The rate-determining step

In a nutshell

The rate-determining step is the slowest step in a multistep reaction. The rate equation can help identify the reactants in the rate-determining step and can be used to predict the reaction mechanism.

The rate-determining step

The rate-determining step in a reaction is the slowest step in a multistep reaction. Since a reaction is a series of steps, every step can have a different rate. The overall rate of reaction is decided by the step with the slowest rate, this is known as the rate-determining step.

The rate equation

The rate equation can be used to figure out the mechanism for a chemical reaction.

Finding out what reactants are in the rate-determining step

To find out what reactants are involved in the rate-determining step follow these steps:

If a reactant appears in the rate equation, it must affect the rate. Therefore this reactant must be in the rate-determining step.

Some important things to note:

The rate-determining step can be any step
The mechanism can't be typically predicted from the chemical equation, other data is typically required.

Predicting the rate equation

The rate equation can be predicted if the rate-determining step is known. The order of a reaction for a particular reactant is the number of molecules of that reactant in the rate-determining step.

Example

For the reaction:

$2NO\ +\ O_2\ \rightarrow\ 2NO_2$

There are two steps to this reaction:

Step 1:	$NO\ +\ NO\ \leftrightharpoons\ N_2O_2$	(fast)
Step 2:	$N_2O_2\ +\ O_2\ \rightarrow\ 2NO_2$	(slow, rate-determining step)

Since $N_2O_2$ and $O_2$ are involved in the rate-determining step the rate equation is:

$rate \ =\ k[N_2O_2][O_2]$

Note, $N_2O_2$ is not in the reaction since it's produced as an intermediate and used up in the subsequent step of the reaction.

Predicting the reaction mechanism

Knowing which reactants are in the rate-determining step can help figure out the mechanism since the reactants and how many of them, are known.

Example

There are two possible mechanisms for the following reaction, identify the mechanism which is most likely to be correct:

$C(CH_3)_3I\ +\ OH^-\ \rightarrow\ C(CH_3)OH\ +\ I^-$

$1$	$2$

The actual rate equation is:

$rate\ =\ k[C(CH_3)_3I]$

Since the rate equation is known (it was determined experimentally), the mechanism can be determined since only the haloalkane is in the mechanism and not $OH^-$ . Therefore, mechanism $2$ is most likely to be correct.

Butanone and iodine

The reaction between butanone and iodine is given below, the reaction is catalysed by hydrogen ions.

The equation for the reaction is:

$C_2H_5COCH_3\ +\ I_2\ \xrightarrow{H^+}\ C_2H_5COCH_2I\ +\ H^+\ +\ I^-$

The rate equation for the above reaction is:

$Rate\ =\ k[C_2H_5COCH_3][H^+]$

Butanone and $H^+$ are in the rate equation, therefore they are part of the rate-determining step.
Iodine is not in the rate equation, it can be involved either before or after the rate-determining step, in this case, it's after.
Both molecules have a reaction order of one, therefore one molecule of each is involved in the rate-determining step.
$H^+$ is a catalyst, it's regenerated in another step.

Step 1: slow (this is the rate-determining step).

Chemistry; Kinetics II; KS5 Year 12; The rate determining step

Step 2: fast

Chemistry; Kinetics II; KS5 Year 12; The rate determining step

Step 3: fast

Chemistry; Kinetics II; KS5 Year 12; The rate determining step

Step 4: fast

Chemistry; Kinetics II; KS5 Year 12; The rate determining step