Step 1: Definition and scope.
The Hell-Volhard-Zelinsky (HVZ) reaction is the selective halogenation of the alpha-carbon of an aliphatic carboxylic acid. It requires the acid to have at least one alpha-hydrogen.
Step 2: Reagents.
The carboxylic acid is treated with chlorine or bromine in the presence of a small amount of red phosphorus. Red phosphorus reacts with the halogen in situ to form $PX_3$, which converts the acid to an acyl halide.
Step 3: Halogenation and hydrolysis.
The acyl halide enolises easily, allowing the halogen to attack at the alpha-position. Subsequent hydrolysis regenerates the carboxylic acid functionality, giving an alpha-halocarboxylic acid.
Step 4: Reaction.
\[ R-CH_2-COOH \xrightarrow{X_2,~\text{Red P}} R-CH(X)-COOH + HX \] (where $X = Cl$ or $Br$). The alpha-hydrogen is replaced by a halogen atom.