Explain the mechanism of action for the esterification of carboxylic acids.

(N/A) The esterification of carboxylic acids with alcohols is a type of nucleophilic acyl substitution. This reaction proceeds through the following steps:
$(i)$ Protonation of the carbonyl oxygen by the $H^{+}$ acid catalyst to produce the protonated carboxylic acid $(X)$.
$(ii)$ The protonated carbonyl group is activated towards nucleophilic attack by the alcohol $(R'-OH)$,forming a tetrahedral intermediate $(M)$.
$(iii)$ $A$ proton transfer occurs within the tetrahedral intermediate $(M)$ to convert the hydroxyl group into a better leaving group,$-OH_2^{+}$,resulting in intermediate $(Y)$.
$(iv)$ The intermediate $(Y)$ eliminates a water molecule to form the protonated ester $(Z)$.
$(v)$ Finally,the protonated ester $(Z)$ loses a proton to yield the final ester $(P)$.