Three Rate-Constant Kinetic Model for Permanganate Reactions Autocatalyzed by Colloidal Manganese Dioxide: The Oxidation of L-Phenylalanine.

The reduction of permanganate ion to MnO(2)-Mn(2)O(3) soluble colloidal mixed oxide by l-phenylalanine in aqueous phosphate-buffered neutral solutions has been followed by a spectrophotometric method, monitoring the decay of permanganate ion at 525 nm and the formation of the colloidal oxide at 420 nm. The reaction is autocatalyzed by the manganese product, and three rate constants have been required to fit the experimental absorbance-time kinetic data. The reaction shows base catalysis, and the values of the activation parameters at different pHs have been determined. A mechanism including both the nonautocatalytic and the autocatalytic reaction pathways, and in agreement with the available experimental data, has been proposed. Some key features of this mechanism are the following: (i) of the two predominant forms of the amino acid, the anionic form exhibits a stronger reducing power than the zwitterionic form; (ii) the nonautocatalytic reaction pathway starts with the transfer of the hydrogen atom in the α position of the amino acid to permanganate ion; and (iii) the autocatalytic reaction pathway involves the reduction of Mn(IV) to Mn(II) by the amino acid and the posterior reoxidation of Mn(II) to Mn(IV) by permanganate ion.


INTRODUCTION
Potassium permanganate is one of the most useful reactants in the chemistry laboratory, and it is widely employed as a versatile oxidizing agent. [1][2][3] On their part, -amino acids are important biological compounds, since they are the essential constituents utilized by nature in the synthesis of proteins. 4 Oxidation of -amino acids is a topic of some interest in relation to cell metabolism. For instance, oxygen free radicals are known to initiate the oxidative degradation of proteins. 5 The oxidation of -amino acids by permanganate ion can be used as a simple chemical model for other related reactions of biological importance. As a result, the scientific literature concerning the permanganate-amino acid reactions is abundant. In particular, these redox reactions have been studied in both acidic 6-24 and neutral solutions. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] An important finding of these kinetic studies is the autocatalysis observed in both media.
Autocatalysis is an interesting phenomenon at the theoretical level because of the relatively scarce information existing on this topic. As happens with all catalytic reactions, in the mechanism of autocatalytic processes at least two reaction pathways are involved, one corresponding to the reaction taking place without involvement of the autocatalytic product and the other corresponding to the autocatalytic process, the rate-determining step being different for each reaction pathway. An integrated rate equation that allows the determination of the two rate constants associated to the non-autocatalytic and autocatalytic reaction pathways has been reported. [42][43][44] However, some deviations from the proposed mathematical model are evident from the experimental kinetic data published for the permanganate-glycine reaction. 45 Moreover, a case of delayed autocatalysis has been reported for the permanganateamino acid reactions under acidic conditions. [46][47][48][49][50] Although delayed autocatalysis is not interpretable by the two rate-constant model, it has also been observed in at least another autocatalytic and autocatalytic reaction pathways, respectively. In the second program k 1 is associated to the non-autocatalytic pathway, whereas both k 2 and k 3 are associated to the autocatalytic one, allowing the introduction into the mathematical model of a long-lived, non in steady-state intermediate. The corresponding calculations were implemented on a Sony Vaio personal computer.

