Free energy electrochemical

Similar to homogeneous electron-transfer processes, one can consider the observed electrochemical rate constant, k, , to be related to the electrochemical free energy of reorganization for the elementary electron-transfer step, AG, by... 

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.

Figure 9.4 Membrane model for electron transfer reaction in photosynthetic cycle with acceptor A and donor D on either side of the membrane (a) P, P. P+ are respectively normal state electronically excited state and oxidised form of pigment molecule, (b) Illustrating energy levels of ground and excited states of pigment molecule in the membrane and acceptor and donor molecules in solution. tk.G=riFE is theoretically available electrochemical free energy e=electron, +=positive hole.

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. 

Electrochemical equilibrium is established at each interface of the cell when the -> electrochemical potentials of the common components of the two phases (a and f) forming the interface are equal, that is pf = ji , and the electrochemical free energy change (AG) for the process occurring at the interface is zero. For the net cell reaction given above, such considerations lead to an expression for the electrochemical equilibrium constant Ka given by [i]... 

Fig. 2. Schematic plots outlining outer-shell free energy-reaction coordinate profiles for the redox couple O + e R on the basis of the hypothetical two-step charging process (Sect. 3.2) [40b]. The y axis is (a) the ionic free energy and (b) the electrochemical free energy (i.e. including free energy of reacting electron), such that the electrochemical driving force, AG° = F(E - E°), equals zero. The arrowed pathways OT S and OTS represent hypothetical charging processes by which the transition state, T, is formed from the reactant.

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 ... 

This equation is equivalent to Eq. 4H, considering that q is nothing but the surface excess of electrons on the metal side of the interphase, and the electrical potential E is the intensive variable determining the electrochemical free energy of electrons in the metal. 

In much the same way we can define the electrochemical free energy of a reaction as follows ... 

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

The thermodynamics of the redox couple in Eq. (a) can be described by an electrochemical free energy of reaction, AG° ... 

A notable feature of electrochemical reactions is that is strongly dependent on the electrode potential. Although (and possibly k ) can be potential dependent, the major part is associated with changes in AG. This dependence can be understood by referring to Fig. 1. The top diagram (A) is a plot of the electrochemical free energy, G, for the electrochemical reaction + e (<)) ) vs. the nuclear reaction coor-... 

Figure 1. Free-energy profile for simple electrochemical reaction + e - Y plotted against the nuclear-reaction coordinate. Fig. lA shows the overall electrochemical free-energy profile I, bulk reactant P, precursor state S, successor state 11, bulk product. Figs. IB and C show the components of the free-energy profile arising from the solution species (Y, Y ), and transferring electron, respectively.

Here x is the transmission coefficient N is the number of reaction centers on a unit surface A, is the reorganization energy for the electrode reaction AG is the electrochemical free energy of the elementary act. 

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... 

Then, the change in the electrochemical free energy of adsorption will be... 

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