Half-wave potential, reversible process

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. 

Half-wave potentials for each of the electron transfer steps shown in Scheme V are listed in Table II. The first oxidations of (0EP)Ge(C6H5)Cl and (0EP)Ge(C H5)0H are irreversible and occur at Ep = 1.00 V for X = 0H. The second oxidations of these complexes are reversible and both occur at Ei/2 = 1.40 V. These second oxidation processes occur at identical to the Ei/2 values for oxidation of (0EP)Ge(C6H5)C10i, and this was presented as strong evidence for an oxidation of Cl on (OEP)Ge(CsHs)Cl and OH on (0EP)Ge(C6Hs)0H(35). 

Benzoquinones are conveniently prepared in solution by the anodic oxidation of catechols. 1,2-Quinones are unstable in solution but they have a sufficient lifetime for the redox process to be reversible at a rotating disc electrode. Reaction involves two electrons and two protons and the half-wave potential varies with pH at 25 °C according to Equation 6.1. Some redox potentials for catechols and hy-droquinones are given m Table 6.6. 

The reversible half wave potential ( 1/2) values became higher with the increase of the concentration of supporting electrolyte, but the a values were practically constant. The rate parameters decreased with increase of radius and charge of the cation of supporting electrolyte at the same ionic strength. The number of water molecules associated with zinc ions in the solutions and with reactant, which directly takes part in the charge-transfer process, was estimated and the following reaction scheme was proposed. 

Bond and coworkers [85] have extended earlier [83] polarographic studies over a wider temperature range from 20 to —60 C. Assuming reversibility (processes 1 and 2), and considering the case of mercury oxidation in the presence of Et2dtp , half-wave potentials depended on Et2dtp concentration ... 

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. 

In aqueous solution nobelium ions are most stable in the 2 oxidation state. In this oxidation state nobelium has a filled f-electron shell, 5f ", which is likely a major factor for its stability. The potential for the No(III)/No(II) couple has been calculated by Nugent et al. as 1.45 0.05 V [177]. A value of —1.4 to —1.5 V was determined by Silva and coauthors from experimental measurements [180]. David et al. have performed electrochemical amalgamation experiments for the reduction of No(II) to No(0) in aqueous acetate and citrate solutions [181]. They determined half-wave potentials of—1.709 0.006 V versus SCE in acetate and —1.780 0.004 V versus SCE in citrate. Their data was consistent with a reversible two-electron reduction process for which the data in acetate solution was taken as representative of a noncomplexing medium. The 1/2 value in acetate was converted to a value of —1.47 0.01 V versus SHE and subsequently used to derive a standard potential value of —2.49 0.06 V for the No(II)/No(0) couple. 

Here, A is the electrode area, C and D are the concentration and the diffusion coefficient of the electroactive species, AE and co(=2nfj are the amplitude and the angular frequency of the AC applied voltage, t is the time, and j=nF (Edc-Ei/2) / RT. For reversible processes, the AC polarographic wave has a symmetrical bell shape and corresponds to the derivative curve of the DC polarographic wave (Fig. 5.14(b)). The peak current ip, expressed by Eq. (5.24), is proportional to the concentration of electroactive species and the peak potential is almost equal to the half-wave potential in DC polarography ... 

If a tetraalkylammonium salt is used as supporting electrolyte, this process is either reversible or quasi-reversible and occurs at around -0.8 V vs aqueous SCE in various aprotic solvents and with various electrode materials (Hg, Pt, GC). If a Bmisted acid is added to the solution, the first step is converted to a two-electron process 0 produced in the first step is protonated to form 02H, which is more reducible than 02. Thus, 02H is further reduced to 02H at the potential of the first step. According to detailed polarographic studies in H20-DMS0 mixtures, about 30% v/v water is needed to convert the one-electron process to the two-electron process [41]. A metal ion, M+, interacts with 02 to fonn an ion-pair M+-02 (often insoluble) and shifts the half-wave potential of the first wave in a positive direction [42]. Electrogenerated superoxide 02 can act either as a nucleophile or as an electron donor and has been used in organic syntheses [43],... 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

Hydration-dehydration equilibria can affect the heights of polarographic waves when they precede the electron transfer, or are interposed between two electron transfers or shift the values of half-wave potentials when they follow after a reversible electrode process. 

When dehydration occurs as a consecutive reaction, its effect on polarographic curves can be observed only, if the electrode process is reversible. In such cases, the consecutive reaction affects neither the wave-height nor the wave-shape, but causes a shift in the half-wave potentials. Such systems, apart from the oxidation of -aminophenol mentioned above, probably play a role in the oxidation of enediols, e.g. of ascorbic acid. It is assumed that the oxidation of ascorbic acid gives in a reversible step an unstable electroactive product, which is then transformed to electroinactive dehydroascorbic acid in a fast chemical reaction. Theoretical treatment predicted a dependence of the half-wave potential on drop-time, and this was confirmed, but the rate constant of the deactivation reaction cannot be determined from the shift of the half-wave potential, because the value of the true standard potential (at t — 0) is not accessible to measurement. 

Sect. 2.2.2.2, and whose intercept coincides with the reversible half-wave potential. In the case of non-reversible processes, it could be thought that these plots would not be linear since this linearity is a direct consequence of... 

The ADDPV curves present a zero current potential, ECIOSS, which can be measured with great accuracy. It coincides with the half-wave potential of a reversible electrode process in planar electrodes and with the formal potential independently of the electrode geometry when the diffusion coefficients of both species are assumed as equal. 

For a reversible process the peak potential can be related to the polarographic half-wave potential Em by the expression... 

Figure 9.1 illustrates the electrochemical reduction of 02 at platinum electrodes in aqueous media (1.0 M NaC104). The top curve represents the cyclic voltammogram (0.1 V s-1) for 02 at 1 atm ( 1 mM), and the lower curve is the voltammogram with a rotated-disk electrode (900 rpm, 0.5 V min-1). Both processes are totally irreversible with two-electron stoichiometries and half-wave potentials (EU2) that are independent of pH. The mean of the Em values for the forward and reverse scans of the rotated-disk voltammograms for 02 is 0.0 V versus NHE. If the experiment is repeated in media at pH 12, the mean Em value also occurs at 0.0 V. 

Fig. 27 Voltammogram obtained for an irreversible one-electron transfer at a hydrodynamic electrode (note a reversible one-electron process is also illustrated with equal half-wave potential for comparison).

For an EC mechanism with a reversible electron-transfer step, the following chemical kinetics will cause the equilibrium associated with the electron-transfer step to shift to the right side. This causes the half-wave potential associated with the E step to move to a less negative potential in the case of a reduction process and to a less positive potential in the case of an oxidation... 

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