Show how you would accomplish the following conversions in good yields. You may use any necessary reagents.
(b)

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Identify the starting material as cyclohexanecarboxylic acid and the product as bromocyclohexanecarboxylic acid, where a bromine atom is added to the alpha-carbon (the carbon adjacent to the carboxylic acid group).

Recognize that this transformation involves alpha-bromination of a carboxylic acid. This can be achieved using the Hell-Volhard-Zelinsky (HVZ) reaction, which selectively brominates the alpha-carbon of carboxylic acids.

First, treat the carboxylic acid with phosphorus tribromide (PBr₃) to form the corresponding acyl bromide. This step activates the carboxylic acid for the subsequent reaction.

Next, add bromine (Br₂) to the reaction mixture. The bromine reacts with the acyl bromide to brominate the alpha-carbon via an enol intermediate.

Finally, hydrolyze the acyl bromide back to the carboxylic acid by adding water, regenerating the carboxylic acid group and yielding the desired brominated product.

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