Question

For a reaction A + B → Products, the rate law is $\mathrm{Rate = k[A][B]^{3/2}}$. Write the overall order of the reaction. Can this reaction be an elementary reaction ? Give reason in support of your answer.

Hint:

Order = sum of powers = 1 + 3/2 = 2.5; a fractional order means a multi-step reaction.

Answer 1

Concept: The overall order of a reaction is just the sum of the powers to which the concentrations are raised in the experimentally found rate law.

Step 1: Add up the powers
In $\mathrm{Rate = k[A][B]^{3/2}}$, the power on [A] is 1 and the power on [B] is $\tfrac{3}{2}$. Add them: \[ \text{order} = 1 + \tfrac{3}{2} = \tfrac{5}{2} = 2.5 \]

Step 2: Can it be elementary
No, it cannot. An elementary reaction takes place in a single step, and for a single step the order must be a whole number, equal to its molecularity (you cannot have half a molecule colliding). Here the order is 2.5, a fraction. A fractional order can only come from a reaction that goes through several steps. So this reaction cannot be elementary.

Answer: The overall order is 2.5, and the reaction is not elementary because its order is fractional.