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9.1.2 Implications of Butler-Volmer model for the one-step, one-electron process In this section, it will be developed a number of operational relationships that will prove valuable in the interpretation of electrochemical experiments. Each is derived under the assumption that the electrode reaction is the one-step, one-electron process for which the primary relations were derived above. The validity of the conclusions for a multistep process will be considered separately. 9.1.2.1 Equilibrium conditions. The exchange current At equilibrium, the net current is zero, and the electrode is known to adopt a potential based on the bulk concentration of O and R as dictated by the Nernst equation. Let us see now if kinetic model yields that thermodynamic relation as a special case. From equation (9.12) we have, at zero current, (9.13) Since equilibrium applies, the bulk concentrations of O and R are found also at the surface; hence which is simply an exponential form of the Nernst relation: Thus, the theory has passed its first test of compatibility with reality. (9.14) (9.15) Even though the net current is zero at equilibrium, we still envision balanced faradic activity that can be expressed in terms of the exchange current, i0, which is equal in magnitude to either component current, ic or ia. That is, If both sides of (9.14) are raised to the –α power, we obtain (9.16) 216PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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