Preferred Label : rate-controlling step;
IUPAC definition : A rate-controlling (rate-determining or rate-limiting) step in a reaction occurring
by a composite reaction sequence 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 ki by: \[{CF} \frac{
(\ln \nu)}{ \ln k_{i}}\] where v is the overall rate of reaction. In performing the
partial differentiation all equilibrium constants Kj and all rate constants except
ki are held constant. The elementary reaction having the largest control factor exerts
the strongest influence on the rate v, 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: table tr td /td td
(1) /td /tr tr td /td td (2) /td /tr /table Assuming that C reaches
a steady state, then the observed rate is given by: \[\nu \frac{k_{1}\,k_{2}\,\left[{A}\right]\left[{B}\right]\left[{D}\right]}{k_{-1}
k_{2}\left[{D}\right]}\] Considering k2[D] a pseudo-first order rate constant, then
k2[D] k-1, and the observed rate v k 1 A B and kobs k1. Step (1) is said to
be the rate-controlling step. If k2[D] k-1, then the observed rate: \[\nu \frac{k_{1}\
k_{2}}{k_{-1}}\left[{A}\right]\left[{B}\right]\left[{D}\right] K\ k_{2}\left[{A}\right]\left[{B}\right]\left[{D}\right]\]
where K is the equilibrium constant for the pre-equilibrium (1) and is equal to k1/k-1,
and kobs K.k2. Step (2) is said to be the rate-controlling step.;
Origin ID : R05139;
See also
A rate-controlling (rate-determining or rate-limiting) step in a reaction occurring
by a composite reaction sequence 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 ki by: \[{CF} \frac{
(\ln \nu)}{ \ln k_{i}}\] where v is the overall rate of reaction. In performing the
partial differentiation all equilibrium constants Kj and all rate constants except
ki are held constant. The elementary reaction having the largest control factor exerts
the strongest influence on the rate v, 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: table tr td /td td
(1) /td /tr tr td /td td (2) /td /tr /table Assuming that C reaches
a steady state, then the observed rate is given by: \[\nu \frac{k_{1}\,k_{2}\,\left[{A}\right]\left[{B}\right]\left[{D}\right]}{k_{-1}
k_{2}\left[{D}\right]}\] Considering k2[D] a pseudo-first order rate constant, then
k2[D] k-1, and the observed rate v k 1 A B and kobs k1. Step (1) is said to
be the rate-controlling step. If k2[D] k-1, then the observed rate: \[\nu \frac{k_{1}\
k_{2}}{k_{-1}}\left[{A}\right]\left[{B}\right]\left[{D}\right] K\ k_{2}\left[{A}\right]\left[{B}\right]\left[{D}\right]\]
where K is the equilibrium constant for the pre-equilibrium (1) and is equal to k1/k-1,
and kobs K.k2. Step (2) is said to be the rate-controlling step.
