New kinetic analysis of the Fenton reaction: Critical examination of the free radical – chain reaction concept

Abstract

Using [H₂O₂] in the molar range, the reaction with Fe²⁺ has two phases: in the first rapid phase, only a small fraction of the total O₂ is evolved; the bulk of the gas is formed in a slow second phase. In interpretations based on the free radical model of Barb et al., the first phase has been identified with the ‘Fenton reaction’ (reaction of Fe²⁺with H₂O₂), while the second with catalytic decomposition of H₂O₂ by Fe³⁺ ions. This interpretation is not correct. A new analysis of the model shows that (1) it is a chain reaction having no termination steps and (2) the ‘Fenton part’ alone consists of two phases. It starts with rapid evolution of O₂ via a five-membered chain reaction (first phase). When [Fe²⁺] becomes low, evolution of O₂ continues in a three-membered chain reaction at a greatly reduced rate (second phase). In later stages of the second phase, Fe³⁺ catalysis contributes to O₂ evolution. Thus, the amount of O₂ formed in the rapid phase cannot be identified with the total amount formed in the ‘Fenton reaction’ but only with that formed in its first phase. Computer simulations of O₂ evolution based on the model of Barb et al. and rate constants show a definite dependence of this quantity on the initial [H₂O₂] – in contrast to the experimentally found independence. More satisfactory, but not complete, agreement with measured data could be reached in simulations using a non-radical model. Some of the difficulty has been due to the determination of the exact position of the end of the first phase. The transition between the two phases of the reaction occurs in a short, but finite time interval. It has been shown that the quantity ‘total amount of O₂ evolved in the Fenton reaction’ (subtracting the part due to Fe³⁺catalysis) is not accessible to experimental determination nor to theoretical calculation.

Introduction

It has been observed that when concentrated H₂O₂ was mixed with a salt of Fe²⁺, there was an initial burst of O₂ followed by a slow evolution of the gas (catalase burst). ¹ The question of the mechanism of the reaction (Fenton reaction) remains the subject of research to this day. Haber and Willstaetter ² suggested that free radicals derived from H₂O₂ are active intermediates in the reaction. Haber and Weiss ³ worked out a model built on a chain reaction carried by free radicals. It offered an explanation for the until-then-unexplained variation of the stoichiometry of the reaction as a function of the concentration of the reactants. Later experiments revealed additional features of the reaction requiring modification of the scheme.

The model of Haber and Weiss

The model (H) consists of four steps

$$\mathrm{F}{\mathrm{e}}^{2+}+{\mathrm{H}}_2{\mathrm{O}}_2\to \mathrm{F}{\mathrm{e}}^{3+}+\mathrm{O}{\mathrm{H}}^{•}+\mathrm{O}{\mathrm{H}}^{-}$$

H1

$$\mathrm{O}{\mathrm{H}}^{•}+{\mathrm{H}}_2{\mathrm{O}}_2\to \mathrm{H}{{\mathrm{O}}_2}^{•}+{\mathrm{H}}_2\mathrm{O}$$

H2

$$\mathrm{H}{{\mathrm{O}}_2}^{•}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{O}}_2+\mathrm{O}{\mathrm{H}}^{•}+{\mathrm{H}}_2\mathrm{O}$$

H3

$$\mathrm{O}{\mathrm{H}}^{•}+\mathrm{F}{\mathrm{e}}^{2+}\to \mathrm{F}{\mathrm{e}}^{3+}+\mathrm{O}{\mathrm{H}}^{-}$$

H4

Step H1 is the initiation reaction, steps H2 and H3 form an O₂-producing chain while H4 is a termination step. The course of the reaction is determined by the relative rates of steps H2 and H4, which in turn depends on the ratio R_R = [H₂O₂]/[Fe²⁺] in the reaction mixture. At low R_R, termination suppresses chain propagation and no O₂ is evolved. The ratio R_P = [O₂]/[Fe³⁺] when the reaction is complete is then 0. On increasing the initial reagent ratio $R_{\mathrm{R}}^{\mathrm{o}}=[{\mathrm{H}}_2{\mathrm{O}}_2{]}_{\mathrm{o}}/[\mathrm{F}{\mathrm{e}}^{2+}{]}_{\mathrm{o}}$ (the symbol []_o denotes initial concentration), increasing amounts of O₂ are formed causing an increase of R_P, in principle without limit. At this point, difficulties arose. Experiments of Barb et al. ⁴ appeared to indicate the existence of a limit, calling for a revision of the Haber–Weiss model.

