Formal potential apparent

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. 

Figure 3.12 gives examples of the dependence of the apparent formal potential on the pH for other organic systems (see also p. 465). 

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... 

The results presented here seem to indicate that 1) the local order about ruthenium centers in the polymers is essentially unchanged from that in the monomer complex and 2) that the interaction with the electrode surface occurs without appreciable electronic and structural change. This spectroscopic information corroborates previous electrochemical results which showed that redox properties (e.g. as measured by formal potentials) of dissolved species could be transferred from solution to the electrode surface by electrodepositions as polymer films on the electrode. Furthermore, it is apparent that the initiation of polymerization at these surfaces (i.e. growth of up to one monolayer of polymer) involves no gross structural change. 

To maximize the current limit that could be shunted by redox additives so that the occurrence of such irreversible processes due to overflowing current could be more efficiently suppressed, the redox additive apparently should be present in the electrolyte at high concentrations, and both its oxidized and reduced forms should be very mobile species. Where the criteria for selecting potential redox additives are concerned, these requirements can be translated into higher solubility in nonaqueous media and lower molecular weight. In addition to solubility and diffusion coefficients, the following requirements should also be met by the potential redox additives (1) the formal potential of the redox couple [R]/[0] should be lower than the onset potential for major decom-... 

Cyclic voltammetry can (i) determine the electrochemical reversibility of the primary oxidation (or reduction) step (ii) allow the formal potential, E°, of the reversible process to be estimated (iii) provide information on the number of electrons, n, involved in the primary process and (iv) allow the rate constant for the decomposition of the M"+ species to be measured. Additional information can often be obtained if intermediates or products derived from M"+ are themselves electroactive, since peaks associated with their formation may be apparent in the cyclic voltam-mogram. The idealized behaviour illustrated by Scheme 1 is a relatively simple process more complicated processes such as those which involve further electron transfer following the chemical step, pre-equilibria, adsorption of reactants or products on the electrode surface, or the attack of an electrogenerated product on the starting material, are also amenable to analysis. 

From the analytical equation (6.105) obtained for CV, the study of the current-potential response in these techniques can be performed along with the analysis of the influence of the key variables. First, the effect of the parameter co (Eq. (6.98)) is shown in Fig. 6.15 where the curves are plotted for a spherical electrode of 50 pm radius. Note that large upvalues relate to the situation where the complexes of the reactant species A are more stable than those of species B, whereas the opposite situation is found for small negative potentials when co increases on account of the hindering of the electro-reduction reaction due to the stabilitization of the oxidized species with respect to the reduced ones. According to Eq. (3.289), an apparent formal potential can be defined as follows ... 

Fig. 6.30 CV curves calculated from Eqs. (6.191) to (6.192) for an EE mechanism ( A = O.OlmV, solid lines) and from (6.166) for two independent electron transfers (idashed lines) and an apparent simultaneous two-electron single transfer (dashed-dotted lines). These curves have been calculated for three values of the dimensionless rate constant of the first step, X2h and three values of AE (shown in the curves). iljj42i = 0.1 for the EE mechanism and the two independent electron transfers. For the two-electron single transfer, it has been assumed that the formal potential coincides with the average potential of the EE mechanism and Q = Qy. a = 0.5. T=29S K. Reproduced with permission from [68]...

When the formal potential of the first step is much more positive than that of the second, AE f < — 200mV (Fig. 7.31c), the intermediate species 02 is stable and two well-separated peaks are obtained, centered on the formal potential of each process and with the features of the voltammograms of one-electron electrochemical reaction. When the A7 ° value increases, the stability of the intermediate decreases and the two peaks are closer, and the transition from two peaks to a single peak is observed (AE —71.2 mV). Eventually, when the formal potential of the second electron transfer is much more positive than that of the first one, AE > 200 mV, the characteristics of the voltammograms are those of an apparently simultaneous two-electron electrochemical reaction (Fig. 7.31a). Note that the... 

Potentials of berkelium redox couples are summarized in Table V. Replicate values for the Bk(IV)-Bk(III) couple are in reasonable agreement with one another. The effect of anions that strongly complex Bk(IV) is clearly reflected in the values of the formal potential for the Bk(IV)-Bk(III) couple and can be seen in the Nemst equation plots for the couple in various media given in Fig. 9 (227). Values of 1.36 (220, 223) and 1.12 V (227) have been reported for the couple in sulfuric and phosphoric acid solutions, respectively. Carbonate ions, apparently... 

