Potential scale, solvent independent

Just as the pH windows are useful in discussing the applicability of solvents as media for acid-base reactions, the potential windows (sometimes called electrochemical windows) are convenient to predict the usefulness of solvents as media for redox reactions. It is desirable that the potential windows are expressed based on a common (solvent-independent) potential scale, like the pH windows based on a common (solvent-independent) pH scale (Fig. 3.6). 

Figure 4.8 shows the potential windows obtained at a bright platinum electrode, based on the Fc+/Fc (solvent-independent) potential scale. Because of the overpotentials, the window in water is 3.9 V, which is much wider than the thermodynamic value (2.06 V). The windows for other solvents also contain some overpotentials for the reduction and the oxidation of solvents. However, the general tendency is that the negative potential limit expands to more negative values with the decrease in solvent acidity, while the positive potential limit expands to more positive values with the decrease in solvent basicity. This means that solvents of weak acidity are difficult to reduce, while those of weak basicity are difficult to oxidize. This is in accordance with the fact that the LUMO and HOMO of solvent molecules are linearly related with the AN and DN, respectively, of solvents [8]. 

The formal potential of the Fe(III)/Fe(II) couple in AN is + 1.57 V vs Ag/O.OIM Ag+(AN), being about 1.3V more positive than in aqueous solutions in a common (solvent-independent) potential scale. This is because Fe(II) in AN is solvated strongly, Fe(III) only moderately. Fe(III) in AN is a strong oxidizing agent. Both Fe(III) and Fe(II) react with moisture in the air and are easily hydrated. The po-... 

In order to use Eq. (6) in electrochemical studies of ion solvation, the problems related to the liquid junction potential have been presented in Sec. 2.2.2. Equation (11) may also be used in such studies, but the measured potentials should be expressed versus the same solvent-independent reference electrode. Such electrodes, which give a basis for the formation of a uniform scale of electrode potentials in different solvents, are available. A scale of this kind is also needed for a correlation of equilibrium potentials (E° 1/2) of electrode systems in various solvents. 

Since the values of AG,r obtained in various solvents for the ions under consideration sometimes differ, one can also obtain slightly different values. We also tried [235] to analyze the kinetic data related to anodic and to cathodic processes separately, by considering the changes of the cathodic rate constant (kfl,) or anodic rate constant (Arth) at constant potential on a solvent-independent scale. Such an analysis is based of the following equations for cathodic (Eq. (57)) and anodic (Eq. (58)) reactions ... 

In conclusion, there is no fully satisfactory system for the construction of a unified potential scale which could be used for mixed solvents of different compositions. In fact, the scales used are the same as those applied for pure solvents, but in the case of mixed solvents the extrathermodynamic assumption may be even less strictly obeyed, especially if there are even small preferential interactions of the reference electrode components with one of the solvents of the mixture. In our work we used the Foe /Foe system as a solvent-independent reference electrode. The consequent use of one reference electrode in a series of experiments with mixed solvents of different composition should diminish the error. 

Superscripts m and w relate to mixed solvent and water, respectively, and the rate constants (Arth) are calculated at constant potential, on the solvent-independent scale. Such formal adoption of Eqs. (57) and (58) gives equations which can be valid only when there is no difference between the composition of the bulk and the surface phases, as in pure solvents where the validity of Eqs. (57) and (58) was proved. 

In practice the main requirement of a reference electrode is that it has a stable potential and that it is not substantially polarised during the experiment. Hence it is common to use the highly convenient aqueous calomel electrode in many experiments in all solvents. Even so, a very wide range of reference electrodes have been used in non-aqueous solvents. Where there is any doubt about the potential of the reference electrode, it is recommended to check the potential of a standard couple, e.g. ferrocene/ferrocinium ion, by cyclic voltammetry. This is also the easiest way to compare potential scales in different solvents it is assumed that the potential of this couple, where both halves of the couple are poorly solvated, is independent of solvent [2j. 

Shortcomings of the choice of the equilibrium state as the electrical reference point in the evaluation of the temperature effect on the rate of electrode reactions, and consequently of the overpotential as an experimental substitute for A(A0) in the WE-RE cell at various temperatures, have been discussed in the previous section. Hence, another reference point should be sought. From a theoretical point of view, the choice is unambiguous—it is the zero point on the relative electrode potential scale, defined by the SHE convention. Basically, this is also an equilibrium state, but of a single reaction selected by convention, namely, the reduction of two hydrogen ions to molecular hydrogen. The value of A0 at the interface when this reaction is held at equilibrium, assuming all species involved are in standard thermodynamic states, is fixed by the SHE convention as zero. The same convention associates additional properties with this reference state temperature, solvent, and solute Independence. Formally, the properties of the SHE satisfy the principal theoretical requirements for the electrical reference point in the evaluation of the effect of temperature on the rate of electrode reactions. 

The quantity Pb is independent of the concentration scale used, being a true property of the solntion, bnt the three standard chemical potentials Pb x), PbV) Pb°°(c) are not eqnal. Conseqnently, differences between the standard chemical potentials of a solnte in the two liqnid phases employed in solvent extraction also depend on the concentration scale nsed. Thus, Pb defined in Eq. (2.23) is specific for the rational concentration scale, and does not equal corresponding quantities pertaining to the other scales. Therefore, Eq. (2.30) might be rewritten with a subscript (x), to designate the rational scale, [i.e., with Z)b(x) and Pb(x)]- Similar expressions would then be... 

Several approaches have been made (see Reference 96 and references cited therein) to establish a quantitative, empirical scale describing the influence of a large collection of ligands of wide structural diversity on the redox potentials of transition metal complexes. All the approaches are based on the assumption that the relative contribution of each ligand to the redox potential of a transition metal complex is independent of the presenee of other ligands, the identity of the transition metal, the oxidation and spin states of this metal, the solvent etc. . Hence the approaches resemble the empirical use of substituent constants in the Hammett relation in organic chemistry. 

Implicit in the recommendations of Pytkowicz and co-workers for pH measurements in seawater is the belief that the liquid junction potential between seawater of a given salinity and a saturated solution of potassium chloride is independent of the nature and concentration of solutes present at low concentrations in the seawater solvent. This would indeed be the case if seawater is a true constant ionic medium. Hawley and Pytkowicz (5) have estimated that this potential difiFerence amounts to 3.2 mV. As already indicated, this constancy of the liquid junction potential is essential for establishing an experimental scale of pmn. 

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