Post on 14-Dec-2015
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Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above activation energy
Rate = k(T) [A][B] Experiment
© University of South Carolina Board of Trustees
Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energy
Rate = pZ0 e-Ea/RT [A][B] Theory
Rate = k(T) [A][B] Experiment
© University of South Carolina Board of Trustees
Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energy
Rate = pZ0 e-Ea/RT [A][B] Theory
Rate = k(T) [A][B] Experiment
correct conc. dependencecorrect temp. dependence rates still too large
© University of South Carolina Board of Trustees
Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energyfraction in a goodorientation
Rate = k(T) [A][B] Experiment
© University of South Carolina Board of Trustees
Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energyfraction in a good (p)orientation
Rate = pZ0 e-Ea/RT [A][B] Theory
Rate = k(T) [A][B] Experiment
© University of South Carolina Board of Trustees
Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energyfraction in a good (p)orientation
Rate = pZ0 e-Ea/RT [A][B] Theory
Rate = k(T) [A][B] Experiment
good agreement with experiment
© University of South Carolina Board of Trustees
Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energyfraction in a good (p)orientation
Rate = pZ0 e-Ea/RT [A][B] = A e-Ea/RT [A][B] “Pre-exponential”Rate = k(T) [A][B] Experiment
© University of South Carolina Board of Trustees
Bimolecular Rate TheoryA + B products
Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energyfraction in a good (p)orientation
= pZ0 e-Ea/RT [A][B]Rate = A e-Ea/RT [A][B]Rate = k(T) [A][B] Experiment
Arrhenius Equation
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Chapt. 13Kinetics
Sec. 4Arrhenius Equation(T dependence of k)
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Arrhenius Equation
k(T) = A e-Ea/RT
or
ln k = ln A - (Ea/R)(1/T)
© University of South Carolina Board of Trustees
Arrhenius Equation
k(T) = A e-Ea/RT
or
ln k = ln A - (Ea/R)(1/T) Graphing y = b + m x
© University of South Carolina Board of Trustees
Arrhenius Equation
k(T) = A e-Ea/RT
or
ln k = ln A - (Ea/R)(1/T) Graphing y = b + m x slope
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k T (oC)
7.8 400
10 410
14 420
18 430
24 440
Using an Arrhenius Plot
Determine Ea for the reaction
2NO2 2NO + O2
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Arrhenius Plot
T (oC)
400 410 420 430 440
k (s
-1)
0
5
10
15
20
25
k T (oC)
7.8 400
10 410
14 420
18 430
24 440
© University of South Carolina Board of Trustees
k ln k T (oC)
7.8 2.05 400
10 2.30 410
14 2.64 420
18 2.89 430
24 3.18 440
Using an Arrhenius Plot
Determine Ea for the reaction
2NO2 2NO + O2
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k ln k T (oC) T (K)
7.8 2.05 400 673
10 2.30 410 683
14 2.64 420 693
18 2.89 430 703
24 3.18 440 713
Using an Arrhenius Plot
Determine Ea for the reaction
2NO2 2NO + O2
© University of South Carolina Board of Trustees
k ln k T (oC) T (K) 1/T (K-1)
7.8 2.05 400 673 1.49x10-3
10 2.30 410 683 1.46x10-3
14 2.64 420 693 1.44x10-3
18 2.89 430 703 1.42x10-3
24 3.18 440 713 1.40x10-3
Using an Arrhenius Plot
Determine Ea for the reaction
2NO2 2NO + O2
© University of South Carolina Board of Trustees
k ln k T (oC) T (K) 1/T (K-1)
7.8 2.05 400 673 1.49x10-3
10 2.30 410 683 1.46x10-3
14 2.64 420 693 1.44x10-3
18 2.89 430 703 1.42x10-3
24 3.18 440 713 1.40x10-3
Using an Arrhenius Plot
Determine Ea for the reaction
2NO2 2NO + O2
© University of South Carolina Board of Trustees
1/T (K-1)
1.40x10-3 1.45x10-3 1.50x10-3
ln k
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
ln k 1/T (K-1)
2.05 1.49x10-3
2.30 1.46x10-3
2.64 1.44x10-3
2.89 1.42x10-3
3.18 1.40x10-3
Arrhenius Plot
T (oC)
400 410 420 430 440
k (s
-1)
0
5
10
15
20
25
k T (oC)
7.8 400
10 410
14 420
18 430
24 440
© University of South Carolina Board of Trustees
ln k = ln A - (Ea/R)(1/T)
y
x
3 3
4
3.04 2.20
1.410 10 1.472 10
1.35 10 aE
R
-1 -1
yslope
x
K K
K
1/T (K-1)
1.40x10-3 1.45x10-3 1.50x10-3
ln k
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
ln k 1/T (K-1)
2.05 1.49x10-3
2.30 1.46x10-3
2.64 1.44x10-3
2.89 1.42x10-3
3.18 1.40x10-3
© University of South Carolina Board of Trustees
Arrhenius Equation
k(T) = A e-Ea/RT
or
ln k = ln A - (Ea/R)(1/T) Graphing y = b + m x (many points)
© University of South Carolina Board of Trustees
Arrhenius Equation
k(T) = A e-Ea/RT
or
ln k = ln A - (Ea/R)(1/T) Graphing (many points)or
Two-PointFormula
1
2 2 1
1 1ln aEk
k R T T
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Activation Energy
What is the activation energy for a reaction if its rate doubles when the temperature increases from 24 ºC to 36 ºC?
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Kinetics vs Thermodynamics
k(T) = A e-Ea/RT
or
ln k = ln A - (Ea/R)(1/T) or
1
2 1 2
1 1aEk
k R T T
ln
Keq(T) = e-G°/RT
or
ln Keq = (S°/R) - (H°/R)(1/T) or
1
2 1 2
1 1K H
K R T T
ln
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Activation Energy Diagram
DGThermodynamics
Kinetics
Reactants
Products
Transition State
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Catalysts
Catalyst: A substance that increases the rate of reaction, but is neither created nor consumed by the reaction
● Changes the activation energy (Ea) by introducing a new mechanism
● Increases the rate● Does not change the thermodynamics
(DG or Keq)
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DGThermodynamics
Ea Kinetics
Kinetics, not Thermodynamics