An Upper Limit to O₂ Evolution as Test for Radical and Nonradical Mechanisms for the Fenton Reaction

Abstract

The origin of an upper limit to the amount of O₂ evolved in the rapid reaction between Fe²⁺ and H₂O₂ was investigated at a high concentration of H₂O₂. Using a nonradical model, including the formation of a primary Fe²⁺–biperoxy complex with a diminished rate of formation of the active intermediate FeO²⁺, agreement has been reached for the first time with the experimental data obtained by Barb et al. A limited formation of O₂ requires that a finite concentration of H₂O₂ should be present in the reaction mixture when [Fe²⁺] falls to zero. It has been shown that in Barb et al.’s model the condition for such a state ([Fe²⁺] = 0, [H₂O₂] > 0) does not exist. Free radical based models fail as mechanisms for the Fenton reaction.

1. Introduction

The question of the mechanism and intermediates in the reaction between Fe²⁺ and H₂O₂ (the Fenton reaction) has been the subject of intensive investigation for over a century [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. The reaction has gained importance as a method for the elimination of industrial waste [1]. In a different field, interest is growing in the possible significance of intermediates of the reaction in processes occurring in living systems [2]. Basic questions relating to the mechanism of the reaction are, however, still open. One of them concerns the variation of the ratio of concentrations of products upon variation of concentrations of reactants. There are two processes occurring in the system: oxidation of Fe²⁺ by H₂O₂ and decomposition of H₂O₂ to O₂ and H₂O. Based on a hypothesis of Haber and Willstaetter regarding the role of free radicals in chemical reactions, Haber and Weiss have proposed a model of the mechanism of the Fenton reaction [3]. It claimed to explain the dependence of the ratio [O₂]/[Fe³⁺], on the ratio [H₂O₂]_o/[Fe²⁺]_o ([O₂] is the number of moles of O₂ evolved per 1 dm³ of reaction mixture, the symbol [ ]_o denotes initial concentration), by attributing it to a competition of the reactions of the radical OH· with Fe²⁺ and H₂O₂, respectively. According to this theory, there should be no upper limit to the amount of O₂ evolved upon increasing the ratio [H₂O₂]/[Fe²⁺] in the reaction mixture. This prediction was found to be in contradiction to the experiment. Using high [H₂O₂]_o/[Fe²⁺]_o, Barb et al. observed a rapid evolution of O₂ followed by a slow one [4]. They found that using [H₂O₂]_o ≥ 0.5 mol dm⁻³, the amount of O₂ evolved in the rapid phase reached a limit. A revision of the Haber Weiss model was suggested by a modification of the O₂ evolution step (see further on for details). It appears, however, that in spite of this and numerous other studies, no positive evidence has yet been provided that the revised scheme does account for the existence of an upper limit. Since the existence of the limit is an experimental fact, it was the aim of the present study to investigate its origin and to give a quantitative explanation for it.

2. The Mechanism

Barb et al. measured the amount of O₂ gas evolved in the time interval of 0–3 min [4]. The first measurement was made at 5 s. Linear [O₂] vs. time plots were obtained with positive intercepts on the [O₂] axis (Figures 1 and 6 in Reference [4]). The existence of these intercepts implied that there was a short and rapid reaction in the system before the first measurement of [O₂] could be made. Since a point at 5 s on a time scale extending from zero to 3 min appears near the origin of the time scale, the intercept on the [O₂] axis could be identified, in good approximation, with [O₂] evolved in the rapid phase. The problem of finding a mechanism for a satisfactory interpretation of the experimental results in the rapid phase presented a serious challenge as no [O₂] vs. time and [Fe²⁺] vs. time data (or their equivalents) were available in the time interval of 0–5 s, only the values of [O₂] at its end in a series of experiments (experimental difficulties being due to gas evolution in the reacting solution in optical measurements, danger of explosion in a closed stopped flow apparatus, etc.). The following interpretation is based on a nonradical model [10,11]. It is presented in Figure 1. It assumes the formation of an active intermediate FeO²⁺, formed from a precursor complex Fe²⁺·H₂O₂ (C₁). In addition, and as a modification of an earlier version of the model, it includes the formation of a biperoxy complex (C₂) yielding FeO²⁺ at a lower rate than C₁ (step 10). This extension proved to be necessary to account for the existence of a limit to the amount of O₂ formed in the reaction at high [H₂O₂]. Neglecting the slow step 10, the mechanism has one path for oxidizing Fe²⁺ to Fe³⁺ (reactions (1)-(3)-(5),) and two reaction cycles ((1)-(3)-(4)-(1) and (1)-(3)-(6)-(7)-(1)) for the production of O₂. Steady state has been assumed to exist for [FeO²⁺], but not for [C₁] and [C₂]. Steady state existed necessarily for [FeOFe⁵⁺]. Its presence in the system was discovered only when [H₂O₂] was reduced to the 10⁻⁵ molar range [10]. A total of 10⁵ fold higher [H₂O₂] reduced [FeOFe⁵⁺] to the steady state range. Assuming negligible rate constants for the back reactions k₂, k_8, k₁₁, the following rate equations were obtained

