Pseudo First Order Reaction

Pseudo First Order Reaction: The reactions which are not truly of first order but become reactions of first-order under certain conditions are called pseudo-first-order reactions.
Let us take a general reaction
A + B → C
The rate of reaction depends upon the concentrations of both A and B but one of the components is present in large excess and thus its concentration hardly changes as the reaction proceeds so the rate is independent of that particular component.
So, if component B is in large excess and the concentration of B is very high as compared to that of A, the reaction is considered to be a pseudo-first-order reaction with respect to A and if component A is in large excess and the concentration of A is very high as compared to that of B, the reaction is considered to be pseudo-first order with respect to B. 

Pseudo First Order Reaction

For example,
i) Hydrolysis of ester in acid (H⁺).
CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH
Rate = k[CH₃COOC₂H₅] [H₂O]
Since water is in excess so its concentrations remain the same during the reaction and [H₂O] is constant and the rate is independent of the concentration of H₂O so
Rate = k[CH₃COOC₂H₅], Where k = k[H₂O]

ii) Inversion of cane sugar (in acid)
C₁₂H₂₂O₁₁ + H₂O → C₆H₁₂O₆   +    C₆H₁₂O₆                 
Cane sugar                   Glucose           Fructose
Since water is in excess and [H₂O] is constant, so
Rate = k [C₁₂H₂₂O₁₁]

(In the above reactions the concentration of H₂O is in excess so the rate of reaction is independent of the concentration of water).