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9 Appendix 9.1 Kinetics of redox reactions 9.1.1 One step, one-electron process Considering the simplest possible electrode process, wherein species O and R engage in one-electron transfer at the interface without being involved in any other chemical step, ‐ (9.1) (9.2) Suppose also that the standard free energy profiles along the reaction coordinate have the parabolic shapes shown in Figure 9.1. The left frame of that figure depicts the full path from reactants to products, while the right is an enlargement of the region near the transition state. It is not important for this discussion that we know the shapes of these profiles in detail222. In developing a theory of electrode kinetics, it is convenient to express potential against a point of significance to the chemistry of the system, rather than against an arbitrary external reference, such as SCE. There are two natural reference points, viz. the equilibrium potential of the system and the standard (or formal) potential of the couple under consideration. It was actually used the equilibrium potential as a reference point in the discussion of the preceding section, and we will use it again in this section. However, it is possible to do so only when both members of the couple are present, so that the equilibrium is defined. The more general reference point is E0’. Suppose the upper curve on the O + e- side of Figure 9.1 applies when the electrode potential is equal to E0’. The cathodic and anodic activation energies are then ΔG‡0c and ΔG‡0a respectively. If the potential is changed by ΔE to a new value, E, the relative energy of the electron resident on the electrode changes by –FΔE= -F(E-E0’); hence the O+e- curve moves up or down by that amount. The lower curve on the left side of Figure 9.1 shows this effect for a positive ΔE. It is readily apparent that the barrier for oxidation, ΔG‡a, has become less than ΔG‡0a by a fraction of the total energy change. 213PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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