13294
J. Phys. Chem. 1994,98, 13294-13299
Reactivity of the Mn(II1) and Mn(IV) Intermediates in the Permanganate/Oxalic Acid/ Sulfuric Acid Reaction: Kinetic Determination of the Reducing Species V. Pimienta, D. Lavabre, G. Levy, and J. C. Micheau* Luboratoire des IMRCP, URA au CNRS 470, Universitg Paul Sabatier, F-31062 Toulouse, France Received: July I S , 1994; In Final Form: September 29, 1994@
UV/visible spectrophotometric analysis of the permanganate/oxalic acid reaction in sulfuric acid demonstrated the presence of two intermediates: bis(oxalato)manganate(III) and a soluble Mn(IV) compound. Their relative proportions were found to depend on the initial concentrations [H2C204]0 and [H2S04]0. The proportion of bis(oxalato)manganate(III) was highest for a rise in [H2C204]0, while those of the soluble Mn(IV) compound increased for a simultaneous fall in [H2C204]0 and [H2S04]0. A kinetic study together with a quantitative study of the effects of displacement of the equilibria of dissociation of the two diacids showed that, from a kinetic point of view, oxalate ion was the reducer of Mn(II1) and molecular oxalic acid that of Mn(1V).
I. Introduction The reaction between permanganate and oxalic acid in sulfuric acid medium (KMn04/H2C204/H2SO4) is regarded as the archetype of autocatalytic reactions. It has features which have intrigued researchers for more than a century.’ For example, an increase in initial concentration of sulfuric acid speeds up the reaction, whereas an increase in the concentration of oxalic acid slows it down2 More recently, several authors have shown that this reaction is bistable in a CSTR at low oxalic acid con~entration.~~~ These findings and the development of new oscillating reactions based on the chemistry of manganese have rekindled interest in this rea~tion.~ It is characterized by two principal processes: Mn(VII) Int
-
-
Int
Mn(II)
where “Int” represents one (or several) reaction intermediate(SI.
Among all the possible intermediates, bis(oxalat0)manganate(111), [Mn(C204)2]- (referred to here as is the most widely recognized.6~~However, using UV/visible spectro~copy,~~~ we demonstrated the presence of a second intermediate containing manganese in oxidation state IV. The intermediate “Int” is in fact a mixture of various proportions of III2 and Mn(1V). The present study was designed to determine the nature of the entities involved in the reduction of Mn(II1) to Mn(I1) and Mn(IV) to Mn(II1). Consideration of the redox potentials indicates that the electrons are provided by oxalic acid, although it is not obvious whether they stem from the nondissociated molecule H2C2O4, the hydrogenooxalate ion HCzO4-, or the oxalate ion C2042-. We thus made a kinetic analysis of the auxiliary reactions {Mn(III)/H2C204/H2S04} (referred to here as RIII) and {Mn(IV)/H2C20&32S04} (referred to here as RIV) using different initial concentrations [H2C204]0 and [H2S04]0 in order to take into account quantitatively the dissociation equilibria of these two diacids in aqueous solution.
n.
Characterization of Intermediates
(1) UVNisible Spectroscopic Analysis of Intermediates. The changes in absorbance between 300 and 700 nm were recorded continuously in a diode array spectrophotometer. @
Abstract published in Advance ACS Abstracts, November 1, 1994.
0022-3654/94/2098- 13294$04.50/0
UJ D Q 0.5
0.0
I
40
80
time (s) Figure 1. (A) Three-dimensional Whisible spectrum recorded during reaction 3 (stoichiometric ratio, see Table 1). (B) Extraction of singlewavelength kinetics from the three-dimensional spectrum: (a) 320 nm; (b) 560 nm; (c) 456 nm (isosbestic point).
