Seoul national university kinetics in many cases r f

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Unformatted text preview: erall reaction order j n j ; partial reaction order, the reaction order with respect to the component j (may not be an integer) k ; rate constant or specific rate Note : dimension of k Solid State Ionics Research Lab. Seoul National University Kinetics 2. Simple reactions and determination of the reaction order 2.1 Integration Method (i) 1st order rate equation A B dc A R kc A dt k Integrating with the I.C., c(t=0)=c0 c ln kt co ln c Often the variable x is convenient t x c0 c i.e. decrease in the reactant dx k (c0 x ) dt Solid State Ionics Research Lab. c0 x ln kt c0 Seoul National University Kinetics (ii) 2nd order rate equation dc A R kc A 2 dt A B dx or k (c0 x )2 dt Integrating 11 1 1 kt c c0 c0 x c0 1 c k 1 c0 t Solid State Ionics Research Lab. Seoul National University Kinetics (iii) 2nd order rate equation: A+B → C R dc A k cAc B dt -In terms of the amount reacted x (much more convenient!) dx k ( A0 x )( B0 x ) dt or dx kdt ( A0 x )( B0 x ) -Rearranging, dx dx kdt ( A0 x )( A0 B0 ) ( B0 x )( A0 B0 ) -Integrating, A0 x 1 ln kdt A0 B0 B0 x Solid State Ionics Research Lab. Seoul National University Kinetics (iv) For an nth order reaction, in general dx k (C 0 x ) n dt -Integrating, 1 1 1 n1 kt n 1 n 1 (C 0 x ) C0 Solid State Ionics Research Lab. Seoul National University Kinetics 2.2 Half-life Method (i) For a 1st order reaction t1/ 2 c0 ln kt c0 x 1 At t=t1/2 ; x= c0 2 ln2=kt1/ 2 or t1/ 2 c0 ln 2 k i.e. The half-life is independent of the initial amount Solid State Ionics Research Lab. Seoul National University Kinetics (ii) For a 2nd order reaction 11 kt c c0 t1/ 2 1 At t=t1/2 ; x= c0 2 1/ k 1/ c0 21 1 kt1/ 2 c0 c0 c0 t1/2 depends on the initial concentration Solid State Ionics Research Lab. Seoul National University Kinetics (iii) For the nth order reaction 1 1 1 n1 kt n 1 n 1 (c0 x ) c0 1 At t=t1/2 ; x= c0 2 t1/2 1 2n1 1 n k (n 1) c0 1 Dependence of t1/2 on co gives n. Solid State Ionics Research Lab. Seoul National University Kinetics 2.3 Method of initial rates to determine the partial rxn order dx x lim kA1n1 B n2 C n3 dt 1 t 0 t 1 x dx x n lim kA2 1 B n2 C n3 dt 2 t 0 t 2 0 t -Solving for n1 log( x / t )1 log( x / t ) 2 n1 log A1 log A2 -Consider why does one have to take the initial rate? Solid State Ionics Research Lab. Seoul National University Kinetics 3. Complex reactions 3.1 Reversible 1st f B A kr k order reaction dx k f ([A]o x) k r ([B]o x) in terms of the reacted amount x dt -Integrating, ln k f [ A ]o k r [B]o (k f k r )t k f ([ A ]o x ) k r ([ B]o x ) or [A]...
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This document was uploaded on 11/26/2013.

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