Page 91 - Bruno Linder Elementary Physical Chemistry

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

76 Elementary Physical Chemistry

The overall rate for d[N 2 O 2 ]/dt is zero. So,

2
k 1 [NO] − k [N 2 O 2 ] − k 2 [N 2O 2][O 2 ] = 0 (7.41)
1
Hence,
2

[N 2O 2]= k 1 [NO] /{k + k 2 [O 2 ]} (7.42)
1
The product NO 2 is produced only in reaction (3), which is the slow reaction
and thus the reaction determining step. For this reaction,

1
r = d[NO 2 ]/dt = k 2 [N 2 O 2 ][O 2 ] (7.43)
2
and thus the rate of production of NO 2 is

2
d[NO 2 ]/dt =2k 1 k 2 [NO] [O 2 ]/(k + k 2 [O 2 ]) (7.44)

1
Finally, assuming that k is much greater than k 2 , we can neglect the term

1
k 2 [O 2] in the denominator, yielding
2
2

d[NO 2]/dt =2(k 1 k 2/k )[NO] [O 2]= k[NO] [O 2] (7.45)
1
which is the expression obtained experimentally.
7.13. The Rate-Determining Step (or Equilibrium)
Approximation
Here, the reaction mechanism is assumed to consist of one or more reversible
reactions that stay close to equilibrium during most of the reaction. This
reaction is followed by a slow step which, as noted before, is the rate-
determining step.

Example 7.8. Consider the reaction catalyzed by Br −

Br
−
+
+
H + HNO 2 +C 6 H 5 NH 2 −→ C 6 H 5 N +2H 2 O (7.46)
2
The observed reaction rate law is
+
r = k[H ][HNO 2 ][Br ] (7.47)
−