# 3.2.3: Rate Determining Step

The rate determining step is the slowest step of a chemical reaction that determines the speed (rate) at which the overall reaction proceeds. The rate determining step can be compared to the neck of a funnel. The rate at which water flows through a funnel is limited/ determined by the width of the neck of the funnel and not by the rate at which the water is poured into the funnel. Like the neck of the funnel, the slow step of a reaction determines the rate of a reaction. Not all reactions have rate determining steps and has one only if one step is significantly slower than the other steps in the reaction.

## Introduction

Rate determining step is the slowest step within a chemical reaction. The slowest step determines the rate of chemical reaction.The slowest step of a chemical reaction can be determined by setting up a reaction mechanisms. Many reactions do not occur in a single reaction but they happen in multiple elementary steps.

Consider this reaction:

$\ce{2NO2 +F2 -> 2NO2 F},$

which occurs via this mechanism

elementary step 1: $\ce{NO2 + F2 ->NO2F +F} \tag{slow}$

elementary step 2: $\ce{NO2+F -> NO2F} \tag{fast}$

For elementary step 1 has a rate constant of k1 and for elementary step 2 it has a rate constant of k2. The slowest step in this mechanism is elementary step 1 which is our rate determining step. Looking at this mechanism I see Intermediates. Intermediates are molecules or elements that are found on the product of one step but are also located in the reactant of another step. In this case we have two intermediates $$\ce{NO2}$$ and $$\ce{F}$$.

The rate equation is derived by the slowest step in the reaction. When writing a rate equation you set up the equation by writing rate is equal to the rate constant of the slowest step times the concentrations of the reactant or reactants raised to there reaction order. Lets look at elementary step one.

elementary step one: $\ce{NO2 +F2 -> NO2F + F}\nonumber$

Here in this example rate=k1[NO2][F2].

Example $$\PageIndex{1}$$

For this reaction

$\ce{2NO + O2 -> 2NO2} \nonumber$

1. What are the intermediates ?
2. What is the rate equation?

elementary step one:

$\ce{NO + NO <=> N2O2 } \tag{fast equilibrium}$

elementary step two:

$\ce{N2O2 + O2 -> 2 NO2 }\tag{slow}$

Solution

1: N2O2 is found on the product side and the reactant side.

2: rate= k2[N2O2][O2]; N2O2 gets canceled out leaving the overall reaction rate.

Example $$\PageIndex{2}$$

1. What is the overall reaction?
2. What is the rate equation?
3. Are there intermediates if so what are they?
4. What is the rate determining step?

elementary step one:

$\ce{Br2 + M <=> Br + Br +M}\tag{fast equilibrium}$

elementary step two:

$\ce{Br +H2 -> HBr +H }\tag{slow}$

elementary step three:

$\ce{H + Br2 -> HBR + Br }\tag{fast}$

Solution

1. H2+Br2 -> 2HBr ; Br and H will be canceled out and therefore they won't appear in the overall reaction.
2. rate=k2 [Br][H2]
3. Br, H are the intermediates in the reaction.
4. elementary step 2 is the slowest step in the mechanism.