A rate-controlling (rate-determining or rate-limiting) step in a reaction occurring
by a
composite reactionsequence is an
elementary reaction the
rate constant for which exerts a strong effect — stronger than that of any other
rate constant — on the overall rate. It is recommended that the expressions rate-controlling, rate-determining
and rate-limiting be regarded as synonymous, but some special meanings sometimes given
to the last two expressions are considered under a separate heading. A rate-controlling
step can be formally defined on the basis of a control function (or control factor)
CF, identified for an
elementary reaction having a
rate constant
by:
where
is the overall
rate of reaction. In performing the partial differentiation all equilibrium constants
and all rate constants except
are held constant. The
elementary reaction having the largest control factor exerts the strongest influence on the rate
, and a step having a CF much larger than any other step may be said to be rate-controlling.
A rate-controlling step defined in the way recommended here has the advantage that
it is directly related to the interpretation of
kinetic isotope effects.
As formulated this implies that all rate constants are of the same dimensionality.
Consider however the reaction of A and B to give an intermediate C, which then reacts
further with D to give products:
Assuming that C reaches a
steady state, then the observed rate is given by:
Considering
a pseudo-first order
rate constant, then
,
and the observed rate
and
.
Step (1) is said to be the rate-controlling step.
If
,
then the observed rate:
where
is the
equilibrium constant for the pre-equilibrium (1) and is equal to
,
and
.
Step (2) is said to be the rate-controlling step.
Source:
PAC, 1994, 66, 1077
(Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994))
on page 1156
See also:
PAC, 1996, 68, 149
(A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC
Recommendations 1996))
on page 182