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Rate law determination 163

Related topics Empirical approaches to kinetics Rate laws in action (F5)

Formulation of rate laws (F4) The kinetics of real systems

Method of isolation

The experimental determination of the rate law is considerably simplified by the method
of isolation in which all the reactants except one are present in large excess. To a good
approximation, the concentrations of the excess reactants remain constant during the
reaction which enables the order of the reaction with respect to the isolated reactant to
be determined directly from observation of the kinetics of just the isolated species. For
example, if the true rate law for a reaction is:
2
rate=k[A][B]
and reactant B is in excess, then the concentration of B throughout the reaction can be
approximated by its initial value [B] 0 and the rate law becomes:
rate=k′[A]

2
where k′=k [B] 0 is still a constant. Since the original third order reaction has been
converted into a first order form the latter rate law is classified as pseudo-first order to
indicate that the rate law disguises intrinsic higher order and only applies under particular
conditions of reactant relative concentrations. k′ is called the pseudo-first order rate
constant.
Similarly, if, instead, reactant A is present in large excess, the rate law becomes
pseudo-second order:
2
rate=k′′[B]
where k′′=k[A] 0 is the pseudo-second order rate constant. Pseudo rate laws of lower
order, and involving only one species, are easier to identify and analyze than the
complete law.

Method of initial rates

A differential rate law is the basic mathematical formulation of a rate law expressing the
rate of change of a species concentration with time. It has the general form:

where α, β,…is the order of reaction with respect to species A, B,…A positive sign to the
differential of a particular species indicates rate of formation of that species, whereas a
negative sign indicates rate of removal of that species.
If [A] 0, [B] 0…are the initial concentrations of species A, B,…then applying logarithms
to this generalized differential rate law at time t=0 gives: