### Definition:
A pseudo-first-order reaction is a reaction that follows first-order kinetics
even though it involves more than one reactant. This happens when one reactant
is present in a large excess, making its concentration effectively constant
during the reaction.
### Difference Between First-Order and Pseudo-First-Order Reactions:
- A true first-order reaction involves only one reactant with a rate directly
proportional to its concentration.
- A pseudo-first-order reaction involves multiple reactants, but the reaction
behaves as first-order because one reactant is in excess.
### Mathematical Derivation:
For a reaction:
A + B -> Products
If B is in large excess, its concentration remains nearly constant. The rate law:
Rate = k[A][B]
Since [B] is constant, we define k' = k[B], so:
Rate = k'[A]
This follows first-order kinetics with respect to A.
### Examples:
1. **Hydrolysis of an Ester in Acidic Medium:**
CH3COOCH3 + H2O -> CH3COOH + CH3OH
Since water is in excess, the reaction follows pseudo-first-order kinetics.