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CE 561 Lecture Notes
Fall 2009
p. 1 of 11
Day 12: Unimolecular Reactions and Pressure Dependent Rate Parameters
A unimolecular reaction is an elementary reaction that nominally involves only one reactant.
This could be an isomerization, such as
CH
3
NC
→
CH
3
CN
In this case, the reaction is also unimolecular in the reverse direction.
A unimolecular
decomposition is a reaction such as
CH
3
CH
2
Cl
→
C
2
H
4
+ HCl, or
C
2
H
6
→
2 CH
3
.
In these cases, the reverse reaction is bimolecular.
These reactions, in the gas phase, have rates
that depend not only on the concentration of the reactant, but also on the total concentration of all
species (or, equivalently, the total pressure).
The first qualitatively correct explanation for the
pressure dependence of these reactions was presented by Lindemann in 1922.
He correctly
reasoned that only molecules with total energies greater than some critical energy were capable
of reacting, and that the molecules must obtain this energy through collisions with other
molecules.
He wrote the overall reaction process as
A + M
→
A* + M with rate constant
k
1
A* + M
→
A + M with rate constant
k
1
A*
→
Products with rate constant
k
2
where A is the reactant, and A* is a reactant molecule with sufficient energy to react.
M is any
molecule.
It is assumed that A is energized and deenergized by a single collision.
This is
known as the
strong collision assumption
.
If we apply the pseudosteadystate approximation to
A* in this mechanism we obtain:
112
[ ]*
0
[ ][
]
[ *][
]
[ *]
dA
k
A
MkA
Mk
A
dt
−
=
=
−−
so the concentration of A* is
1
12
[ ][
]
[ *]
[]
kAM
A
kM k
−
=
+
The reaction rate (the production rate of products) is
2
[ ][
]
[Products]
[ ]
[ *]
kk A M
d
kA
dt
dt
k
M
k
−
=
−=
=
+
and the effective unimolecular rate constant is given by
uni
kk M
k
−
=
+
.
At high pressures ([M]
→
∞
) this becomes
k
uni
=
k
1
k
2
/
k
1
(
≡
k
∞
), and the effective rate constant is
independent of pressure.
At low pressures ([M]
→
0) this becomes
k
uni
=
k
1
[M] (
≡
k
o
), and the
effective rate constant is directly proportional to pressure.
This lowpressure limit is called the
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View Full DocumentCE 561 Lecture Notes
Fall 2009
p. 2 of 11
bimolecular limit, since the reaction behaves as a second order (bimolecular reaction).
k
1
can be
identified as the bimolecular rate constant.
It is reasonable to assume that every collision of A*
leads to deenergization, and therefore
k
1
can be equated to the gaskinetic collision rate
constant.
However, only a small fraction of the collisions of A lead to energization (creation of
A*) so
k
1
is not simply a collisional rate constant.
For this simple theory, called the
LindemannHinshelwood
or
LindemannChristiansen
theory, a
loglog plot of the unimolecular rate constant (
k
uni
) looks like:
The pressure range where the rate goes from the high pressure regime (rate independent of
pressure) to the lowpressure regime (rate proportional to total pressure) is known as the
falloff
regime
.
The pressure range over which this happens is frequently identified by stating the
pressure (
p
1/2
)
at which the observed rate constant (
k
uni
) is onehalf of the high pressure rate
constant (
k
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 Fall '09

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