Under what conditions a bimolecular reaction may be kinetically of first order ?

Options

A. when both reactants have same concentration
B. when one of the reacting species is in large excess
C. when the reaction is at equilibrium
D. when the activation energy of reaction is less

Answer

To determine the conditions under which a bimolecular reaction can be kinetically of first order, we need to analyze the nature of bimolecular reactions and how their rate laws are formulated.

### Step-by-Step Solution:

1. **Understanding Bimolecular Reactions**:
- A bimolecular reaction involves two reactant molecules. These can either be two different molecules (A + B) or two identical molecules (2A).
- The general form of a bimolecular reaction can be represented as:
\[ A + B \rightarrow P \]

2. **Rate Law for Bimolecular Reactions**:
- The rate law for a bimolecular reaction is typically expressed as:
\[ \text{Rate} = k [A]^m [B]^n \]
- For a bimolecular reaction, the sum of the orders \(m + n\) is 2 (since it involves two reactants).

3. **Condition for First Order Kinetics**:
- For a bimolecular reaction to exhibit first-order kinetics, we need to manipulate the concentrations of the reactants.
- This can be achieved if one of the reactants is in large excess compared to the other.

4. **Mathematical Representation**:
- If we assume that the concentration of reactant A is much larger than that of B, we can consider [A] to be constant.
- Thus, we can rewrite the rate law as:
\[ \text{Rate} = k' [B] \]
- Here, \(k' = k [A]^m\) becomes a new rate constant that incorporates the constant concentration of A.

5. **Conclusion**:
- Therefore, under the condition where one of the reactants (say A) is in large excess, the bimolecular reaction can be simplified to a first-order reaction with respect to the other reactant (B).

### Summary of Conditions:
- A bimolecular reaction can be kinetically first order when one reactant is in large excess, making its concentration effectively constant throughout the reaction.