$$\begin{aligned} \text{Anhydride Formation:} &\quad 2\text{R-COOH} \xrightarrow{\text{P}_2\text{O}_5 \, / \, \text{Conc. H}_2\text{SO}_4, \, \Delta} (\text{RCO})_2\text{O} + \text{H}_2\text{O} \\ \text{Fischer Esterification:} &\quad \text{R-COOH} + \text{R'-OH} \xrightarrow{\text{Conc. H}_2\text{SO}_4} \text{R-COOR'} + \text{H}_2\text{O} \end{aligned}$$
Concept: Fischer esterification operates via a fully reversible nucleophilic acyl substitution mechanism, where isotopic labeling proves that the bridging oxygen atom in the final ester product comes entirely from the reacting alcohol reactant.
Notation:
- $$\text{P}_2\text{O}_5$$ = Phosphorus pentoxide dehydrator;