d[C₁]/dt = k₁ [Fe²⁺] [H₂O₂] − (k₃ + k₉ [H₂O₂]) [C₁]

(1)

d[C₂]/dt = k₉ [H₂O₂] [C₁] − k₁₀ [C₂]

(2)

d[Fe³⁺]/dt = 2 v_R R2

(3)

d[O₂]/dt = v_R (R1 + R3)

(4)

v_R = k₃ [C₁] + k₁₀ [C₂]

(5)

[FeO²⁺] = v_R/(k₄ [H₂O₂] + k₅ [Fe²⁺] + k₆ [Fe³⁺])

(6)

R1 = [H₂O₂]/([H₂O₂] + (k₅/k₄) [Fe²⁺] + (k₆/k₄) [Fe³⁺])

(7)

R2 = [Fe²⁺]/((k₄/k₅)[H₂O₂]+[Fe²⁺]+(k₆/k₅)[Fe³⁺])

(8)

R3 = [Fe³⁺]/((k₄/k₆) [H₂O₂] + (k₅/k₆) [Fe²⁺] + [Fe³⁺])

(9)

[Fe²⁺] = [Fe²⁺]o − [Fe³⁺] − [C₁] − [C₂]

H₂O₂] = [H₂O₂]o − 2 [O₂] − 0.5 [Fe³⁺]

In the calculation of [H₂O₂], [C₁] and [C₂] could be neglected because of the large excess of [H₂O₂] over [Fe²⁺] in the experiments. The differential equations were integrated numerically by using the method of Gear. The initial value of [Fe²⁺] in the simulations was 4 × 10⁻² mol dm⁻³. To cover the range of [H₂O₂] in the experiments of Barb et al. (Figure 6, pH = 1.8, T = 0 °C, [4]), seven simulation runs were performed at seven [H₂O₂]_o with equal intervals between them in the range 0.5–3.5 mol dm⁻³ (among them concentrations identical with those used in the experiments). [Fe³⁺], [C₁] and [C₂] at time = 0 were set to zero. Trial values of rate constants k₁, k₃, k₉, k₁₀, k₄/k₅, k₆/k₅ were inserted as initial parameters. (Other rate constants appearing in the rate equations were calculated as combinations of the parameters of the basis set.) [C₁], [C₂], [Fe³⁺] and [O₂] vs. time curves were simulated. For a successful simulation, the convergence of all [O₂] vs. time curves at 5 s at the target value of 1.40 × 10⁻² mol dm⁻³ (upper limit at pH = 1.8 in the experiments of Barb et al. [4]) was a necessary but not sufficient condition. As around 5 s, or before it, there is a sharp fall in the rate of O₂ evolution, the limit must be approached in all runs with diminishing slopes of the [O₂] vs. time curves. To this end, simulations were continued beyond 5 s and values obtained at 6, 7, and 8 s were also included in the summation of squared deviations of calculated values of [O₂] from 1.40 × 10⁻² mol dm⁻³. The total sum of squared deviations was minimized by varying rate parameters using a combination of Migrad and Simplex minimum searching routines.

