Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

8.2 Lindemann mechanism 180
I Half-pressure: We have found the following results:
=
2 1 [M]
−1 [M] + 2
(8.17)
Thus, if −1 [M] = 2 ,wehave
1
∞ = 2
−1
(8.18)
0 = 1 [M] (8.19)
=
2 1 [M]
= 2 1 [M]
−1 [M] + 2 2 −1 [M] = 1 2 1
= 1 2 −1 2 ∞ (8.20)
Half “pressure”:
[M] 12
= 2
−1
(8.21)
I Lifetimes of energized molecules: It is instructive to look at the reciprocal values:
1
−1 [M] = 1 2
(8.22)
1
• is the time between two collisions. This is, in fact, the lifetime of the
−1 [M]
energized molecules with respect to collisional deactivation.
• 1 is the lifetime of the excited molecules with respect to reaction.
2
Thus, at the half pressure, we have
Collisional Deactivation = Unimolecular Decay (8.23)
I Determination of k ∞ :
y
=
2 1 [M]
−1 [M] + 2
(8.24)
1
= −1
+ 1 1
1 2 1 [M]
(8.25)
= 1 + 1 1
∞ 1 [M]
(8.26)
= 1 + 1 ∞ 0
(8.27)
y Plot of −1 vs. [M] −1 should give a straight line with slope 1 −1 and intercept
∞ −1 .