Solid state ionics research lab seoul national

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Unformatted text preview: o [B] k f [ A ] k r [B ] e ( k f k r )t k f [ A ]o k r [B]o Chem. equilibrium [A] [B]o -As t→∞, kf[A]=kr[B] or 0 [B ] k f K eq (T) [ A] k r t→ Thermodynamic equilibrium Solid State Ionics Research Lab. Seoul National University Kinetics -Actually at the thermodynamic equilibrium, R dx k f ([A]o x) k r ([B]o x) 0 dt k f ( A o x eq ) k r (B o x e q ) G o k f Bo xeq Beq K eq exp RT k r Ao xeq Aeq where ΔGo, the standard reaction free energy for the reaction A=B. Solid State Ionics Research Lab. Seoul National University Kinetics 3.2 Consecutive 1st order reaction k1 k2 A B C d [ A] k1 [ A] dt d[ B] k1 [ A] k 2 [ B ] dt d [C ] k2[ B] dt [A] [A]o ek1t where [A] [A]o at t 0 d[B] k 1[ A]o e k1t k 2 [B] dt Solid State Ionics Research Lab. Seoul National University Kinetics -Trial solution: [ B ] A e k1t Be k 2 t d[B] k 1Ae k1t k 2Be k 2t k 1[ A]o e k1t k 2 Ae k1t Be k 2t dt -Comparing the both sides, one obtains k 1A k 1[ A]o k 2 A - As [B] [B]o [B ] A k 1[ A]o k 2 k1 at t 0, [B]o A B. B [B]o k 1[ A ]o k 2 k1 k 1[ A]o k1t e e k 2t [B]o e k 2t k1 k 2 d[C] d[ A] d[B] dt dt dt [ A] [B] [C] [ A]o [B]o [C]o [C] ([ A]0 [B]0 [C]0 ) ([ A] [B]) Solid State Ionics Research Lab. Seoul National University Kinetics -Steady state approximation k1 k2 A B C d[ A ] k 1[ A ] dt d[B] k 1[ A ] k 2 [ B ] dt d[C] k 2 [B ] dt Very often, d[ A ] d[C] d[B] , 0 : Steady state approximation dt dt dt Solid State Ionics Research Lab. Seoul National University Kinetics d[B] 0 k 1[ A ] k 2 [ B ] dt [B ] k 1 constant [ A] k 2 [A] d[C] d[ A] k 1[ A ] k 2 [ B ] dt dt [C] -The steady state solution t [ A] [ A]0 e k1t [B ] k1 [ A]0 e k1t k2 When [B]=const? k [C] [ A]0 [B]0 [C]0 [ A]0 1 1 e k1t k 2 The assumption of steady state approx. makes the problem extremely easy sometimes !! Solid State Ionics Research Lab. Seoul National University Kinetics 3.3 Another application of the steady state approximation (optional) k1 k2 B C A k 1 k 2 d [ A] k1 [ A] k 1[ B ] dt d[ B] k1 [ A] k 2 [ B ] k 2 [C ] k 1[ B ] dt d [C ] k 2 [ B ] k 2 [C ] dt Solid State Ionics Research Lab. Seoul National University Kinetics -Direct integration is extremely difficult. Now assume a steady state with respect to [B] or d [ B] 0 dt Then k1[ A] k 2 [C ] ( k 1 k 2 )[B ] Thus [ B ] k1 [ A] k 2 [C ] k 1 k 2 d [ A] k k [ A] k...
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This document was uploaded on 11/26/2013.

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