ELECTROCHEMISTRY - Wits Structural Chemistry

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Exchange Current Density Under zero current conditions: Dynamic Equilibrium Ox + ne - Red o RT a Eeq = E − ln nF a Re d Ox EQUILIBRIUM! Overpotential (η): the difference between the applied potential and the equilibrium potential. η = E – E eq Equilibrium potential: potential where i = 0 By definition, no net chemical change occurs i = 0 However, this is a dynamic equilibrium! i = ia + ic = 0 Increasing rate of reduction η = E – E eq E eq Increasing rate of oxidation η = E – E eq i.e. there is still current flowing: i a = −ic = io E eq exchange current η > 0 Recall: current is the variation of charge with time: current ∝ rate of electron transfer dq i = dt η < 0 i o is a measure of the electron transfer activity in both cathodic and anodic directions at equilibrium. It is a very useful kinetic parameter in dynamic electrochemistry. Rate of e - transfer depends on the electrode potential which drives the transfer of e - ’s. Current is defined as: i = nFAν A = surface area of electrode ν = reaction rate Forward reaction: Reverse reaction: k k ox Ox + ne - red Red Red Ox + ne- ν red = k red C i ν c red = nFA Butler-Volmer Equation ox 1 st order Current at electrode: ν = k C ox ox i ν a ox = nFA Overall rate: 1 ν = νox − νred = koxCred − kredCox = (ia − ic ) nFA i = ia − ic = nFA(k oxCred − kredCox ) red Note: c red or c ox refers to the conc’s near the electrode surface Forward reaction: Reverse reaction: k Ox + ne - red k ox Red Red Ox + ne- Current at electrode: The rate constant varies with applied potential (in an exponential way): (1−α )nF −αnF η η o o RT RT k = kred = k e ox k e k o = standard rate constant (k when potential applied is E eq ) α = transfer coefficient (0 < α < 1) → symmetry factor (1− α)nF o i = nFAk C RT rede i = ia − ic = nFA(k oxCred − kredCox ) η − Coxe − αnF η RT (1− α)nF − αnF η η i = i RT − RT o e e Butler-Volmer equation and o io = nFAk C Current (rate of reaction) depends on: • Electrode area, A • Concentration of reactant, C • Temperature • The kinetic parameters i o and α • Overpotential, η Current density, j: i j = A (1− α)nF − αnF η η j = j RT − RT o e e (1−α)nF − αnF η η i = i RT − RT o e e i = nFAν j is independent of electrode area Butler-Volmer equation in terms of current density For small overpotentials (η < ~10 mV): nF j = joη RT In most practical situations, only the forward or the reverse reaction is significant and a simplified equation is sufficient. Large, positive overpotential predominantly oxidation: In practise, η ≥ ~ +0.12/n V j (1−α )nF η RT = j e o (1− α)nF ln j = ln jo + η RT Large, negative overpotential predominantly reduction: In practise, η ≤ ~ -0.12/n V j −αnF η RT = j e o αnF ln j = ln jo − η RT (1− α)nF j = j RT o e η − e Anodic current − αnF η RT Cathodic current i.e. η nF < 1 RT Low field region High field region Tafel equations 8
(1− α)nF ln j = ln jo + η RT Tafel Plot Tafel Plot Anodic current Butler-Volmer: No Mass Transport Effects j j a High field Oxidation: Red → Ox + ne - For oxidation reaction anodic current: nF slope = (1− α) RT ∴ find α j = j a + j c Low field i ∝ E E ln j o Deviation from linearity at low η as the reverse reaction can no longer be ignored High field j c Reduction: Ox + ne - → Red j = jo e Anodic current (1−α )nF η RT − e Cathodic current −αnF RT η Focusing on low field region j Oxidation j a Effect of transfer coefficient (α) on j vs η relationship: j α = 0.25 α = 0.5 η0 Oxidation favoured α = 0.75 j a = j o -j c = j o E = E eq potential at zero current flow E Reduction: Ox + ne - → Red Oxidation: Red → Ox + ne - η j c Reduction Reduction favoured (1− α)nF − αnF η η j = j RT − RT o e e α = the fraction of applied potential that influences the rate of electrochemical rxn Butler-Volmer: Mass Transport Effects Assumption in derivation of Butler-Volmer equation: negligible conversion of electroactive species at low current densities uniformity of concentration near the electrode j Predicted by the Butler-Volmer equation The Butler-Volmer equation fails at high current densities → current is limited by transport of ions towards the electrode. Larger η is needed to produce given current. η Current controlled only by mass transport This effect is called concentration polarisation and its contribution to the total overpotential is called the polarisation overpotential, η c . Current controlled only by electron transfer and j 0 Exponential increase in current with η (B-V equation) Current controlled by η and transport 9
Page 1 and 2: ELECTROCHEMISTRY Mrs Billing GH840
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