Reaction Rate Theory

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Reaction Rate Theory
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Partition Functions
Similarly can we separate the internal motions of
a molecule in Part involving vibrations, rotation
and nuclei motion, and electronic motion i.e.
for a mulecule we have
Now we create a system of many molecules N that
are in principle independent and as they are
indistinguishable we get an overall partition
function Q
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Partition Functions Summary
s
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Partition Functions
What was the advantage of having the Partition
Function?
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Surface Collisions
Consider a box with volume V
What are the numbers?
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Surface Collisions
How many are successful in reacting? Simple
Maxwell-Boltzman distribution
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Transition State Theory
Consider the following reaction
q
How?
We assume that R and R are in Equilibrium
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Transition State Theory
By splitting the partition function in the
transition state
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Transition State Theory
The partition function q can conveniently be
split further
Which basically is the Arrhenius form If q0 q
n 1x1013s-1
Relation to Thermodynamics
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Transition State Theory
Think of some examples
Temperature dependence of prefactor
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Transition State Theory on Surfaces
Indirect adsorption of atoms
An atom adsorbs into a 2-dim mobile state, we
have Ng gas atoms, M sites on the surface, and N
atoms in the transition state
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Transition State Theory on Surfaces
Now what is K ?
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Transition State Theory on Surfaces
This corresponds to the collision on a surface
since the atoms are still free to move in two
dimensions
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Transition State Theory on Surfaces
Direct adsorption of atoms
M is total number of sites M is number of free
sites
Why?
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Transition State Theory on Surfaces
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Transition State Theory on Surfaces
Notice adsorption always result in loss of entropy
There may also be steric hindrance leading to
reduced S
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Transition State Theory on Surfaces
What happens in the regime between direct and
indirect adsorption?
The atoms breaks free of the site and start to
diffuse around in
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Transition State Theory on Surfaces
Indirect adsorption of molecules
Notice that if the precursor is sufficiently
loose S0(T)1.
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Transition State Theory on Surfaces
Direct adsorption of molecules
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Transition State Theory on Surfaces
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Transition State Theory on Surfaces
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Transition State Theory on Surfaces
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Transition State Theory on Surfaces
Notice how the Keq is alone determined from
initial and final state partition functions.
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Transition State Theory on Surfaces
Desorption
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Transition State Theory on Surfaces
System Prefactor s-1 Ea
kJ/mol CO/Co(0001) 1015
118 CO/Ni(111) 1015
130 CO/Ni(111) 1017
155 CO/Ni(111) 1015
126 CO/Ni(100) 1014
130 CO/Cu(100) 1014
67 CO/Ru (001) 1016
160 CO/Rh(111) 1014 134
How?
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Transition State Theory on Surfaces
If the details of the transition state can be
determined can the rate over the barrier be
calculated.

• Details of the transition state are difficult to
  access
• Low concentration
• Short lifetime.

Often determined by First Principle
calculations, but are only accurate to say 0.1
eV or 10 kJ/mol.