The model of Barb et al

To account for a limit to the production of O₂ when [H₂O₂] is increased, step B4 has been substituted for H3 of the Haber and Weiss ³ scheme

$$\mathrm{F}{\mathrm{e}}^{2+}+{\mathrm{H}}_2{\mathrm{O}}_2\to \mathrm{F}{\mathrm{e}}^{3+}+\mathrm{O}{\mathrm{H}}^{•}+\mathrm{O}{\mathrm{H}}^{-}$$

B0

$$\mathrm{O}{\mathrm{H}}^{•}+{\mathrm{H}}_2{\mathrm{O}}_2\to \mathrm{H}{{\mathrm{O}}_2}^{•}+{\mathrm{H}}_2\mathrm{O}$$

B2

$${\mathrm{HO}}_2^{•}+\mathrm{F}{\mathrm{e}}^{3+}\to {\mathrm{O}}_2+\mathrm{F}{\mathrm{e}}^{2+}+{\mathrm{H}}^{+}$$

B4

$$\mathrm{O}{\mathrm{H}}^{•}+\mathrm{F}{\mathrm{e}}^{2+}\to \mathrm{F}{\mathrm{e}}^{3+}+\mathrm{O}{\mathrm{H}}^{-}$$

B1

$${\mathrm{HO}}_2^{•}+\mathrm{F}{\mathrm{e}}^{2+}\to \mathrm{F}{\mathrm{e}}^{3+}+\mathrm{H}{{\mathrm{O}}_2}^{-}$$

B3

It is a chain reaction in which B0 has a double role: it both initiates and propagates the chain. In contrast to the Haber–Weiss model, this chain reaction has no termination steps. Namely, by substituting step B4 for H3, steps B1 and B3 (which only appear to be termination steps) become chain carriers as their product Fe³⁺ reacts again in B4 while HO₂⁻ will react, after protonation, in B0. Such a reaction stops only if one of the reactants in the initiation step has been used up.

There are two reaction chains possible in the system: (a) a long one involving all five reactions and (b) a short one involving B0, B2, and B4 only. This fact has a decisive influence on the course of the reaction. Let us consider the case of the long chain (a). $\mathrm{O}{\mathrm{H}}^{•}$ and ${\mathrm{HO}}_2^{•}$ being extremely reactive intermediates, the steady state approximation applies to their concentrations during the reaction

$$\left[\mathrm{O}{\mathrm{H}}^{•}\right]=k_o\left[\mathrm{F}{\mathrm{e}}^{2+}\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]/(k_1\left[\mathrm{F}{\mathrm{e}}^{2+}\right]+k_2\left[{\mathrm{H}}_2{\mathrm{O}}_2\right])$$

(1)

$$\left[\mathrm{H}{{\mathrm{O}}_2}^{•}\right]=k_o{k}_2\left[\mathrm{F}{\mathrm{e}}^{2+}\right]{\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}^2/\left\{(k_1\left[\mathrm{F}{\mathrm{e}}^{2+}\right]+k_2\left[{\mathrm{H}}_2{\mathrm{O}}_2\right])(k_3\left[\mathrm{F}{\mathrm{e}}^{2+}\right]+k_4\left[\mathrm{F}{\mathrm{e}}^{3+}\right])\right\}$$

(2)

Subscripts of the rate constants refer to scheme B and follow the designation of Barb et al. The rate of O₂ evolution is given by

$$\mathrm{d}\left[{\mathrm{O}}_2\right]/\mathrm{dt}=k_o\left[\mathrm{F}{\mathrm{e}}^{2+}\right]\left[{\mathrm{H}}_2{\mathrm{O}}_2\right](\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]/\mathrm{A})(\left[\mathrm{F}{\mathrm{e}}^{3+}\right]/\mathrm{B})$$

(3)

where A = (k₁/k₂) [Fe²⁺] + [H₂O₂] and B = (k₃/k₄) [Fe²⁺] + [Fe³⁺].