Figure 1A shows two spectral zones: (a) Between 490 and 650 nm, the characteristic peak complex of MnO4- ions collapses without deformation, as only permanganate absorbs significantly in this region. The corresponding wavelengths are said to be pure, as they can be used to follow the change in concentration of permanganate at any instant. The kinetics at 560 nm, represented in Figure lB(b), shows the autocatalytic nature of the disappearance of MnO4- ions. (b) Between 300 and 400 nm, a transient absorbance is observed, which passes through a maximum and then falls until the reaction mixture is completely bleached (Figure lB(a)). This 0 1994 American Chemical Society
Reactivity of the Mn(II1) and Mn(IV) Intermediates
J. Phys. Chem., Vol. 98,No. SO, 1994 13295
TABLE 1: Relative Proportion of Bis(oxalato)manganate(III) (I&) and x as a Function of [ H z C ~ Oand ~ ] ~[HzSO& (in m0l.L-l) in the Reaction Intermediate Observed during the PermanganatdOxalic Acid Sulfuric Acid Reactiod
1200
A 800
no. 1
::
W
2
400
3
4
400
450
0.2 0.025 0.0013 0.0013
[H2S0410 0.27 0.27 0.27
0.09
tin
240 220 80 180
%X
As,
450 452 456 456
91
9
69 40
31
32
60 68
mol.L-'. The values of tln (in s) correspond [Mn04-]0 = 5 x to the half-life of permanganate during the reaction. Note the shift of the isosbestic point (Aisos) as a function of initial concentrations.
I 500
wavelength (nm)
la,
[HzCz041o
I
relative initial concentrations [H2Cz04]0 and [H2S04]0 (Table 1). Examination of spectrum 1 in Figure 2A, for which [HzC204]0 = 0.2 mo1.L-' and [H2S04]0= 0.27 mol-L-' (a = 0.91), shows that, in this case, the intermediate consists almost exclusively of III2. The first step of the reaction can thus be schematized by W 111, as suggested by Adler et aL6 However, in their study, in which the concentration of oxalate ion was high, they only detected Mn(II1). Spectra 2 and 3 were obtained for a lower [HzCZO~IO: a falls progressively to a value of 0.40; for spectrum 4, where [H2C204]0 and [H2S04]0 are both low, a = .32; the overall spectrum of the intermediates is effectively constituted by 68% of compound x. Its exact structure could not be readily determined since (i) it could not be isolated and (ii) its spectrum did not resemble that of any known species of manganese in any oxidation state between VI1 and II. A partial identification was made on searching the literature and by successive elimination. (2) Identification of the Second Intermediate, x. Mn(V1) and Mn(V) were ruled out, as they are highly unstable in acid medium." Furthermore, their spectra display peaks at 600 and 660 nm, respectively.12 With respect to Mn(III), various complexes with oxalate ions have been described,13J4 such as mono(oxalato)manganese(III) ([Mn(C204)]+, referred to here as IIIl) and tris(oxalato)manganate(III) ([Mn(C204)3I3-, referred to here as III3). The intermediate IIIl is unstable and is not readily observed experimentally. Species 1113, however, is readily isolated, but only at much higher concentrations of oxalate ions than those employed in the present experiments. It exhibits a peak at 510 nm. We thus concluded that the second intermediate was a Mn(IV)species. This oxidation state is commonly involved in the oxidation of organic compounds by permanganate. The spectra of such species depend on the nature of the reducing agent and the experimental conditions (acidity of the solution, presence or absence of stabilizing ions such as phosphate). None of the spectra are identical, which complicates the attribution to a chemically defined species.15-17 Nevertheless, the spectra display the same general shape, with a decreasing absorption between 300 and 600 nm with a shoulder whose position ranges from 375 to 475 nm. They are attributed to either a soluble species of Mn(N), which could be HZMn03," or colloidal Mn02.18 In our experiments, it was attributed to a soluble species of Mn(IV), as the solution was completely clear and because Rayleigh scattering was not verified.
-
"350
400
450
500
wavelength (nm)
Figure 2. (A) Overall spectra of intermediates obtained after subtraction of the spectrum of permanganate using formula 3 (see Experimental Section). The indices 1, 2,3, and 4 refer to the initial concentrations listed in Table 1. Since these spectra changed over time, they were chosen to correspond to around 40% disappearance of the initial permanganate. The spectra shown by solid lines were reconstructed numerically from relationship 2; they fit perfectly the experimental spectrum. The values of a are given in Table 1, and the calculated spectrum of x is plotted in Figure 2B. (B) Spectrum of I& from an authentic sample. The spectrum of x = Mn(1V) was derived by numerical analysis of the four intermediate spectra, 1-4, using formula
4.
