To identify product (P) of the given reaction, analyze reaction conditions and reactants.
- The starting material is a cyclic carboxylic acid, as depicted in the provided image.
- The reaction sequence, \({\text{Br}_2/\text{Red P}}\) followed by hydrolysis (\({\text{H}_2\text{O}}\)), is indicative of the Hell-Volhard-Zelinsky (HVZ) reaction, used for α-bromination of carboxylic acids.
- Within the HVZ reaction:
- \({\text{Br}_2}\) and red phosphorus (Red P) generate \({\text{PBr}_3}\), a brominating agent.
- The carboxylic acid is converted to an acyl bromide intermediate, which then undergoes α-halogenation.
- Hydrolysis with water reforms the carboxylic acid functional group, incorporating a bromine atom at the α-position.
- Consequently, product (P) will be the original cyclic carboxylic acid with a bromine atom substituted at the α-carbon, adjacent to the carboxyl group.
- Referring to the provided options, the correct structure for the α-brominated product is illustrated in the following figure:
This selection accurately represents the cyclic structure with an α-carbon bromination, aligning with the established reaction mechanism.