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

Concept: The order of a reaction is defined as the sum of the powers of the concentration terms appearing in the experimentally determined rate law. For a rate law: \[ \text{Rate}=k[A]^m[B]^n \] the overall order is: \[ m+n \] The molecularity of an elementary reaction, however, is always a whole number because it represents the actual number of reacting species participating in a single elementary step.

Step 1: Identify the powers of concentration terms. Given: \[ \text{Rate}=k[A]^{\frac{3}{2}}[B] \] Power of concentration of A: \[ \frac{3}{2} \] Power of concentration of B: \[ 1 \]

Step 2: Calculate overall order. Overall order \[ =\frac{3}{2}+1 \] \[ =\frac{5}{2} \] \[ =2.5 \] Therefore, \[ \boxed{\text{Overall Order}=\frac{5}{2}} \]

Step 3: Can the reaction be elementary? An elementary reaction occurs in a single step. For elementary reactions:

• Molecularity is always an integer.

• Rate law follows directly from the stoichiometric equation.

• Fractional powers do not appear.
In the given rate law: \[ [A]^{\frac{3}{2}} \] contains a fractional exponent. A fractional order indicates that the reaction mechanism involves multiple steps and intermediates. Therefore, the reaction cannot be represented by a single elementary step.

Step 4: Conclusion. Since the rate law contains a fractional exponent, the reaction is not elementary and must proceed through a complex mechanism. \[ \boxed{\text{Overall Order}=\frac{5}{2}} \] \[ \boxed{\text{The reaction cannot be elementary.}} \]

Reason: Elementary reactions have integral molecularity, whereas the given rate law exhibits a fractional order.