Page 93 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch07 Elementary Physical Chemistry

78 Elementary Physical Chemistry

It is assumed that a molecule A collides with another molecule A
to produce an energetically excited molecule A . The following reactions
∗
(assumed to be elementary) occur. In all these reactions, the rate constants
k 1 and k 2 are in the forward direction, and k is in the reverse direction.

1
∗
1) A + A → A +A
∗
d[A ]/dt = k 1 [A] 2 (7.54)
∗
The A molecule may lose its energy by colliding with another molecule A.
∗
2) A +A → A+A
−d[A ]/dt = k [A ][A] fast (7.55)
∗

∗
1
or A may shake itself apart, by undergoing a unimolecular reaction
∗
∗
3) A → P
∗
∗
−d[A ]/dt = k 2[A ] slow (7.56)
Assuming that A is the intermediate, and thus
∗
∗
d[A ]/dt =0
2

∗
∗
= k 1 [A] − k [A ][A] − k 2 [A ] (7.57a)
1
which gives
∗ 2
[A ]= k 1 [A] /{k 2 + k [A]} (7.57b)
1
Finally, if (not always true) reaction (3) is very much slower than (2), and
thus k k 2 ,we obtain

1
∗
[A ]= k 1 /k [A]= k[A} (7.58a)
1
and therefore,

−d[A ]/dt =d[P]/dt = k[A] (7.58b)
∗

which is first order.