Redox couple thermodynamic parameters

Tables I and II contain electrochemical kinetic and related thermodynamic parameters for several transition-metal redox couples gathered at the mercury-aqueous interface. These systems were selected since the kinetics can be measured accurately under experimental conditions where the diffuse-layer potentials, , are small and/or could be estimated with confi-...

Let us finally point out that the characterization of an electrochemi-cally reversible step lies on the only thermodynamic parameter the formal electrode potential of the redox couple Ox/Red, L ox/Red) which is commonly measured as the average value ... 

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. 

As noted earlier, the polarographic half-wave potential Estandard redox potential of the couple because EVl is governed by kinetic as well as thermodynamic parameters, so that attempts to correlate EVl for irreversible couples with structural features of the complex have been very difficult to obtain. One moderately successful correlation, however, was obtained by Vlcek13 and by Crow14 for a fairly extensive series of complexes of Co111, Crm and Rhm. It was suggested that before reduction of the metal complex... 

CV has become a standard technique in all fields of chemistry as a means of studying redox states. The method enables a wide potential range to be rapidly scanned for reducible or oxidizable species. This capability, together with its variable time scale and good sensitivity, makes CV the most versatile electroanalytical technique thus far developed. It must, however, be emphasized that its merits are largely in the realm of qualitative or diagnostic experiments. Quantitative measurements (of rates or concentrations) are best obtained via other means (e.g., step, pulse, or hydrodynamic techniques). Because of the kinetic control of many CV experiments, some caution is advisable when evaluating the results in terms of thermodynamic parameters (e.g., measurement of E° for irreversible couples). 

The possibility of predicting thermodynamic properties of redox couples and solutes in different solvents is very important. It should be very useful to develop procedures of transferring thermodynamic data such as redox potentials from solvent to solvent. In fact, the correlation found between kinetic and thermodynamic parameters of reactions in solutions, and solvent parameters such as DN, AN, dielectric constant, etc., indicates that it may be quite feasible to draw empirical formulas which predict, for instance, redox potentials in some solvents, based on well-established data obtained experimentally with other solvents. Thus, it may be possible to define transfer parameters (AG , AH , ASf, etc.) reflecting the difference between aqueous and polar aprotic solutions in the thermodynamic properties of solutes. 

The above considerations show how important it is to find a relationship between /If and the characteristic parameters of a redox couple. To this end, we shall consider a solution containing one red particle. Denoting the most probable thermodynamic energy of the electron level of the red particle by E°ed and that of the ox particle by Eox we shall analyze, following papers, the thermodynamic cycle (a-d) shown in Fig. 1 [in Eq. (1), n = is assumed for simplicity) ... 

Redox parameters analogous to those for acid-base chemistry can be defined for all aqueous systems. The redox intensity factor pE is an energy parameter in non-dimensional form that describes the ratio of electron acceptors (oxidants) and donors (reductants) in a redox couple. The redox potential (Ej ) of the system is an alternative and equivalent intensity factor. Table I summarizes the complete thermodynamic analogy between pH and pE. An analogy between acid-base and redox systems can also be made for capacity factors. 

Certain advantages arise in the use of electrochemical techniques compared to chemical redox titrations in the determination of biological molecule thermodynamic parameters. Electrochemical techniques which couple the principle of mediation between electrodes and biological molecules to overcome irreversible electrode reactions with optical monitoring of the redox state of the sample have recently been developed. The following two sections address the principles and applications of these techniques in the study of biological molecule thermodynamics. 

Ogino,H., Nagata,T. and Ogino,K. (1989) Redox potentials and related thermodynamic parameters of (diaminopolycarboxylato)metal(III/II) redox couples , Inorg. Chem. 28, 3656-3659. 

Ey2,r which will be encountered also when dealing with different voltammetric techniques in the following parts of this chapter, is most often a very good approximation of the thermodynamic quantity, E°. It should be emphasized that a dynamic technique may be invaluable tool for evaluating this parameter, for example whenever one partner of the redox couple is not stable enough to make a potentiometric measurement, but it is over the much shorter time scale of a potentiodynamic measurement. 

FIG. 3 Comparison of potential scales for redox species in aqueous and DCE phases versus SHE. Redox potentials in DCE were experimentally measured against the couple Fc /Fc. The formal redox potential of this couple in DCE was obtained by evaluating the parameters in the thermodynamic cycle given by Eq. (7). 

Equation (6) links, in a simple way, the thermodynamically important stability constants Kox and /Cred of a complex in different oxidation states with experimentally measurable redox potentials EH and EHa. Therefore it provides an easy way to obtain the ratio of KoxIKted, which is a theoretically useful parameter known as the binding enhancement factor (BEF). We propose that a better description for this ratio would be the reaction coupling efficiency (RCE) since binding by so-called molecular switches may be reduced or enhanced, depending upon the particular system involved. Equation (6) also allows the calculation of Kox if Kted is known or vice versa. 

Lever has successfully predicted Mn"/ potentials of 24 Mn-carbonyl complexes containing halide, pseudohalide, isonitrile, and phosphine co-ligands, with additivity parameters derived from the potentials of Ru "/" couples [39]. An important consideration for heteroleptic complexes is the influence of isomerism on redox thermodynamics. For Mn(CO) (CNR)6- complexes, with n = 2 or 3, the Mn"/ potentials for cis/trans and fac/mer pairs differ by as much as 0.2 V [40]. The effect arises from the different a-donor and 7r-acceptor abilities of carbonyl (CO) and isocyanide and their influence on the energy of the highest energy occupied molecular orbital (HOMO). 

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