The term d[O₂]/dt will become zero (apart from at t = 0 when [Fe³⁺] is zero) only if [H₂O₂] or [Fe²⁺] becomes zero. It has been shown that, in a sufficiently large initial excess of H₂O₂, the final concentration of Fe²⁺ is zero. ⁵ The decrease of [Fe²⁺] in the course of the reaction will lead, at some stage, to a state in which the following relations will exist: v_B1 << v_B2 and v_B3 << v_B4 (v denotes rate). As a result, the course of the reaction will change and will include steps B0 – B2 – B4 only (short chain). The kinetics will change from those of phase (a) to those of phase (b). There will be a sharp decrease in the rate of evolution of O2, because low [Fe2+] will cause a low rate in step B0, causing low rates of reaction in the chain including in the O2 producing step B4. In phase (b), in every cycle B0–B2–B4, two molecules of H₂O₂ disappear with no loss of Fe²⁺. It can be regarded as a decomposition of H₂O₂ catalysed by Fe²⁺. As stated above, at this stage the rate of step B1 is negligible compared to those constituting the short chain, but it is not zero. From time to time, step B1 occurs, causing a small disturbance in the balance among the chain reactions. After a few cycles, a new balance will be established at a lower [Fe²⁺]. Catalytic decomposition of H₂O₂ will go on at this lower level. Because of lower [Fe²⁺], but mainly due to the loss of H₂O₂ through catalytic decomposition, the rate of step B0 will decrease. As a consequence, the rates of all reactions of the chain will decrease. This sequence of events with ever-slowing chain reactions will repeat itself many times until the final stage of the reaction has been reached. It follows then from the two-phase evolution of O₂ that the amount of O₂ evolved per dm³ of reaction mixture (ΔO₂) in the rapid phase is not the total amount formed in the Fenton reaction. The interpretation of this quantity by Barb et al. was incorrect. Ferric catalysis (starting with a direct reaction between Fe³⁺ and H₂O₂) plays no part in these considerations. It does occur also, but only in the later stages of the slow phase, in overlap with it.

Making no distinction between rapid and slow phases, Barb et al. have derived equations for the dependence of ΔO₂ on the concentration of the reactants. For high [H₂O₂]/[Fe²⁺], the expression becomes

$$\mathrm{\Delta }{\mathrm{O}}_2=(k_4/k_3)({\left[\mathrm{F}{\mathrm{e}}^{2+}\right]}_{\mathrm{o}}/2)\{\ln ({\left[\mathrm{F}{\mathrm{e}}^{2+}\right]}_{\mathrm{o}}/\left[\mathrm{F}{\mathrm{e}}^{2+}\right])+\left({\left[\mathrm{F}{\mathrm{e}}^{2+}\right]/\left[\mathrm{F}{\mathrm{e}}^{2+}\right]}_{\mathrm{o}}\right)-1\}$$

(4)

(equation (AVIII) in Kremer ⁵ (with term [Fe²⁺]/[Fe²⁺]_o missing) and the equation on p. 480 in Barb et al. ⁴ ). [Fe²⁺]_o is the initial concentration of Fe²⁺, [Fe²⁺] is its concentration after time t and ΔO₂ is the amount of O₂ evolved in time t. The equation is based on the set of all five free radical reactions. Its notable feature is the absence of [H₂O₂] in the equation, implying that, under these circumstances, ΔO₂ is independent of [H₂O₂]. Experimental results supported this conclusion (Figure 6 in Barb et al. ⁴ ). However, there were difficulties in using this equation. Namely, the meaningful range of its application is the time interval in which there is a substantial change of [Fe²⁺] (say 90%). Computer simulations show that this occurs during the first second of the reaction (Figures 1 and 2). During 1 s, no measurements of both ΔO₂ and [Fe²⁺] could be made. To overcome this difficulty, [Fe²⁺] was taken at the end of the reaction ([Fe²⁺]_e) and, accordingly, ΔO₂ as the total amount of O₂ formed in the Fenton reaction. Thus, this leaves only a single point in a run with a given [Fe²⁺]_o. Far more disastrous is the fact that it has been shown that [Fe²⁺]_e is zero, causing the right hand side of equation (4) to become infinite! ⁵ In order to avoid the ‘infinity catastrophe’, Barb et al. ⁶ have substituted ‘the stationary concentration of Fe²⁺ during the subsequent ferric ion + peroxide reaction’ for [Fe²⁺]_e. This idea is, however, unsound. In calculating [Fe²⁺]_e, it was not logical to introduce the ‘ferric ion + peroxide reaction’ only at the endpoint of the Fenton reaction and to neglect it during all other parts of it. This step was even less justified in interpreting results of experiments in which Fe³⁺ was added initially to the reaction mixture ‘in a big excess over [Fe²⁺]_o’. The way out of this dilemma is a computer simulation of the reaction – a facility not available at the time when the classical investigations of Barb et al. were performed.