corresponds to the appearance and disappearance of one or more reaction intermediates. An isosbestic point is observed at 456 nm (Figure lB(c)), but only at the start of the reaction. At this wavelength, we assumed that €Int m E ~ Q - . We have discussed the validity of this assumption in an earlier paper,1° and it appears to be well justified in this case. During this phase, the conservation of matter is approximated by the overall equation (1): [Mn04-], - [Mn04-]
= [Int]
(1)
However, for [H~C204]0ranging from 1.25 x to 0.2 mol-L-', there is a shift in isosbestic point between 456 and 450 nm, indicating that the intermediate must comprise at least two chemically distinct species in variable proportions. The overall spectrum of the intermediates (gint) is obtained after subtraction of the permanganate spectrum (Figure 2). Assuming that there are only two intermediates, the value of the molar extinction coefficient of Int (€int) is governed by a relationship of the following type:
where € 1 is~known, ~ a represents the relative proportion of IIIz, and (1 - a) is that of the second intermediate, another compound of Mn (referred to here as x); the spectrum of x and a were calculated numerically. The value of a depends on the
111. Determination of the Actual Reducing Agent of Each Intermediate The following experiments were designed to obtain a qualitative analysis of these two intermediates' reactivity during the complete permanganate/oxalic acidsulfuric acid reaction. The
Pimienta et al.
13296 J. Phys. Chem., Vol. 98, No. 50, 1994 actual reducing agents were determined with the aid of two auxiliary reactions. (1) Reactivity of I&. With some modification and simplification, the mechanism described by Taube13may be employed to interpret the reactivity of III2. This mechanism involves the equilibria of complexation of Mn(1II) with oxalate ions (steps A and B). In addition, these ions also donate electrons: the two complexes of Mn(III) (In1 and III2) spontaneously decompose to give Mn(I1) (steps C and D):
+ c,o,2- =111, 111, + c,o,2- 111, 111, - I1 + c0,'- + CO, 111, - I1 + c,o,2- + c0,'- + CO, I11
f
HC,04- -I-H+
+ Hf HS04- + H+ S O : + H+
HC204- f Cz0,2-
H2S04f HS0,-
f
-u N
(A) O.C.3-X
,I
0.0
(B) (C)
(D)
The effect of inhibition by oxalic acid, which is observed in the complete reaction (see Table 1, experiments 1, 2, and 3) can be explained by assuming that the rate of reduction of complex III1 (step C) is higher than that of II12 (step D). As [H2C204]0 increases, the concentration of oxalate ions rises, the proportion of III2 increases by displacement of the equilibria A and B, and so the proportion of IIIl falls with a reduced rate of disappearance of Mn(II1). To account for the accelerating effect of H2SO4 (see Table 1, experiments 3 and 4),the equilibria of dissociation of the two diacids (steps E, F, G, and H) must be taken into consideration. H,C204
I
t 0
pK,, = 1.3
(E)
pK, = 4.3
(F)
pK, = -9
(GI
pKa4 = 2
(H)
Calculation of the concentrations of each species at equilibrium shows that an increase in H2SO4 shifts the equilibria of dissociation of HzCzO4 toward an increase in molecular [H2C204] (nondissociated) and a decrease in [HC204-] and [C2042-]. Complex IIIl is thus favored by the shift in equilibria E and F, and the rate of disappearance of Mn(III) increases. We show in section lII.3 that this interpretation is quantitatively correct. (2) Reactivity of Mn(n7). Inspection of Table 1 shows that the proportion of Mn(1V) falls (i) as [H2Cz04]0 increases (experiments 3, 2 , and 1) and (ii) as [H2S04]0 increases (experiments 4 and 3). Between experiments 4 and 3, the effect of acceleration by sulfuric acid leads to a faster formation of the intermediate. Since under these conditions the relative proportion of Mn(IV) falls, one can assume that sulfuric acid speeds its disappearance. The effect of an increase in [HzC204]0, at constant [HZSO~IO, (experiments 3, 2, and 1) does not allow identification of the actual reducer of Mn(IV), since under these conditions [H2C2041, [HC204-1, and [C2042-] all increase along with [HZCZO~~O. On the other hand, as we have seen above, the addition of sulfuric acid at constant oxalic acid concentration (experiments 4 and 3) gives rise to a different effect: [HzCZO~] increases, while [HC204-] and [ C ~ 0 4 ~ decrease. -] If as mentioned above one assumes that the acceleration of the reduction of Mn(1V) by sulfuric acid is simply induced by shifting the dissociation equilibria of oxalic acid, the reducer is
0.oeXyII
OoecoO
2oe-04
400-04
kI2C2041,
Figure 3. (A) Chart used for RIII to determine the concentration at equilibrium of oxalate ion [CZO~~-], for a mixture of [H&204]0 from 0 to 0.25 mo1.L-1 and [HzSO& from 0.022 to 0.18 mol-L-'. The horizontal lines correspond to situations for which the oxalate concentration at equilibrium [C204*-], is kept constant. (B) Chart used for RIV for the determination of [HzC~04], for a mixture of [HzCZO~IO m0l.L-l to 6 x m0l.L-I and [&SO&, from 5.6 from 1.4 x x to 0.09 mol.L-'. The horizontal lines correspond to situations for which the concentration of molecular oxalic acid at equilibrium [HzCzO& is kept constant. Each point labeled with a letter (a, b, ...) gives the experimental conditions for each auxiliary reaction.
