Question

For a reaction \(A+B\rightarrow\) products, the rate law is: \[ Rate=k[A][B]^{\frac{3}{2}} \] Write the overall order of the reaction. Can this reaction be an elementary reaction? Give reason.

Hint:

Order can be fractional, but molecularity cannot be fractional. So fractional order usually indicates a complex reaction.

Answer 1

Concept:
Order of reaction is the sum of powers of concentration terms in the rate law. For elementary reactions, powers in rate law are usually equal to stoichiometric coefficients and must represent molecularity. Molecularity cannot be fractional.

Step 1: Write the given rate law.
\[ Rate=k[A][B]^{\frac{3}{2}} \] Power of \([A]\): \[ 1 \] Power of \([B]\): \[ \frac{3}{2} \]

Step 2: Calculate overall order.
\[ \text{Order}=1+\frac{3}{2} \] \[ \text{Order}=\frac{2}{2}+\frac{3}{2} \] \[ \text{Order}=\frac{5}{2} \]

Step 3: Check whether it can be elementary.
For an elementary reaction, molecularity must be a whole number. But here the order is fractional: \[ \frac{5}{2} \] A fractional order suggests that the reaction is complex and occurs through multiple steps. Therefore, it cannot be an elementary reaction. Hence: \[ \boxed{\text{Overall order}=\frac{5}{2}} \] \[ \boxed{\text{It cannot be elementary because molecularity cannot be fractional.}} \]