Figure 1.

Simulated curve of O₂ evolution (Barb et al.’ scheme): k_o = 12.6 mol dm^-3; k₁/k₂ = 69; k₃/k₄ = 3.3; [Fe²⁺]_o = 0.04 mol dm^-3; [H₂O₂]_o = 1 mol dm^-3.

Figure 2.

[O₂] and [Fe²⁺] versus time at the beginning of the reaction (Barb et al.’s scheme). Rate constants as in Figure 1, [Fe²⁺]_o = 0.04 mol dm⁻³ and [H₂O₂]_o = 1 mol dm⁻³.

Simulation of the Fenton reaction using the model of Barb et al

The set of differential rate equations relevant to reactions of model B0–B4 were integrated numerically. [Fe²⁺] and [O₂] versus time curves were constructed. Rate constants of Barb et al. (k₀ = 12.6 mol⁻¹ dm³ s⁻¹, k₁/k₂ = 69, k₃/k₄ = 3.3, at 0°C and pH = 1.8) were used as parameters. Figure 1 shows the evolution in time of O₂ at [H₂O₂]_o = 1 mol dm⁻³ ([Fe²⁺]_o = 0.04 mol dm⁻³). The evolution of O₂ in two phases is clear from the graph: an initial rapid phase followed by O₂ production at a reduced rate. It is reasonable to identify the first phase with the five-membered chain reaction (phase a) and ΔO₂ as the amount of O₂ evolved in it ([O₂]_a). Figure 2 shows in more detail phase (a) lasting for about 1 s. In 1 s, Fe²⁺ disappears nearly completely, while only about 5% or less of the maximum possible amount of O₂ is formed. Transition between the phases has been defined as the state in which both ratios v_B1/v_B2 and v_B3/v_B4 have decreased to ≤ 10⁻³.

Since k₁/k₂ and k₃/k₄ are not identical, reaching this state between steps 1 and 2, and steps 3 and 4, respectively, occurs at different times: there exists no single transition point, but there is a transition period, the length of which varies with [H₂O₂]. Table 1 shows the results of some calculations. Data in the second and third columns are time elapsed since the start of the reaction until the respective transition. The upper entry in the last column gives the number of moles of O₂ evolved until the first transition. The lower entry is the total amount when both transitions are complete ([O₂]_a). The data in the table show that by increasing [H₂O₂], transitions occur at shorter times and that the time difference between the transitions decreases. At high R_R, transition 1–2 occurs first and transition 3–4 occurs second. The phenomenon is due to competition between steps 1 and 2.

Table 1.

Transition points between five- and three-membered chain reactions in the free radical model.

[H2O2]o (mol dm−3)	1–2 (min)	3–4 (min)	[O2] (mol dm−3)
0.2	–	7.11 × 10−1	6.81 × 10−3
0.2	3.46	–	8.41 × 10−3
0.5	–	5.31 × 10−1	1.43 × 10−2
0.5	9.71 × 10−1	–	1.56 × 10−2
2	1.11 × 10−1	–	2.57 × 10−2
2	–	2.51 × 10−1	2.91 × 10−2
4	3.12 × 10−2	–	2.71 × 10−2
4	–	1.41 × 10−1	3.39 × 10−2

Rate constants as given in the text. [Fe²⁺]_o = 0.04 mol dm⁻³.

