Electrode potential, absolute formal

Let us choose, as an arbitrary reference level, the energy of an electron at rest in vacuum, e ) (cf. Section 3.1.2). This reference energy is obvious in studies of the solid phase, but for the liquid phase, the Trasatti s conception of absolute electrode potentials (Section 3.1.5) has to be adopted. The formal energy levels of the electrolyte redox systems, REDox, referred to o, are given by the relationship ... 

This equation is virtually identical to the Jdnetically deduced version of Eq. (7.40). However, it is not yet formally identical with that of Nernst, which was deduced long before the concept of a Galvani potential difference (MdS< >) across the metal/solution interface was introduced (Lange and Misenko, 1930). Nernst s original treatment was in terms of the electrode potential and symbolized by V. It is possible to show (see Section 3.5.15) that for a given electrode, M S< > - V + const. (i.e., the factors that connect the measured electrode potential to the potential across the actual interface) do not depend on the activity of ions in the solution. Hence, using now the relative electrode potentials, Vt in place of the absolute potentials ,... 

For a reversible process involving species in solution, the absolute value of the peak potential separation, - EpcI, approaches 59/n (mV at 298 K), whereas the half-sum of such potentials can, in principle, be equal to the formal electrode potential of the couple. Under the above conditions, the peak current is given by the Randles-Sevcik equation (Bard et ak, 2008) ... 

The voltammetric features of a reversible reaction are mainly controlled by the thickness parameter A = The dimensionless net peak current depends sigmoidally on log(A), within the interval —0.2 < log(A) <0.1 the dimensionless net peak current increases linearly with A. For log(A )< —0.5 the diSusion exhibits no effect to the response, and the behavior of the system is similar to the surface electrode reaction (Sect. 2.5.1), whereas for log(A) > 0.2, the thickness of the layer is larger than the diffusion layer and the reaction occurs under semi-infinite diffusion conditions. In Fig. 2.93 is shown the typical voltammetric response of a reversible reaction in a film having a thickness parameter A = 0.632, which corresponds to L = 2 pm, / = 100 Hz, and Z) = 1 x 10 cm s . Both the forward and backward components of the response are bell-shaped curves. On the contrary, for a reversible reaction imder semi-infinite diffusion condition, the current components have the common non-zero hmiting current (see Figs. 2.1 and 2.5). Furthermore, the peak potentials as well as the absolute values of peak currents of both the forward and backward components are virtually identical. The relationship between the real net peak current and the frequency depends on the thickness of the film. For Z, > 10 pm and D= x 10 cm s tlie real net peak current depends linearly on the square-root of the frequency, over the frequency interval from 10 to 1000 Hz, whereas for L <2 pm the dependence deviates from linearity. The peak current ratio of the forward and backward components is sensitive to the frequency. For instance, it varies from 1.19 to 1.45 over the frequency interval 10 < //Hz < 1000, which is valid for Z < 10 pm and Z) = 1 x 10 cm s It is important to emphasize that the frequency has no influence upon the peak potential of all components of the response and their values are virtually identical with the formal potential of the redox system. 

Nemst s law (Eq. II. 1.7, which is simply the Nernst equation written in the exponential form) defines the surface concentrations of the oxidised, [A]jc=o. and die reduced form, [B] =o. of the redox reagents for a reduction process A + n e B as a function of E t) and, the applied and the formal reversible potential [4], respectively, where t is time, n is the number of electrons transferred per molecule of A reacting at the electrode surface, F, the Faraday constant, R, the constant for an ideal gas, and T, the absolute temperature. Pick s second law of diffusion (Eq. II. 1.6) governs the mass transport process towards the electrode where D is the diffusion coefficient. The parameter x denotes the distance from the electrode surface. 

Nearly a century has passed since Ostwald formally introduced the use of absolute potentials in his Lehrbuch der Allgem. Chemie. Although the Nernst forces carried the day and established the normal hydrogen electrode as the basis of the redox scale, Ostwald s elegant concept of an absolute potential as a base for the system has attracted attention of prominent scientists from time to time since then. New concepts and new experimental approaches have been tested, but in no case does there seem to be a system developed likely to supplant hydrogen. The chemistry of the time led both Nernst and Ostwald to believe that they were dealing with systems much less complex than the experience of a century of research has proved. 

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