Conditional (apparent) equilibrium constants - Equilibrium constants that are determined for experimental conditions that deviate from the standard conditions used by convention in - thermodynamics. Frequently, the conditional equilibrium conditions refer to - concentrations, and not to - activities, and in many cases they also refer to overall concentrations of certain species. Thus, the formal potential, i.e., the conditional equilibrium constant of an electrochemical equilibrium, of iron(II)/iron(III) may refer to the ratio of the overall concentrations of the two redox forms. In the case of complex equilibria, the conditional - stability constant of a metal ion Mm+ with a ligand L" refers to the overall concentration of all complex species of Mm+ other than Conditional equilibrium... 

Formal potential — Symbol Efr (SI Unit V), has been introduced in order to replace the standard potential of -> cell reaction when the values of - activity coefficients of the species involved in the cell reaction are unknown, and therefore concentrations used in the equation expressing the composition dependence of ceii instead of activities. It also involves the activity effect regarding the -+ standard hydrogen electrode, consequently in this way the formal electrode potential is also defined. Formal potentials are similar to conditional (apparent) equilibrium constants (-> equilibrium constant), in that, beside the effect of the activity coefficients, side reaction equilibria are also considered if those are not known or too complex to be taken into account. It follows that when the logarithmic term which contains the ratio of concentrations in the -> Nernst... 

Fig. 20. Variation of the product of the apparent standard rate constant Atq and the viscosity // of (O) the aqueous or ( ) the organic solvent phase with the formal potential difference the transfer of acetylcholine across the (O) (water-tsucrose)-1,2-dichloroethane or ( ) water-(nitrobenzene-Ketrachloromethane) interface. Concentration of sucrose (wt.%) (1) 4, (2) 10, (3) 20, (4) 30, and (5) (40) data taken from [124]. Concentration of tetrachloromethane (wt.%) (T) 10, (2 ) 23, (3 ) 47, (4 ) 57 and (5 ) 71 data taken from [139]. The broken line corresponds to a = 0.5.

Note that the only difference in the expressions for the two sets of a values is the two different formal potentials, = 0.68 V and Eq = 1.44 V in 1 M H2SO4. The effect of this difference will be apparent in the a-plots. Since n= 1 for both couples, it does not appear in these equations for a. 

Another consequence of the anionic nature of the DNA films is the restricted transfer of ions across the monolayer-solution interface. The resulting interfacial Donnan potentials are expected to shift the apparent formal potentials of redox molecules bound within the film, by analogy to polyelectrolyte film coatings.In the general case of an -electron, m-proton redox couple (Equation 5-3), the apparent formal potential shifts as a function of both pH and cation concentration according to 5-4. 

Here E app is the apparent formal potential, E is the formal potential in solution, z is the charge of the cation in the supporting electrolyte, Q is the concentration of the cation in solution, and Q is the concentration of the cation within the film, which is effectively constant at low loadings of cationic reporters.) As illustrated in Fig. 5-9, a plot of vs. log[KCl] for the reduction of Ru(NH3)fA is linear with slope of 60 mV/log unit, in excellent agreement with the 59 mV slope predicted by eqn. 5-4 (7 = 25 °C). 

Figure 5-9. Plot of the apparent formal potential of Ru(NI at a DNA-modified electrode. The concentration of Ru(NH3) " was adjusted such that I j , remained -10-20 pmol cm or approximately 5-10% of the value at saturation.

From the foregoing discussion, it is apparent that a study of a given biological molecule by mediated ottle will require access to a mediator having the desired formal potential as well as optical properties in both the oxidized and reduced forms which do not interfere with the optical response of the biological sample. Many mediators suitable for use in ottle studies of biological molecules have been described. 

Sokol et showed that the voltammetric response of cytochrome C3 arises from four relatively independent hemes with closely spaced formal potentials. Digital simulation results fitted to experimental data indicated four independent heme redox centers having formal potentials of -0.226, -0.278, -0.298, and -0.339 V. Each heme is apparently chemically unique and does not interact significantly with the other hemes in electron transfer. 

Table 10-4. Formal potentials of SAM of MNC and anodic peak potentials, current densities and apparent rate constants (A at) for the electrocatalytic oxidation of NADH at SAM of 1 in different supporting electrolytes. ...

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