the species whose concentration increases as [HzC204]0 and [HzSO410 both increase together. This is true only for molecular oxalic acid, H2C204. Kinetic study of the two auxiliary reactions RIII, {Mn(III)/ HzC20&2S04), and RIV,{ M ~ ( I V ) / H Z C Z O ~ / H for ~ S ~dif~}, ferent values of the initial concentrations [H2C20410 and [H2S04]0provides a quantitativevalidation of these assumptions. (3) Kinetic Analysis of the Two Auxiliary Reactions RIII and RIV. If the two diacids are both present in solution, the equilibria E-H are set up, and each of the two potential reducing species attain concentrations [ C Z O ~ ~and - ] ~[H2C204le4,respectively. We have calculated numerically these concentrations from the values of PKAfor the different initial concentrations [HzCzOalo and [H2S04lo. Different pairs of initial concentrations [H~C204]0and [HzSO410 can be determined by tracing horizontal lines on Figure 3A, all giving rise to the same concentration of oxalate ions at equilibrium: [C2042-],. Figure 3A was thus employed to study the degradation of III2 (auxiliary reaction RIII). Similarly, Figure 3B was employed to obtain the conditions required to maintain [H2C204], in the case of Mn(IV) (auxiliary reaction FUV). It can be seen from Table 2 that the concentrations of all the other species depend on [HzCz04]0and [HzS04]0except one, namely, the species voluntarily kept constant. Although IIIz is readily obtained from commercial compounds, we were not able to synthetize any compounds of Mn(IV) with a UV/visible spectrum resembling the one observed in our experiments. Nonetheless, MnOz derived from the
Reactivity of the Mn(II1) and Mn(IV) Intermediates
J. Phys. Chem., Vol. 98, NO.50, I994 13297
TABLE 2: Calculated Equilibrium Concentrations of Six Mixtures of [H~CZO~IO + [HZSO~IO~ no. d e f k 1
[HzCZO~IO [H~SO~IO [HzCz041q mol%-' mo1.L-l mo1.L-l
[HCz04-leq
[ C Z O ~ ~ - I ~[HzS041eq ~ mol%-' mo1.L-l
[HS04-1ul mol.L-'
[so42-1w
2.4 x 6.3 x 1.9 x lo-' 4.5 x 3.1 x 2.4 x
1.4 x 2.6 x 5.2 x lo-* 2.9 x 1.6 x 8.5 x
1.7 x 1.7 x 1.7 x 5.0 x 1.5 x 4.2 x lo-*
1.7 x lo-' 3.9 x 8.3 x 1.6 x 3.6 x lo-' 8.0 x lo-'
5.2 x 6.3 x 7.1 x 6.7 x 8.6 x 1.0 x lo-*
2.2 x 4.5 x 9.0 x 2.2 x 4.5 x 9.0 x
1.0 x 3.7 x 1.4 x 10-' 1.5 x low4 1.5 x 1.5 x
mol%-'
6.9 x lo-" 3.0 x 1.2 x lo-" 4.6 x 1.9 x 8.0 x
mo1.L-l
[Hf1e4
mol%-' 4.1 x 7.8 x 1.5 x 2.9 x 5.4 x 1.0 x
lo-' lo-'
lo-'
lo-' m Experiments d, e, and f (from Figure 3A) produce a constant concentration of oxalate ions, while experiments k,1, and m (from Figure 3B) are for constant molecular oxalic acid. Note the changes in concentrations of all the other species. The validity of these values was verified by experimental determination of pH. In all cases, the difference between experimental and calculated values did not exceed 0.03 pH units. 6.00-03
I
1.e-01r----
1
using MnO2 from the Guyard reaction as a source of Mn(1V). Complex 1112 is the direct product of the reduction, although under our experimental conditions it did not accumulate due to the very low concentration of oxalate ions. The MnO2 spectrum decayed without deformation. The observed kinetics were first order and could be also characterized by a value of Kobs. Figure 4B shows that we obtained almost identical values of Kobs (within experimental error) for all the kinetics corresponding to the same value of [HZC~O~], whatever the concentrations of the other ions. (4) Discussion. Our results throw light on the mechanism of these reactions and may help decide among various hypotheses proposed to date: (i) In a recent study of the Mn(III)/H2C204 reaction in sulfuric acid medium, Adamsikova et al.