What do you mean by rate determining step

One or more molecules are involved in a chemical reaction. As a result, a chemical reaction occurs in one step or more than one step. Writing differential rate equation for one step reaction is easy but writing differential rate equation for more than one step reaction is the biggest problem. To solve the problem of writing differential rate equations for multistep reactions, we study the rate determination step. It helps us to write differential rate equation for a multistep reaction.

One Step Reaction?? 

A single-step reaction which takes place in one single step is called an elementary reaction. The differential rate equation can be easily written for the initial reactions. 

More Than One Step Reaction?? 

While the chemical reaction that involves a series of two or more steps is called a complex or complicated reaction or non-elementary reaction. The rate law cannot be easily written for non-elementary reactions. The rate law for these types of reaction is dependent on the rate determination step.

In a non-elementary reaction, the sequence of steps through which the reaction takes place is called the mechanism of the chemical reaction. Each sequential step in the mechanism is an elementary step reaction. During the course of chemical reaction, these molecules constantly bump into each other and based on that, the chemical reaction takes place.

RATE DETERMINING STEP

When a reaction is completed in more than one elementary step, then the rate of reaction depends on the slowest step at which the overall reaction proceeds, out of all the other steps. And this slow step is called as "Rate Determining Step". 

("Rate determining step is the one which is the slowest step. Slowest step is the one that control the overall rate of reaction and therefore the overall conversion")

The rate determining step is only considerable in the case of complex reaction that takes place more than one step as shown in below figure. 

For Example

1)                 NO₂ + CO ➝ NO + CO₂

The above reaction is proceeding in more than one step;

         Step-1:  NO₂ + NO₂ ➝ NO₃ + NO (slow) 

         Step-2:  NO₃ + CO ➝ NO₂+ CO₂ (fast) 

Here, Step-1 is the slowest step that determine the rate of overall reaction. Hence, step-1 is the rate determining step in this case.

Now, the rate of reaction based on the reaction step-1 is given as;

                     ➩   r = k [NO₂]²

2)                 2 NO₂+ Cl₂ ➝ 2NO₂Cl

The above reaction is proceeding in more than one step;

Step-1:  NO₂ + Cl₂ ➝ NO₂Cl + Cl     (Slow)

Step-2:  NO₂ + Cl ➝ NO₂Cl          (Fast)

Here, Step-1 is the slowest step or rate determining step that determine the rate of overall reaction.

Thus, the rate law will depend on the rate determining step of reaction and given as;

➩ Rate, r= k₁[NO₂][Cl₂]

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