# 12.4: The Rate Determining Step Approximation

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The rate determining step approximation is one of the simplest approximations one can make to analyze a proposed mechanism to deduce the rate law it predicts. Simply stated, the rate determining step approximation says that a mechanism can proceed no faster than its slowest step. So, for example, if the reaction

$A + B \rightarrow C \nonumber$

is proposed to follow the mechanism

$\underbrace{A +A \xrightarrow{k_1} A_2}_{\text{slow}} \nonumber$

$\underbrace{ A_2 \xrightarrow{k_2} C + A}_{\text{fast}} \nonumber$

the rate determining step approximation suggests that the rate (expressed in terms of the appearance of product $$C$$) should be determined by the slow initial step, and so the rate law will be

$\dfrac{[C]}{dt} = k_1[A]^2 \nonumber$

matching the order of the rate law to the molecularity of the slow step. Conversely, if the reaction mechanism is proposed as

$\underbrace{A \xrightarrow{k_1} A^*}_{\text{slow}} \nonumber$

$\underbrace{ A^* + B \xrightarrow{k_2} C}_{\text{fast}} \nonumber$

the rate determining step approximation suggests that the rate of the reaction should be

$\dfrac{[C]}{dt} = k_1[A] \nonumber$

again, with the order of the rate law matching the molecularity of the rate determining step.

This page titled 12.4: The Rate Determining Step Approximation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Patrick Fleming.