*O observed either an acceleration of the reduction with increase in [HS04-] or a slowing down with increase in [Sod2-]. They proposed the intervention of a further complex, [Mn(C204)(HSO4)], to account for the accelerating effect of HS04-. Our results indicate that the effect of displacement of the dissociation equilibria of the two diacids should also be taken into account. By calculating the concentrations of each species at equilibrium, it can be seen that addition of HS04- induces a fall in [C2042-], and hence an increase in the IIIl/III2 ratio, which in turn increases kobs. It can also be seen that addition of S042- leads to an increase in [C~04~-]; the IIIl/III2ratio drops and so does kobs. Thus, from sole consideration of the displacement of the dissociation equilibria, the two effects observed can be interpreted qualitatively without involving a further complex. However, we could not rule out involvement of such a complex, as our experimental conditions were somewhat different from those of Adamsikova et al. Under our conditions, there is no effect of HS04-, as, for example, in reactions d, e, and f the kobs are very close, whereas the corresponding values of [HSOd-], ranged from 1.7 x to 8.3 x mol-L-', a more than 4-fold difference. (ii) With respect to the reduction of Mn(IV), further light can be thrown on the results of Bradley et a1.21 on the mechanism of the Mn(IV)/HzC204/H2S04 reaction. These authors proposed a prior adsorption of the reducer on the surface of colloidal MnOz, although they did not determine its exact nature (H2C204, HC204-, or C20&). Our results, along with those of Bradley, indicate that the reduction of the intermediate Mn(IV) in the permanganate/oxalic acid reaction in sulfuric acid medium occurs in the following two reaction steps: Mn(1V)
+ H2C204
[Mn(IV).H2Cz04]
f
-
Mn(II1)
[Mn(IV).H2Cz04]
+ C0,'- -I-C 0 2 f 2H'
(1)
(J)
In the first step (I), Mn(IV) associates with molecular oxalic acid. The higher the value of [H2C204], the more the equilibrium will be shifted in favor of association. During step J, this
Pimienta et al.
13298 J. Phys. Chem., Vol. 98, No. 50, 1994 complex decomposes, and Mn(IV) is reduced to Mn(1II) with molecular oxalic acid as electron donor. Kinetic study of the two auxiliary reactions {Mn(III)/H2C204/ HzSO~}and {M~(IV)/HZCZO~/H~SO~} for different values of the initial concentrations [ H Z C Z O ~and ] ~ [H2S04]0 provides a quantitative validation of these assumptions.
I
1
h
ln
0 -f
IV. Conclusion Multiwavelength analysis of the permanganate/oxalic acid reaction in sulfuric acid detected the presence of two intermediates: bis(oxalato)manganate(III) (III2) and a soluble Mn(IV) compound. Two separate auxiliary reactions were developed to study the reactivity of these intermediates. Although LTI2 could be obtained directly, the Mn(IV) species could not be identified experimentally, and its reactivity was thus modeled using MnOz obtained by the Guyard reaction. MnOz had a reactivity toward the oxalic acidsulfuric acid mixtures comparable to that of the Mn(1V) intermediate. Various mixtures of the two diacids were prepared whose initial concentrations were chosen to produce a constant concentration of the reducing species (molecular HzC204 or C Z O ~ ~at- )equilibrium. The proportions of the two diacids were selected from appropriate charts. The kinetic study using auxiliary reactions showed that, from the kinetic point of view, the reducer of IIIz was the oxalate ion, whereas that of Mn(IV) was molecular oxalic acid. This difference in reactivity between III2 and Mn(IV) can account for the variations in relative proportions of these two intermediates in the permanganate/ oxalic acid reaction. The role of sulfuric acid is restricted to the displacement of the dissociation equilibria of oxalic acid. The concentrations of oxalic and sulfuric acids that we employed in the auxiliary reactions were within the domain of concentrations in which the dynamic features of the overall permanganate/oxalic acidsulfuric acid reaction are observed (acceleration by sulfuric acid, inhibition by oxalic acid, bistability in a CSTR). The use of charts rather than a large excess of reagent ensures that the processes demonstrated were those that actually take place in the complete reaction KMnOd H2CzO4/HzS0 4 .
