Initial Steps in the Reaction of H₂O₂ with Fe²⁺ and Fe³⁺ Ions: Inconsistency in the Free Radical Theory

Abstract

Consideration of the changes in free energy shows that the assumed initial steps in reactions of H₂O₂ with Fe²⁺ and Fe³⁺ in the free radical theory are not consistent. The free radical theory is unable to account for the Fe³⁺-initiated decomposition of H₂O₂ or for oxidations by it. In reactions with Fe²⁺ ions at high [H₂O₂], where O₂ evolution reaches a limit, such limit is not foreseen by the free radical model. At lower [H₂O₂], because of a disallowed substitution in the equation used, the interpretation is not valid. It appears, therefore, that free radicals derived from H₂O₂ do not provide a suitable basis for constructing models for these reactions. Non-radical models are more successful in interpreting experimental results.

1. Introduction

The search for the mechanism of the reaction of H₂O₂ with Fe²⁺ and Fe³⁺ ions has lasted for over a hundred years. The question has still not been settled satisfactorily, and many researchers are basing their interpretations of experimental results on the free radical theory that was introduced by Haber and Weiss [1]. The subject of the present discussion is to address some thermodynamic and kinetic aspects of O₂ evolution and oxidation in these systems. It is divided into two parts. In the first part, reactions involving Fe³⁺ and H₂O₂ are discussed. The corresponding reactions of Fe²⁺ are discussed in the second part.

2. Free Radical Model of the Fe³⁺ Ion-Catalyzed Decomposition of H₂O₂

In the free radical theory, free radicals originating from H₂O₂ are produced in the reaction between H₂O₂ and Fe²⁺ or Fe³⁺ ions. According to the version proposed by Barb et al., and shown in Appendix A, the initial steps of the respective reactions are [2,3]

Fe³⁺ + HO₂⁻ → Fe²⁺ + HO₂^•

(1)

Fe²⁺ + H₂O₂ → Fe³⁺ + OH^• + OH⁻

(2)

H₂O₂ is presented in step 1 in its anionic form, Appendix A [4]. In these reactions, the molecule H₂O₂ is broken up in various ways to yield free radicals. In one way, the O–O bond is split by absorbing an electron and yielding the radical OH^•

e + H₂O₂ → OH^• + OH⁻

(3)

In another way, the radical HO₂^• is formed by the ejection of an electron from the anion HO₂⁻

HO₂⁻ → HO₂^• + e

(4)

The donor and the acceptor of electrons in these processes is the oxidation–reduction pair Fe²⁺–Fe³⁺

Fe²⁺ → Fe³⁺ + e

(5)

e + Fe³⁺ → Fe²⁺

(6)

After coupling the appropriate processes, we obtain the following identities: (1) = (4) + (6) and (2) = (3) + (5). Denoting the total free energy changes accompanying various processes by F, we have F₁ = F₄ + F₆ and F₂ = F₃ – F₆ (note that F₅ = −F₆). Adding F₁ and F₂ we get F₁ + F₂ = F₃ + F₄. This sum is positive, because in reactions (3) and (4) free radicals are produced requiring the investment of free energy. On the other hand, the experiment shows that upon mixing Fe²⁺ and H₂O₂ react spontaneously and quantitatively. Therefore, F₂ must be negative (Appendix B). Consequently, F₁ must be positive. If F₁ is positive, then the initial and all the following steps of the Fe³⁺ ion-catalyzed decomposition of H₂O₂ cannot occur. In reality, the Fe³⁺ ion does catalyze the decomposition of H₂O₂. Therefore, the conclusion must be drawn that, due to considerations of free energy, the model of Barb et al. failed to account for the occurrence of this reaction [3]. Modifications of Barb et al.’s scheme were suggested by including additional O₂ producing steps involving radical–radical reactions [5,6,7]. Since all these free radical models for the decomposition of H₂O₂ by Fe³⁺ start with step 1, the conclusion reached above applies to all of them. Mixtures of Fe²⁺ + H₂O₂ and of Fe³⁺ + H₂O₂ are able to oxidize a variety of organic compounds [8,9,10]. According to the free radical theory, the active intermediate involved in the oxidations is the OH^• radical. In the case of Fe²⁺, OH^• is formed during step 2. In the case of Fe³⁺, it is formed in a two-stage process: step 1 followed by step 2. Since a free energy barrier prevents step 1 from happening, the following step 2 cannot occur either. Under such circumstances, the oxidation of substrates by H₂O₂ + Fe³⁺ becomes impossible. Summing up: all free radical schemes beginning with reaction 1 are nonstarters [3,4,5,6,7,8,9,10].

