Question

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

Hint:

Fractional or zero order reactions always indicate a complex reaction mechanism. Molecularity can never be fractional, whereas order can be fractional.

Answer 1

Step 1: Calculate overall order.
Rate $= k[\text{A}]^{3/2}[\text{B}]^1$. Overall order $= \dfrac{3}{2} + 1 = \dfrac{5}{2} = 2.5$.
Step 2: Requirement for elementary reactions.
An elementary reaction occurs in a single molecular event. For any elementary step, the exponents in the rate law must be positive whole numbers equal to the stoichiometric coefficients. Fractional orders NEVER arise in elementary reactions.
Step 3: Conclusion.
The exponent $\dfrac{3}{2}$ on $[\text{A}]$ is fractional. You cannot have half a molecule reacting in a single step; this is physically impossible. A fractional order always signals a complex multi-step mechanism involving intermediates. This reaction CANNOT be elementary.