A lower pK$_a$ value corresponds to a higher K$_a$ value, which indicates a stronger acid. The strength of an acid depends on the stability of its conjugate base: electron-withdrawing groups (-I, -M) stabilize the conjugate base and increase acidity, whereas electron-donating groups (+I, +M) destabilize it, decreasing acidity.
1. Phenols vs. Carboxylic acids:
- Carboxylic acids are stronger acids than phenols because the carboxylate anion (RCOO$^-$) delocalizes its negative charge over two oxygen atoms, whereas the phenoxide ion delocalizes it over one oxygen and the aromatic ring.
- Thus, (B), (C), and (D) are stronger acids than (A).
2. Substituted benzoic acids (B, C, D):
- (B) Benzoic acid: reference compound.
- (C) 4-Methoxybenzoic acid: The methoxy group (-OCH$_3$) is para to the -COOH group. It has a strong +R effect that donates electron density to the ring, destabilizing the carboxylate ion and decreasing acidity relative to benzoic acid.
- (D) 4-Nitrobenzoic acid: The nitro group (-NO$_2$) is para. It has a strong -I and -R effect, withdrawing electron density from the ring and stabilizing the carboxylate anion. This makes it more acidic than benzoic acid.
Order of acidity:
\[
\text{4-Nitrobenzoic acid}>\text{Benzoic acid}>\text{4-Methoxybenzoic acid}>\text{4-Nitrophenol}
\]