Heterogeneous redox equilibria

In an electrochemical cell, electrons maybe accepted from or donated to an inert metaUic conductor (e.g., platinum). A reduction process tends to charge the electrode positively (remove electrons), and an oxidation process tends to charge the electrode negatively (add electrons). By convention, a heterogeneous redox equilibrium (equation 2) is represented by the cell... 

When the heterogeneous electron-transfer process at the electrode becomes slow and irreversible, the use of the direct OTTLE/Nernst experiment is inconvenient because of the uncertainties associated with a slow equilibration process. A mediated OTTLE/Nernst experiment should rather be considered, where a redox mediator Mox/Mred characterized by a high heterogeneous rate constant is added to the cell (Eq. 111). The concentration ratio of the mediator couple will be adjusted quickly to the applied electrode potential E and, furthermore, it will be in a redox equilibrium (Eq. 112) with the redox pair O/R in the bulk solution, according to Eq. 113. 

In contrast to a mixture of redox couples that rapidly reach thermodynamic equilibrium because of fast reaction kinetics, e.g., a mixture of Fe2+/Fe3+ and Ce3+/ Ce4+, due to the slow kinetics of the electroless reaction, the two (sometimes more) couples in a standard electroless solution are not in equilibrium. Nonequilibrium systems of the latter kind were known in the past as polyelectrode systems [18, 19]. Electroless solutions are by their nature thermodyamically prone to reaction between the metal ions and reductant, which is facilitated by a heterogeneous catalyst. In properly formulated electroless solutions, metal ions are complexed, a buffer maintains solution pH, and solution stabilizers, which are normally catalytic poisons, are often employed. The latter adsorb on extraneous catalytically active sites, whether particles in solution, or sites on mechanical components of the deposition system/ container, to inhibit deposition reactions. With proper maintenance, electroless solutions may operate for periods of months at elevated temperatures, and exhibit minimal extraneous metal deposition. 

In the real world, the simple redox couple may be perturbed by finite ET rates, by adsorption of O and/or R on the electrode surface, and by homogeneous (i.e., in solution) chemical kinetics involving O and/or R. Various combinations of heterogeneous ET steps (E) with homogeneous chemical steps (C) are encountered. It should be clear that if one or more species in equilibrium in solution are electroactive, electrochemistry can be used to perturb the equilibrium and study the solution chemistry. 

If the rate of electron transfer is low (or the scan rate is too high), electron transfer will not be able to adjust the surface concentrations of -Fc and -Fc+ to values that are at equilibrium with the applied potential (quasireversible or totally irreversible case, see Chap. 3). In this case, the anodic peak and the cathodic peaks will not be at the same potential that is, AEpk will be greater than zero volts. Kinetic information about the surface-bound redox couple can be obtained from such quasireversible or irreversible voltammograms. For example, methods for obtaining the standard heterogeneous rate constant (see Chap. 2) for the surface-confined redox couple have been developed [41,42]. 

In soil solutions the most important chemical elements that undergo redox reactions are C, N, O, S, Mn, and Fe. For contaminated soils the elements As, Se, Cr, Hg, and Pb could be added. Table 2.4 lists reduction half-reactions (most of which are heterogeneous) and their equilibrium constants at 298.15 K under 1 atm pressure for the six principal elements involved in soil redox phenomena. Although the reactions listed in the table are not full redox reactions, their equilibrium constants have thermodynamic significance and may he calculated with the help of Standard-State chemical potentials in the manner... 

However, in heterogeneous catalysis, metals are usually deposited on nonconducting supports such as alumina or silica. For such conditions electrochemical techniques cannot be used and the potential of the metallic particles is controlled by means of a supplementary redox system [8, 33]. Each particle behaves like a microelectrode and assumes the reversible equilibrium potential of the supplementary redox system in use. For example, with a platinum catalyst deposited on silica in an aqueous solution and in the presence of hydrogen, each particle of platinum takes the reversible potential of the equilibrium 2H+ + 2e H2, given by Nemst s law as... 

In this manner, it is possible to measure Eq with a precision of a few mV or better. Although Eq might be determined more easily and with a similar precision for a reversible system by the CV technique, the OTTLE/Nernst experiment is very useful for the study of quasi-reversible systems. The presence of slow heterogeneous kinetics means that the equilibrium is attained relatively slowly upon changing the potential, but this presents no problem as long as the redox pair is kinetically stable. The technique has therefore been used in the measurement of Eq and n for a large number of inorganic salts and enzymes [70, 82]. 

Most applications of coupled models use the local equilibrium assumption. It is well known that most heterogeneous and redox reactions in the low temperature, near-surface systems are kinetically controlled (Hunter et al., 1998). However, we lack both theory and data to model kinetic reactions satisfactorily. In addition, inclusion of kinetic reactions makes the results even more difficult to comprehend completely and hence more costly. 

These observations can be summarised in the general statement that at equilibrium all of the species involved in the reversible reaction must be present simultaneously. It is particularly important to remember this when a heterogeneous reaction is involved, e.g. in the solubility and redox reactions the solid phases BaS04 and Ag must be present at equilibrium. 

The last step in complexity that we will explore in detail for the construction of diagrams to illustrate redox equilibria involves the addition of heterogeneous equilibria to redox and acid-base equilibrium diagrams. We will illustrate this system with a ps-pH diagram for iron species in aqueous solution containing no anions other than hydroxide, We will expand on this diagram later in this chapter during the discussion of iron chemistry. 

Even the earliest H NMR studies of PfFd revealed that the protein can exist in multiple forms, in addition to its alternate cluster redox states, Fd and Fd, with PfVA capable of existing in no less than six discrete molecular states. Some of these states are only metastable, " while others are clearly equilibrium structural heterogeneities. Similar molecular heterogeneity was not detected in the H NMR spectra of either 7m or ... 

In LSV and CV, a redox system may show a Nernstian, quasireversible or totally irreversible behavior depending on the scan rate employed, since V determine the time available for the electrodesolution interphase to attain the equilibrium condition dictated by the Nernst equation. Such a dependence is usually rationalized by the following dimensionless parameter, comparing the standard heterogeneous rate constant with the scan rate v ... 

ABSTRACT. The electrochemical behaviour of tetraazamacrocyc-lic Ni(II) complexes containing a pendant amino group has been studied by cyclic voltammetry at glassy carbon electrodes in function of pH and kind of solvent. The internal pH-dependent equilibrium between the open and chelated form of the pendant arm, the influence of solvent on the heterogenous kinetics of Ni(III)/Ni(II) redox couple in these complexes, formation of the modified electrode in strongly alkaline solutions and its application to the electrocatalytic oxidation of simple alcohols have been studied and discussed. 

Electron transfer reactions at the electrode may not be rapid enough to maintain equilibrium concentrations of the redox couple species near the electrode surface. It is therefore necessary to consider the kinetics of the electron transfer process. The rate equation for heterogeneous electron transfer (Equation 8) expresses the flux of electrons at the electrode surface (Figure 1-9) ... 

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