110c-lecture25 - Reversible First-order Kinetics k1 A k-1 B...

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Reversible First-order Kinetics AB k 1 k -1 [ ] [] [] B k A k dt A d 1 1 + = [ ] [] 1 1 = = k k A B K EQ EQ c If [A] = [A] 0 and [B] = 0 at t=0, then [A] 0 =[A]+[B] and [ ] [ ] A A B = 0 : [] [] [] {} () + + = + = = 0 1 1 1 1 1 0 1 1 1 0 1 1 ) ( A k k k A k k A k A k k A A k A k dt A d [ ] EQ EQ EQ EQ c A A A A B k k K = = = 0 1 1 0 1 1 1 A k k k A EQ + = [ ] [][] { } EQ A A k k dt A d + = 1 1 [ ] [ ] [ ] { } EQ EQ EQ A A k k dt A A d dt A d dt A d dt A d + = = + = 1 1 { } dt k k A A A A d EQ EQ 1 1 + = { } t k k A A A A EQ EQ 1 1 0 ln + = [ ] [ ] ( ) [ ] [ ] ( ) ( ) t k k A A A A EQ EQ 1 1 0 ln ln + = [ ][ ] { } + = t A A EQ EQ dt k k A A A A d 0 1 1 ] [ ] [ 0
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[] [] [] () [ ] EQ t k k EQ A e A A t A + = + 1 1 0 ) ( [ ] EQ A [ ] EQ B Reversible First Order Kinetics AB k 1 k -1 [ ] [] [] [ ] 0 1 1 = = = dt B d B k A k dt A d [ ] [] 1 1 = = k k A B K EQ EQ eq [ ] [ ] A A B = 0 [] [] [ ] [ ] ( ) ( ) { } EQ t k k EQ A e A A A t A A t B + = = + 1 1 0 0 0 ) ]( [ ] [ ) ( (dashed line) (solid line) [ ] [ ] B k A k 1 1 = At equilibrium: exchange rate = k 1 + k -1 ( ) ( ) t k k EQ e B t B 1 1 1 ) ( + = [ ] [ ] ( ) [ ] t k k A e B t A + = + 1 1 ) (
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A+B C k 1 k -1 Bimolecular Reversible Association [ ] [] [] [] [ ] [ ] dt C d dt B d C k B A k dt A d t v = = = = 1 1 ) ( Analytical solution amazingly complex – Numerical integration used instead Use Mathematica to calculate [A](t), [B](t) and [C](t) (see kinetics-math.pdf) [][] [] [ ] constant A k k where C k B k dt B d t v dt C d dt B d C k B A k dt A d t v = = = = = = 0 1 1 1 1 1 0 1 ) ( ) ( [ ] [ ] 0 0 B A >> If (pseudo first-order in B) then rate law simplifies to: 1 k is a pseudo first-order rate constant Ex: peptide + H 2 O products [H 2 O] >> [peptide] v(t) = k[H 2 O][peptide] = k’[peptide] t k peptide peptide ' ] ln[ ] ln[ 0 = [ ] t k e peptide peptide ' 0 = k’ = k[H 2 O]
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Pseudo First-order Kinetics A+B C k 1 k -1 [ ] [] [] [] [] [] C k B k C k B A k dt B d 1 ' 1 1 1 = = [ ] [] [] C k B k dt B d 1 ' 1 = [] [] [] () EQ t k k EQ B e B B t B + = + 1 ' 1 0 ) ( [ ] [ ] ] [ 0 B B C = + = + EQ t k k EQ B e B B B t C 1 ' 1 0 0 ) ( [A] 0 >> [B] 0 and [C] 0 = 0 [ ] EQ B [ ] EQ C [B](t) [C](t) k 1 ’=k 1 [A] [ ] [ ] dt C d dt B d C k B A k rate = = = 1 1 ( ) ( ) t k k EQ e C t C 1 ' 1 1 ) ( + =
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A+B C k 1 k -1 [ ] [] 1 1 1 1 1 = = s s M k k B A C K a A+B C k d k a Reversible Association vs. Dissociation Kinetics Association Constant Dissociation Constant [ ][ ] 1 1 1 = = s M s k k C B A K a d d a d K K 1 =
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Diffusion Controlled Kinetics Fastest reactions have rate constants ~10 9 –10 12 s -1 .
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This note was uploaded on 06/22/2010 for the course CHEM 21360 taught by Professor Ame during the Spring '09 term at East Los Angeles College.

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110c-lecture25 - Reversible First-order Kinetics k1 A k-1 B...

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