lec 3 - Rate Depends on Collision Frequency (ZAB) and...

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A + B Product E a Rate = (# of collisions per second) X (# of collisions having E > E a ) Z AB c and density exp(-E a /RT) 2 2 mv Rate Depends on Collision Frequency (Z AB ) and Boltzmann Factor (e -Ea/RT ) M RT c π 8 = P 2 2 2 2 z y x v v v v c + + = =
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Collision Frequency (Z 1 ) For one molecule: Volume of cylinder: ( ) ( ) t c d 2 π Z 1 = Volume of cylinder X density of molecules time Number density: V N collisions s -1 V N c d Z 2 1 ~10 9 Collisions by a single molecule in one second. 1 9 1 3 19 4 2 8 1 10 5 ) 5 . 2 )( / 5 ( ) 4 ( × × × × = s Z cm s Z area x length at 298 K
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1 8 3 23 1 3 35 11 10 1000 10 022 . 6 1 10 × s M m mol s m collisions Z l Binary Collision Frequency (Z 11 ) Binary collision frequency (Z 11 ) includes all N molecules in volume (V): A B B A () 1 3 35 3 25 9 1 11 10 10 5 . 2 2 / 10 2 = × = = s m collisions m s collisions V N Z Z Divide by 2 Plug in numbers for air (N 2 ): Collisions per molecule (Z 1 ) X N molecules 2 X Volume (V) Z 11 = 2 2 1 11 2 2 2 = = V N c d V N Z Z π
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Mean Free Path ( λ ) λ is average distance traveled between collisions. λ = average speed (c) X average time between collisions (1/Z 1 ) 640 / 10 4 . 6 / 10 5 . 7 10 8 . 4 6 9 1 4 1 = × = × × = = collision cm s collisions s cm Z c Ǻ P d T k V N d V N c d c Z c B 2 2 2 1 2 2 1 2 π = = = = T k P RT PN V N B A = =
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Sucrose + Air Metabolic Energy Chemical Kinetics (Chapter 9) O 11H 12CO 12O O H C 2 2 2 11 22 12 + + Δ = -5693 kJ/mol Ch. 9 Homework : 2,4,6,8,10,12,14,16,20,22,23,26,27,32,34,38,56,57,64 Δ Sucrose CO 2 + H 2 O E a Rate (k) exp(-E a /RT) K eq exp(- Δ Gº/RT) Enzyme Catalyzed (fast) No enzyme (slow) K eq ~ 10 100
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Reactant and Product vs Time Why Study Chemical Kinetics? Learn how to control and optimize reactions Predict the yield and outcome of a reaction Deduce the molecular mechanism a reaction (i.e. how many steps) What is Chemical Kinetics? Kinetics investigates the rate of chemical reactions and how rate depends on temperature, concentration and catalysts. P R Reactant Product [R](t) [P](t) Time Concentration [] [ ] Δ t P Δ = Δ Δ = t R rate
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