The Formal Potential

Substituting these concentrations into equation 9.17 along with the formal potential for the Fe 3-/pg2+ half-reaction from Appendix 3D, we find that the potential is... 

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

The standard redox potential is 1.14 volts the formal potential is 1.06 volts in 1M hydrochloric acid solution. The colour change, however, occurs at about 1.12 volts, because the colour of the reduced form (deep red) is so much more intense than that of the oxidised form (pale blue). The indicator is of great value in the titration of iron(II) salts and other substances with cerium(IV) sulphate solutions. It is prepared by dissolving 1,10-phenanthroline hydrate (relative molecular mass= 198.1) in the calculated quantity of 0.02M acid-free iron(II) sulphate, and is therefore l,10-phenanthroline-iron(II) complex sulphate (known as ferroin). One drop is usually sufficient in a titration this is equivalent to less than 0.01 mL of 0.05 M oxidising agent, and hence the indicator blank is negligible at this or higher concentrations. 

The standard or formal potential of ferroin can be modified considerably by the introduction of various substituents in the 1,10-phenanthroline nucleus. The most important substituted ferroin is 5-nitro-l,10-phenanthroline iron(II) sulphate (nitroferroin) and 4,7-dimethyl-1,10-phenanthroline iron(II) sulphate (dimethylferroin). The former (E° = 1.25 volts) is especially suitable for titrations using Ce(IV) in nitric or perchloric acid solution where the formal potential of the oxidant is high. The 4,7-dimethylferroin has a sufficiently low formal potential ( e = 0.88 volt) to render it useful for the titration of Fe(II) with dichromate in 0.5 JVf sulphuric acid. 

Mention should be made of one of the earliest internal indicators. This is a 1 per cent solution of diphenylamine in concentrated sulphuric acid, and was introduced for the titration of iron(II) with potassium dichromate solution. An intense blue-violet coloration is produced at the end point. The addition of phosphoric(V) acid is desirable, for it lowers the formal potential of the Fe(III)-Fe(II) system so that the equivalence point potential coincides more nearly with that of the indicator. The action of diphenylamine (I) as an indicator depends upon its oxidation first into colourless diphenylbenzidine (II), which is the real indicator and is reversibly further oxidised to diphenylbenzidine violet (III). Diphenylbenzidine violet undergoes further oxidation if it is allowed to stand with excess of dichromate solution this further oxidation is irreversible, and red or yellow products of unknown composition are produced. 

The equilibrium potential for a given reaction is related to the formal potential ... 

FIGURE 2-3 Concentration distribution of the oxidized and reduced forms of the redox couple at different times during a cyclic voltammetric experiment corresponding to the initial potential (a), to the formal potential of the couple during the forward and reversed scans (b, d), and to the achievement of a zero reactant surface concentration (c). 

The position of the peaks on the potential axis (Ep) is related to the formal potential of the redox process. The formal potential for a reversible couple is centered between E and E ... 

Example 2-2 The following cyclic voltammogram was recorded for a reversible couple Calculate the number of electrons transferred and the formal potential for the couple. 

The potential at which the current is one-half of its limiting value is called the half-wave potential, El/1. The half-wave potential (for electrochemically reversible couples) is related to the formal potential, E°, of the electroactive species according to... 

Voltammograms of a polythiophene film showing reasonably reversible electrochemistry of both types are shown in Fig. 2.M The formal potentials (average of the anodic and cathodic peak potentials) for p- and n-doping can provide useful estimates of the energies of the polymer s valence and conduction bands and its band gap35... 

Rotating-disk voltammetry is the most appropriate and most commonly employed method for studying mediation. In most systems that have been studied, there has been little penetration of the substrate in solution into the polymer film. This can be demonstrated most easily if the polymer film is nonconductive at the formal potential of the substrate. Then the absence of a redox wave close to this potential for an electrode coated with a very thin film provides excellent evidence that the substrate does not penetrate the film significantly.143 For cases where the film is conductive at the formal potential of the substrate, more subtle argu-... 

The electrochemical characteristics of an electroactive ion immobilized in a conducting polymer film depend on whether the film is conductive at the formal potential of the ion.243... 

If the film is nonconductive, the ion must diffuse to the electrode surface before it can be oxidized or reduced, or electrons must diffuse (hop) through the film by self-exchange, as in regular ionomer-modified electrodes.9 Cyclic voltammograms have the characteristic shape for diffusion control, and peak currents are proportional to the square root of the scan speed, as seen for species in solution. This is illustrated in Fig. 21 (A) for [Fe(CN)6]3 /4 in polypyrrole with a pyridinium substituent at the 1-position.243 This N-substituted polypyrrole does not become conductive until potentials significantly above the formal potential of the [Fe(CN)6]3"/4 couple. In contrast, a similar polymer with a pyridinium substituent at the 3-position is conductive at this potential. The polymer can therefore mediate electron transport to and from the immobilized ions, and their voltammetry becomes characteristic of thin-layer electrochemistry [Fig. 21(B)], with sharp symmetrical peaks that increase linearly with increasing scan speed. 

