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1 Kinetics of Electrode Reactions For an electrochemical reaction, O + n e « R N = Q / nF where N is the number of moles oxidized or reduced (mol) Q is the charge passed in electrochemical reaction (C) n is the stoichiometric number of electrons (e.g 2 for Cd² reduction) F is the Faraday constant (96,485 C/mol) Since electrode reactions are heterogeneous, their reaction rates are usually described in mol/s cm 2 . Reaction rate (mol/s cm 2 ) = dN/Adt =(1/nFA)(dQ/dt) = i/nFA ⇒ Rate of an electrode reaction is proportional to current. Rate of Electrode Reaction

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2 For an electrode reaction, equilibrium is characterized by the Nernst equation, which links the electrode potential to the bulk concentrations of the participants. O + n e « R E = E o’ + (RT/nF) ln (C O */C R *) where C O * and C R * are the bulk concentrations E o’ is the formal potential. Current is related exponentially to the overpotential h . i = a’ exp ( h /b’) or, as given by Tafel in 1905, h = a + b log i ~ Tafel equation Essentials of Electrode Reaction k f k b O + ne R ) , 0 ( ) , 0 ( nFA i t C k nFA i t C k a R b b c O f f = = = = u § The forward reaction rate v f is proportional to the surface concentration of O. § Let C O (x,t) be the concentration at distance x from the electrode surface at time t, then C O (0,t) is the surface concentration at t. where i c is a cathodic current and i a is an anodic current. § Let’s begin by considering that reaction has forward and backward paths as shown below. Likewise we have for the backward reaction
) , 0 ( ) , 0 ( nFA i t C k t C k R b O f b f net = - = - = u Thus the net reaction rate is and we have overall i = i c – i a = nFA [k f C O (0,t) – k b C R (0,t)] § Rate constants have units of cm/s. Since the interface can respond to its immediate surroundings, the concentrations entering rate expressions are always surface concentrations, which may differ from those of the bulk solution. § The potential of an electrode strongly affects the kinetics of reactions occurring on its surface. ex) Hydrogen evolves rapidly at some potentials, but not at others. Copper dissolves from a metallic sample in a clearly defined potential range, but it is stable outside that range. § Let's consider the following reaction Na(Hg) « Na + + e where Na + is dissolved in acetonitrile or dimethylformamide. § By plotting the free energy profile along the reaction coordinate, we can see how BUTLER-VOLMER MODEL Effects of Potential on Energy Barriers

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