Formal electrode potentials

Parameter E° in Eqs. (3.30) and (3.32) is called the standard electrode potential it corresponds to the value of electrode potential that is found when the activities of the components are unity. Values E° differ somewhat from values E°. For a more distinct differentiation between these parameters, E° is called the formal electrode potential. 

Obviously 0electrode potential we obtain... 

Very often, the value of the formal electrode potential E 0 is not known for an irreversible electrode reaction. The overpotential f] cannot, therefore,... 

The charge transfer reaction (5.2.39) is characterized by the formal electrode potential the conditional rate constant of the electrode reaction kf and the charge transfer coefficient aly while the reaction (5.2.40) is characterized by the analogous quantities E2y kf and a2. If the rate constants of the electrode reactions, which are functions of the potential, are denoted as in Eqs (5.2.39) and (5.2.40) and the concentrations of substances Au A2 and A3 are cly c2 and c3, respectively, then... 

This value is close to the formal electrode potential and independent of the convection velocity. The plot of log(/d — j)/j versus E is linear with the slope nF/2.303RT. 

C = concentration of the active species in the bulk of the solution E° = formal electrode potential of the couple Ox/Red. It differs from the thermodynamic standard potential E° by a factor related to the activity coefficients of the two partners Ox and Red ... 

We must however note that even if one partner of a redox couple does not possess a high propensity to exchange electrons with the electrode (i.e. low k°), we can force it to increase its electron transfer rate by applying to the working electrode a potential value higher than the formal electrode potential Eo of the couple itself (i.e. more negative for a reduction process more positive for an oxidation process). In fact, as seen ... 

As noted above, often the kinetic equations are written as a function of i0 rather than k°. One of the advantages of using i0 is that the faradaic current can be described as a function of the difference between the potential applied to the electrode, E, and the equilibrium potential, Eeq, rather than with respect to the formal electrode potential, E01, (which, as previously mentioned, is a particular case of equilibrium potential [COx(0,f) = CRed(0,t)], and at times may be unknown). In fact, dividing the fundamental expression of i by that of i0 one obtains ... 

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 ... 

If the rate of the electron transfer is lower than that of the mass transport, or in the case of irreversible processes (see Chapter 1, Section 4.3), the potential at which the reduction reaction Ox + neT— Red takes place can be much more cathodic than the formal electrode potential of the couple Ox/Red. In addition, commonly the separation between the forward peak and the reverse peak is so large that the reverse peak is undetected. 

Standard potential of the second electron transfer more cathodic than that of the first electron transfer (AE0 negative). One can consider the case where the formal electrode potential of the second couple is more cathodic, by at least 180 mV, with respect to the first couple (which has, for example, E01 = 0.00 V). If kf is low (compared to the intervention times of cyclic voltammetry i.e. if k[< n F- v/R T), the response will be due to the first electron transfer process, without complications caused by the following chemical reaction. As increases, the second process will have increasing effect up to the limiting case in which kt >n-F-v/R-T. In this limiting case the voltammogram will display two forward peaks, but only the second electron transfer will exhibit a return peak. 

The peak potential Ep is correlated with the formal electrode potential E° of the couple Ox/Red by the expression ... 

As mentioned, DPV is particularly useful to determine accurately the formal electrode potentials of partially overlapping consecutive electron transfers. For instance, Figure 40 compares the cyclic voltammogram of a species which undergoes two closely spaced one-electron oxidations with the relative differential-pulse voltammogram. As seen in DPV the two processes are well separated. 

As it happens in DPV, if A Sw is small (about 50fn mV), the peak-potential for a reversible process virtually coincides with the formal electrode potential. 

It is often useful to carry out voltammetric measurements at low temperatures in order to evaluate both the stability of an electrogenerated species (the decrease in temperature will slow down the kinetics of any decomposition processes of the species formed in the electrode process) and the variation in formal electrode potential of a redox couple as a function of temperature. The latter point regards thermodynamic considerations of the redox processes, which will be discussed in Chapter 13, Section 3. 

Table 2 Formal electrode potentials (V vs. SCE, at 25° C) and peak-to-peak separation (mV) for the couple [Fe(t]5-C5H5)2]/[Fe(t]5-C5H5)2] in different solutions. Platinum working electrode (measured in our laboratory)...

Table 6 Formal electrode potential (V vs. SCE, at 25° C) for the one-electron oxidation of a few substituted ferrocenes. Dichloromethane solution [NBu4][CIO4] supporting electrolyte...

Table 8 Formal electrode potentials ( V, vs. SCE), and relative separation (V), for the two one-electron oxidations of a few diferrocenyl molecules...

Table 11 Formal electrode potentials (V vs. SCE) for the redox processes exhibited by a few cobaltocenes in different solvents...

Table 4 Formal electrode potentials (V, vs. Ag/AgCl) for the redox changes exhibited by [V bipy)3J2+ and [V(pheri)3J2+...

Table 14 Formal electrode potentials (V, vs. SCEj for the reduction processes exhibited by complexes [NiX(triphos) ]+ in MeCN solution...

Table 5 Formal electrode potentials (V, vs. SCE) andpeak-to-peak separation (mV) for the fullerene-centred reductions of [MfCsolCyo)(CO)2 (phen) (dbm)] in CH2Cl2 solution. T= —10° C...

Table 7 Formal electrode potentials ( V, vs. AgjAgCl) for the reduction processes of [Fe2(H S)2(h2-C6o)(CO)6] m 1,2-dichlorobenzene solution...

Table 1 Formal electrode potentials (V vs. NHE) for the one-electron reduction of substrate-free cytochrome P450cam under different experimental conditions...

Another interesting blue protein is stellacyanin (FW = 20 000) from the Japanese lacquer tree Rhus vernicifera, in which, with respect to the other cupredoxins, glutamine replaces the methionine ligand.64 Stellacyanin also bears an overall positive charge (p/=9.9). It, therefore, gives a reversible Cu(II)/Cu(I) response at a glassy carbon electrode in aqueous solution (pH 7.6).61 The formal electrode potential of the Cu(II)/Cu(I) reduction (E01 = + 0.18 V vs. NHE) is the lowest among cupredoxins. 

Figure 1 Dependence of the formal electrode potentials of the Co(II)/Co(III) oxidation for [Co(R-X-Saldpt) ] derivatives on the electronic effects of the substituents (M) R=H (%) R=Me...

These complexes undergo two consecutive one-electron reductions with features of chemical and electrochemical reversibility both in MeCN and CH2C12 solution.2 Table 2 summarizes the formal electrode potentials for the first reduction process and the sums of the Taft constants of the various substituents for each complex. 

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