At high R_R, step 2 suppresses step 1. It retards the formation of Fe³⁺, and therefore tips the balance of the rates of steps 3 and 4 in favour of step 3: it retards the transition 3–4. At low R_R, the situation is reversed: the competition between reactions 1 and 2 is in favour of reaction 1 (transition 1–2 retarded), formation of Fe³⁺ is favoured: step 4 is favoured in comparison to step 3 (transition 3–4 favoured). Viewed differently, high R_R increases the rate of formation of ${\mathrm{HO}}_2^{•}$ , therefore the rate of formation of O₂, but by retarding the rate of increase of Fe³⁺, a smaller fraction of ${\mathrm{HO}}_2^{•}$ will produce O₂. At low R_R, fewer ${\mathrm{HO}}_2^{•}$ radicals are formed, but a larger fraction of them will produce O₂. Variation of R_R has thus opposing effects on the rate of evolution of O₂. [O₂]_a as function of [H₂O₂]_o is shown in Figure 3. The values of ΔO₂ = [O₂]_a are in the right order of magnitude, but they show a clear dependence on [H₂O₂]_o, in disagreement with a reported constant value (Figure 6 in Barb et al. ⁴ ; however, see below).

Figure 3.

[O₂] at the end of phase (a) as a function of [H₂O₂]_o (Barb et al.’s scheme).

Non-radical model of the Fenton reaction

The alternative, non-radical model for the Fenton reaction is presented in Figure 4.^5,7 The scheme departs from the principle of ‘compulsory one-eq14 oxidation and reduction of H₂O₂’ requiring the formation of free radicals. It starts with the formation of a precursor complex {Fe²⁺•H₂O₂}. The active intermediate FeO²⁺ is formed from the precursor by an internal rearrangement involving the splitting off of H₂O. The active intermediate is involved in (1) the evolution of O₂, (2) the oxidation of Fe²⁺ and (3) the oxidation of substrates, if present. There exist two channels for O₂ evolution: steps 4 and 7. Step 4 is a direct reaction of the active intermediate with H₂O₂, and step 7 requires the participation of Fe³⁺ ions.

Figure 4.

FeO²⁺ ion-based model of the Fenton reaction.

To reconstruct the experimental results of Barb et al., it was necessary to find rate constants which yielded [O₂] versus t curves such that (1) they had a rapid initial part followed by a slow, approximately linear section and (2) when using [H₂O₂]_o in the range 1–3.5 mol dm⁻³ at constant [Fe²⁺]_o (0.04 mol dm⁻³), a back extrapolation of the linear section to t = 0 yielded a constant intercept (equated with the amount of O₂ evolved in the rapid phase). This mode of calculation follows closely the method used by Barb et al. to determine this quantity experimentally. The curve chosen for simulation corresponds to experimental results obtained at pH = 1.8 and 0°C (Figure 6 in Barb et al. ⁴ ). The constant intercept to simulate was 1.4 × 10⁻² mol dm⁻³. Rate constants for the non-radical scheme have been obtained at 25°C using low concentrations of reactants (10⁻⁴–10⁻⁵ mol dm⁻³).^5,7 Modifications of the kinetic treatment were therefore necessary:

1. Due to a 10⁴ times increase of [H₂O₂] and the proportional increase of the rate of production of FeO²⁺, its concentration could not be assumed to be in a steady state, at least not as an initial assumption.

2. Due to increased [H₂O₂], [FeOFe]⁵⁺ could be regarded as being in a steady state. In addition, the validity of the approximation k₇ [H₂O₂] + k₈≈k₇ [H₂O₂] at high [H₂O₂] was assumed.

