Kinetic Aspects of Electrochemistry Overpotential

The foregoing considerations are based on the concepts of reversible thermodynamics the electrochemical cells are considered to be operating reversibly, which means in effect that no net current is drawn. Real cell EMFs, however, can differ substantially from the predictions of the Nernst equation because of electrochemical kinetic factors that emerge when a nonnegligible current is drawn. An electrical current represents electrons transferred per unit of time, that is, it is proportional to the extent of electrochemical reaction per unit of time, or reaction rate. The major factors that can influence the cell EMF through the current drawn are 

Factor (a) can be minimized by making the internal resistance of the cell as small as possible, for example, by having a high concentration of an inert electrolyte in the cell. Factor (b) can be reduced by stirring the cell contents vigorously. Factor (c), since it originates in chemical reaction kinetics, can 

These considerations refer to the formation of H2(g) from H+(aq), but any forward pathway for a reaction is necessarily a reverse pathway, too (cf. the principle of microscopic reversibility Section 2.5), so the same factors create an overpotential for the oxidation of H2(g) to H+(aq). In particular. 

Quantitative treatment of overpotential and related phenomena goes back to 1905, when Tafel showed empirically that, for an electrochemical half-cell from which a net electrical current I is being drawn, an excess potential AE away from the equilibrium potential will inevitably exist, and AE will be a linear function of the logarithm of the current density i i = //area of interface)  

For the forward reaction, the sign of b is negative, so 77 reduces the EMF. Equations 15.65, 15.68, and 15.69 can be combined and rearranged to give the Butler-Volmer equation (Eq. 15.70) for the net current density, i, of an electrode process involving a single electrochemical step  

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