Show how free-radical halogenation might be used to synthesize the following ­compounds. In each case, explain why we expect to get a single major product.
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Free-radical halogenation is a reaction where alkanes react with halogens (like bromine) in the presence of heat or light to form alkyl halides. This process involves the generation of free radicals, which are highly reactive species with unpaired electrons. The reaction proceeds through three main steps: initiation, propagation, and termination, leading to the substitution of hydrogen atoms with halogen atoms.

Selectivity in free-radical halogenation refers to the preference for the formation of certain products over others. This is influenced by the stability of the free radicals formed during the reaction. More stable radicals (like tertiary radicals) are favored, leading to a single major product when the substrate has a clear preference for one site of substitution, as seen in the provided compound.

The mechanism of bromination involves the formation of a bromine radical that abstracts a hydrogen atom from the substrate, creating a new radical. This radical can then react with another bromine molecule to form the brominated product. The specific structure of the compound in the image suggests that bromination will occur at a position that leads to a stable radical, thus resulting in a single major product due to the lack of competing sites for substitution.