Electron transfer equilibrium potential

From the measured electron-transfer equilibrium constant and the known standard potential for the reference D /D- couple it has been possible to determine E for the PhO /PhO- couple. The method, however, is non-trivial and does not lend itself to the rapid determination of standard potentials for a large series of related compounds. 

In the case of nonpolaiizable interfaces, the inner and the outer potential differences, 4>a/b and v a/b, are determined by the equilibrium of chai transfer that occurs across the interface. Figure 4—8 shows the electron energy levels in two sohd metals A and B before and after they are brought into contact with each other. As a result of contact, electrons in a metal B of the hi er electron level (the lower work function ) move into a metal A of the lower electron level (the higher work fiuiction), and the Fermi levels of the two metals finally become equal to each other in the state of electron transfer equilibrium. The electrochemical... 

Next, we consider the interface M/S of a nonpolarizable electrode where electron or ion transfer is in equilibrium between a solid metal M and an aqueous solution S. Here, the interfadal potential is determined by the charge transfer equilibrium. As shown in Fig. 4-9, the electron transfer equilibrium equates the Fermi level, Enn) (= P (M)), of electrons in the metal with the Fermi level, erredox) (= P s)), of redox electrons in hydrated redox particles in the solution this gives rise to the inner and the outer potential differences, and respectively, as shown in Eqn. 4-10 ... 

The electrode potential. , in the electron transfer equilibrium does not depend on the nature of the electrode. However, determined by the electron transfer equilibrium (P (m> = P.(rsdox, s>), the potential across the electrode interface, = (He(M) - l eatEDox,s))/-e,does depend upon the nature of electrodes involved, because the chemical potential lt) of electron in the electrode differs with different electrode materials. 

For the hydrogen electrode, the interfadal potential between the electrode metal and the hydrogen gas film is determined by the electron transfer equilibrium and the interfacial potential between the hydrogen gas film and the aqueous... 

Since the electron transfer of the interfacial redox reaction, + cm = H.a> on electrodes takes place between the iimer Helmholtz plane (adsorption plane at distance d ) and the electrode metal, the ratio of adsorption coverages 0h,j/ in electron transfer equilibrium (hence, the charge transfer coefficient, 6z) is given in Eqn. 5-58 as a function of the potential vid /diOMn across the inner Helmholtz layer ... 

In addition, electrode reactions are frequently characterized by an irreversible, i.e., slow, electron transfer. Therefore, overpotentials have to be applied in preparative-scale electrolyses to a smaller or larger extent. This means not only a higher energy consumption but also a loss in selectivity as other functions within the molecule can already be attacked. In the case of indirect electrolyses, no overpotentials are encountered as long as reversible redox systems are used as mediators. It is very exciting that not only overpotentials can be eliminated but frequently redox catalysts can be applied with potentials which are 600 mV or in some cases even up to 1 Volt lower than the electrode potentials of the substrates. These so-called redox reactions opposite to the standard potential gradient can take place in two different ways. In the first place, a thermodynamically unfavorable electron-transfer equilibrium (Eq. (3)) may be followed by a fast and irreversible step (Eq. (4)) which will shift the electron-transfer equilibrium to the product side. In this case the reaction rate (Eq. (5)) is not only controlled by the equilibrium constant K, i.e., by the standard potential difference be-... 

Because of the high concentration of isomer molecules (>0.1 mol-dm 3), the equilibrium depicted is established instantaneously. The ionization potential of trans-decalin is 0.02 eV lower than the ionization potential of d.v-dccalin (9.24 eV vs. 9.26 eV). Therefore, the electron-transfer equilibrium is shifted slightly to the left side. Thus, in terms of charge-transfer kinetics, the two ions behave as a single species. 

Electron-transfer equilibria of the organometallic anions TpM(CO)3- can be examined by coupling them with a graded series of triarylpyrylium cations (TaP+) for which 1-electron reduction potentials are known to be strongly dependent on the substituents (88). The evaluation of the constant K for the electron-transfer equilibrium in Eq. (39) requires the quantitative analysis of the anionic organometallic redox couple in Eq. (38), as well as that of triarylpyrylium cation. 

These equations assume that only the lowest energy state mixes with the ground state, that the potential energy surfaces are harmonic and have the same force constants, and that the displacement of the ground state potential energy surface compensates for the stabilization and destabilization of the states that mix [116]. The use of electrochemical data in the evaluation of parameters that contribute to hvmax leads to a significant correction term in strongly coupled donor-acceptor systems since the excited state species is not involved in the electrochemical processes [9, 116]. The optical and electrochemical processes are related by means of the electron-transfer equilibrium in Eq. 29. 

