Question

For a reaction $A + B \to {\text{Products}}$, the rate law is $ - Rate = K\left[ A \right]{\left[ B \right]^{3/2}}$. Can the reaction be an elementary reaction? Explain.

Answer 1

Hint: An elementary reaction is the one in which there are no intermediates formed during the reaction. For the above reaction, the rate law equation has been given. One can calculate the intermediates formed and the steps taken by the reaction to complete the reaction and decide whether the reaction is elementary or not.

Complete step by step answer:
1) First of all we will learn about the concept of elementary reaction. The elementary reaction has only one step that means the reaction completes in only one step. This also means that there are no intermediates formed during the reaction process. If there is the formation of one or more intermediates then the reaction will not be an elementary reaction.
2) Now let us discuss the given reaction in question where the rate of reaction is given as,
The reaction is $A + B \to {\text{Products}}$,
$ - Rate = K\left[ A \right]{\left[ B \right]^{3/2}}$
3) Now let us find out the order of the reaction based on the above rate equation as below,
Order of reaction $ = 1 + \dfrac{3}{2} = \dfrac{5}{2}$.
The order of a reaction is the sum of molecularity of the components present in the reaction. In this reaction, reactant A has molecularity 1 and reactant B has the molecularity $\dfrac{3}{2}$ and the sum of both the molecularities will be $\dfrac{5}{2}$ which is the order of the reaction.
4) Now the order of the reaction is $\dfrac{5}{2}$ which is not equal to the stoichiometric coefficient of both reactants. This means there are multiple steps taken and the reaction is not completed in a single step.
Therefore, this reaction is not an elementary reaction.

Note: An elementary reaction can be as unimolecular, bimolecular, and termolecular elementary reaction based on the stoichiometry and the order of the reaction. The order of reaction and the stoichiometry of the reaction must be in integral form to become an elementary reaction.