Electrochemical free energy activation

Twice the intrinsic electrochemical free energy of activation, obtained from value of ks... 

Figure 2. The electrochemical free energy of activation, AGe, for Cr(OHt)6s+/2+ at the mercury-aqueous interface, plotted against the electrode potential for both anodic and cathodic overpotentials. Solid lines are obtained from the experimental rate constant-overpotential plot in Ref. 14, using Eq. 6 (assuming A = 5 X 10s cm S1). Dashed lines are the predictions from Eq. 16.

Forward and backward reaction rate coefficients can be expressed, according to eqns. (64) and (65) with AG, the standard free energy of formation of one mole of activated complex from reactants in eqn. (126), and should be replaced by the electrochemical free energy of activation, AG, for charged particles. 

Now, we have already seen that the electrochemical free energy of activation is linearly related to the applied potential, giving us a powerful tool wilh which we can 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 density. 

The symmetry factor has already been defined (Eq. 7D) in terms of the ratio between the effect of potential on the electrochemical free energy of activation and its effect on the electrochemical free energy of the reaction ... 

For the standard electrochemical free energy of activation we may write,... 

While the derivative dj]/d n i is used commonly to characterize the dependence of current density on potential and is referred to as the Tafel slope, b = RT/aF, we suggest that there is some advantage to using its reciprocal, d In i/drf = aF/ RT, as this corresponds directly to the exponential term in the electrochemical free energy of activation [Eq. (9)]. Then reciprocal Tafel slopes can conveniently be referred directly to factors that affect the activation process in charge transfer reactions [Eqs. (4) and (9)]. 

For an electrochemical rate process, the rate constant i is determined by an electrochemical free energy of activation, AG , related to AG , the chemical free energy of activation, by... 

The electrochemical free energy change at equihbrium and reduction is depicted in Fig. 3.1. As shown in Fig. 3.1a, the difference between the cathodic and anodic activation... 

Here and in the following, e is the charge of an electron, k and h are Boltzmann s constant and Planck s constant respectively, is the transmission coefficient, a - the activity, y the activity coefficient, G - the Gibbs free energy, and G - the Gibbs electrochemical free energy. The superscript 7 denotes the transition state, the subscripts i and f indicate the initial and final states, "a" stands for the adsorbed particles, and the superscript 0 means that the corresponding values refer to standard conditions. 

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