3. Results

To calculate meaningful values of standard deviations, the number of simulations was increased to 31 by changing [H₂O₂]_o between 0.5 and 3.5 mol dm⁻³ in steps of 0.1 mol dm⁻³. The standard deviation of calculated [O₂] values at 5 s from the target of 1.40 × 10⁻² mol dm⁻³ was 1.4 × 10⁻⁴ mol dm⁻³. The optimal set of rate parameters together with conditional standard deviations were: k₁ = (3.84 ± 0.13) × 10 mol⁻¹ dm³ s⁻¹, k₃ = (1.19 ± 0.03) × 10² s⁻¹, k₉ = (3.16 ± 0.04) × 10 mol⁻¹ dm³ s⁻¹, k₁₀ = 2.02 × 10⁻⁴ s⁻¹, k₄/k₅ = (2.82 ± 0.06) × 10⁻³, k₆/k₅ = (1.52 ± 0.05) × 10⁻¹. (Due to step 10 being a slow parallel path to FeO²⁺ formation, it was not possible to determine the conditional standard variation of k₁₀.) Similar values of k₁ and k₉ indicate similar energetic conditions for the first and second H₂O₂ molecules to enter the coordination sphere of Fe²⁺ ions. The difference between them appears in the rate of their decomposition to yield FeO²⁺. Here C₂ shows more stability and consequently lower rate constant of decomposition (k₁₀ << k₃). This difference is at the root of the existence of a limit to O₂ evolution at high [H₂O₂]. In Figure 2, simulated curves of [O₂] vs. t are shown at [H₂O₂]_o = 0.5 and 3.5 mol dm⁻³, (triangles and squares, respectively) representing the lower and upper limits of the concentration range in the experiments.

[Fe2+]o = 4.00 × 10−2 mol dm−3
[H2O2]o = 0.5 mol dm−3 (triangles)	[H2O2]o = 3.5 mol dm−3 (squares)
k1 = 3.84 × 10 mol−1 dm3 s−1	k3 = 1.19 × 102 s−1
k9 = 3.16 × 10 mol−1 dm3 s−1	k10 = 2.02 × 10−4 s−1
k4/k5 = 2.82 × 10−3	k6/k5 = 1.52 × 10−1

At high [H₂O₂], it showed a very rapid approach (measured on the timescale of milliseconds) to an upper limit of [O₂]. The curve with low [H₂O₂] reached the same limit in about 1.5 s. Figure 3 presents calculated (circles) and experimental (triangles) values of the amount of O₂ evolved at 5 s.

Table 1. Simulated and experimental values of [O₂] evolved in 5 s.

[O2]exp mol dm−3	[O2]sim mol dm−3	[H2O2]o mol dm−3
1.40 × 10−2	1.41 × 10−2	0.5
1.40 × 10−2	1.38 × 10−2	1
-----	1.40 × 10−2	1.5
1.40 × 10−2	1.41 × 10−2	2
-----	1.41 × 10−2	2.5
-----	1.40 × 10−2	3
1.37 × 10−2	1.39 × 10−2	3.5

Standard deviation of 31 values of [O₂]_sim from 1.40 × 10⁻² mol dm⁻³ (target) = 1.38 × 10⁻⁴ mol dm⁻³. Values of [O₂]_exp from the work of Barb et al. ([Fe²⁺]_o = 4.00 × 10⁻² mol dm⁻³, T = 0 °C, pH = 1.8, Ref. [4], Figure 6).

lists the numerical results.

Data both in the Figure and in the Table show that agreement has been reached between calculated and experimental values of [O₂] evolved in 5 s both showing constancy in the range of [H₂O₂]_o = 0.5–3.5 mol dm⁻³. (It may be added at this point that a previous attempt to account for the existence of the upper limit to O₂ evolved; using the nonradical model without the inclusion of C₂, was not successful [11].)

4. Discussion

To investigate the source of convergence of [O₂] vs. time curves at 5 s, the terms contributing to the rate of O₂ formation were examined. These were v_R, R1, R2 and R3. By definition, R terms vary between 0 and 1, some decreasing and some increasing in the course of the reaction. Plots of the terms R1 (circles), R2 (squares) and R3 (triangles) are shown in Figure 4. (Initial conditions [H₂O₂]_o = 2 mol dm⁻³ and [Fe²⁺]_o = 4 × 10⁻² mol dm⁻³ and [Fe³⁺]_o = 0.) Plots were obtained by entering the numerical values of the rate parameters and of their combinations into Equations (7)–(9). The following results were obtained:

• The starting value of R1 was 0.12. It rose in 0.2 s to 0.59 and remains constant.
  (Although [H₂O₂] is decreasing, R1 is increasing due to the steep decrease in the [Fe²⁺] term in the denominator.)
• The starting value of R2 was 0.88. It decreased in 0.2 s to practically zero.
• The starting value of R3 was 0. It rose in 0.2 s to 0.41 and remained constant.

