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![Page 1: Reaction Mechanisms in Inorganic Chemistry. Elementary Reaction Kinetics: A Review of the Fundamentals.](https://reader033.fdocuments.us/reader033/viewer/2022061612/56649f205503460f94c387c4/html5/thumbnails/1.jpg)
Reaction Mechanisms in Inorganic Chemistry
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Elementary Reaction Kinetics: A Review of the Fundamentals
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The Arrhenius equation
A + B Pk2
2
P[A][B]
dk
dt
Experimental rate law
• Describes temperature dependence of the reaction rate constant.
k2 = A.exp[-Ea/RT]
ln k2 = -(Ea/RT) + constant
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Activated Complex Theory (ACT)
1
1
A + B C
C P
k
k
k
Transition state or activated
complex
A +B
P
C ‡G
Reaction coordinate
K‡ = k1/k-1
[P] = [C ]
t
dk
d
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Principal aim of kinetics:
Relating experimental (“macroscopic”) rate and equilibrium constants to theoretical (“microscopic”) rate and equilibrium constants
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What is the relationship between k2, k‡ and K‡?
2
P[A][B] experimental
dk
dt
P[C ] theory
dk
dt
2[A][B] = [C ]k k
1
1
[C ]
[A][B]
[C ] = [A][B]
kK
k
K
2[A][B] [A][B]
and
k k K
≠ ≠2k =k K
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2k k K
and it can be shown (see notes) that
2 exp( / )kT
k G RTh
2 exp( / ) exp( / )kT
k H RT S Rh
Gibbs energy of activation
Entropy of activation
Enthalpy of activation
The Eyring EquationThe Eyring Equation
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2 exp( / ) exp( / )kT
k H RT S Rh
2lnk h H S
kT RT R
ln (
kh/
kT)
2
1 /T
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2lnk h H S
kT RT R
2ln lnh H S
kkT RT R
So:
2
2
ln
ln
k H
k S
If S‡ increases, ln k2 increases and reaction is entropy driven
If H‡ decreases, ln k2 increases and reaction is enthalpy driven
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If S‡ increases, ln k2 increases and reaction is entropy driven
more disordered transition state
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If H‡ decreases, ln k2 increases and reaction is enthalpy driven
less energy in total needed to break chemical bonds
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2 exp( / ) exp( / )kT
k H RT S Rh
Transition state theory
2 exp( / )ak A E RT
Arrhenius equation
2aH E RT
In solution
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Example (p. 1.5)
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Excel
Example (p. 1.5)
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-38.5
-38
-37.5
-37
-36.5
-36
-35.5
0.00375 0.0038 0.00385 0.0039 0.00395 0.004 0.00405
Example (p. 1.5)
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y = -10093x + 2.3527
R2 = 0.9985
-38.5
-38
-37.5
-37
-36.5
-36
-35.5
0.00375 0.0038 0.00385 0.0039 0.00395 0.004 0.00405
Excel
Example (p. 1.5)
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Excely = -10093x + 2.3527
R2 = 0.9985
-38.5
-38
-37.5
-37
-36.5
-36
-35.5
0.00375 0.0038 0.00385 0.0039 0.00395 0.004 0.00405
Example (p. 1.5)
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Excel
Example (p. 1.5)
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Excel
Example (p. 1.5)
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So report results as:
H‡ = 84 2 kJ mol-1
S‡ = 20 7 J K-1 mol-1
Example (p. 1.5)
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The kinetic salt effect
1
1
A + B Ck
k
Define
C C
A B A
[C ] = =
[A][B]
=
B
aK
a a
K K
But2k k K
So2
Kk k
K
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2
Kk k
K
If i = 1 ∀ i, then K = 1 and k2o = k‡K
o2
2
kk
K
From Debye-Hückel theory:
2 1/ 2j jlog Az I
constant charge
I = ½ mjzj2
is the ionic strength
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o2
2
kk
K
o2 2
o2 A BC
o 2 2 2 1/ 22
log log log
log log log log
log ( )A B C
k k K
k
k A z z z I
But
A BCz z z
o 2 2 2 1/ 22 2
o 1/ 22
log log ( ( ) )
log 2
A B A B
A B
k k A z z z z I
k Az z I
1/ 22o2
log 2 A B
kAz z I
k
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1/ 22o2
log 2 A B
kAz z I
k
A = 0.509 M-½ in aqueous solution at 25 oC
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1/ 22o2
log 2 A B
kAz z I
k
o ++
zA = 0 zB = +1
1/ 2
02 2
02 2
2 0
log( / ) 0
( . ., )
A BAz z I
k k
i e k k
log(
/)
kk
220
I1 /2
0
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1/ 22o2
log 2 A B
kAz z I
k
+ ++
zA = 1 zB = +1
0 1/ 22 2log( / ) 2k k AI
log(
/)
kk
220
I1 /2
0
2A
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The pressure dependence of rate constants
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2(ln )V
kP RT
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‡
V‡ > 0
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‡
V‡ < 0