ϩ H2O
ϩ
ؒ
2
2
2
2
ϩ
(2)
3
variation of [Hϩ] from 0.10 to 0.90 mol dmϪ (Table
II) resulted in rate constants, with no control of ionic
strength, larger than those at constant ionic strength;
and both showed the trend to a limiting value and that
at higher concentrations of sulfuric acid the oxidation
capacity decreases. The experimental rate laws that
represent the kinetic data are given as
and
Y*2ϩ 9Ј
k2
9
: HOOCCH C (OH)CH Cϩ(OH)
ؒ
2 2 2
ϩ
ϩ CO2 ϩ V(OH)(HSO4)2 ϩ H2O (2Ј)
In the absence of ionic strength control, the free radical
produced is rapidly oxidized through another mole of
V(V), yielding one more carbon dioxide; a charged
intermediate, V(IV); and H2O according to the follow-
ing scheme:
d[V(V)]
␯ ϭ Ϫ
ϭ kobs[HCi]0.5[Hϩ][V(V)]
dt
with no control of ionic strength
and
ϩ
(HO) CϩCH C (OH)CH Cϩ(OH) ϩ V(OH) HSO
ؒ
2
2
2
2
3
4
d[V(V)]
k3
␯ ϭ Ϫ
ϭ kobs[HCi]0.5[Hϩ]0.5[V(V)]
99
: (HO)2CϩCH2COCH3 ϩ CO2
dt
ϩ V(OH)2HSO4 ϩ Hϩ ϩ H2O (3)
ϩ
with control of ionic strength
and, in a similar way, between the cation radical
HOOCCH C (OH)CH Cϩ(OH) and
mole of
The fractional dependence on the citric acid concen-
tration with no control of ionic strength may be due
to the participation in two steps of the mechanism and
protonation of citric acid prior to equilibrium accord-
ing to
a
ؒ
2
2
2
V(OH)2(HSO4)2ϩ at constant ionic strength.
In the last step, the formation of acetone takes place
with the liberation of the third mole of carbon dioxide
with no control of ionic strength, according to the fol-
lowing reaction:
ϩ
V(OH)3HSO4 ϩ H
K1
R
ϩ
ϩ [HOOCCH2(OH)C(COOH)CH2COOH] E
F X*2
ϩ
(HO)2CϩCH2COCH3 ϩ V(OH)3HSO4
(1)
k4
99: CH3COCH3 ϩ CO2
ϩ
The fractional orders with respect to [HCi] and [Hϩ]
provide a concerted equilibrium among vanadium(V),
HCi, and Hϩ when the ionic strength is controlled:
ϩ V(OH)2HSO4 ϩ H2O (4)
and, in a similar manner, at fixed ionic strength.

CITRIC ACID OXIDATION BY VANADIUM(V) IN SULFURIC ACID MEDIUM
571
The increase of the ionic strength from 0.30 to 1.25
k2K1 [HCi][Hϩ][V(V)]t
1 ϩ K1 [HCi]
␯ ϭ
(5)
3
mol dmϪ doubled the rate constants (Table II) and
presented a linear dependence on the plot of log kobs
against the square root of the ionic strength, giving an
ionic charge product of 0.60. From this value alone it
is difficult to suggest that the vanadium(V) reacts with
citric acid either as the protonated form or in the mo-
lecular form. The application of the primary salt effect
[9] in ionic strengths up to 0.05 mol dmϪ3 also works
in this oxidation. This may indicate that some other
factors, such as size and structure of the substrate and
oxidant, compensate the ionic charge and concentra-
tion of the species in the solution and lead to the ap-
plication of the expression for a primary salt effect.
