Half-wave potentials reactions from

Figure 11.19. Correlation between the second-order rate constants for reactions of substituted phenoxide anions with chlorine dioxide and estimated values of AG°. The circles are experimental data and the curves represent fits of the data to the Marcus equation. The solid curve corresponds to equation 46 (X = 30.1 kcal moP ). AG° (and log K) values were calculated from electrode half-wave potentials. (Adapted from Tratnyek and Hoigne, 1994.)...

If the shape of the wave shows a reversible process, when the limiting current is diffusion controlled, but the half-wave potentials differ from those measured at the equilibrium conditions and are dependent on the drop-time ( x/2 = const. 2-303RTInFlogiff, then the product of the reversible electrode reaction is inactivated by a fast chemical reaction, e.g. in the case of the anodic waves for ascorbic acid.< > > It was supposed that the inactivation reaction is the hydration of dehydroascorbic acid, but the polarographic behaviour of dehydroascorbic acid does not agree with this simple explanation. 

Using these assumptions and conventions, Imoto and co-workers have correlated a number of series of reactions of thiophenes and furans. The reactions studied are the acid-base equilibria pK values) and the acid catalyzed methylations (thiophenes only) of thiophene-and furan-carboxylic acids and the alkaline hydrolyses of their ethyl esters the side-chain bromination of the a-acetylthiophenes, and the a-mercuration of thiophenes and the polarographic half-wave potentials of the methyl esters of thiophene- and furan-carboxylic acids and of nitrothiophenes. The pK values were determined and the ester hydrolyses studied for all three substitution orientations in the thiophene series. For the 4-R-2-Y and 5-R-2-Y series, the p-values do not appear significantly different and the data could probably be combined into a single series unfortunately, however, no limits of accuracy are reported for the p-values, and some of the raw data are not readily available so recalculation is not easily possible. For the 5-R-3-Y series the p-values deviate considerably from the other values however, whereas they are higher for the pK values, they are lower for the ester hydrolyses, and it is possible that the differences are neither systematic nor significant. 

The oxidation or reduction of a substrate suffering from sluggish electron transfer kinetics at the electrode surface is mediated by a redox system that can exchange electrons rapidly with the electrode and the substrate. The situation is clear when the half-wave potential of the mediator is equal to or more positive than that of the substrate (for oxidations, and vice versa for reductions). The mediated reaction path is favored over direct electrochemistry of the substrate at the electrode because, by the diffusion/reaction layer of the redox mediator, the electron transfer step takes place in a three-dimensional reaction zone rather than at the surface Mediation can also occur when the half-wave potential of the mediator is on the thermodynamically less favorable side, in cases where the redox equilibrium between mediator and substrate is disturbed by an irreversible follow-up reaction of the latter. The requirement of sufficiently fast electron transfer reactions of the mediator is usually fulfilled by such revemible redox couples PjQ in which bond and solvate... 

The ET reaction between aqueous Fe(CN)g and the neutral species, TCNQ, has been investigated extensively with SECM, in parallel with microelectrochemical measurements at expanding droplets (MEMED) [84], which are discussed in Chapter 13. In the SECM studies, a Pt UME in the aqueous phase generated Fe(CN)g by reduction of Fe(CN)g. TCNQ was selected as the organic electron acceptor, because the half-wave potential for TCNQ ion transfer from DCE to water is 0.2 V more positive than that for ET from Fe(CN)g to TCNQ [85]. This meant that the measured kinetics were not compromised by TCNQ transfer from DCE to the aqueous phase within the potential window of these experiments. 

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.)... 

For reversible transfer reactions of a simple ion, may be expressed in terms of the half-wave potential, A (pi/2, by direct transposition from the case of reversible eleetron transfer at a metal electrode-electrolyte solution interface [234] ... 

Finally, a remark should be made on the effect of the scan rate an increase in the scan rate, e.g., from 50 through 100 to 200mV s 1, causes a sharper and apprecially higher peak, as expected. If the electrode reaction is reversible, the half-wave potential, Up/2, remains nearly unaltered, otherwise there is a shift to the right (more negative in reductive LSV). It should be borne in mind that in a follow-up reaction such as the system EC (see p. 124) an increase in scan rate may cause a transition from irreversibility to apparent reversibility if the charge-transfer reaction E becomes predominant. 

The constants characterizing the electrode reaction can be found from this type of polarization curve in the following manner. The quantity k"e is determined directly from the half-wave potential value (Eq. 5.4.27) if E0r is known and the mass transfer coefficient kQx is determined from the limiting current density (Eq. 5.4.20). The charge transfer coefficient oc is determined from the slope of the dependence of In [(yd —/)//] on E. 

