Question

State the condition under which a bimolecular reaction may be kinetically a first order reaction.

Hint:

"Pseudo" means false. These reactions are not "true" first-order reactions because they require two different molecules to collide, but they appear first-order in experiments.

Answer 1

Concept:

• Molecularity is the number of reacting species taking part in an elementary step, whereas the order is determined experimentally.

• A bimolecular reaction involves the collision of two molecules.

• If a bimolecular reaction follows first-order kinetics, it is called a pseudo-first-order reaction.

• This usually happens when the concentration of one reactant remains practically unchanged during the reaction.
Step 1: Analyze the rate law for a bimolecular system
Consider a reaction between two species \( A \) and \( B \): \[ A + B \rightarrow \text{Products} \]
The general experimental rate law is: \[ \text{Rate} = k'[A][B] \]
This is a second-order reaction (1st order with respect to \( A \) and 1st order with respect to \( B \)).

Step 2: Apply the condition of large excess
If the reactant \( B \) is present in a very large excess (for example, if \( B \) is the solvent), its concentration will not change significantly as the reaction proceeds.
Therefore, \( [B] \) can be treated as a constant. The rate law is modified to: \[ \text{Rate} = (k'[B]) [A] \] \[ \text{Rate} = k[A] \]
where \( k = k'[B] \). The reaction now behaves as a first-order reaction kinetically.

Step 3: Illustrate with a chemical example
The inversion of cane sugar is a bimolecular reaction: \[ C_{12}H_{22}O_{11} + H_{2}O \xrightarrow{H^{+}} C_{6}H_{12}O_{6} + C_{6}H_{12}O_{6} \]
Because water is present in such a massive excess, its concentration remains nearly constant at \( 55.5 \, M \). The rate depends only on the concentration of the sugar, making it a pseudo-first-order reaction. The final answer is one reactant must be in large excess.