Page 199 - Instant notes

Rate laws in action 185

not overwhelmingly in favor of products, the back reaction converting products into
reactants becomes important since the overall net rate of reaction must decrease (and is
zero at equilibrium) (see Topic C1). Consider a general case of an isomerization reaction
between A and B in which the opposing kinetics are first order (or pseudo-first order):

and the equilibrium concentrations are [A] e and [B] e. When the reaction is not at
equilibrium the concentrations of A and B can be written as [A] e+x and [B] e−x, where x
represents some arbitrary displacement in concentration (positive or negative) away from
equilibrium. The net reaction towards equilibrium at this instant is described by the rate
law:

or, on rearrangement, by:

At equilibrium, x=0, and there is no net reaction so:

which on substitution above gives:

This equation shows that the approach to equilibrium of opposing first order reactions is
also a first order process with a first order rate constant equal to the sum of the forward
and reverse first order rate constants, i.e. opposing reactions approach equilibrium at a
rate faster than either the forward or backward reactions alone. The relaxation to
equilibrium of a mixture initially containing concentration [A] 0 of A and zero
concentration of B is shown in Fig. 1.