Thermodynamic Considerations of Redox Reactions

We start with a simple reversible redox reaction for which we can directly measure the free energy of reaction, Ar 7, with a galvanic cell. This example helps us introduce the concept of using (standard) reduction potentials for evaluating the energetics (i.e., the free energies) of redox processes. Let us consider the reversible interconversion of 1,4-benzoquinone (BQ) and hydroquinone (HQ) (reaction 14-5 in Table 14.1). We perform this reaction at the surface of an inert electrode (e.g., 

Note that by convention we always write a half reaction such as Eq. 14-14 as a reduction that is, the oxidized species appears on the left side of the equation. Also, 

The platinum electrodes serve to transport electrons from H2 on one side to BQ on the other. Hence, the reaction we are actually considering is given by  

With a potentiometer we can now measure the potential difference, AE, between the two electrodes. During our potentiometric measurement, no current is flowing between the two electrodes. If we assume electrochemical equilibrium at the electrode surface (which implies that we have a fast reversible half reaction at each electrode), then the potential difference, AE, is directly related to the ArG of the reaction (e.g., Atkins, 1998) by  

Since in experiments such as the one we have just discussed, it is only possible to determine potential differences between two electrodes (and not the absolute potential of each half cell), it is now useful to choose a reference system to which all measured potential differences may be related. In accord with the IUPAC 1953 Stockholm convention, the standard hydrogen electrode (SHE) is commonly selected as the reference electrode to which we arbitrarily assign a zero value of electrical potential. This is equivalent to assigning (arbitrarily) a standard free energy change, ArG°, of zero at all temperatures to the half reaction  

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The thermodynamic feasibility of redox reactions at the semiconductor-electrolyte interface can be assessed from thermodynamic considerations. Since typical redox potentials for many redox couples encountered in electrolytes of natural or technical systems often lie between the band potentials of typical semiconductors, many electron transfer reactions are (thermodynamically) feasible (Pichat and Fox, 1988). With the right choice of semiconductor material and pH the redox potential of the cb can be varied from 0.5 to 1.5 V and that of the vb from 1 to more than 3.5 V (see Fig. 10.4). 

In many cases, redox reactions that are favorable from a thermodynamic point of view may not actually take place sometimes, the activation energy barriers for such reactions are too high to allow fast transformation, according to the preferred thermodynamic considerations. For example, the complete oxidation of any organic molecule to carbon dioxide and water is thermodynamically favorable. However, such oxidation is not favorable kinetically, which implies that organic molecules— including all forms of living species—are not oxidized immediately this fact explains the ability to sustain life. The reason for this difference between kinetic and thermodynamic considerations, for redox reactions, is partly because redox reactions are relatively slow compared to other reactions and partly due to the fact that, in many cases, reactions are poorly coupled because of slow species diffusion... 

Let us now turn to some kinetic considerations of NAC reduction. As an example, consider the time courses of nitrobenzene (NB) concentration in 5 mM aqueous hydrogen sulfide (H2S) solution in the absence and presence of natural organic matter (Fig. 14.7). As is evident, although reduction of NB by H2S to nitrosobenzene and further to aniline (Eq. 14-31) is very favorable from a thermodynamic point of view (see Fig. 14.4), it seems to be an extremely slow process. However, when DOM is added to the solution, reduction occurs at an appreciable rate (Fig. 14.7). In order to understand these findings, some general kinetic aspects of redox reactions involving NACs should be recognized. 

The majority of this chapter is devoted to thermodynamic prediction. The last section mentions some kinetic considerations about redox reactions. 

It follows from the electrochemical mechanism of corrosion that the rates of the anodic and cathodic reactions are interdependent, and that either or both may control the rate of the corrosion reaction. It is also evident from thermodynamic considerations (Tables 1.9 and 1.10) that for a species in solution to act as an electron acceptor its redox potential must be more positive than that of the M /M equilibrium or of any other equilibrium involving an oxidised form of the metal. 

Cyclic voltammetry is the most widely used technique for acquiring qualitative information about electrochemical reactions. The power of cyclic voltammetry results from its ability to rapidly provide considerable information on the thermodynamics of redox processes, on the kinetics of heterogeneous electron-transfer reactions, and on coupled chemical reactions or adsorption processes. Cyclic voltammetry is often the first experiment performed in an electroanalytical study. In particular, it offers a rapid location of redox potentials of the electroactive species, and convenient evaluation of the effect of media upon the redox process. 

In the presence of trace amounts of iron, superoxide can then reduce Fe3+ to molecular oxygen and Fe2+. The sum of this reaction (13.2) plus the Fenton reaction (13.1) produces molecular oxygen, hydroxyl radical and hydroxyl anion from superoxide and hydrogen peroxide, in the presence of catalytic amounts of iron. This is the Haber-Weiss reaction (13.3), originally described by Haber and Weiss (1934), but manifestly impossible from thermodynamical considerations in the absence of catalytic amounts of redox metals such as iron and copper ... 

In both reactions, electron transfer induces the dissolution of the solid phase i.e., reductive and oxidative dissolution, respectively. Although no kinetic implications follow directly from the thermodynamic considerations, there are cases where the redox rate is related to the redox equilibrium (see e.g., Eq. 9.12). 

Catalysts and their effects on chemical reactions aid in efficiency, effectiveness and selectivity. A recent example of current research is redox and ligand exchange reactions of the oxygenation catalyst (N,N -bis(salicylidene)ethylenediaminato)co-balt(II), Co(SALEN)2 (below), and its one-electron oxidation product, Co(salen) 2-These were investigated in DMF, pyridine, and mixtures of these solvents. Solvent effects on the potentials, the thermodynamics of cross reactions, and the distribution of Co(II) and Co(III) species as a function of the solvent composition are important considerations (Eichhorn, 1997). The results in these solvents should be compared with other work with catalysts using more environmentally benign media (Collins et al., 1998). 

From thermodynamic considerations, the course of such redox reaction > can be expressed in terms of the redox potentials of the two couples Ed and Er... 

A consideration of these relationships reveals8 that because E° is a thermodynamic parameter and represents an energy difference between two oxidation states and in many cases the spectroscopic or other parameter refers to only one half of the couple, then some special conditions must exist in order for these relationships to work. The special conditions under which these relationships work are that (a) steric effects are either unimportant or approximately the same in both halves of the redox couple and (b) changes in E° and the spectroscopic or other parameters arise mainly through electronic effects. The existence of many examples of these relationships for series of closely related complexes is perhaps not too unexpected as it is likely that, for such a series, the solvational contribution to the enthalpy change, and the total entropy change, for the redox reaction will remain constant, thus giving rise to the above necessary conditions. 

In several cases it has been found that the oxidation of the redox system occurs entirely via hole transfer directly from the valence band to the reduced form of the couple. Then both processes, oxidation of the redox system and corrosion, proceed independently. This is usually not visible from measurements with an n-type electrode, because the photocurrent is entirely determined by the light intensity. As already mentioned above, p-type electrodes are more suitable, because the current is determined by majority carrier transfer (reaction rate Vf, in Fig. 21). From the thermodynamic point of view, the oxidation of Cu at GaAs is an interesting case. The corresponding current-potential curves are given in Fig. 22 [93]. The corrosion current is not changed upon addition of Cu, i.e. corrosion and redox process are completely independent. In this case, the kinetics of the direct hole transfer is obviously very fast, i.e. the redox current is considerably larger than the corrosion current. Both processes occur indepen-... 

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