In the following compounds:

I. Phenol

II. p-Cresol

III. m-Nitrophenol

IV. p-Nitrophenol

The order of acidity is:

IV > III > I > II

The correct answer is option 2. IV > III > I > II.

Let us dive into the detailed reasoning behind the order of acidity for the given compounds:

Acidity of Phenols:

The acidity of a phenol is determined by how easily it can lose a proton (\(H^+\)) from the hydroxyl group \((-OH)\). When a phenol loses a proton, it forms a phenoxide ion (\(C_6H_5O^-\)). The stability of this phenoxide ion is crucial in determining the acidity of the phenol. Electron-Withdrawing Groups (EWGs), like nitro groups (-NO\(_2\)), stabilize the negative charge on the oxygen atom in the phenoxide ion, making the phenol more acidic. Electron-Donating Groups (EDGs), like methyl groups (-CH\(_3\)), destabilize the phenoxide ion by increasing electron density on the oxygen, making the phenol less acidic.

Analysis of Each Compound:

I. Phenol:

Substituents: No substituents other than the hydroxyl group.

Acidity: This is the reference compound. The hydroxyl group attached to the benzene ring can lose a proton, but there's no additional stabilizing or destabilizing influence from other groups.

Acidity: Baseline acidity.

II. p-Cresol: 

Substituent: A methyl group (-CH\(_3\)) at the para position relative to the hydroxyl group.

Effect of Methyl Group: The -CH\(_3\) group is an electron-donating group. It pushes electron density towards the benzene ring and the hydroxyl group, making it harder for the hydroxyl group to lose a proton.

Acidity: Lower than phenol because the methyl group reduces the acidity.

III. m-Nitrophenol: 

Substituent: A nitro group (-NO\(_2\)) at the meta position relative to the hydroxyl group.

Effect of Nitro Group: The nitro group is a strong electron-withdrawing group. In the meta position, it withdraws electron density through the benzene ring, making it easier for the hydroxyl group to lose a proton. However, its effect is less pronounced than if it were in the para position.

Acidity: Higher than phenol due to the electron-withdrawing effect of the nitro group, but less acidic than p-nitrophenol.

4. p-Nitrophenol:

Substituent: A nitro group (-NO\(_2\)) at the para position relative to the hydroxyl group.

Effect of Nitro Group: In the para position, the nitro group strongly withdraws electron density from the benzene ring and the hydroxyl group, stabilizing the phenoxide ion significantly after deprotonation.

Acidity: Highest among the four due to the strong electron-withdrawing effect of the nitro group in the para position.

Conclusion: Order of Acidity

p-Nitrophenol (IV): Most acidic due to the strong electron-withdrawing nitro group in the para position.

m-Nitrophenol (III): Less acidic than p-nitrophenol but more acidic than phenol because of the electron-withdrawing effect of the nitro group in the meta position.

Phenol (I): Baseline acidity with no additional effects.

p-Cresol (II): Least acidic due to the electron-donating effect of the methyl group in the para position.

The correct order of acidity is IV > III > I > II.