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(a) p-dichlorobenzene: $$\mu = 0$$ because the single-atom $$\text{-Cl}$$ substituents align linearly along the para-axis and cancel each other completely.
(b) p-dicyanobenzene: $$\mu = 0$$ because the $$\text{-C}\equiv\text{N}$$ groups are strictly linear ($$sp$$-hybridized) and their opposite dipole vectors cancel out perfectly.
(c) p-dihydroxybenzene: $$\mu \neq 0$$ because the $$\text{-OH}$$ groups are bent ($$sp^3$$-hybridized), and their rotating conformations prevent perfect vector cancellation.
(d) p-dimercatobenzene: $$\mu \neq 0$$ because the $$\text{-SH}$$ groups are bent ($$sp^3$$-hybridized), resulting in a net structural dipole moment during rotation.
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