Simulated concentration versus time curves of [FeO²⁺], [Fe²⁺] and [O₂] were calculated using rate parameters $k{\prime }_1$ , k₄, k₅, and k₆ ( $k{\prime }_1$ = k₁k₃ / (k₂ + k₃) is the overall second order rate constant of formation of FeO²⁺) . For $k{\prime }_1$ , the value of k₀ = 12.6 mol⁻¹ dm³ s⁻¹ at 0°C of Barb et al. was taken. The rate constants k₀ and $k{\prime }_1$ are identical kinetically. They refer to reactions between identical reactants, only the products being different. Their measured values at 25°C obtained both on the basis of the radical and non-radical models showed excellent agreement (53.0 vs 52.4 mol⁻¹ dm ³  s⁻¹, independent of pH).^4,7 This agreement was assumed to hold also at 0°C. Other rate constants have been treated as variable parameters. Rate equations were integrated numerically. The step size of time increments in the integrations had to be carefully controlled. It had to be adapted to the rate of the fastest changing concentration ([Fe²⁺]) and kept small enough so that the concentration change at every step was not more than a few percent. The step size was increased when concentration changes became small. Step sizes ranging from 1 × 10⁻⁷ to 0.1 min were used. Variation of rate constants required occasionally an adjustment of step sizes. Calculations with [H₂O₂] in the range of 1–3.5 mol dm⁻³ were carried out. [Fe²⁺]_o was kept constant at 0.04 mol dm⁻³ (additional simulations were carried out with 0.5 and 0.2 mol dm⁻³ [H₂O₂], but these runs were not taken into account in the adjustment of rate constants). Plots which did not show a rapid initial phase followed by a slow second phase approaching linearity were rejected. Slopes and intercepts of straight lines running through points [O₂] (2.5 min) and [O₂] (4.5 min) were evaluated. Deviations of intercepts from the target value of 1.4 × 10⁻² mol dm⁻³ were determined and their squared sum (RSS) was calculated. RSS was reduced by variation of rate parameters. [FeO²⁺] versus time curves were calculated both with and without making the steady state assumption in respect of [FeO²⁺]. Using either assumption, when minimum of RSS was approached, identical [O₂] vs time and intercept vs [H₂O₂] curves were obtained. This implied that (1) during the entire reaction, [FeO²⁺] remained near its steady state value and (2) the truly independent rate parameters were k₄/k₅ and k₆/k₅. Furthermore, towards the end of parameter fitting, k₄/k₅ became insignificant so that there remained only two rate parameters which determined the shape of the curves: $k{\prime }_1$ and k₆/k₅ (their best values were 12.6 mol⁻¹ dm³ s⁻¹ and 7.09 × 10⁻², respectively). This meant that evolution of O₂ through direct reaction between FeO²⁺ and H₂O₂ (step 4) was insignificant at 0°C. The result of the calculations for [H₂O₂]_o = 2 mol dm⁻³ is shown in Figure 5. This shows the initial rapid rise of [O₂] and the subsequent slow phase. The latter is approximately, but not strictly linear as those shown in Figure 1 of Barb et al. ⁴ Actually, Figure 1 in the present work also shows that computer simulations of the free radical scheme do not yield plots with linear sections either. In Figure 6, the calculated intercepts of the quasi-linear sections of the plots are shown as a function of [H₂O₂]. It is seen that with increasing [H₂O₂], the intercepts approach a constant limiting value in the range 1.40 × 10⁻² to 1.50 × 10⁻² mol dm⁻³.

Figure 5.

Simulated curve of O₂ evolution (non-radical model). $k{\prime }_1$  = 12.6 mol dm³ s⁻¹; k₆/k₅ = 7.09x10^-2; k₄/k₅ negligible; [Fe²⁺]_o = 0.04 mol dm^-3; [H₂O₂]_o = 2 mol dm^-3

Figure 6.

Intercepts of quasi-linear sections of simulated [O₂] versus time curves (radical and non-radical models).

It seemed of interest to investigate the results of a curve fitting process using the free radical scheme of Barb et al. as a basis. This implied varying k₁/k₂ and k₄/k₃ while keeping k₀ = 12.6 mol⁻¹ dm³ s⁻¹ constant. Reagent concentrations were identical to those used in simulations of the non-radical model. The legend to Figure 6 shows that identical fits were obtained when kinetically equivalent rate constants were used. An explanation of this result is given in Appendix 1. The difference between the two simulations lies in the matter of compatibility of rate constants in the models obtained under different experimental conditions. In the non-radical model, the (pH dependent) value of k₆/k₅ was found to be 8.1 × 10⁻² (25°C, pH = 1.8, see Kremer, ⁷ Table 4). Taking into account compensating changes in rate constants upon reducing the temperature to 0°C, the value obtained in the present work (7.09 × 10⁻²) is reasonable. k₄/k₅ is about 40 times lower than k₆/k₅ at 25°C. This ratio may become even lower at 0°C. In Table 2 the free radical rate parameters (0°C, pH = 1.8) from Barb et al.’s work are summarized. A comparison of these data with those appearing in the Legend to Figure 6 shows that there is no agreement between them. It appears thus that a more consistent, though still not complete account of O₂ evolution data of Barb et al. can be given on the basis of the non-radical model. It may be noted however that there are uncertainties (1) in determination of the transition point between the two phases of the reaction (there is a finite time interval) and (2) identification of the intercept, obtained by back extrapolation, with [O₂]_a is only an approximation. It gives only an approximate value. Discussion of further aspects of radical versus non-radical mechanisms can be found in the literature.^7–10

Table 2.

