Concise Physical Chemistry

c10 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

152 CHEMICAL KINETICS

approach to equilibrium is always less than either the forward reaction or the back

reaction becausekfandkbwork in opposition to one another.

For simple reversible systems,

A→←B

A+B←→C

A+B←→C+D

etc.

equations can be worked out that relate the observed rate constantkobsfor the approach

to equilibrium tokf andkb, the elementary reactions that contribute to it (Metiu,

2006).

The concept of equilibrium as the result of opposite forward and back reactions is

called the principle of detailed balance; for example, at equilibrium,

kfA−kbB= 0

The equations implied by the principle of detailed balance rest on the assumption that

the concentrations of reactant and product vary in the simplest possible way. This

assumption is often violated and must never be taken for granted.

Some enzyme-catalyzed reactions, including the famous Michaelis–Menten

(Houston, 2001) mechanism, are examples of more complicated reaction mecha-

nisms. Despite their complexity, they can often be broken down into elementary steps

and equilibriums. The kinetics of complex reactions can sometimes be simplified by

regarding one component of the reaction as a constant during part of the chemical

process. This is thesteady-state approximation(Metiu, 2006).

An especially important class of reaction mechanisms is that of the chain reactions

in which one molecular event leads to many, possibly very many, products. The classic

example for chemists is production of HBr from the elements:

H 2 +Br 2 →2HBr

for which we might guess the rate law to be

1

2

d[HBr]

dt

=k[H 2 ][Br 2 ] wrong

but that guess would be wrong. Instead, the rate law is

1

2

d[HBr]

dt

=k[H 2 ][Br 2 ]^1 /^2 right