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