Consider the following acid catalysed reaction:
Hydrolysis of ethyl acetate:
CH3COOC2H5 + H2O + H+→CH3COOH + C2H5OH
The above reaction is bimolecular but is found to be of first order, as experimentally it is observed that: The rate of reaction proportional to [CH3COOC2H5] only.
The reason for such a behavior is that water is present in such a large excess that its concentration remains almost constant during the reaction.
Such reactions which are not truly of the first order but under certain conditions become reactions of the first order are known as pseudo unimolecular reactions.