Rate parameters from Barb et al. ⁴

	k 2 /k 1	k 4 /k 3
Fe2+ kinetics	(9 ± 2) × 10−2 (p. 497)	0.30 (Table III)
O2 evolution	(1.45 ± 0.08) × 10−2 (Table XI)	0.25 (Table IV)

Total amount of O₂ formed in the Fenton reaction

An important quantity in the analysis of the kinetics of the free radical model is the total amount of O₂ formed in the Fenton reaction. This term deserves a closer examination. It is defined as O₂ formed from the initial amounts of Fe²⁺ and H₂O₂ via reactions B0–B4. It consists of O₂ formed partly in phase (a) and partly in phase (b) of the reaction. Phase (b) itself can be divided into two sections. Section 1 covers the time interval before the onset of the direct reaction between the Fe³⁺ ion and H₂O₂

$$\mathrm{F}{\mathrm{e}}^{3+}+{\mathrm{H}}_2{\mathrm{O}}_2\to \mathrm{F}{\mathrm{e}}^{2+}+{\mathrm{H}}^{+}+\mathrm{H}{{\mathrm{O}}_2}^{•}$$

Bi

As the reaction progresses, Bi becomes important once the ratio [Fe³⁺]/[Fe²⁺] in the reacting mixture increases beyond a certain limit (section 2). It starts a catalytic cycle for the decomposition of H₂O₂ (Fe³⁺ catalysis). ⁶ However, Bi will also change the course of the Fenton reaction itself (B0–B4): it will reduce the rate of disappearance of Fe²⁺ in two ways: (1) directly by regeneration of Fe²⁺ and (2) indirectly by formation of $\mathrm{H}{{\mathrm{O}}_2}^{•}$ (producing more Fe²⁺ via step B4). A single unified mechanism will operate which has two initiation steps: B0 and Bi. Under these conditions, it is impossible to distinguish between O₂ produced in chain reactions initiated by B0 (Fenton reaction) and in chain reactions initiated by Bi (Fe³⁺ catalysis). As a consequence, the total amount of O₂ formed in the Fenton reaction becomes undefined and cannot be determined. Thus, any proof in support of the free radical model based on this quantity is not valid.

Finally, we note that the observation of coupling of the formation of O₂ to the regeneration of Fe²⁺ is accounted for equally well by the radical and non-radical models^4,5

$$\mathrm{F}{\mathrm{e}}^{3+}+\mathrm{H}{{\mathrm{O}}_2}^{•}\to {\mathrm{O}}_2+\mathrm{F}{\mathrm{e}}^{2+}+{\mathrm{H}}^{+}$$

B4

$$\mathrm{Fe}{\mathrm{O}}^{2+}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{O}}_2+\mathrm{F}{\mathrm{e}}^{2+}+{\mathrm{H}}_2\mathrm{O}$$

Non-radical analogue

Conclusion

The Haber Weiss reaction

The basic assumption of Haber and Weiss was the formation of OH^•. radicals in the reaction between H₂O₂ and Fe²⁺. It was regarded as the key intermediate involved in the formation of O₂. Reacting with H₂O₂ it was assumed to produce $\mathrm{H}{{\mathrm{O}}_2}^{•}$ radicals (H2 or B2) which in turn can form O₂ either in reaction with H₂O₂ (H3) or with Fe³⁺ (B4). Barb et al. have shown that reaction H3 doesn’t occur, the present work proves that reaction B4 leads to wrong kinetics. There remain the radical – radical reactions:

$${{\mathrm{HO}}_2}^{•}+{{\mathrm{HO}}_2}^{•}\to {\mathrm{O}}_2+{\mathrm{H}}_2{\mathrm{O}}_2$$

$${{\mathrm{HO}}_2}^{•}+{\mathrm{OH}}^{•}\to {\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}$$

These reactions have been examined and found also to lead to incorrect kinetics. ⁹ This exhausts the possibilities of forming O₂ within the free radical scheme. It is concluded therefore that the reaction.

$${\mathrm{Fe}}^{2+}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{Fe}}^{3+}+{\mathrm{OH}}^{•}+{\mathrm{OH}}^{-}$$

does not occur.