Physical Chemistry Third Edition

584 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics

Let us see what would be the consequence of assuming that equilibrium corresponds

to a large forward rate of the two-step mechanism and a large reverse rate of the one-

step mechanism with smaller rates for the reverse rate of the two-step mechanism and

the forward rate of the one-step mechanism. If a solid substance can be found that

removes iodine atoms, insertion of this substance into the reaction vessel would slow

down the forward rate of the two-step reaction but would do nothing to the rate of the

one-step mechanism. The system would no longer be at equilibrium and would have to

change its composition to restore equilibrium. Removal of the solid substance would

cause the system to return to its original equilibrium state, so that one could at will

change the equilibrium composition back and forth. It would be possible to harness

some of the Gibbs energy change of the forward reaction or the reverse reaction, and

one would have a perpetual motion machine of the second kind, which violates the laws

of thermodynamics. These two mechanisms must therefore conform to the principle of

detailed balance.

By analogy with Eq. (11.4-7), the equilibrium constant for the mechanism of

Eq. (13.2-1) is given by

K 1 a

k 1 a

k′ 1 a

(13.2-2)

By analogy with Eq. (11.5-12), the equilibrium constant for the mechanism of

Eq. (12.5-15) is

K

k 1 k 2

k 1 ′k′ 2

(13.2-3)

Since both equilibrium constants refer to the same reaction, they must be equal:

k 1 k 2

k 1 ′k 2 ′



k 1 a

k′ 1 a

(13.2-4)

This relation provides a condition that the rate constants for the two mechanisms must

obey. Of the six rate constants, only five are independent of each other. If we apply the

principle of detailed balance to a catalyzed and an uncatalyzed mechanism for a given

reaction, we can see thata catalyst must catalyze the reverse reaction if it catalyzes the

forward reaction, since it cannot change the equilibrium constant of the reaction.

The principle of detailed balance is related to theprinciple of microscopic rever-

sibility, which states that mechanical processes are time-reversible. That is, the equa-

tions governing these processes must be unchanged if the value of the time is replaced

by its negative so that time appears to run backward. If it were possible to take a moving

picture of the motions of molecules, the mechanical laws of motion would still apply

if the movie were run backward. If equilibrium corresponded to the forward reaction

of one mechanism being balanced by the reverse reaction of the other mechanism, a

moving picture run backwards would be different from the same moving picture run

in the forward direction.

Irreversible macroscopic processes do not obey time reversibility. A moving picture

of a macroscopic diffusion process or a chemical reaction would appear to violate the

second law of thermodynamics if the movie were run backwards. The entropy of the

universe would seem to decrease. However, a microscopic movie of the molecular

motions during the irreversible process must appear normal if run backwards. One of

the most interesting questions of science:How can irreversible macroscopic processes

result from time-reversible molecular processes?We believe that macroscopic proper-

ties are determined by microscopic properties and that macroscopic states are equivalent