© University of South Carolina Board of Trustees Bimolecular Rate Theory A + B products Rate...

$: © University of South Carolina Board of Trustees Bimolecular Rate Theory A + B products Rate =frequency of collisions( Z 0 [A][B]) fraction above activation.$
© University of South Carolina Board of Trustees

Bimolecular Rate TheoryA + B products

Rate = frequency of collisions (Z0[A][B])fraction above activation energy

Rate = k(T) [A][B] Experiment



Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energy

Rate = pZ0 e-Ea/RT [A][B] Theory




Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energy



correct conc. dependencecorrect temp. dependence rates still too large



Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energyfraction in a goodorientation




Rate = frequency of collisions (Z0[A][B])fraction above (e-Ea/RT) activation energyfraction in a good (p)orientation








good agreement with experiment




Rate = pZ0 e-Ea/RT [A][B] = A e-Ea/RT [A][B] “Pre-exponential”Rate = k(T) [A][B] Experiment




= pZ0 e-Ea/RT [A][B]Rate = A e-Ea/RT [A][B]Rate = k(T) [A][B] Experiment

Arrhenius Equation


Chapt. 13Kinetics

Sec. 4Arrhenius Equation(T dependence of k)


Arrhenius Equation

k(T) = A e-Ea/RT


Arrhenius Equation

k(T) = A e-Ea/RT

or

ln k = ln A - (Ea/R)(1/T)


Arrhenius Equation

k(T) = A e-Ea/RT

or

ln k = ln A - (Ea/R)(1/T) Graphing y = b + m x


Arrhenius Equation

k(T) = A e-Ea/RT

or

ln k = ln A - (Ea/R)(1/T) Graphing y = b + m x slope


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


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


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



2NO2 2NO + O2


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



2NO2 2NO + O2


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



2NO2 2NO + O2


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


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


Arrhenius Equation

k(T) = A e-Ea/RT

or

ln k = ln A - (Ea/R)(1/T) Graphing y = b + m x (many points)


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


Activation Energy

What is the activation energy for a reaction if its rate doubles when the temperature increases from 24 ºC to 36 ºC?


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


Activation Energy Diagram

DGThermodynamics

Kinetics

Reactants

Products

Transition State


Chapt. 13Kinetics

Sec. 5Catalysts


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)


DGThermodynamics

Ea Kinetics

Kinetics, not Thermodynamics


Types of Catalysts

Homogeneous:everything is in the same phase

Heterogeneous:catalyst is a different phase (usually solid)

Enzymes:large protein molecules (100’s-1000’s of atoms) that speed biochemical reactions

© University of South Carolina Board of Trustees Bimolecular Rate Theory A + B products Rate...

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