2. THEORIES OF UNIMOLECLAR
GASEOUS REACTION
It is easy to understand a bimolecular reaction on the basis of
collision theory. Thus, when two molecules A and B collide, their
relative kinetic energy exceeds the threshold energy with the result
that the collision results in the breaking of bonds and the formation of
new bonds .
But how can one account for a unimolecular reaction ? If we
assume that in such a reaction (A P ),the molecule A acquires the
necessary activation energy by colliding with another molecule , then
the reaction should obey second-order kinetics and not the first order
kinetics which is actually observed in several unimoleclar gaseous
reaction.
3. According to this theory , a unimolecular reaction A P
proceeds following mechanism;
A + A A* + A
Here A* is the energized A molecule which has acquired sufficient vibrational
energy to enable it to isomerize or decompose.
A* is simply a molecule in a high vibrational energy level and not an activated
complex. In first step what actually happen is that the kinetic energy of the
second molecule is transferred into the vibrational energy of the first.
1.Lindemann theory
K-1
K1
A P
K2
4. .In the lindemann mechanism , a time lag exists between the energization A to A*
and the decomposition (or isomerization) of prodcts . during this time lag , A* can
be de-energized back to A.
The rate of formation = k1 [A]2 and
The rate of decomposition = K-1 [A][A*] +K2 [A*]
According to study state approximation(s.s.a),
d[A*]/dt = K1[A]2 _ K-1 [A][A*] – K2 [A*] = 0 …………….(1)
so that [A*] = K1 [A]2 / K-1 [A]+ K2 …………………………………………(2)
The rate of the reaction is given by
r = - d[A] / dt = k2 [A*] ……………………………(3)
sbstituting Eq. (2) in Eq. (3),
r = K1 K2 [A]2 / K-1 [A] + K2 ………….(4)
5. The rate law given by Eq.( 4) has no definite order . we can , however, two limiting cases ,
Case 1 ;
If k-1[A] >> K2
Then the K2term in the denominator can be neglected ,
r = ( k1 k2 / k-1 )[A] …………………(5)
which is the rate equation for a first order reaction. In a gaseous reaction , this is the high –
pressure limit because at very high pressure ,[A] is very large so that k1[A]>>K2.
Case 2 ;
If k2 >>k-1[A]
then the k-1 [A] Term in denominator can be neglected,
r = k1[A]2 ……………….(6)
6. Which is the rate equation for a second –order reaction . This is
the low pressure limit.
The experimental rate is defined as
……………………….(7)
Where kuni is the unimolecular rate constant .
Comparing eqs.(4) and (5),we have
kuni = k’ = k1k2[A] /k-1[A]=K2 ……………..(8)
r = kuni [A]
7. LIMITATION OF LINEMANN THEORY
Equ. 8 becomes
k’ = k1 k2[A]/k-1[A] = K2 ……………(9)
Case 1;
K-1[A] >> K2
K1 = K1 K2 [A] / K-1[A]
K1 = K1 K2 / K-1 = K∞ …………(10)
K’ = CONSTANT(K∞ )
ZERO ORDER REACTION
Case 2;
k-1 << k2
k’ = k1 k2 [A] / K2
K’ = K[A] …………..(11)
FIRST ORDER REACTION
.
.
.
.
.
.
.
.
.
.
.
.
.
.
8. K ∞ ………………..........................……....
K’
[A]
Plot of k’ verses [A]
According to equ.(9), the plot of the first order rate constant K’ verses [A] is
HYPERPOLA.
The rate constant K’ is a constant in the heigher concentration range
.but falls of low concentration.
9. Application of this relationship to experimental data raises some difficulties
Another difficulty with lindemann mechanism becomes evident when experimental
results are in another way.
Rewritting eq.(8) as,
1 /k’ = k-1[A] + K2 /K1K2 [A]
= K-1[A]/K1K2[A] + K2 / K1K2[A]
1 /K’ = K-1 /K1K2 + 1/K1[A] ………………..(12)
Y = C + M x stright line equation
10. Ploting 1 / K’ VS 1 / [A] give stright line . However ,deviation
from linearity heave been found (fig -2.)
EXPERIMENTAL
THEORITICAL
1 / [A]
1 / K’
Theoretical rate is heigher than the
experimental rate .
From this graph theoretical curve is stright
line and the experimental line is hyperpola.
The variation between the two lines is one of the limitation of lindemann theory.
The variation is further explained by the RRK and SLATERS theory.
