Indicators half-wave potentials

Two waves arise with the indicated half-wave potentials. The wave height for the process P2 + Zb -> P3 occurring at the more negative potential will obviously depend on the rate at which electroactive P2 is generated from Pi, which is itself assumed to be electroinactive. Examples where this type of behavior arises are the reductions of a-substituted ketones, aromatic bicarbonyl compounds such as p-diacetylbenzene, terephthaldialdehyde and a,/8-unsaturated ketones. Restricting ourselves to one type of example discussed by Zuman, " the following is the scheme for reduction of an a-substituted... 

As already indicated, quantitative conventional d.c. polarography is limited at best to solutions with electrolytes at concentrations greater than 10-5M, and two different ions can only be investigated when their half-wave potentials differ by at least 0.2 V. These limitations are largely due to the condenser current associated with the charging of each mercury drop as it forms, and various procedures have been devised to overcome this problem. These include ... 

The half-wave potentials of (FTF4)Co2-mediated O2 reduction at pH 0-3 shifts by — 60 mV/pH [Durand et ah, 1983], which indicates that the turnover-determining part of the catalytic cycle contains a reversible electron transfer (ET) and a protonation, or two reversible ETs and two protonation steps. In contrast, if an irreversible ET step were present, the pH gradient would be 60/( + a) mV/pH, where n is the number of electrons transferred in redox equilibria prior to the irreversible ET and a is the transfer coefficient of the irreversible ET. The —60 mV/pH slope is identical to that manifested by simple Ee porphyrins (see Section 18.4.1). The turnover rate of ORR catalysis by (ETE4)Co2 was reported to be proportional to the bulk O2 concentration [Collman et ah, 1994], suggesting that the catalyst is not saturated with O2. 

Voltametric studies (34, 37) have revealed the electron transfers Mo(R2c/fc)4 Mo(R2C fc)4° MoCRjdfc) Mo(R2half wave potentials for the processes 0 +1 and + - + 2 depend upon the nature of R. The dependency can be described by the Taft relation =p2a where a is the Taft constant for the N-bonded substituents R. The rather low values of p indicate that the redox orbitals have mainly a metal character, the mixing of these orbitals with those of the ligands is rather small. This conclusion is in accordance with the interpretation of the electronic spectra and the results of Extended Hiickel MO calculations (37). Only the compound with R = Ph does not fit into the Taft relation, the Ej 2 value is lower than... 

The electron transfer Au(R2voltametric measurements 163). The half-wave potentials of the quasi-reversible process depends on the substituent R according to the Taft relation, as was described for Mo, W and Mn 37). The value of p decreases in the series Au > Mn > Mo = W, which indicates that in this sequence the mixing of ligand orbitals into the redox orbital decreases. The dominant ligand character of the unpaired electron MO in Au(R2dtc)2 relative to those in copper and silver compounds is found from Extended Hiickel MO calculations, as will be discussed later on. 

The FR polarograms of 5-nitrobenzimidazole in a buffer of pH 7.0 are shown in Fig. 33. The FR polarograms are obtained on the negative side of the abscissa, indicating that a should be less than 0.5. The FR summit peak is obtained at the half-wave potential -0.65 V and it is conspicuous up to 100 Hz. As the reaction involves a six-electron charge transfer, it may be assigned the following mechanism ... 

Figure 6.9 Polarogram showing a time-averaged current, i.e. redrawn without the sawtoothed effect caused by the cyclic nature of the mercury drops the half-wave potential, 1/2, and the residual current are also indicated. The magnitude of the diffusion current, 7a, is determined with respect to the residual current.

Almost all reactions of alkylidenecycloproparenes lead to opening of the cyclopropane ring. A notable exception to this is the reversible electrochemical reduction of237 and 240 which leads to the stablfe radical anions 396 and 397, with half-wave potentials of -2.32 and -1.93 V, respectively, and their oxidation to the quasi-stable radical cations 398 and 399 ( i/2(ox) = +0.68 and +0.81). The cations may be further oxidized to the corresponding very short-lived dications. In contrast, the photoelectron spectra of 237 and 240 reveal practically identical first-oxidation potentials of both compounds, which indicates that the difference in half-wave potentials for oxidation (in condensed phase) of 237 and 240 does not exist in the gas phase. This has been attributed to structure-specific solvation energies in the radical cations 398 and 399. °... 

Kihara et al. employed flow coulometry to study the electrode reactions for Np ions in various acidic media [49]. Flow coulometry has an inherent advantage over the conventional hulk coulometry methods in that the electrolysis can be achieved rapidly to aid in the characterization of unstable electrode products. The resulting coulopo-tentiograms for the Np02 /Np02 and Np /Np " " couples indicate reversible processes in nitric, perchloric, and sulfuric acids. The differences in potentials between the various acids are attributed to the associated stability constants of the electrode products with the anion of the acid in each case. Table 2 contains the half-wave potentials for each couple in the various acids. 

Comparison between the half-wave potentials (equations 2 to 4) of [Cr(CNR)6](PF6)2, e.g. for R = Bu , -1.04, -0.28 and 0.84 V (versus SCE),22 with those for [Cr(CNPh)6](PF6)2, i.e. -0.35, 0.25 and 1.00 V,20 shows that alkyl and aryl isocyanides favour respectively the higher and the lower oxidation states as expected from the greater a-donor and weaker jr-acceptor capabilities of the alkyl over the aryl isocyanides. Similarly, the phosphines in the mixed ligand complexes (Table 3), 23 relative to isocyanide ligands, stabilize the Cr111 oxidation state. The great difference in the relative stabilities of Cr—C bonds in the cyano and phenyl isocyanide complexes is indicated by the magnitude of the shift (ca. 2.0 V) between the Cr(CN) "/Cr(CN)r (-1.130 V) and the Cr(CNPh)i+/Cr(CNPh)i+ reduction potentials.28... 

