Exchange reaction current at the equilibrium potential

In equilibrium of redox reactions, the Fermi level of the electrode equals the Fermi level of the redox particles (ckm) = p iusdox)) and the anodic reaction current equals, but in the opposite direction, the cathodic reaction current (io = io = io). It follows from the principle of micro-reversibility that the forward and backward reaction currents equal each other not only as a whole current but also as a differential current at constant energy level e io(e) = tS(e) = io(e). Referring to Eqns. 8-7 and 8-8, we then obtain the exchange reaction ciurent as shown in Eqn. 8-18  

At equilibrium the Fermi level is equilibrated between the electrode and the redox particles (erm) = erredox)) hence, Eqn. 8-18 gives Eqn. 8-19  

Equation 8-19 indicates that the rate constant of electron transfer by tunneling is the same in the forward and backward directions at constant electron energy. The same tunneling rate constant of electrons in the forward and backward directions is valid not only in the equilibrium state but also in the nonequlibrium state of electron transfer [Gerischer, I960]. 

Integration of Eqn. 8-18 with respect to electron energy e to produce Eqn. 8-20 yields the exchange reaction current io  

Introducing Eqn. 8-17 into Eqn. 8-20, we obtain Eqn. 8—21 as an approximate equation for the exchange reaction current io  

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