## Wikipedia - Stadio cineticamente determinante rate-controlling step

https://doi.org/10.1351/goldbook.R05139
A rate-controlling (rate-determining or rate-limiting) step in a reaction occurring by a @C01211@ @ST06775@ is an @E02035@ the @O04322@ for which exerts a strong effect — stronger than that of any other @O04322@ — 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 @E02035@ having a @O04322@ $$k_{i}$$ by: $\text{CF}=\frac{\partial (\ln \nu)}{\partial \ln k_{i}}$ where $$\nu$$ is the overall @R05156@. In performing the partial differentiation all equilibrium constants $$K_{j}$$ and all rate constants except $$k_{i}$$ are held constant. The @E02035@ having the largest control factor exerts the strongest influence on the rate $$\nu$$, 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 @K03405@. 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:
 R05139-1.png (1) R05139-2.png (2)
Assuming that C reaches a @S05962@, then the observed rate is given by: $\nu = \frac{k_{1}\,k_{2}\,\left[\text{A}\right]\left[\text{B}\right]\left[\text{D}\right]}{k_{-1}+k_{2}\left[\text{D}\right]}$ Considering $$k_{2}\left[\text{D}\right]$$ a pseudo-first order @O04322@, then $$k_{2}\left[\text{D}\right]\gg k_{-1}$$, and the observed rate $$\nu = k_{1}\ \left[\text{A}\right]\left[\text{B}\right]$$ and $$k_{\text{obs}}=k_{1}$$. Step (1) is said to be the rate-controlling step. If $$k_{2}\left[\text{D}\right]\ll k_{-1}$$, then the observed rate: $\nu = \frac{k_{1}\ k_{2}}{k_{-1}}\left[\text{A}\right]\left[\text{B}\right]\left[\text{D}\right]=K\ k_{2}\left[\text{A}\right]\left[\text{B}\right]\left[\text{D}\right]$ where $$K$$ is the @E02177@ for the pre-equilibrium (1) and is equal to $$\frac{k_{1}}{k_{-1}}$$, and $$k_{\text{obs}}=K\ k_{2}$$. Step (2) is said to be the rate-controlling step.