Added stability in PEC can be attained through the use of non-aqueous solvents. Noufi et al. [68] systematically evaluated various non-aqueous ferro-ferricyanide electrolytes (DMF, acetonitrile, PC, alcohols) for use in stabilizing n-CdSe photoanodes. Selection of the solvent was discussed in terms of inherent stability provided, the rate of the redox reaction, the tendency toward specific adsorption of the redox species, and the formal potential of the redox couple with respect to the flat band potential (attainable open-circuit voltage). On the basis of these data, the methanol/Fe(CN)6 system (transparent below 2.6 eV) was chosen as providing complete stabilization of CdSe. Results were presented for cells of the type... 

FIG. 21 Plot of log ki2 vs. AEi/2 showing the dependence of ET rate on the driving force for the reaction between ZnPor and four aqueous reductants. The difference between the half-wave potentials for an aqueous redox species and ZnPor, AE-i/2 = AE° + A°0, where AE° is the difference in the formal potentials of the aqueous redox species and ZnPor and A° is the potential drop across the ITIES. The solid line is the expected behavior based on Marcus theory for X = 0.55 eV and a maximum rate constant of 50 cm s M . (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)... 

However, under most conditions the activity coefficients cannot be neglected, certainly for a single redox couple where the ox/red concentration ratio cannot be simply calculated from the true standard potential and the potential directly observed. In order to overcome this difficulty the concept of the formal potential was introduced, which represents a formal standard potential E ° measured in an actual potentiometric calibration and obeying the Nernst equation, E = E ° + (0.05916/n) log ([ox]/[red]) at 25° C, E"0 must meet the conditions under which the analytical measurements have to be made. Sometimes the formal potential values are decisive for the direction of the reaction between two redox couples even when the E° values do not differ markedly10. 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

The formal potential of a reduction-oxidation electrode is defined as the equilibrium potential at the unit concentration ratio of the oxidized and reduced forms of the given redox system (the actual concentrations of these two forms should not be too low). If, in addition to the concentrations of the reduced and oxidized forms, the Nernst equation also contains the concentration of some other species, then this concentration must equal unity. This is mostly the concentration of hydrogen ions. If the concentration of some species appearing in the Nernst equation is not equal to unity, then it must be precisely specified and the term apparent formal potential is then employed to designate the potential of this electrode. 

Standard redox potentials can be determined approximately from the titration curves for suitably selected pairs of redox systems. However, these curves always yield only the difference between the standard potentials and a term containing the activity coefficients, i.e. the formal potential. The large values of the terms containing the activity coefficients lead to a considerable difference between the formal potential and the standard potential (of the order of tens of millivolts). 

An electrode reaction in which the oxidized form accepts more than one electron usually proceeds as a series of one-electron reaction steps. As will be demonstrated below, if the formal potentials of these partial electrode reactions satisfy certain conditions, then the electrode reaction simulates the transfer of several electrons in one step (Eq. 5.2.5) and obeys Eq. (5.2.24). An example is the two-electron reaction of substance Au converted to substance A3 by the transfer of two electrons, where the reaction occurs through the unstable intermediate A2 ... 

The formal potentials ( ° ) of the three kinds of SODs were found to be dependent on solution pH as displayed in Fig. 6.6. As shown, the formal potential of bovine erythrocyte Cu, Zn-SOD decreases linearly with increasing solution pH with a slope of ca. -60mV/pH from pH 5.8 to pH 9.5 (curve b), indicating one proton and one electron are included in the electrode reaction of Cu, Zn-SOD, which is similar to previously proposed enzymatic catalytic mechanistic scheme of the Cu, Zn-SOD [139— 144], In contrast, the pH dependency of Fe-SOD from E. coli was complicated (curve a) the formal potential changes linearly with solution pH in a range from pH 5.8 to 8.5 with a slope of ca. -60mV/pH, and becomes pH-independent at above pH > 8.5. Previous studies have observed that the Fe (III) form of the protein ionizes with an apparent pKa of 9.0 0.3 and such ionization effect has been interpreted in terms of hydrolysis of a bound water molecule with p/<"a of ca. 8.5 [145], The C -pII profile of... 

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