Potential formal standard

However, under most conditions the activity coefficients cannot be neglected, certainly for a single redox couple where the ox/red concentration ratio cannot be simply calculated from the true standard potential and the potential directly observed. In order to overcome this difficulty the concept of the formal potential was introduced, which represents a formal standard potential E ° measured in an actual potentiometric calibration and obeying the Nernst equation, E = E ° + (0.05916/n) log ([ox]/[red]) at 25° C, E"0 must meet the conditions under which the analytical measurements have to be made. Sometimes the formal potential values are decisive for the direction of the reaction between two redox couples even when the E° values do not differ markedly10. 

According to the Nemst equation, E = E0 + (RT/F) In ([ox]/[red]) (cf., p. 29), where E0 represents the formal standard potential allowing for the direct use of concentration values within the logarithmic term, the application of a specific potential E to the electrode leads to the establishment of a certain equilibrium [ox]/[red], It is clear, that if Eappl - Em = AE becomes positive there will be a shift to greater [ox] and if negative a shift to lower [ox] than at the original ratio [ox]/[red]. 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

The first term on the right-hand side in eqn. (75) is the conditional or formal standard electrode potential E ° which contains the activity coefficients of O and R since a ratio of concentrations appears in the second term. 

From the identity (77), a standard exchange rate coefficient at the conditional or formal standard potential E ° is defined as... 

In Fig. 9, each transition state can be identified and is characterized by Jo j, Ea i and at j0 measures the barrier height of each transition state in the respective standard conditions, whereas at the formal standard potential, E° for the overall reaction, kf = kh and this potential value is half way between E and E2. 

As in BV, the MHC model describes the electrode kinetics as a function of three parameters the formal potential, the standard heterogeneous rate constant, and the reorganization energy. Nevertheless, important differences can be observed between the two kinetic models with respect to the variation of the rate constants with the applied potential. Whereas in BV rate constants vary exponentially and... 

The formal standard redox potential of the 0H/0H"(H20) couple being equal to 2,85 V versus i.e. quite close to the valence band edge of Ti02, reaction (25)... 

The gathering of fundamental information concerning the initial electron transfer, such as standard potentials, E°, or rather formal potentials, E° for radical cation formation, was earlier greatly hindered by the occurrence of rapid reactions of the intermediates. (See Chapter 1 for a discussion of the difference between formal potentials and standard potentials.) Reaction with impurities in the solvent, or even the solvent itself, and/or rapid proton loss are common reasons for not observing reversible formation of radical cations the consequent irreversibility is in CV associated with a shift in Ep, in the negative direction, from that for reversible oxidation. Considerable progress has been made in countering these difficulties. 

Substitution of formal potentials for standard electrode potentials in the Nernst equation yields better agreement between calculated and experimental results—... 

Usually join and are called formal standard potential. Then the Nernst equation assumes the format... 

In the case of irreversible reactions, the polarographic half-wave potential also depends on the standard potential (formal potential) however, the kinetics of the electrode reaction lead to strong deviation as an overpotential has to be applied to overcome the activation barrier of the slow electron transfer reaction. In the case of a totally irreversible electrode reaction, the half-wave potential depends on the standard rate constant ks of the electrode reaction, the transfer coefficient a, the number e- of transferred electrons, the diffusion coefficient T>ox, and the drop time t [7] as follows ... 

It should be noted that in order to apply this refined model in general it is necessary to know the potential drop across the inner layer. We can recover Eq. (56) if we make the assumption that a is independent of A

following equation valid at equihbrium at the formal standard transfer potential ... 

The peak potentials and half-peak potentials, respectively, can be referred either to the formal standard potential E of the redox system A B or to the half-wave potnetial E,/2- The latter quantity can be determined by an appropriate extrapolation eliminating the kinetic perturbations. Then, the following equations hold for the reversible electron transfer at 25°C ... 

The formal standard potential of a redox system. Closely related to the thermodynamic standard potential. 

In many centred molecules the interactions between the electro-active centres in a given molecule modify the spacing of the formal Standard Potentials of the successive processes by an amount that depends in the case of coulombic forces in part on the dielectric properties of the local surrounding electrolyte solution. This feature has been observed in Ae case of bimetallic complexes in mixed solvent systems of relatively low bulk dielectric constants, has been used to ascertain Ae impact of electrolyte concentration in particular ion-pairing on electrolyte dielectric behaviour. 

From this equation we can establish the definition of formal standard potential E°, where concentrations are used rather than activities. 

For convenience, the formal standard potential is often taken as the reference point of the potential scale in reversible systems. 

The exchange current Iq is a measure of the rate of exchange of charge between oxidized and reduced species at any equilibrium potential without net overall change. The rate constant k, however, has been defined for a particular potential, the formal standard potential of the system. It is not in itself sufficient to characterize the system unless the transfer coefficient is also known. However, Eq. (2.21) can be used in the elucidation of the electrode reaction mechanism. The value of the transfer coefficient can be determined by measuring the exchange current density as a function of the concentration of the reduction or oxidation species at a constant concentration of the oxidation of reduction species, respectively. A schematic representation of the forward and backward currents as a function of overvoltage, 7] = E - E, is shown in Fig. 2.6, where the net current is the sum of the two components. 

Reduction. The uranyl ion, U02 is readily reduced to U, stable in air-free H2O, by Nang, Mg, Cr Fe, Co, Cu, Zn, ZnHg, Cd, Sn, Pb, etc., but not appreciably by SnCl2, despite moderately favorable (formal) standard electrode potentials for the latter, even with heat in chloride media (i.e., absent the tightly ligating... 

Providing that the vanadium ion activity coefficients do not change, the formal standard potential of vanadium remains constant. The second term appears when the concentration of the potential-determining component in the near-electrode layer is substituted into the Nemst equation. This concentration can be expressed... 

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