These results showed that, except for a short initial period, all R terms were constant during the time interval ending at 5 s. The reason for the particular shape of the [O₂] vs. time curves must therefore be found in the time variation of v_R. Since k₃ >> k₁₀, the time variation of v_R was determined almost entirely by the time variation of [C₁] but indirectly also by that of [C₂]. Figure 5 shows this variation. In the Figure, plots of [C₁] vs. t (triangles) and [C₂] vs. t (squares) are shown at [H₂O₂]_o = 0.5 mol dm⁻³ (empty markers) and 3.5 mol dm⁻³ (full markers). The form of the curves in the Figure is the result of two opposing effects of [H₂O₂] on the kinetics of the reaction. At high [H₂O₂], the rate of formation of C₁ was high, [C₁] reaching a (relatively) high maximum. Up to the maximum, conversion of C₁ into C₂ decreased the rate of increase of [C₁]. After the maximum, it increased the rate of decrease of C₁. The second effect was more pronounced as [C₂] was higher after the maximum than before it. At low[H₂O₂], there was slow accumulation of C₁ with a low maximum of [C₁].

There was little formation of C₂ with little retardation of the increase in [C₁] and little acceleration of its decrease. Because of the rapid fall of [C₁] after the maximum at a relatively high value of [H₂O₂] and its damped change at low [H₂O₂], the decreasing parts of [C₁] vs. time plots a high and low [H₂O₂] had a point of intersection. This implies, that up to the point of intersection, the rate of formation of the active intermediate FeO²⁺ (v_R ≈ k₃ [C₁]) was higher with high [H₂O₂], but after the point of intersection, it became relatively higher with lower [H₂O₂]. Since under the conditions of the experiments [Fe²⁺] << [H₂O₂], practically all FeO²⁺ will produce O₂. Therefore, v_R can be equated, in good approximation, with the rate of production O₂ (v_O2). We can summarize the results of this section as follows. Denoting high and low [H₂O₂] by (a) and (b), and the time interval up to and after the point of intersection by (α) and (ß), respectively, we have the following relationships between rates of evolution of O₂ in the two phases of the reaction in the time interval 0–5 s:

v_O2(aα) > v_O2 (bα) and v_O2(aβ) < v_O2(bβ)

(10)

This is shown in Figure 6. Full triangles represent simulations with [H₂O₂]_o = 3.5 mol dm⁻³ (case a), empty triangles with [H₂O₂]_o = 0.5 mol dm⁻³ (case b).

The two curves have a point of intersection at about 40 ms. The similarity between the corresponding curves of [C₁] in Figure 5 and of v_O2 in Figure 6 is clear. The total amount of O₂ evolved at high and low [H₂O₂] during the time interval 0–5 s can be written as

O₂(a) = O₂(aα) + O₂(aβ) and O₂(b) = O₂(bα) + O₂(bβ)

(11)

Considering the inequalities in Equation (10), the difference in rates during phase α between case a and b are larger than the reversed differences during phase β. The duration of phase β is, however, considerably longer than that of phase α, (about 125 times longer in the present case). Thus, in case b, a lesser amount of O₂ produced during phase α may be balanced by a larger amount produced during phase β. The extent of balancing depends on the amounts of O₂ produced during phases α and β in cases a and b. The fact that in the simulations a constant amount of O₂ was calculated in all runs in 5 s proves that for the sums in Equation (11) exists

O₂(aα) + O₂(aβ) = O₂(bα) + O₂(bβ) = constant

(12)

The existence of an upper limit to O₂ evolved is thus due to the constancy of the sum of pairs of O₂(xα) and O₂(xβ) terms where x denotes any concentration of H₂O₂ between 0.5 and 3.5 mol dm⁻³.

