Page 80 - Bruno Linder Elementary Physical Chemistry

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

Chemical Kinetics 65

Plot of ln[A]vs. t in a first-order reaction.
Fig. 7.1

Plot of 1/[A]vs. t in a second-order reaction.
Fig. 7.2

In a second-order reaction, such as

−d[A]/dt = k A [A] 2 (7.19a)
2
−d[A]/[A] = k Adt (7.19b)
2
we have dx/x = −1/x and so integration of Eq. (7.19b) between the
limits [A] 0 and [A], gives
1/[A] − 1/[A] 0 = k A t (7.19c)

Accordingly, a plot of 1/[A]vs. t gives a straight line (Fig. 7.2).

Note: The foregoing does not apply to all second-order reactions.
For example, for a reaction of the type A + B → C in which the
concentrations of A and B are not equal, the rate law is much more
complicated.