Answer the question on basis of passage given below:

Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(pK_a\) is ∼16 for ethanol and 10 for phenol) The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabalized by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol,a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalized over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalized over one oxygen atom and less electronegative carbon atoms in phenoxide ion.Thus, the carboxylate ion is more established than phenoxide ion, so carboxylic acids are more acidic than phenols.

Effect of substituents on the acidity of carboxylic acids: substituents may affect the stability of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilizing the conjugate base through delocalization of the negative charge by by inductive and /or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.

Arrange the following acids in order of their increasing \(pK_a\) value:

(A) Benzoic acid

(B) 2-Nitrobenzoic acid

(C) 4-Nitrobenzoic acid

(D) 4-Methoxybenzoic acid

Choose the correct answer from the options given below:

B < C < A < D

The correct answer is option 4. B < C < A < D.

To arrange the given acids in order of their increasing \(pK_a\) values, we need to understand how different substituents attached to the benzoic acid ring influence the acidity of the acid. The \(pK_a\) value is inversely related to acidity: lower \(pK_a\) values correspond to stronger acids.

Factors Influencing Acidity:

Electron-Withdrawing Groups (EWGs):

Effect: EWGs increase acidity by stabilizing the negative charge on the carboxylate ion formed after the acid donates a proton. This stabilization occurs through inductive and/or resonance effects.

Common EWGs: Nitro (\(-NO_2\)) groups are strong electron-withdrawing groups.

Electron-Donating Groups (EDGs):

Effect: EDGs decrease acidity by destabilizing the carboxylate ion, as they push electron density toward the negatively charged oxygen atom.

Common EDGs: Methoxy (\(-OCH_3\)) groups are electron-donating groups.

Analysis of the Given Acids:

B. 2-Nitrobenzoic Acid :

Substituent: Nitro group (\(-NO_2\)) at the ortho (2-) position relative to the carboxyl group.

Effect on Acidity: The nitro group is a strong EWG. At the ortho position, it exerts both inductive effects (due to proximity) and resonance effects, significantly stabilizing the carboxylate ion after deprotonation. This makes 2-nitrobenzoic acid the strongest acid among the four, and thus it has the lowest \(pK_a\) value.

C. 4-Nitrobenzoic Acid:

Substituent: Nitro group (\(-NO_2\)) at the para (4-) position relative to the carboxyl group.

Effect on Acidity: The nitro group is still a strong EWG, but its effect is slightly reduced compared to the ortho position. The resonance stabilization is present but less direct than in 2-nitrobenzoic acid. Therefore, 4-nitrobenzoic acid is also quite acidic, though slightly less so than 2-nitrobenzoic acid, giving it a slightly higher \(pK_a\) than B.

A. Benzoic Acid:

Substituent: None; only the carboxyl group is attached to the benzene ring.

Effect on Acidity: Without any additional substituents, benzoic acid's acidity is moderate. There are no strong EWGs or EDGs to alter its acidity significantly. The \(pK_a\) of benzoic acid is higher than both 2-nitrobenzoic acid and 4-nitrobenzoic acid but lower than 4-methoxybenzoic acid.

D. 4-Methoxybenzoic Acid:

Substituent: Methoxy group (\(-OCH_3\)) at the para (4-) position relative to the carboxyl group.

Effect on Acidity: The methoxy group is an EDG, which destabilizes the carboxylate ion by donating electron density. This effect weakens the acidity of the acid, resulting in the highest \(pK_a\) value among the acids listed.

Order of Increasing \(pK_a\) Values:

B. 2-Nitrobenzoic Acid : Lowest \(pK_a\) (strongest acid) due to the strong electron-withdrawing effect of the ortho nitro group.

C. 4-Nitrobenzoic Acid : Slightly higher \(pK_a\) than 2-nitrobenzoic acid, as the para nitro group still withdraws electrons but with less influence.

A. Benzoic Acid : Higher \(pK_a\) than both nitro-substituted acids, as it lacks additional electron-withdrawing groups.

D. 4-Methoxybenzoic Acid : Highest \(pK_a\) (weakest acid) due to the electron-donating effect of the para methoxy group, which decreases acidity.

Conclusion:

The correct order of increasing \(pK_a\) values is: B < C < A < D

This sequence reflects the increasing \(pK_a\) values, meaning decreasing acidity as you move from 2-nitrobenzoic acid to 4-methoxybenzoic acid.

Thus, the correct option is: 4. B < C < A < D