Figure 7 shows the variation in time of the rates of reaction in the two O₂ producing cycles denoted as v₄ and v₆, respectively. Their values are presented as empty triangles and full squares. Values of the total rate of evolution of O₂, v_O2 = v₄ + v₆, are shown as full triangles. Initially, [Fe³⁺] = 0 and v_O2 = v₄; the two curves coincided. As Fe³⁺ began to be formed, the rate of the Fe³⁺ ion catalyzed path of O₂ evolution became significant too. The maximum of the total rate of formation of O₂ occurred near 20 ms, while at about 100 ms, most of the O₂ measured at 5 s had already been formed. It explains why it appeared as an initial burst (catalase burst). Reducing the concentration of [H₂O₂] by a factor of 10³ to 10⁴, the role of C₂ in the mechanism became insignificant [10]. The influence of C₂ on the kinetics of C₁ at high [H₂O₂] provides indirect proof of the formation of the primary intermediate C₁, until now only assumed to exist. It should be noted that the inclusion of C₂ in the mechanism implies that when using the mixture Fe²⁺ + H₂O₂ in oxidation of substrates, the increase in [H₂O₂] beyond a certain limit decreases the efficiency of the mixture as it decreases the rate of formation of FeO²⁺. In agreement with this prediction, Barb et al. report that “dilute solutions of methyl orange are readily oxidized to colorless compounds by 10⁻⁴ mol dm⁻³ Fe²⁺ and 10⁻⁴ mol dm⁻³ H₂O₂ to give completely colorless solutions [4]. When the hydrogen peroxide concentration is increased, the extent of this oxidation is decreased, and with 1 mol dm⁻³ H₂O₂, no destruction of color is observed” (Ref. [4], p. 464). The simulations showed only the increasing part of the [C₂] vs. t curve up to a plateau. Concerning the decreasing part, the half time of decay from the maximum value can be calculated to be 58 min, a time span much longer than that in which measurements were made (3 min). Therefore, in the time range of the experiments C₂ can be regarded as an inert intermediate. The quantitative aspect of the discussion on this point is, however, only approximate, due to the difficulty of determining the value of k₁₀ with sufficient accuracy.

The concept of FeO²⁺ as intermediate in the Fenton reaction has been supported by density functional studies of Baerends and coworkers and also by Lu and coworkers. They have shown that the energetically favorable path of the reaction between Fe²⁺ and H₂O₂ led to the formation of FeO²⁺ rather than free radicals [15,16].

5. Free Radical Models of the Mechanism of the Fenton Reaction

In free radical models based on one-equivalent oxidation/reduction reactions, the precursor of O₂ is the radical HO₂·. The first model, proposed by Haber and Weiss, consists of the following steps:

Fe²⁺ + H₂O₂ → Fe³⁺ + OH· + OH⁻

(13)

OH· + H₂O₂ → HO₂· + H₂O

(14)

HO₂· + H₂O₂ → OH· + O₂ + H₂O

(15)

OH· + Fe²⁺ → Fe³⁺ + OH⁻

(16)

It is a chain reaction in which (13) is the initiation step, (14) and (15) are chain carriers, and (16) is the chain termination step. OH· and HO₂· are free radicals derived from H₂O₂. The balance between the oxidation of Fe²⁺ and O₂ evolution depends on the ratio r = [H₂O₂]/[Fe²⁺], i.e., on the balance between reactions (14) and (16). At low r, (16) is dominant and the reaction is restricted to steps (13) and (16), resulting in oxidation of Fe²⁺ and no evolution of O₂. At increasing r, (14) begins to compete with (16) and evolution of O₂ accompanies the oxidation of Fe²⁺, as observed experimentally. In deriving rate expressions for the formation of products, free radical intermediates are assumed to be in steady states. Their concentrations are given by the equations

[OH·] = (k₁₃/k₁₆) [H₂O₂] and [HO₂·] = {k₁₃k₁₄/(k₁₅k₁₆)} [H₂O₂]

The rate of O₂ evolution becomes (Ref. [3], Equation (6))

d[O₂]/dt = (k₁₃k₁₄/k₁₆) [H₂O₂]²

(17)

This equation cannot be the correct expression for the rate of O₂ evolution in the Fenton reaction. Namely, according to it, the rate should be no function of [Fe²⁺], thus that of r. The model, on the other hand, requires that d[O₂]/dt should approach zero with decreasing r by increasing [Fe²⁺] at a finite [H₂O₂]. According to Equation (14) d[O₂]/dt becomes zero only for [H₂O₂] = 0. The rate equation is therefore not consistent with the model: the Haber Weiss scheme falls short of accounting for the course and kinetics of the Fenton reaction.

A modification of the Haber and Weiss model has been suggested by Barb et al. [4].

Fe²⁺ + H₂O₂ → Fe³⁺ + OH· + OH⁻

(18)

OH· + Fe²⁺ → Fe³⁺ + OH⁻

(19)

OH· + H₂O₂ → HO₂· + H₂O

(20)

HO₂· + Fe²⁺ → Fe³⁺ + HO₂⁻

(21)

HO₂· + Fe³⁺ → Fe²⁺ + O₂ + H⁺

(22)