Visible Spectra.
A periodical scanning of the reaction mixture revealed the existence of two isosbestic points at 467 and 692 nm (Figure 1, top). The spectrum of the manganese reduction product showed the typical upward-concave band covering the whole visible region corresponding to absorption + dispersion by soluble colloidal MnO 2 , 57 as well as a shoulder corresponding to light absorption by Mn(III). [58][59][60] On standing and at high L-phenylalanine concentration, the peak at 462 nm corresponding to Mn(III) became more definite as the spectrum decayed because of the reduction of Mn(IV) by the amino acid ( Figure 1, bottom).
The stability of this Mn(III) species (detectable for one week after completion of the permanganate/amino acid reaction) suggests that it was a colloidal oxide (Mn 2 O 3 ) rather than an aqueous species, either Mn 3+ (instable by dismutation) or a Mn(III) complex with Lphenylalanine (instable by internal redox reaction).  The values of the reaction rate were obtained from those of the permanganate concentration by means of the finite difference method. This mathematical procedure of approximate derivation allows the calculation of the rate at time t + t/2 from the permanganate concentrations (c) at times t and t + t as: This method allows calculating the reaction rate with a very low systematic error provided that the time interval chosen (t) is small enough.
The rate of the permanganate/L-phenylalanine reaction has been plotted as a function of time. We can see that the rate versus time plots are bell-shaped and that the ratio between the maximum value of the reaction rate and its initial value tended to decrease as the initial permanganate concentration decreased. For instance, whereas at high initial permanganate concentration (1.0010 -3 M) a ratio of 2.36 was found (Figure 2, top), at low initial permanganate concentration (4.0010 -4 M) the ratio was only 1.53 (Figure 2, bottom).

Figure 2
3.3. Two Rate-Constant Kinetic Model for Autocatalysis. The simplest form of the differential rate law for an autocatalytic reaction assumes that both reaction pathways are of first order in the limiting reactant (permanganate ion) and that the autocatalytic pathway is also of first order in the autocatalyst (colloidal manganese dioxide). Hence: where k 1 and k 2 (the pseudo-rate constants for the non-autocatalytic and autocatalytic reaction pathways, respectively) are dependent on both the amino acid concentration (in large excess) and the pH. Now, assuming that all the manganese intermediates are in steady state and, so, in negligible concentration with respect to Mn(VII) and Mn(IV), eq 3 can be rewritten as: where c o is the initial permanganate concentration.
This two-rate constant kinetic model can explain the fact that the bell-shaped profile of the reaction rate versus time plots tends to disappear as the initial concentration of the limiting reactant decreases (Figure 2), since it is easy to demonstrate from eq 4 that those plots show a maximum only when: can be rewritten in a linearized way as: Equation 6 predicts a linear plot when the rate-permanganate concentration ratio is plotted against the permanganate concentration at different instants during the course of the reaction.
A typical example can be seen in Figure 3. For a pseudo-first order kinetics (k 2 = 0) the v/c ratio would be expected to remain constant (v/c = k 1 ) as the reaction progresses. However, an increase of that ratio can be observed in Figure 3, indicating again the existence of an autocatalytic phenomenon. Although the first stretch is approximately linear, a definite upward-concave curvature can be seen at high reaction times, indicating that the two rateconstant kinetic model is insufficient to explain the behavior of the permanganate/Lphenylalanine reaction.

Scheme 1
The differential equations corresponding to this simplified mechanism are the following: where k 1 , k 2 and k 3 are pseudo-rate constants (L-phenylalanine assumed in large excess with respect to permanganate ion). Equations 7-9 have been integrated for each kinetic experiment by means of a numerical approximate procedure, the fourth order Runge-Kutta method. 64 In   3.7. Kinetic Results. Rate constants k 1 and k 3 decreased as the initial permanganate concentration increased, whereas k 2 increased (Table 1). Although true rate constants should not depend on the initial concentration of the limiting reactant, the existence of such dependence is a phenomenon rather generalized in kinetic studies of autocatalytic reactions concerning not only the reduction of permanganate ion, 65 but also that of colloidal MnO 2 . 66 This dependence can be partially explained by a change in the size and surface composition of the colloidal species. Actually, an increase of the initial permanganate concentration is expected to result in an increase of the average colloidal particle size as well as in a decrease of the level of reduction of surface Mn(IV) to the lower Mn(III)/Mn(II) oxidation sates.

Table 1
Rate constants k 1 and k 3 increased linearly as the L-phenylalanine concentration increased (order 1), whereas k 2 remained almost unchanged (order 0), as can be seen in and a decrease of k 2 , whereas k 3 showed no appreciable effect (Table 2).

