Title: Kinetics
1Kinetics
2What is Kinetics ?
- Analysis of reaction mechanisms on the molecular
scale - Derivation of rate expressions
- Design and analysis of experiments to test rate
equations and derive kinetic parameters - Theoretical prediction of rate constants
- How can we improve it?
3Basic surface interactions
- Reactions take place on the metal surface
4Reaction Scheme
O2
CO
CO2
catalyst
Adsorption
Desorption
Reaction
Energy
adsorption
reaction
desorption
reaction coordinate
5Heterogeneous Catalysis
Adsorption
Reaction
Desorption
6The Mean-FieldApproximation
Ntotal number of sites NANumber of sites
occuppied by A NBNumber of sites occuppied by
B NNumber of free sites
?ANA/N ?BNB/N ?(N-NA-NB)/N
7Monte Carlo Simulations
8Experimental Evidence by STM
a
b
8x8 nm
9The Heat of Adsorption is Always
Negative !!!!
10Reaction Scheme
O2
CO
CO2
catalyst
Adsorption
Desorption
Reaction
Energy
adsorption
reaction
desorption
reaction coordinate
11Adsorption
- Associative Adsorption CO, N2, Ar, He, etc
At equilibrium
12Langmuir Isotherm
13Irving Langmuir(1881 - 1957)
- worked at General Electrics
- oxygen adsorption on tungsten
- filaments of light bulbs
- 1932 Nobel Prize in Chemistry
- Langmuir Adsorption Isotherm
KA pA
?A
1 KA pA
14Adsorption
- Dissociative Adsorption N2, O2, CO, H2 etc.
For equilibrium 0
15Adsorption
16The Fuel Cell
17CO severely reduces efficiency
18Langmuir - Hinshelwood Kinetics
Cyril Norman Hinshelwood 1897 - 1967 Nobel Prize
1956
19Eley - Rideal Mechanism
direct reaction between gas phase and adsorbed
species
Unlikely !!
20The Langmuir-Hinselwood (LH) mechanism
Net reaction over catalyst
Elementary steps
21The Complete Solution
22The Steady State Approximation
Interesting solution for many processes, but we
lose time dependence
Last eq. not independent, i.e. n-1 eq. for n
elementary steps
23The Quasi-equilibrium Approximation
Assumes one step is rate limiting while the rest
are in Quasi-equilibrium
RLS
24The Quasi-equilibrium Approximation
Notice only valid when step 3 is rate limiting!
25Steps with Similar Rates
Assume step 1 and 3 are slow i.e. rate limiting
steps (rls)
while step 2 and 4 are in quasi-equilibrium
Resulting in a reduced problem as comparred to
the complete solution
26Simplifications to the Quasi-equilibrium
Approximation Irreversible steps
How does this approximation describe the approach
towards equilibrium?
27Simplifications to the Quasi-equilibrium
Approximation The MARI Approximation
The Most Abundent Reaction Intermediate
approximation (MARI)
Assume for example that specie A bonds much
stronger than B and AB- A will then become MARI
What are examples of MARI??
28Simplifications to the Quasi-equilibrium
Approximation Nearly empty Surface
Typical for high temperatures
In that case is it simple to find the maximum of
the rate as a function of gas-composition
29Reaction order
What is the reaction order nAB?
30Apparent activation energy as function of
molefraction
31Apparent activation energy as function of
molefraction
Asumptions
p are assumed independent of T, i.e. we keep the
pressure fixed.
Notice that n3 and DSx both depends on T, but in
a more weak manner than exponential. It can give
problems in an Arrhenius plot.
32Coverage and reaction order and apparent
activation energy as function of molefraction
Notice nA, nB, and Eapp varies with pressure for
fixed temperature
33CO Oxidation Reaction Scheme
The overall reaction is
The elementary step on a surface are
34CO Oxidation the mechanics
For the 3 elementary steps in Quasi equilibrium
we easily obtain the langmuir equation for
adsorption and desorption
35CO Oxidation- the rate
The rate limiting step
From equilibrium we have
36CO Oxidation- Temperature limits
The CO2 interacts so weakly that step 4 can be
considered irreversible
Low Temperature limit CO will become MARI
Find reaction orders in this limit.
nO20.5, nCO-1
37CO Oxidation- Temperature limits
The CO2 interacts so weakly that step 4 can be
considered irreversible
High Temperature limit Very low concentration of
surface species
Find reaction orders in this limit.
nO20.5, nCO1
38CO Oxidation-Results