Electrochemical Gibbs energy

A distinguishing aspect in electrode kinetics is that the heterogeneous rate constants, kred and kox, can be controlled externally by the difference between the inner potential in the metal electrode (V/>M) and in solution (7/>so1) that is, through the interfacial potential difference E = electrode setup (typically, a three-electrode arrangement and a potentiostat), the E-value can be varied in order to distort the electrochemical equilibrium and favor the electro-oxidation or electro-reduction reactions. Thus, the molar electrochemical Gibbs energy of reaction Scheme (l.IV), as derived from the electrochemical potentials of the reactant and product species, can be written as (see Eqs. 1.32 and 1.33 with n = 1)... 

Electrochemical potential — (SI unit J mol-1) The notion introduced by -> Butler [i] and Guggenheim [ii] for consideration of equilibria in electrochemical systems with participation of charged species on the basis of the relationship for the electrochemical -> Gibbs energy G ... 

A is the sum of the solvent and intramolecular reorganization energies, and AG = F(A 0 - A 0J) is the standard electrochemical Gibbs energy of the electron transfer from x = a to x = b. Parabolic dependence of AG on AG was demonstrated [viii]. Electrochemical behavior including the kinetic analysis of various ET systems was reviewed [ix]. A special type of the ET reaction is the deposition of a metal at ITIES, e.g., the deposition of Au particles by the interfacial reaction between AUCI4 in 1,2-dichloroethane and Fe(CN)6 in water [x]. 

Because a chemical reaction always preserves the charge (identical overall charge on both sides of the balanced equation), then the electrochemical Gibbs energy of reaction, AfG, and the chemical Gibbs energy of reaction, A G, are identical (see the example below). 

By analogy with the case of chemical reactions in volumes, the state of thermodynamic electrochemical equilibrium corresponds to a zero value for the electrochemical Gibbs energy of reaction ... 

When several reactive phenomena co-exist at the same interface, it is necessary to express the equilibrium state by writing that the electrochemical Gibbs energies of reaction are zero for each phenomenon. In particular, keep in mind that when writing the equation for a combination of different equilibria in the form of a single overall equilibrium, this does not provide all the information necessary to give a thorough description of the interface equilibrium, as explained below in the example of multiple junctions. 

In equilibrium, the electrochemical Gibbs energy of reaction is equal to zero. So, assuming that the Volta and Galvani potential differences are equal, the following is obtained ... 

This function is confused with Gibbs energy if, as well as the amount of matter, only the thermomechanical couples S, T and V, -P ate considered. In the case where an electrical potential is added, the function is called electrochemical Gibbs energy and its variables ate temperatute, pressure, electrical potential and amount of matter. For surface phenomena, we encounter capillary Gibbs energy which involves the following variables temperature, pressure, surface tension and amount of matter. 

According to Guggenheim,the electrochemical Gibbs energy of activation can be conceptually represented by... 

In much the same way, we can express the change in standard electrochemical Gibbs energy of a reaction as ... 

For the standard electrochemical Gibbs energy of activation, we write... 

Now, we have already seen that the electrochemical Gibbs energy of activation is linearly related to the applied potential, giving us a powerful tool to control the rate of electrode reactions over many orders of magnitude. At the other extreme, we can also use the potential to probe the reaction under conditions close to equilibrium, by applying small values of the overpotential in both directions around zero, and measuring the resulting current densities. 

The relationship between the Gibbs energy and potential was discussed in Section 4.1.2. For the standard electrochemical Gibbs energy of a reaction, we wrote Eq. (4.6) and for the standard electrochemical Gibbs energy of activation, Eq. (4.7). 

The symmetry factor has already been defined (Eq. (4.9)) in terms of the ratio between the effect of potential on the electrochemical Gibbs energy of activation and its effect on the electrochemical Gibbs energy of the reaction ... 

The results of the Marcus theory can be extended to electrode reactions by replacing the standard Gibbs energies by the standard electrochemical Gibbs energies, AG and AG. Equation (5.40) is thus rewritten as... 

Curve 1 applies to the system at equilibrium. A value of = 0.5 eV was chosen here for the electrochemical Gibbs energy of activation, and the position of the activated complex was taken to be closer to the initial state of the solvated ion (which is... 

The peak in the electrochemical Gibbs energy in Figure 19.5 was chosen to be at one quarter of the distance between the initial and final states, when the system is at equilibrium (ifl = 0). This leads to a numerical value of = 0.25 for the cathodic process of metal deposition. The corresponding rate equation, at high cathodic overpotential and in the absence of mass-transport limitation, is given by... 

Figure 19.6 Schematic plots, showing the variation of the electrochemical Gibbs energy with distance, for systems at equilibrium, having different values of u and consequently of jq. (c.f. E. Gileadi, IsraelJ. Chem. 48 (2008) 121)...

When an overpotential is applied, the chemical part of the electrochemical Gibbs energy, AG , does not change, hence all the change in AG, induced by imposing an overpotential, is electrostatic. Consequently, it is correct to consider only the electrostatic field created by application of an overpotential as the driving force... 

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