Question

Explain the rate determining step with an example.

Answer 1

1. Most of the chemical reactions occur by multistep reactions. In the sequence of steps, it is found that one of the steps is considerably slower than the others. The overall rate of the reaction cannot be lower in value than the rate of the slowest step.

2. Thus in a multistep reaction the experimentally determined rate corresponds to the rate of the slowest step. The step which has the lowest rate value among the other steps of the reaction is called as the rate determining step (or) rate limiting step.

3. Consider the reaction,

\[\ce{2A + B -> C + D}\]

going by two steps as follows,

\[\ce{A + B ->[k1] C + Z}\] ...........[1 step (slow)]

\[\ce{Z + A ->[k2] D}\] ............[2 step (fast)]

\[\ce{2A + B -> C + D}\]

Here the overall rate of the reaction corresponds to the rate of the first step which is the slow step and thus the first step is called as the rate determining step of the reaction. In the above equation, the rate of the reaction depends upon the rate constant k only. The rate of the second step doesn't contribute experimentally determined overall rate of the reaction.

For example,

\[\ce{NO2_{(g)} + CO2_{(g)} -> NO_{(g)} + CO2_{(g)}}\]

Which occurs in two elementary steps:

\[\ce{NO2 + NO2 -> NO + NO3 (Slow)}\]

\[\ce{NO3 + CO -> NO2 + CO2 (Fast)}\]

Because the first step is the lowest step, the overall reaction cannot proceed any faster than the rate of the first elementary step. The first elementary step in this example is therefore the rate determining step.

The rate equation for this reaction is equal to the rate is constant of step-1 multiplied by the reactants of that first step. If the rate constant of step-1 is denoted as k₁ then the rate of the first step in the reaction (and the total reaction) will be,

Rate = k₁ [NO₂] [NO₂]

= K₁ [NO₂]₂