The crucial change in the model is the replacement of H₂O₂ by Fe³⁺ in (22) as the O₂ producing step. With this modification, the model ceases to be a chain reaction. Namely, there are three pathways along which the reaction can proceed: (1) (18)-(19) (Fe²⁺ oxidation), (2) (18)-(20)-(21) (Fe²⁺ oxidation), and (3) (18)-(20)-(22) (O₂ evolution). The last one is a self-repeating cycle. The Barb model is not a chain reaction, because the initiation step (18) is part of the O₂ producing cycle. (In a chain reaction the product forming cycle cannot include the initiation step). The following description of the course of the reaction is valid for concentrations of reactants used in the experiments of Barb et al.: [H₂O₂]_o = 0.5–3.5 mol dm⁻³ and [Fe²⁺]_o = 4 × 10⁻² mol dm⁻³ [4]. Regarding rate constants, in the present context it is sufficient to note that rate constants of reactions involving free radicals (k₁₉, k₂₀, k₂₁, k₂₂) are extremely high while that of a reaction between an ion and a molecule (k₁₈) is in comparison low. The kernel of the model is the cycle consisting of (18), (20), and (22). Their sum is 2 H₂O₂ = O₂ + 2 H₂O. It presents the path for the decomposition of H₂O₂. Fe²⁺ and Fe³⁺ ions participate in these reactions but are cancelled out in the summation. It means that they are neither formed nor consumed in the cycle; their concentrations remain constant. Thus, the cycle of the three reactions presents a scheme for the catalytic evolution of O₂ by the pair Fe³⁺–Fe²⁺. Reactions (20) and (22) have high rate constants, while that of (18), is low; (18) is, therefore, the rate determining step in the cycle. In the absence of further reactions, there is mutual balance among the rates of the reactions of the cycle; all rates are equal. Reactions (19) and (21) act as perturbations; they remove the carriers of the cycle: HO₂^., OH· and Fe²⁺. At the start of the reaction, the course involves both the steps of the kernel and the perturbations. Due to perturbations, the rate of the evolution of O₂ (22) will be less than the rate of production of free radicals (18), because a fraction of free radicals has been removed in perturbation reactions. In these reactions Fe²⁺ ions are oxidized to Fe³⁺. As a result, [Fe²⁺] and the rate of initiation becomes lower. A new cycle will end with an additional amount of Fe²⁺ ions oxidized to Fe³⁺. As the cycles are repeated, [Fe²⁺] will be reduced continuously until it will become negligible beside both [H₂O₂] and [Fe³⁺]. Perturbation reactions will then become insignificant and the course of the reaction will be reduced to reactions of the kernel. From this point on, O₂ will be evolved in a steady state at a constant and low [Fe²⁺]; the reaction will become a catalytic decomposition of H₂O₂. With the existing rate constants, the rate of O₂ evolution in the initial phase, in spite of perturbation reactions, is high (measured on a timescale of seconds). In the catalytic phase in contrast, the reaction is slow, even on the timescale of minutes. This description explains the observed “initial burst of O₂”, the amount of which is not identical with “the total amount of O₂ evolved in the Fenton reaction”. It represents only the amount of gas evolved during the rapid phase. To calculate its magnitude theoretically, the rate equations of Barb et al. were integrated numerically using their rate constants and the value of [O₂] was determined at a point where both conditions v₁₉/v₂₀ < 10⁻³ and v₂₁/v₂₂ < 10⁻³ were satisfied [4]. The results have shown a definite dependence of this value on [H₂O₂]_o (Ref. [11], Figure 3). It is concluded, therefore, that the existence of an upper limit in the amount of O₂ evolved in the Fenton reaction during the initial burst at high [H₂O₂] has not been explained satisfactorily by the model of Barb et al [4].

A radical—radical reaction has also been suggested as the source of O₂ [20].

HO₂· + HO₂· → O₂ + H₂O₂

(23)

This reaction severs, however, the connection between O₂ evolution and the regeneration of Fe²⁺, a phenomenon demonstrated experimentally (Ref. [4], p. 476). It is, therefore, unacceptable. The same applies also to the reaction

HO₂· + OH· → O₂ + H₂O

(24)

This exhausts the possibilities of constructing mechanisms for the Fenton reaction based on free radicals.

6. Conclusions

There are three basic facts for which any mechanism of the Fenton reaction must account:

• Change in the ratio of concentrations of the products when the ratio of concentrations of reactants is varied.
• Coupling of the evolution of O₂ with the regeneration of Fe²⁺.
• The existence of an upper limit to the amount of O₂ formed when [H₂O₂] is increased beyond a certain value.
  The mechanism of Haber and Weiss fails to explain all three points.
  The mechanism of Barb et al. explains points one and two but fails to explain point three [4].
  The nonradical mechanism explains all three points.