3. Free Radical Model of the Fenton Reaction

A new direction in the search for the mechanism of the reaction of Fe²⁺ and H₂O₂ started when Haber and Weiss introduced their model in 1934 (Appendix A) [1]. It was a chain reaction based on the participation of OH^• and HO₂^• radicals. This mechanism was criticized later as it could not account for the existence of a limit in the evolution of O₂ when [H₂O₂] was increased at a constant [Fe²⁺]. The discoverers of this limit, Barb et al., modified the scheme of Haber and Weiss, by substituting Fe³⁺ for H₂O₂ in the O₂ evolution step (Appendix A) [2]. With the change, the chain reaction has been turned into a catalytic reaction. Namely, as the result of this substitution, (1) the cycle of the two chain-carrying radicals has been eliminated and (2), in the O₂-producing step, Fe²⁺ has been regenerated. Fe²⁺ became thus a catalyst, as it was both a reactant in the initial step and was regenerated in the product-forming step [11]. This fact is generally overlooked, although it is significant for understanding the free radical model (it is to be noted, that there is no regeneration of Fe²⁺ in the Haber–Weiss scheme). The modified scheme of Barb et al. is shown in Appendix A. It is a combined model for both the Fenton reaction and the Fe³⁺ ion catalyzed decomposition of H₂O₂. The set of reactions A2 to A6 present the Fenton part. Concerning the limit to the evolution of O₂, it is observed in a large excess of [H₂O₂] over [Fe²⁺]. In the model, it causes step A3 to become insignificant beside A4. The same excess will cause a rapid oxidation of Fe²⁺ to Fe³⁺ and will cause A5 to become insignificant beside A6. The model will then be reduced to steps A2–A4-A6. This combination is a catalytic cycle for the conversion of H₂O₂ to O_2, carried by the free radicals OH^• and HO₂^.. Due to their high reactivity, (a) their concentrations are in steady states and (b) the rates of all reactions in the cycle are equal: v₂ = v₄ = v₆ (v denoting rate). By inserting v₆ = d[O₂]/dt and v_{2 =} k₂ [Fe²⁺] [H₂O₂], we obtain

d[O₂]/dt = k₂ [Fe²⁺] [H₂O₂]

(7)

(Indexing of rate constants follows the numbering of the corresponding Equation in the Appendix A with the omission of the prefix A.)

Clearly, an equation of this form cannot explain the phenomenon of an upper limit to O₂. Barb et al. also performed O₂ evolution experiments at lower [H₂O₂], but still in excess over [Fe²⁺]. In this range, the following relation exists between the amount of O₂ evolved (per 1 dm³ of the reaction mixture) and [Fe²⁺] at various times [2,11,12]

ΔO₂ = (k₆/k₅) ([Fe²⁺]_o/2) {ln([Fe²⁺]_o/[Fe²⁺]) + ([Fe²⁺]/[Fe²⁺]_o) − 1}

(8)

The symbol [ ]_o denotes initial concentration. Since the measurement of pairs of simultaneous values of ΔO₂ and [Fe²⁺] at different times was not feasible due to the speed of the reaction, Equation (8) was applied to the “total amount of O₂” evolved in the Fenton reaction (ΔO₂^T). If ΔO₂ = ΔO₂^T then [Fe²⁺] is the concentration of Fe²⁺ at the end of the reaction ([Fe²⁺]_end). [Fe²⁺]_end can be calculated by solving the rate equation for d[Fe²⁺]/dt = 0. It was found to be zero [11,12]. This implies that the logarithmic term and the entire r.h.s. of Equation (8) became infinite. As a consequence, at this point Equation (8) has lost its physical meaning. In an attempt to treat the problem, Barb et al. added A1 to the set of reactions from A2 to A6. Consider then all reactions occurring in the system when Fe²⁺ and H₂O₂ are mixed with no Fe³⁺ being present initially. Reaction A1 can be neglected in the initial phase (phase A, Fenton reaction). As the reaction progresses, [Fe²⁺] will decrease with simultaneous increase of [Fe³⁺]. The reaction will reach a stage at which initiation will occur via both steps A1 and A2 (phase AB). With further decrease of the ratio [Fe²⁺]/[Fe³⁺], step 1 will become the only starting point of the reaction (phase B, Fe³⁺ catalysis). During phase B, [Fe²⁺] will reach a steady state denoted as [Fe²⁺]_s.s [3]. There is no identity between the steady state during phase B and the endpoint of phase A. In the calculations, Barb et al. have inserted a quantity defined in phase B ([Fe²⁺]_s.s) in an equation the validity of which is restricted to phase A. This substitution is not permissible. There is also problem with the determination of ΔO₂^T: in the transition phase, O₂ evolved in the Fenton reaction path and in Fe³⁺ catalysis are inseparable [12]. Finally, there is a very short proof of inadequacy of the free radical model. A rate equation should be able to describe the course of the reaction from the beginning to the end. If it leads to an infinity catastrophe at the end, it is sign that the model is wrong.

4. Conclusions

Consideration of kinetics and of free energy changes in reactions of Fe²⁺ and of Fe³⁺ with H₂O₂ shows that there are deficiencies in proofs for free radical models of these reactions. Thus, the concept of Haber and Weiss, according to which interatomic bonds in H₂O₂ can be broken to form free radicals in thermal reactions with ions of iron in an aqueous media is not well supported by experimental evidence. The reactions can proceed through non-radical intermediates of the type FeO²⁺ and FeO³⁺ [11,12,13,14]. A non-radical model on this basis was able to offer an explanation for the existence of an upper limit to O₂ evolution—70 years after it has been found experimentally [2,13].