Prior to this discussion, we would like to refer to a qualitative introduction given by Bard and Faulkner (ref. 21, Sect. 11.1.2 and 11.2.3). In a few pages they give a clear indication of the effect of the chemical reaction on the several characteristic electrochemical quantities (e.g. half-wave potential, limiting current, etc.). In addition, it is argued that a chemical rate constant, ft,-, is measurable by a given technique if its reciprocal value, 1/fc, falls within the experimental time range accessible for the technique (the so-called time window ). 

As is known in the reaction centres of PSl, there are at least two molecules of iron-sulphur protein which can be reduced photochemically [46-48]. Observations of the simultaneous decay at low temperatures of P700 and reduced molecules of iron-sulphur protein with a half-wave potential of 530 mV indicate that, at least at such temperatures, it is this iron-sulphur protein that serves as the stable primary acceptor A [40,49]. This conclusion is also corroborated by the results of EPR and optical experiments which show the yield of P700+ to decrease upon preliminary (previous to illumination) redox titration of subchloroplasts leading to the... 

The establishment of equilibria (7), in some cases requires a considerable time. The wave corresponding to coumarin reduction after a time such that the wave shows no further decrease (11) can be utilized to calculate the equilibrium constants Kq and the effect of R1, R2 = alkyl or aryl can be shown (10). The linear dependence found between the half-wave potentials of coumarin and the 6-values indicates that the relative... 

The plot of the pH-dependence (Fig. 18) indicates qualitatively a participation of an intermediate acid-base equilibrium. Evaluation of rate constants kr and kg is made difficult by the inaccessibility of the dissociation constant of reaction (24 b) which corresponds to protonation of a radical anion. ESR would be a suitable method for the determination of the dissociation constants of at least the more stable radical anions. Another possibility for obtaining at least an approximate value of the equilibrium constant is the measurement of the shifts of the half-wave potentials of the more negative wave at potential 3 with pH. Because the half-wave potential of this wave is known to be sensitive to the... 

These conditions are fulfilled for the reduction of phenacylsulpho-nium salts at low pH values cleavage of the C—S bond occurs in the first step and proton transfer is involved only in the consecutive steps. The observed shift of half-wave potentials (74) with pH follows the plot predicted by equation (27). The intersection of the two linear parts indicates that phenacylsulphonium salts are moderately strong acids with pK values between 7 and 8 (Fig. 20). Potentiometrically measured pK values, used for verification, are in good agreement with the approximate pK values obtained from polarographic data. The system involved in the first step can be described by scheme (28) ... 

An effect of the ring-size in addition to that observed in the elimination taking place in the reduction of vicinal dibromides, has been observed for medium-sized ring compounds which carry the electro-active group either in the side-chain or directly attached to the ring. The half-wave potentials of cycloalkyl bromides can be correlated with the half-wave potentials of cyclic ketones and their derivatives (Fig. 29). The observed relation indicates that the relative effect of ring-size on the reactivity is similar in all the reaction series compared. 

It is worth highlighting that, when different diffusion coefficients are considered, the half-wave potential depends on the characteristics of the diffusive field (geometry and size of the electrode), as indicated in Sect. 2.5.1. The variation of the... 

All general typical variables considered in this chapter for a particular reaction scheme, for example the half-wave potential, are of fundamental interest for its characterization in any electrochemical technique. Moreover, as indicated in the previous chapter, all the current-potential expressions deduced here under stationary conditions (when microelectrodes are used) are applicable to any multipotential step or sweep electrochemical techniques like Staircase Voltammetry or Cyclic Voltammetry. 

Fig. 4.7 Variation of the DDPV peak potential (solid line) and the half-wave potential (dotted line) with respect to the formal potential with the electrode sphericity parameter corresponding to the second pulse (Rq = rs/ D0Ti ) for different values of y indicated on the graph. AE = -50 mV, n = 5 s, t2 = 0.025 s...

To check this behavior, in Fig. 5.5 are plotted the voltammograms corresponding to a planar electrode calculated from Eq. (5.50) (Fig. 5.5a), those calculated from Eq. (5.63) for different values of the electrode radius (Fig. 5.5b), and, finally, the current corresponding to a spherical electrode, calculated as the sum of these two contributions (Fig. 5.5c). Thus, the decrease of the electrode size leads to an increase of the dimensionless current of the spherical electrode and to a change of the voltammogram shape in the way indicated above. For small electrodes (see curves in Fig. 5.5c for a radius rs = 10 microns), the peak of the second scan has disappeared and that corresponding to the first scan is poorly defined. Therefore, in these conditions the determination of thermodynamic parameters of the experimental systems under study lies in the study of the half-wave potential of the voltammograms (see below). 

However, under close examination this reaction was found to correspond to the simple case shown in Fig. 2 48 50 Sodium acetate-acetic acid has an anodic limit of about 2.0 V vs. SCE, whereas both anisole and naphthalene (and a large number of other substrates) have half-wave potentials far below this value. Controlled potential electrolysis (cpe) at low anode potentials showed that aryl acetates indeed were formed via discharge of the aromatic compound and not acetate ion. Another case in which the mechanism is clearly indicated by results from cpe is anodic acetamidation of alkylaromatics 1 and aliphatic compounds 44l... 

---