reaction mechanisms in inorganic chemistry. elementary reaction kinetics: a review of the...
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Reaction Mechanisms in Inorganic Chemistry
Elementary Reaction Kinetics: A Review of the Fundamentals
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
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
Principal aim of kinetics:
Relating experimental (“macroscopic”) rate and equilibrium constants to theoretical (“microscopic”) rate and equilibrium constants
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
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
2 exp( / ) exp( / )kT
k H RT S Rh
2lnk h H S
kT RT R
ln (
kh/
kT)
2
1 /T
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
If S‡ increases, ln k2 increases and reaction is entropy driven
more disordered transition state
If H‡ decreases, ln k2 increases and reaction is enthalpy driven
less energy in total needed to break chemical bonds
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
Example (p. 1.5)
Excel
Example (p. 1.5)
-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)
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)
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)
Excel
Example (p. 1.5)
Excel
Example (p. 1.5)
So report results as:
H‡ = 84 2 kJ mol-1
S‡ = 20 7 J K-1 mol-1
Example (p. 1.5)
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
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
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
1/ 22o2
log 2 A B
kAz z I
k
A = 0.509 M-½ in aqueous solution at 25 oC
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
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
The pressure dependence of rate constants
2(ln )V
kP RT
‡
V‡ > 0
‡
V‡ < 0