lec 5 - Second-Order Kinetics 2A Products rate = d A 2 =...

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Second-Order Kinetics Products 2A Products B A + [] 0 1 1 A kt A + = [] [] [ ][ ] kt B A A B A B = 0 0 0 0 ln 1 2 d d A k t A rate = = [ ] [ ] B A k t B t A rate = = = d d d d

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Second-order Half-life = kt + 1 [A] 0 [A] t 1 2A products = kt 1/2 + 2 [A] 0 [A] 0 1 = k[A] 0 1 t 1/2 t 1/2 = 0.5[A] 0 /k (zero-order) t 1/2 = 0.693 k (1 st -order) (2 nd -order)
t 1/2 t 1/2 t 1/2 Zero-order 1 st -order 2 nd -order t 1/2 = 0.5[A] 0 /k t 1/2 = 0.693 k = k[A] 0 1 t 1/2 time [A] Half-life vs Zero-, 1st- and 2nd-order Reactions [A] [A] [A] t = - kt + [A] 0 [A] t = [A] 0 exp(-kt)

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Second-order Kinetics Sample Problem The second order reaction (2A product) has the following kinetic data: Time (min) [A] (M) 0 0.0169 12.18 0.0144 24.55 0.0124 42.50 0.0103 68.05 0.00845 What is the value of the rate constant, k? At what time is [A] t = 0.005M? = kt + 1 [A] 0 [A] t 1 k = 1 [A] 0 [A] t 1 - 1 t = 1 ( 0.0169 ) (0.00845) 1 - 1 68.05 k = 0.87 M -1 min -1 t = 1 [A] 0 [A] t 1 - 1 k = 1 ( 0.0169 ) ( 0.00423 ) 1 - 1 0.87 = 2.0 x 10 2 min
Pseudo First-Order Kinetics CH 3 COOC 2 H 5 + H 2 O l CH 3 COOH + C 2 H 5 OH [ ] [ ] O H H COOC CH k Rate 2 5 2 3 = [H 2 O] = 55.5 M and remains nearly constant during rxn. Therefore reaction becomes zero order with respect to H 2 O [] 5 2 3 H COOC CH k Rate = O H k k 2 = (k´ = pseudo 1 st order rate constant) (k = 2 nd order rate constant) ethyl acetate acetic acid ethanol = k[H 2 O] time ln[A] t -k’

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2 nd Order Kinetics if [A] = [B] products B A ⎯→ + [] B A k dt A d r = ] [ = ate kdt - = B A ] A [ d [] [] [ ][ ] 0 0 0 0 ln 1 A B B A B A kt = [ ] () [ ] 0 0 0 0 ln ln A B B A kt B A = [ ] B A ln time [ ] 0 0 ln A B [ ] [ ] ( ) 0 0 B A k Slope = Can simplify kinetic expression if set initial concentrations equal ( [ ] [ ] 0 0 B A = ). Since 1 = = B A ν , then [ ] B A = throughout the course of the reaction: [ ] 2 A k B A k dt A d = = , which we solved already. kt A A + = 0 1 1 or kt B B + = 0 1 1 [ ] [ ] 0 0 0 0 A B e B A B A kt =
Second-Order Renaturation of DNA A G G C A C T C G T A G G C A C T C G T [ ][ ][ ] 2 A k B A k rate = = [] 0 1 1 A kt A + = [ ] kt A f A A 0 0 1 1 + = = kt A A A 0 0 1 + = or [A] = [B] because AB B A + k

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Renaturation Kinetics of DNA [] kt A f A A 0 0 1 1 + = = [A] 0 = Concentration of strand A at t=0 [A] = Concentration of strand A at t f=fraction of strands that dissociate [A] o vs total strand concentration (C 0 ): N C A 2 0 0 = N is the smallest repeating sequence (i.e. complexity of the DNA) Strand A Strand B