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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 activationcontrolled 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 EinsteinStokes 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 onedimension
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. Temperaturedependence of the ratelaw 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.
 Fall '13

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