Seoul national university optional kinetics 4

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Unformatted text preview: he overallreactionrate for the reaction A B P kk d dP k AB [ A ][ B] dt k k d k eff Solid State Ionics Research Lab. kk d ; overall rate law constant k k d Seoul National University Kinetics -Two extreme cases (or limiting cases) are thought out : i) k k (i.e., Forming products are very rare event) d k eff kk d kk d kK k kd kd where K k d / k equilibrium constant for the reaction A B AB d k ⇒ Rate – determining step is AB P called an activation-controlled reaction ii) k k d k eff k d Solid State Ionics Research Lab. Called a diffusion – controlled reaction Seoul National University (optional) Kinetics 4.2 Derivation of kd r A [B] [B]∞ (matrix concentration) 0 R r Once B is transporte d within R * , it disappears to make P d AB dt k A B B Q B 4 r D B r Solid State Ionics Research Lab. 2 in spherical symmetry Seoul National University Kinetics dAB A J B R* dt (where we s upposed that Ais immobile in space) At t he s teady s tate, Q B constant Thus, B 0 QB dB 4DB 1 QB dr B R* r 2 4DB Q B 4 DB R* B 1 R* The average number of B particles / unit time passing through any spherical surface centered on any A d[ AB] 4R DB [ A] [B] dt k d 4R DB [ A] [B] As far we have assumed that A is immobile and only B is approaching A. Let`s now remove this constraint: Solid State Ionics Research Lab. Seoul National University Kinetics k d 4 R ( D A D B ) DB DA DB D According to the Einstein-Stokes equation kT kT DA ; DB 6 RA 6 RB 2kT 1 Taking RA R RB , then D 2 3 R 8 RT Finally we have k d 3 kd depends only on the viscosity of the solvent and temperature. Independent of the identifies of the reactants Solid State Ionics Research Lab. Seoul National University (optional) Kinetics 4.3 The Details of Diffusion ( optional ) Concentration change in a volume element fixed at the laboratory reference fame due to diffusion and convection. L V J Cv u Velocity relative to the laboratory frame 0 When, the matrix flows at a speed u relative to the lab. frame J C( v u) C u DC C u Diffusion frame Convection frame C DC (Cu) D 2C uC t Solid State Ionics Research Lab. Seoul National University Kinetics The same thing may be analyzed in a little bit different way : C C (r , t ) Thus, dC C d r C dt t r dC d r C C dt dt t r or in general C dC u C t r dt Concentration change due to diffusion Concentration change due to convection DC uC Local variation of concentration If now, there is a chemical reaction of e.g. the 1 st order C D 2C uC kC t Or in one-dimension Solid State Ionics Research Lab. C 2C C D 2 u kC t x x Seoul National University Kinetics Solution of the 2nd order partial differential equation is by no means trivial. As an example, put u 0 (i.e. no convection ) C 2C D 2 kC t x One may solve the equation by Laplace transform method. Solid State Ionics Research Lab. Seoul National University Kinetics 5. Temperature-dependence of the rate-law constant justificatio n v v Ordinary Collision Molecular collision frequency Leading to Chemical reaction Empirically, ln k vs. 1/T gives a straight line. ln k Ea R k Ae Ea / RT -Arrhenius equation 1/ T -Sometimes, Solid State Ionics Research Lab. k AT ne Ea / RT Seoul National University...
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This document was uploaded on 11/26/2013.

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