The effect of solvent on the reaction rate was stud-
ied varying the methanol-water composition (Table
III). Plots of ln kobs against the reciprocal of the di-
electric constant of the binary mixtures [11], with no
control or constant ionic strength, resulted in straight
lines with positive slopes. This is similar to malic and
lactic acids oxidations and unlike that of tartaric acid,
that is, an increase in the oxidation rate with the de-
crease in the solvent polarity. Thus, the transition state
is either less polar than the reactants [13] or the solvent
is providing more hydrogen bonding, which can sta-
bilize the activated complex and in this manner de-
crease the next step in the reaction mechanism.
and
k2 K1 [HCi][Hϩ][V(V)]t
Ј
Ј
␯Ј ϭ
(5Ј)
1 ϩ K1 [HCi][Hϩ]
Ј
where the total or analytical concentrations of V(V)
are given by
ϩ
[V(V)]t ϭ [(X*2 )] ϩ [V(OH)3HSOϩ4 ]
or
ϩ
[V(V)]t ϭ [(Y*2 )] ϩ [V(OH)2(HSO4ϩ)2]
The rate laws, (5) and (5Ј), are in agreement with the
experimental data in sulfuric acid medium. The inves-
tigated reactions are of first order with respect to the
vanadium(V) and hydrogen ion concentrations, and of
The negative values of the entropy of activation,
1
Ϫ93 and Ϫ101 J molϪ1 KϪ , calculated from the val-
ues of the apparent second-order rate constant, are ex-
pected because there is a charge increase of reactive
vanadium(V) species in the rate-determining species,
which undergo electrostriction with the solvent mol-
ecules [14]. However, when compared with the other
␣-hydroxyacids investigated [4–6], it is clear that the
complex stability is practically the same when the
1
1
ionic strength is fixed (Ϫ101 J molϪ KϪ ) compared
1
1
with no control (Ϫ93 J molϪ KϪ ). This means that
in the activated complex formation the presence of
three carboxyl groups of the citric acid is predominant
with respect to the coordinated forms of vanadium(V).
While the oxidation rates are systematically greater in
the fixed ionic strength, the difference between the ac-
tivation energy with fixed control and without control
of ionic strength is slightly lower than that previously
observed [4–6]. The same trend occurs with the en-
thalpy of activation, and this may be justified by the
steric hindrance, which is caused by the carboxyl
groups of the citric acid in this oxidation.
Assuming the slow step as the rate-determining one
(k2 , and k2Ј, respectively), these mechanisms lead to
the rate laws (5) and (5Ј) for the oxidation of citric
acid by V(V) in sulfuric acid medium with no control
and with fixed ionic strength, respectively:
Figure 1 A double reciprocal plot of the pseudo-first-order
rate constant, kobs, and citric acid concentration; [HCi] for
Ϫ
Ϫ
Ϫ3
V(V)] ϭ 1.00 ϫ 10 2 mol dm 3, [H2SO4] ϭ 0.20 mol dm
at 303 K. (᭿) No control of the ionic strength and (᭹) con-
Ϫ
stant ionic strength (I ϭ 1.00 mol dm 3).

572
RAMINELLI ET AL.
Paulo) for valuable suggestions concerning this study, and
Ivanira Moreira for technical assistance.
fractional order with the respect to the citric acid with-
out ionic strength control. When it was controlled, the
rate was of first order only for vanadium(V) concen-
tration since for citric acid and hydrogen ion concen-
trations the order was fractional. From the slopes and
intercepts of the double reciprocal plots at constant
vanadium(V) and citric acid concentrations (Figure 1,
r Ն 0.97548 and s Յ 7.8210) the equilibrium con-
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2
stant, K1 , was determined as 0.178 molϪ dm6 at
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1
1
constant k2 was obtained as 1.60 ϫ 10Ϫ molϪ dm3
sϪ with no control of ionic strength control. When
1
this was adjusted to 1.00 mol dmϪ , these values be-
3
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In conclusion, the decrease of the oxidation rate as
a function of the vanadium(V) concentration as well
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the activated species, X*2 and Y*2 , leading to the
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ϩ
ϩ
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This work was made possible through the financial support
of PADCT/FINEP, PADCT/CAPES, CNPq, and CPG/UEL.
We thank Professor Jose´ Manuel Riveros (University of Sa˜o