V. Experimental Section (1) Preparation of Solutions. All the solutions were prepared from commercial compounds: KMnO4 (M = 158.03); MnS04*H20(M = 169.02); Mn(CH3COO)3*2H20(M= 268.1); HzSO4 ( M = 98.07); HzCz04-2H20 (M = 126.07). They were dissolved in double-distilled water and used immediately. A set of experiments were carried out in no more than 2 days. The solution of permanganate was acidified, [H2S04] = 0.02 mol*L-', to limit formation of Mn02. (2) Reduction of Mn(II1) (Auxiliary Reaction RIII). Mn(CH3C00)3*2HzOwas dissolved in a mixture of oxalic and sulfuric acids whose concentrations [H~CZO~IO and [H2S04lo were obtained from Figure 3A. [Mn(CH3C00)3.2HzO]o = 6 x IOb3 mo1.L-l. (3) Reduction of Mn(IV) (Auxiliary Reaction RIV). MnO2 was prepared by the Guyard method: 2H20 4- 2Mn0,-
+ 3Mn2+ = 5Mn0, + 4H+
The Mn02 prepared was used immediately. [MnOzlo = 7.5 m0l-L-I; the concentrations [HzCz041o and [H2S0410 were obtained from Figure 3B. (4) Recording Kinetics. The reagents were mixed directly in quartz cuvettes (2 mL with 1 cm optical path length). The measurements were made in a diode array spectrophotometer x
time(s) Figure 5. First-order fitting of two auxiliary reactions. RIII: experiment h, l o b s = 456 nm; Abs scale 0-1.2; time scale 0 - 1 m s; kobs = 4.6 x s-'. RIV: experiment I , &bs = 400 nm; Abs scale 0-0.6; time scale 0-50 s; kobs = 1.3 x lo-' s-l.
(HP 8451), the temperature was maintained at 25 "C, and the solution was stirred continuously. (5) Data Processing. (a) Spectra of Intermediates: Subtraction of Permanganate Spectrum. The overall absorbance of the intermediates was calculated from relationship 3: Ab$(int), = Absp - Abs"-,(Abs:60/Absz)
(3)
Over the duration of the isosbestic point, the equation of conservation of mass, [Int] = [Mn04-]0 - [Mn04-], gives the total concentration of the intermediates. Dividing Abs(int) by [Int] gives the overall spectrum of the intermediates €int in mol-'*L-cm-' (units of molar extinction coefficient). (b) Calculation of Spectrum of Mn(N). The permanganate spectrum was subtracted for n (=4) different experiments observed at m different wavelengths. This gives rise to nm equations of type 2, in which there are n m unknown variables (n values of a and m values of E ~ W ) )This . set of equations can be resolved by an iterative procedure minimizing term 4:
+
n
m
(c) Calculations Assuming First-Order Kinetics. The absorbance over time of a first-order reaction is given by the following equation: Abs = (Abs,,
- Abs,)e-k"bs'
+ Abs,
(5)
The values of the parameters kobs and Abs, were obtained by minimization of the residual error (RE) using a nonlinear optimization program of the Powell type?
where n is the number of experimental points; Abs,dci is given by relationship 5 . In our case, Abs, was always 0. Examples of first-order fittings of auxiliary reactions RIII and RIV using eq 5 are shown in Figure 5 . (d) Calculations of Equilibrium Concentrations. Values shown in Table 2 were obtained by numerical integration using the Runge-Kutta procedure. Each equilibrium constant was split into two individual elementary rate processes. To obtain the corrected value [Cz042-],, of oxalate ions in auxiliary reaction RIII, the dissociation equilibria of the two diacids and the dissociation equilibria of Mn(II1) (K(A)= 2.5 x
Reactivity of the Mn(II1) and Mn(1V) Intermediates 10' mol-'.L; K(B)= 4 x lo6 mo1-I-L) were computed together with the dissociation equilibrium of acetic acid (pK, = 4.5).
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