Inorganic Oxidation-Reduction Reactions in Solution Electron Transfers

A theoretical treatment has been developed for the rates of electron-transfer reactions in aqueous solution, with particular reference to the ferric-ferrous system. T h e reactions are considered to be diffusion-co~ltrolled processes, the approach of the ions being hindered by the electrostatic repulsion between them. Calculations have been ~u a d e of the free energy of the diffusion process and for the repulsion, account being taken of the variation in dielectric constant with the electric field. The form of the potential-energy barrier between the ions is calculated for various separations, and the transmission coefficient calculated using the quantum-mechanical expression corresponding to a rectangular barrier. The total free energy of activation for the reaction, which is the sum cf the contributions due to diffusion, repulsion, and tunnelling, is found to pass through a minimum a t a separation of about 4 A.The calc~~lated free energy of activation for the reaction is 15.4 kcal, in good agreement with the experimental value of 16.8 lccal. The energy and entropy of activation for the reaction arc also briefly discussed. INTRODUCTIONDuring the past few years a considerable number of kinetic studies have been concerned with electron-transfer processes between ions in different valency states. A well-known process of this type is that between ferric and ferrous ions in aqueous solution,Although many complexities exist, the evidence indicates that in some cases these reactioils occur by a simple transfer of an electron from one ion to another. This is possibly true of the ferric-ferrous reaction, and Silverman and Dodson (1) have determined values of 9.9 kcal and -25 e.u. for the energy and entropy of activation of the process.This paper is concerned with the theory of simple electron-transfer reactions, and for the most part deals quantitatively with the factors influencing the rate of the Fe++-Fe++f reaction. Several previous theoretical discussioils of these reactions have been presented, notably by Libby (2), Weiss (3), Eyring and co-workers (4, 5 ) , and by Marcus (Ge). In the case of the latter two treatments, an attempt was made to calculate the free energies of activation (AF;" of a number of reactions, including the Fe++-Fe+++ one. The quantitative agreement with experiment was not, however, completely satisfactory. T h e experimental AF" for the Fe++-Fe+++ system is 16.8 kcal a t 25' C: Eyring et al. obtain agreement only by arbitrarily adding a term of 8.1 kcal, while Marcus (Ga) calculated a value of 9.8 ltcal.* I t has appeared to the present writer that this lack of good agreement could be attributed to failure to take into consideration certain important factors which must influence the rate. In particular it would seem that neither Eyring nor Marcus treated in sufficient detail the collisions (or, more correctly, encounters) between the reacting ions.I n the present work an attempt has been made to bring about some improvement, particularly with respect to the two points noted above. If ...

Section: Introductionmentioning

confidence: 99%

Some Theoretical Aspects of Electron-Transfer Processes in Aqueous Solution

Laidler¹

1959

“…Several review articles have recently appeared in which the current status of theory and experiment have been summarized for both isotopic and nonisotopic clcctron transfer reactioils (1,14,19). The proceedings of a symposium held in 1954 on this subject have also been published (12).…”

Section: Introductionmentioning

confidence: 99%

“…Such results have reawakened interest in the whole subject of both isotopic and ilo~lisotopic electron transfer reactioils between cations in solution. Some kinetic information is now available relating to the reactioils between the nonisotopic pairs Sn (11) -Fe (111) (5), T1 (111) -Fe (11) (2), and N p (IV) -Fe (111) (10).Several review articles have recently appeared in which the current status of theory and experiment have been summarized for both isotopic and nonisotopic clcctron transfer reactioils (1,14,19). The proceedings of a symposium held in 1954 on this subject have also been published (12).…”

mentioning

confidence: 99%

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Kinetics of the Oxidation of Uranium (Iv) by Iron (Iii) in Aqueous Solutions of Perchloric Acid

Betts¹

1955

The kinetics of oxidation of uranium (IV) b y iron (111) in aqueous solutions of perchloric acid have been investigated a t four temperatures between 3.1°C. and 24.8"C. The reaction was followed by measurement of the amount of ferrous ion formed. For the conditions (Il+) = 0.1-1.0 iM, ionic strength = 1.02, (FelII) = 10-'-10-5 hf, and (UIV) = lO-'-lO-6 ill, the observed rate law is d(FeZ+)/dt = -2d(UIV) /dt -K1 and Kn are the first hydrolysis constants for Fe3+ and U4+, respectively, and K'and K" are pseudo rate constants. At 24.8"C., K' = 2.98 sec.-I, and K" = 10.6 mole liter-' sec-'. The corresponding temperature coefficients are AH' = 22.5 kcal./mole and AH" = 24.2 kcal./mole. The kinetics of the process are consistent with a mechanism which involves, as a rate-controlling step, electron transfer between hydrolyzed ions. INTRODUCTIONOxidation-reduction reactions between cations in aqueous solution have been thought until recently t o proceed very rapidly, and the term "instantaneous" has frequently been used to characterize their rates. However recent studies with radioactive tracers have shown that even such elementary reactions as electron transfer between iron (11) and iron (I 11), or between Ce (I 11) and Ce (IV), do not proceed instantaneously (18,8). Such results have reawakened interest in the whole subject of both isotopic and ilo~lisotopic electron transfer reactioils between cations in solution. Some kinetic information is now available relating to the reactioils between the nonisotopic pairs Sn (11) -Fe (111) (5), T1 (111) -Fe (11) (2), and N p (IV) -Fe (111) (10).Several review articles have recently appeared in which the current status of theory and experiment have been summarized for both isotopic and nonisotopic clcctron transfer reactioils (1,14,19). The proceedings of a symposium held in 1954 on this subject have also been published (12).As a further example of this type of reaction, the present paper describes experiments relating to the kinetics of the oxidatioil of uranium (IV) by iron (111) in aqueous acidic media. Perchloric acid and sodium perchlorate were chosen as the principal electrolytes, since amongst the common inorganic anions, perchlorate has the least tendency to form ion-pairs with cations. T o bring the rate of reaction into a range suitable for study, it has been necessary to work with solutions to 10-5 M in uranium (IV) and iron (111). T h e course of the reaction has been followecl by measurement of the rate of formatioil of iron (11). Such measurements, in conju~lction with a knowledge of the stoichiometry of the reaction, were sufficient to enable a kinetic analysis of the results to be made. I t would have been useful, as confirmatory evidence, lMa?zz~script

“…OH-and C1-) exert in other electron transfer reactions such as the exchange between isotopic metal ions of different valence. I t has been suggested that the anion forms a polarizable bridge between the two reacting species, thereby lowering the electrostatic repulsion barrier t o their mutual approach and facilitating electron transfer between them (14). I t is possible that some of the anion influences observed in the present reaction should also be regarded in this light.…”

Section: S H G ( I I ) a (Concentrations Expressed I N Mole Litermentioning

confidence: 88%

Effects of Complexing on the Homogeneous Reduction of Mercuric Salts in Aqueous Solution by Molecular Hydrogen

Korinek¹,

Halpern²

1956

The effects of various complexing agents on the homogeneous reduction of mercuric salts by molecular hydrogen in aqueous solution were determined. In all cases the kinetics suggest that the rate-determining step is a bimolecular reaction between a mercuric ion or complex and a hydrogen molecule, probably leading t o the formation of an intermediate mercury atom. The reactivity of various mercuric complexes was found to decrease in the following order:HgSOl > Hg++ > HgAc?, HgPrz > HgClz > HgBr:! > Hg(EDA)zf+. Addition of anions such as OH-, COZ' , Ac-, Pr-, and C1-, in excess of the amounts required to form stable mercuric complexes, was found to increase the rate. An interpretation of these effects is given.