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p-Nitrophenol (III): The $$-NO_2$$ group is a powerful electron-withdrawing group. At the para position, it effectively withdraws electron density through resonance ($$-M$$), making it the most acidic among the given options.
p-Chlorophenol (I): Chlorine is electronegative and exerts a $$-I$$ effect. Although it has a $$+M$$ effect, the $$-I$$ effect is more significant in halogens. It is more acidic than alkyl-substituted phenols but less than nitro-substituted ones.
p-Cresol (II): The methyl group is electron-donating through hyperconjugation ($$+H$$) and inductive effect ($$+I$$). This destabilizes the phenoxide ion relative to phenol, making it less acidic than (I) and (III).
p-Methoxyphenol (IV): The methoxy group exhibits a very strong $$+M$$ effect due to the lone pair on the oxygen atom. At the para position, this effect is dominant over its $$-I$$ effect, making it the most electron-donating and thus the least acidic.
The order of decreasing acidity is: III > I > II > IV
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