Page 65 - Basic physical chemistry for the atmospheric sciences

Chemical kinetics .4i l

k r
A + B � AB
be an elementary process . Then, the rate of increase of [AB] 1s
kr[A][B] . The reverse elementary process is
k.
AB� A + B
Hence, the rate of decrease of [AB] is k.[AB] . At equilibrium there s
i
n o net change of [A ] . Therefore,
B
kr[A][B] = k.[AB]

or ,
kr [AB]
- --
k. [A][B]
But the right-hand side of the last relation is the equilibrium constant
K for the forward reaction. Therefore,
c
kr
k = K c (3 .8)
r
which is the required relationship for an elementary process .
In the case of a chemical reaction that proceeds by a multistep
process, each elementary process must be in equilibrium if Eq. ( 3 . 8 ) is
to be applied to each step. This is called the principle o f detailed
balancing; it permits a relationship to be derived between the rate
coefficients for the elementary processes and the equilibrium constant
2
for the overall reaction .
Exercise 3 .4. If the reaction mechanism for

IS
N02(g) + 03(g)� N03(g) + 02(g) (i)
N03(g) + N0 (g) + M � N205(g) + M (ii)
2
derive an expression for the equilibrium constant Kc for the forward
reaction of the overall equation in terms of the forward and reverse
rate coefficients for the elementary processes .
Solution . The condition for equilibrium is that each elementary pro­
cess be in equilibrium. Hence, if k1r and k1• are the forward and reverse