The correct order of acid character of the following compounds is:

• Compound I (Phenol): Phenol is inherently a much weaker acid than any carboxylic acid. When it loses a proton, its conjugate base (the phenoxide ion) must disperse its negative charge into the carbon ring. This is far less stable than a carboxylate ion, which perfectly distributes its negative charge across two highly electronegative oxygen atoms. Therefore, this is the weakest acid of the group.
• Compound II (p-Nitrobenzoic acid): This molecule features a nitro group ($$-NO_2$$), which is powerfully electron-withdrawing due to both the resonance (-R) and inductive (-I) effects. It continuously pulls electron density away from the carboxylate group, which deeply stabilizes the negative charge of the resulting conjugate base. This intense stabilization makes it the strongest acid in the lineup.
• Compound III (Benzoic acid): This is the standard, unsubstituted aromatic carboxylic acid. It possesses no extra groups to push or pull electrons, making it the perfect neutral baseline to compare against the other carboxylic acids.
• Compound IV (p-Methylbenzoic acid): This molecule features a methyl group ($$-CH_3$$), which is an electron-donating group through hyperconjugation and the positive inductive (+I) effect. It pushes excess electron density into the ring and toward the carboxylate group. This extra negative charge severely destabilizes the conjugate base, making it a weaker acid than the neutral baseline (Compound III).

Thus, the electron-withdrawing group makes II the strongest, III serves as the neutral baseline in the middle, the electron-donating group makes IV weaker than the baseline, and the phenol I is the weakest functional group overall.

Therefore, the correct decreasing order of acid character is:

$$II > III > IV > I$$