FIGURE 2.48. Electrochemical reduction of the diphenylmethyl radical produced by the reaction of diphenylmethyl chloride by photo-injected electrons in dimethylformamide in the presence of increasing amounts of benzimidazole. Variations of the half-wave potential the concentrations of acid added, from bottom to top, 0, 0.018, 0.049, 0.11, 2.8, 6.7 mM. Solid lines, simulations for each acid concentration. Adapted from Figure 1 of reference 50b, with permission from the American Chemical Society. 

The competition between substrate and cosubstrate also shows up in the variations of the half-wave potential. The wave is centered on the standard potential pQ when reaction (2) is the RDS (i.e., when k2Cp(l/k2>2+ l/ i, 2 + 1/kiCg) —>0). The wave then shifts toward positive values as kinetic control passes from reaction (2) to reaction (1), with, for example, decreasing substrate concentration. When these conditions are fulfilled [i.e., when fc2Cp(l/k2>2 + l/h, 2 + 1/kiCg) — oo], the wave equation becomes... 

E1/2 being the reversible half-wave potential of the electron-transfer reaction with respect to ferrocene. The suggested offset value, however, differs somewhat from group to group. 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

Fig. 5 Electrochemical stepwise electron-transfer-bond-breaking reactions. Competition between electron transfer, bond breaking and diffusion. E i2, Half-wave potential RX/RX- standard potential. The horizontal scale is given both in terms of X and k. The number on each curve is the value of A, and the value of log ky is given in parentheses. 5 is taken as 10 cm and D as 10" cm s" . (Adapted from Andrieux et al., 1978.)...

The outcome of the competition is represented in Fig. 5 in terms of the location of the half-wave potential of the RX reduction wave (i.e. the current-potential curve), relative to the standard potential of the RX/ RX- couple, E° (Andrieux et al., 1978). As concerns the competition, three main regions of interest appear in the diagram. On the left-hand side, the follow-up reaction is so slow (as compared to diffusion) that the overall process is kinetically controlled by the parameter A, i.e. by electron transfer and diffusion. Then, going upward, the kinetic control passes from electron transfer to diffusion. In the upper section d in the lower section... 

When the follow-up reaction becomes so fast that the thickness of the reaction layer comes close to molecular dimensions, the above analysis breaks down because the diffusion of RX- ceases to obey Pick s law. An extreme situation in this connection is when the reaction is so fast that RX- has no time to diffuse away from the electrode and collapses instead at the surface. The follow-up reaction should then be viewed as a surface reaction and the half-wave potential is given (Saveant, 1980b, 1983) by (55), where... 

Nevertheless, the mid-peak potentials determined by cyclic voltammetry and other characteristic potentials obtained by different electroanalytical techniques (such as pulse, alternating current, or square wave voltammetries) supply valuable information on the behavior of the redox systems. In fact, for the majority of redox reactions, especially for the novel systems, we have only these values. (The cyclic voltammetry almost entirely replaced the polarography which has been used for six decades from 1920. However, the abundant data, especially the half-wave potentials, 1/2, are still very useful sources for providing information on the redox properties of different systems.)... 

This chapter gives a selected compilation of the standard and other characteristic (formal, half-wave) potentials, as well as a compilation of the constant of solubility and/or complex equilibria. Mostly, data obtained by electrochemical measurements are given. In the cases when reliable equilibrium potential values cannot be determined, the calculated values (calcd) for the most important reactions are presented. The data have been taken extensively from previous compilations [5-13] where the original reports can be found, as well as from handbooks [13-16], but only new research papers are cited. The constant of solubility and complex equilibria were taken from Refs 6-11,13,17-21. The oxidation states (OSs), ionization energies (IBs) (first, second, etc.), and electron affinities (EAs) of the elements and the... 

Equation (4.5) is also valid in this case. Reactions of this type are realized in polarography at a dropping mercury electrode, and the standard potentials can be obtained from the polarographic half-wave potentials ( 1/2)- Polarographic studies of metal ion solvation are dealt with in Section 8.2.1. Here, only the results obtained by Gritzner [3] are outlined. He was interested in the role of the HSAB concept in metal ion solvation (Section 2.2.2) and measured, in 22 different solvents, half-wave potentials for the reductions of alkali and alkaline earth metal ions, Tl+, Cu+, Ag+, Zn2+, Cd2, Cu2+ and Pb2+. He used the half-wave potential of the BCr+/BCr couple as a solvent-independent potential reference. As typical examples of the hard and soft acids, he chose K+ and Ag+, respectively, and plotted the half-wave potentials of metal ions against the half-wave potentials of K+ or against the potentials of the 0.01 M Ag+/Ag electrode. The results were as follows ... 

---