The silver-silver chloride electrode is an example of a metal electrode that participates as a member of a redox couple. The silver-silver chloride electrode consists of a silver wire or rod coated with AgCl(s) that is immersed in a chloride solution of constant activity this sets the half-cell potential. The Ag/AgCl electrode is itself considered a potentiometric electrode, as its phase boundary potential is governed by an oxidation-reduction electron transfer equilibrium reaction that occurs at the surface of the silver ... 

Rate constants for electron transfer equilibrium reactions of phenoxyl radicals (Table 10) have been determined in conjunction with measurements of reduction potentials of phenoxyl radicals. Since most phenoxyl radicals in aqueous solutions are relatively short-lived, it was not possible to determine their reduction potentials by cyclic voltammetry. Therefore, it was necessary to utilize the pulse radiolysis technique to determine the reduction potentials from equilibrium constants, using a reference compound with which a phenoxyl radical can establish equilibrium conditions. Equilibrium concentrations were determined at short times, after the electron transfer equilibrium was achieved but before any significant decay of the radicals took place. The equilibrium constants were determined either from the concentrations at equilibrium, derived from absorbance, or from the rate constants for the forward and reverse reactions, derived from the rate of approach to equilibrium. Further details were given before . 

Equilibrium Constant. For those cases in which the electron transfer equilibrium is overwhelmingly on the side of the acceptor anion, the rate of the back reaction, as has been pointed out (2), is negligible. In some cases where this is not true, as for diphenyl-naphthalene, the equilibrium with respect to Reaction 4 may be quenched by the protonation of the acceptor anion in Reaction 2. In the case of pyrene-anthracene and pyrene-9,10-dimethylanthracene, where equilibration occurs, the back reaction has a measurable effect upon the electron transfer kinetics, and k4b has been determined. From these data, the equilibrium constant may also be reliably estimated since it is given by the ratio Kc = k4a/k4b. The values obtained at 25°C. are (1) pyrene-anthracene —86 and (2) pyrene-9,10-dimethylanthracene —35. These values for Kc may also be determined from the difference in the reduction potentials of the pair as measured potentiometrically (5, 8, 9, 18). The equilibrium constant is related to the reduction potential difference, AF, by ... 

When hydronium or hydroxide ions are involved in redox equilibria without being themselves reduced or oxidized, it is essential to define standard potentials for the overall reaction, not only for the electron transfer equilibrium. An example is the following reaction ... 

Consider two or more electron conductors that are so arranged that electrons can freely transfer among them. There is the usual condition for transfer equilibrium in these phases the chemical potential (in this case /J,e) is the same in each phase. Thus, electron transfer equilibrium between phases a and requires and to be equal. We equate and /Xe,... 

In a zero-eurrent equilibrium state, there is electron transfer equilibrium between the left electron conductor and the left terminal, and between the right eleetron eonductor and the right terminal /Xe(LE) = /Xe(LT) and /ie(RE) = /ie(RT), where /Te(LT) and /Te(RT) are the chemical potentials of electrons in the left terminal and right terminal, respectively. Thus we can rewrite Eq. 14.3.6 as... 

The first redox potentials of ferryl complexes were measured by cyclic voltammetry in dry acetonitrile [48] but the instability of the reduced form [(L)Fe -O] leads to observed data that are not unambiguous. Two other types of experiments have been described more recently to obtain valuable information on the oxidation power of ferryl complexes (i) the spectropotentiometric oxidation of the Fe " - OH complex in acetonitrile with added water [49] and (ii) the titration of the ferryl complex with ferrocene derivatives (Fc) in dry acetonitrile to determine the Fc + Fe" =0/Fc -1- Fe -0 electron transfer equilibrium constant and, together with the kno wn redox potential of the Fc derivative used, the Fe =0/Fe -0 potential [48b]. Note that the two potentials (i) and (ii) describe two entirely different processes, both of importance for ferryl-catalyzed oxidation reactions, that is, (i) a H -coupled electron transfer and (ii) a pure electron transfer. That is. 

For a simple electron transfer reaction containing low concentrations of a redox couple in an excess of electrolyte, the potential established at an inert electrode under equilibrium conditions will be governed by the Nemst equation and the electrode will take up the equilibrium potential for the couple 0/R. In temis of... 

Determining Equilibrium Constants for Coupled Chemical Reactions Another important application of voltammetry is the determination of equilibrium constants for solution reactions that are coupled to a redox reaction occurring at the electrode. The presence of the solution reaction affects the ease of electron transfer, shifting the potential to more negative or more positive potentials. Consider, for example, the reduction of O to R... 

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