Activation free energy forward rate constant

The free energy of activation or the forward rate constant may thus be obtained as a function of Ep for each scan rate. The nonlinear character of the rate law, if any, will then become apparent in the way in which AG p varies with the peak potential, which provides a point-by-point description of the activation-driving force relationship (one point per scan rate). The nonlinear character of the rate law will also transpire in the variation of ap, derived from ctp = 2A2 1ZT/F)(Ep/2 — Ep) with the scan rate. 

The forward and backward rate constants are related to the corresponding activation free energies, AG and AGf, by equation (1.25) below, introducing koo (and kf ) as the maximal rate constants, reached when A Gf or A Gf vanish. The main laws and models describing the way in which the forward and backward rate constants, or the corresponding free energies of activation, vary with the driving force are discussed in Section 1.4.2. 

AGq is the standard activation free energy, also termed the intrinsic barrier, which may be defined as the common value of the forward and backward activation free energies when the driving force is zero (i.e., when the electrode potential equals the standard potential of the A/B couple). Expression of the forward and backward rate constants ensues ... 

The forward and backward activation free energies and the corresponding rate constants thus depend on an extrinsic factor, the standard free energy of the reaction, AG° = E — E°, and an intrinsic factor, the standard activation free energy, that reflects the solvent and internal reorganization energy, Aq and A [equation (1.31)]. 

The situation for a chemical, as opposed to an electrochemical, reaction is considered first. Simplified activated complex theory assumes an Arrhenius-type dependence of the forward rate constant, kf, on the chemical free energy of activation, AC, according to the following equation ... 

Variational transition-state theory (VTST), as its name implies, variationally moves the reference position along the MEP that is employed for the computation of the activated complex free energy, either backwards or forwards from the TS sttuctme, until the rate constant is minimized. Notationally... 

The rate expressions for the forward and reverse reactions, having rate constants kt and k x and free energies of activation AGf and AG11s respectively, may be written as ... 

Equation 24E gives the chemical rate constant of the forward reaction as a function of the standard free energy of activation. To use this equation for electrode kinetics, it is necessary to relate the standard free energy of activation to the potential drop At]) across the interphase. 

As shown in Figure 5.8, the rate constants and depend on the free energies of activation AGf and AG for forward and backward reactions. The reaction rate constant in general is given by the Arrhenius expression... 

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