Kinetics

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Kinetics
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What 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?

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Basic surface interactions

• Reactions take place on the metal surface

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Reaction Scheme

• Reaction

O2
CO
CO2

catalyst
Adsorption
Desorption
Reaction
Energy
adsorption
reaction
desorption
reaction coordinate
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Heterogeneous Catalysis
Adsorption
Reaction
Desorption
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The 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
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Monte Carlo Simulations

• r ltlt N k ?A?B

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Experimental Evidence by STM
a
b
8x8 nm
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The Heat of Adsorption is Always

• Negative !!!!

Negative !!!!
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Reaction Scheme

• Reaction

O2
CO
CO2

catalyst
Adsorption
Desorption
Reaction
Energy
adsorption
reaction
desorption
reaction coordinate
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Adsorption

• Associative Adsorption CO, N2, Ar, He, etc

At equilibrium
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Langmuir Isotherm
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Irving 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
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Adsorption

• Dissociative Adsorption N2, O2, CO, H2 etc.

For equilibrium 0
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Adsorption

• Competitive Adsorption

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The Fuel Cell
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CO severely reduces efficiency
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Langmuir - Hinshelwood Kinetics
Cyril Norman Hinshelwood 1897 - 1967 Nobel Prize
1956
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Eley - Rideal Mechanism
direct reaction between gas phase and adsorbed
species
Unlikely !!
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The Langmuir-Hinselwood (LH) mechanism
Net reaction over catalyst
Elementary steps
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The Complete Solution
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The 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
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The Quasi-equilibrium Approximation
Assumes one step is rate limiting while the rest
are in Quasi-equilibrium
RLS
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The Quasi-equilibrium Approximation
Notice only valid when step 3 is rate limiting!
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Steps 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
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Simplifications to the Quasi-equilibrium
Approximation Irreversible steps
How does this approximation describe the approach
towards equilibrium?
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Simplifications 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??
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Simplifications 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
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Reaction order
What is the reaction order nAB?
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Apparent activation energy as function of
molefraction
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Apparent 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.
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Coverage and reaction order and apparent
activation energy as function of molefraction
Notice nA, nB, and Eapp varies with pressure for
fixed temperature
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CO Oxidation Reaction Scheme
The overall reaction is
The elementary step on a surface are
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CO Oxidation the mechanics
For the 3 elementary steps in Quasi equilibrium
we easily obtain the langmuir equation for
adsorption and desorption
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CO Oxidation- the rate
The rate limiting step
From equilibrium we have
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CO 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
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CO 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
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CO Oxidation-Results