Initial Steps in the Reaction of H 2 O 2 with Fe 2+ and Fe 3+ Ions: Inconsistency in the Free Radical Theory

: Consideration of the changes in free energy shows that the assumed initial steps in reactions of H 2 O 2 with Fe 2+ and Fe 3+ in the free radical theory are not consistent. The free radical theory is unable to account for the Fe 3+ -initiated decomposition of H 2 O 2 or for oxidations by it. In reactions with Fe 2+ ions at high [H 2 O 2 ], where O 2 evolution reaches a limit, such limit is not foreseen by the free radical model. At lower [H 2 O 2 ], because of a disallowed substitution in the equation used, the interpretation is not valid. It appears, therefore, that free radicals derived from H 2 O 2 do not provide a suitable basis for constructing models for these reactions. Non-radical models are more successful in interpreting experimental results.


Introduction
The search for the mechanism of the reaction of H 2 O 2 with Fe 2+ and Fe 3+ 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 O 2 evolution and oxidation in these systems. It is divided into two parts. In the first part, reactions involving Fe 3+ and H 2 O 2 are discussed. The corresponding reactions of Fe 2+ are discussed in the second part.

Free Radical Model of the Fe 3+ Ion-Catalyzed Decomposition of H 2 O 2
In the free radical theory, free radicals originating from H 2 O 2 are produced in the reaction between H 2 O 2 and Fe 2+ or Fe 3+ 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] Fe 3+ + HO 2 − → Fe 2+ + HO 2

•
(1) H 2 O 2 is presented in step 1 in its anionic form, Appendix A [4]. In these reactions, the molecule H 2 O 2 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 In another way, the radical HO 2 • is formed by the ejection of an electron from the anion HO 2 The donor and the acceptor of electrons in these processes is the oxidation-reduction pair Fe 2+ -Fe 3+ Fe 2+ → Fe 3+ + e e + Fe 3+ → Fe 2+ (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 F 1 = F 4 + F 6 and F 2 = F 3 -F 6 (note that F 5 = −F 6 ). Adding F 1 and F 2 we get F 1 + F 2 = F 3 + F 4 . 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 Fe 2+ and H 2 O 2 react spontaneously and quantitatively. Therefore, F 2 must be negative (Appendix B). Consequently, F 1 must be positive. If F 1 is positive, then the initial and all the following steps of the Fe 3+ ion-catalyzed decomposition of H 2 O 2 cannot occur. In reality, the Fe 3+ ion does catalyze the decomposition of H 2 O 2 . 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 O 2 producing steps involving radicalradical reactions [5][6][7]. Since all these free radical models for the decomposition of H 2 O 2 by Fe 3+ start with step 1, the conclusion reached above applies to all of them. Mixtures of Fe 2+ + H 2 O 2 and of Fe 3+ + H 2 O 2 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 Fe 2+ , OH • is formed during step 2. In the case of Fe 3+ , 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 H 2 O 2 + Fe 3+ becomes impossible. Summing up: all free radical schemes beginning with reaction 1 are nonstarters [3][4][5][6][7][8][9][10].

Free Radical Model of the Fenton Reaction
A new direction in the search for the mechanism of the reaction of Fe 2+ and H 2 O 2 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 HO 2 • radicals. This mechanism was criticized later as it could not account for the existence of a limit in the evolution of O 2 when [H 2 O 2 ] was increased at a constant [Fe 2+ ]. The discoverers of this limit, Barb et al., modified the scheme of Haber and Weiss, by substituting Fe 3+ for H 2 O 2 in the O 2 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 O 2 -producing step, Fe 2+ has been regenerated. Fe 2+ 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 Fe 2+ in the Haber-Weiss scheme). The modified scheme of Barb  ]/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 Fe 2+ and H 2 O 2 are mixed with no Fe 3+ being present initially. Reaction A1 can be neglected in the initial phase (phase A, Fenton reaction). As the reaction progresses, [Fe 2+ ] will decrease with simultaneous increase of [Fe 3+ ]. The reaction will reach a stage at which initiation will occur via both steps A1 and A2 (phase AB  [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 ([Fe 2+ ] 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 ∆O 2 T : in the transition phase, O 2 evolved in the Fenton reaction path and in Fe 3+ 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.

Conclusions
Consideration of kinetics and of free energy changes in reactions of Fe 2+ and of Fe 3+ with H 2 O 2 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 H 2 O 2 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 FeO 2+ and FeO 3+ [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 O 2 evolution-70 years after it has been found experimentally [2,13].
Funding: This research was supported by a grant from the Hebrew University for Emeriti.

Conflicts of Interest:
The author declares no conflict of interest.

Appendix A
The free radical model of Haber  It does not affect the change of the free energy in step A1. Namely, by taking the difference of the free energy (F) changes in steps (A7) and (A1), we obtain the following: Because of the equilibrium between H 2 O 2 and its dissociation products, the r.h.s. of this equation must be zero. Thus, F A7 = F A1 .