每日一句
少年中国的人生观的仇敌：
第一种是醉生梦死的无意识生活。
第二种是退缩的人生观，如坐禅学佛的人，都是消极的缩头主
义。这些人没有生活的胆子，不敢冒险，只求平安。
第三种是野心的投机主义，这种人虽不退缩，但为完全自己的
私利起见，不惜利用他人，不惜牺牲他人和自己的人
格，到了紧要关头，不惜作伪，不惜作恶，不顾社会
公共幸福。
胡适
1919.3.22
9.8 The rate theory of unimolecular reaction
Decomposition; isomerization
Pseudo-unimolecular reaction
9.8 The rate theory of unimolecular reaction
9.8.1 Puzzling problems
(1) Activation of the molecules
It is obvious that a single molecule at ground state will not undergo
any reaction except that it was activated by energy of some types.
A  A*  P
For unimolecular reaction, the puzzling question is that how do
reactant molecules acquire necessary activation energy.
(a) Activation through collision—heat?
(b) Activation by energy radiation—work?
9.8 The rate theory of unimolecular reaction
9.8.1 Puzzling problems
(a) Activation by collision:
Before reaction takes place, reactants must collide with each other to
acquire enough activation energy. This may lead to a conclusion that all
gaseous reaction should be second-ordered.
A+M
 A*
dP
*

k
[A
]  k[A][M]
P
1
dt
At early 19th century, it was found that all unimolecluar reaction,
such as gaseous decomposition and isomerization, is of first-order.
9.8 The rate theory of unimolecular reaction
9.8.1 Puzzling problems
(b) Activation by radiation:
In 1919, Perrin proposed that, for unimolecular reaction, the reactant
molecule was activated by absorption of infrared radiation from the
container or other molecules – radiation activation theory.
A 
 A 
P
radiation
*
k1
dP
 k1[A* ]
dt
The result is in good accordance with the early observation of kinetic
characteristics of the unimolecular reaction, i.e., unimolecular reaction is
of first-order.
9.8 The rate theory of unimolecular reaction
9.8.1 Puzzling problems
Problems proposed by Langmuir :
1) The energy of the infrared radiation of the wall of container is
very low and is not sufficient for activation.
2) some reactant molecules do not have an absorption band in the
wave-length region of infrared radiation.
3) Latterly, it was observed that
k∞
the unimolecular reaction is of
second-order at low pressure and
first-order at high pressure.
[A]
9.8 The rate theory of unimolecular reaction
9.8.2 Christiansen and Lindemann’s consideration
(1) Special consideration
In 1921, Christiansen postulated that the activation of molecules in
unimolecular reaction is also through intermolecular collision.
For this theory, it is easy to explain the second-ordered feature of
unimolecular reaction at low pressure but it is impossible to gave any
reasonable explanation to its first-ordered feature at high pressure.
In 1922 Lindemann and Christiansen postulated that the activated
molecules react long after the collision. There is a time lag between
activation and reaction. During the stay of activated molecules, some of
them may lose their energy due to the further collision (deactivation).
Only part of the activated molecules form product.
9.8 The rate theory of unimolecular reaction
9.8.2 Christiansen and Lindemann’s consideration
(2) Lindemann Mechanism
1) Activation through collision:
A  M 
 A*  M
k1
2) deactivation through collision
during time lag
A  M  A  M
k1
*
3) decomposition of activated molecule after time lag
A 
P
*
k2
The activation and the deactivation processes are bimolecular reactions
and the decomposition process is truly a unimolecular reaction.
9.8 The rate theory of unimolecular reaction
9.8.2 Christiansen and Lindemann’s consideration
(3) Rate equation of Lindemann mechanism
The rate of the reaction can be given
as:
d [P]
r
 k2 [A* ]
dt
To determine the concentration of activated molecules, the
stationary- state approximation should be used.
Stationary-state approximation
If A* is very active, its concentration is very low and after a
short time, its concentration does not vary with time:
d [A* ]
0
dt
9.8 The rate theory of unimolecular reaction
9.8.2 Christiansen and Lindemann’s consideration
(3) Rate equation of Lindemann mechanism
d [A* ]
?
dt
d [A* ]
0
dt
r  k2 [A* ]
[A* ]  ?
k1k2 [A][M]
r
k1[M]  k2
This equation suggests that unimolecular reaction have no
definite reaction order.
9.8 The rate theory of unimolecular reaction
9.8.2 Christiansen and Lindemann’s consideration
(3) Rate equation of Lindemann mechanism
Case I:
k1k2 [A][M]
r
k1[M]  k2
When the pressure of the system is low enough. When the pressure
and the concentration of A and M is low, the collision frequency is
low and thus the deactivation is rare.
Case II:
At high pressure. The collision frequency is high and thus the
deactivation is fast. When the rate of deactivation is much higher
than the rate of decomposition.
k1k2
r
[A]  k [A]
k1
This is an expression for the pseudo-first-order reaction.
9.8 The rate theory of unimolecular reaction
9.8.2 Christiansen and Lindemann’s consideration
(3) Rate equation of Lindemann mechanism
k
r  k [A]
r
k1k2 [A][M]
k1[M]  k2
r  k1[A][M]
[A]
The Lindemann mechanism can satisfactorily explain the phenomena
of the unimolecular reaction.
9.8 The rate theory of unimolecular reaction
9.8.2 Christiansen and Lindemann’s consideration
(3) Rate equation of Lindemann mechanism
experimental
Lindemann
The quantitative calculation of Lindermann mechanism was poor. To
modify Lindemann mechanism, Hinshelwood used theory of energy
partition to calculate k1, but the result is still not satisfactory.
9.8 The rate theory of unimolecular reaction
9.8.3 RRKM theory
In 1930s, Rice-Ramsperger-Kassel
established another mechanism for
unimolecular reaction.
In 1950, Marcus innovated the
mechanism and introduced TST into the
treatment of unimolecular reaction.
Rudolph A. Marcus
1992 Noble Prize
USA
Theories of electron transfer
In which A is energized molecules
9.8 The rate theory of unimolecular reaction
9.8.3 RRKM theory
They postulated that, before A* decomposed to product, the energy
they attained must be transferred to the chemical bond to break and the
molecules must attain the transition state (A, energized molecule) with
special configuration similar to product.
The time needed for configuration transformation corresponds to the
time lag proposed by Lindemann.
experimental
RRKM
9.8 The rate theory of unimolecular reaction
Summary
To discus the following reaction based on different reaction
theories: simple collision theory, transition state theory and
unimolecular reaction.
2HI
H 2  I2