Figure 7
Table 2 The three experimental rate constants increased with increasing pH (base catalysis), and

Figure 8
Application of both the Arrhenius and Eyring equations allowed the determination of the apparent (pH-dependent) activation parameters associated to the rate constants k 1 (Table 3), k 2 (Table 4) and k 3 ( Table 5). The apparent activation energy obtained for k 1 was roughly independent of pH, whereas that of k 2 increased strongly with increasing pH and that of k 3 decreased slightly. The apparent values of the standard activation enthalpy at different pHs were strongly correlated with those of the standard activation entropy for rate constants k 2 and k 3 , but weakly correlated in the case of k 1 (Figure 9). The corresponding slopes for the linear enthalpy-entropy plots yielded the values of the isokinetic temperatures T ik = 229 ± 99 (for k 1 ), 277 ± 6 (for k 2 ) and 350 ± 29 (for k 3 ) K. It thus seems that stronger pH dependence of the apparent activation energy correlates with higher coupling of the apparent activation enthalpyentropy values. Table 3   Table 4 Table 5

Figure 9
The intercepts and slopes of both the k 1 Figure 10). Moreover, they also fulfilled the Eyring equation, yielding the pH-independent activation parameters listed in Table 6.  increasing pH (base catalysis) provided that k III > k II . Fulfillment of this condition is indeed plausible because the anionic form of the amino acid has a higher electronic density (and so a higher reducing power) than the zwitterionic form.

Figure 10
The value of the equilibrium constant associated to eq 13 has been reported (K I = 5.16 10 -10 M, pK a = 9.29, at zero ionic strength and 25.0 ºC). 73  in agreement with the existence of k 1 versus [H + ] -1 linear plots (Figure 8, top), the intercepts corresponding to the reaction of permanganate ion with the zwitterionic form of the amino acid in the solution and the slopes to the reaction with the anionic form. Hence, according to eq 24 and the activation parameters given in Table 6, we can conclude that the pH independence of the apparent activation energy associated to rate constant k 1 experimentally observed ( Application of eq 24 to the pH-temperature crossed experimental data, along with the thermodynamic parameters reported for equilibrium constant K I , 73 allowed the determination of rate constants k II and k III as well as their associated activation parameters (Table 7). The value obtained for the ratio of those two rate constants was k III / k II = 248 ± 96, and the activation energy associated to k III (23 ± 2 kJ mol -1 ) was much lower than that associated to k II (70 ± 2 kJ mol -1 ). These findings are again consistent with the higher electronic density of the amino acid anionic form (strong reducing agent) with respect to the zwitterionic form (weak reducing agent).

Table 7
The kinetics of the reaction of permanganate ion with L-phenylalanine in neutral aqueous solutions resembles those of its reactions with other -amino acids. For instance, besides being all of them autocatalyzed by colloidal MnO 2 , the activation energy for the nonautocatalytic reaction pathway in the oxidation of L-alanine is 74.0 kJ mol -1 , 29 quite close to the values found in Table 3 for the same reaction pathway in the oxidation of Lphenylalanine. This suggests that the permanganate/-amino acid reactions follow a common mechanism, the side group R not being directly attacked by the oxidant.
Phosphate ions, used to buffer the solutions, are known to fix at the colloidal MnO 2 surface, thus allowing that the negatively charged colloid particles be stable in solution for a long period. 75 In the case of the permanganate/glycine reaction, an inhibition of the autocatalytic pathway with increasing phosphate concentration was found, 65   Thus, the intercepts of those plots are associated to the reaction on the colloid surface involving the zwitterionic form of the amino acid and the slopes to the reaction involving the anionic form.
Hence, according to eq 36 and the activation parameters given in Table 6, we can conclude that the slight decrease of the apparent activation energy associated to rate constant k 3 with increasing pH (Table 5) (Table 3) and of positive values for that associated to rate constant k 3 (Table 5)