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.

Which of the following compounds would have the smallest value of \(pK_a\)?

\(O_2NCH_2COOH\)

The correct answer is option 1. \(O_2NCH_2COOH\).

To determine which compound has the smallest \( pK_a \) value (indicating the highest acidity), we need to examine the effect of different substituents on the carboxyl group in the carboxylic acids provided. The \( pK_a \) of a compound is inversely related to its acidity; a lower \( pK_a \) corresponds to a stronger acid.

Effect of Substituents on Acidity

1. Nitroacetic Acid (\(O_2NCH_2COOH\)):

Substituent: Nitro group \((NO_2)\).

Effect on Acidity: The nitro group is a very strong electron-withdrawing group due to both inductive and resonance effects. It pulls electron density away from the carboxyl group, stabilizing the negative charge on the carboxylate ion after deprotonation. This increased stabilization makes the acid more acidic.  Nitroacetic acid is expected to have the lowest \( pK_a \) value (strongest acid) due to the strong electron-withdrawing effects of the nitro group.

2. Cyanacetic Acid (\(NCCH_2COOH\)):

Substituent: Cyano group \((CN)\).

Effect on Acidity: The cyano group is also an electron-withdrawing group but mainly through inductive effects. It also stabilizes the carboxylate ion, although not as effectively as the nitro group. Cyanacetic acid is more acidic than simple acetic acid but less acidic than nitroacetic acid due to the weaker electron-withdrawing effect compared to the nitro group.

3. Fluoroacetic Acid (\(FCH_2COOH\)):

Substituent: Fluoro group \((F)\).\

Effect on Acidity: The fluoro group is an electron-withdrawing group via inductive effects. While it does increase the acidity of the carboxyl group, it is less effective compared to the nitro and cyano groups because fluorine's inductive effect is less pronounced over the distance compared to nitro and cyano groups. Fluoroacetic acid is more acidic than simple acetic acid but less acidic than both cyanacetic acid and nitroacetic acid.

4. Benzylacetic Acid (\(C_6H_5CH_2COOH\)):

Substituent: Phenyl group \((C_6H_5)\).

Effect on Acidity: The phenyl group has a slight electron-donating effect through resonance. This effect reduces the acidity of the carboxyl group by increasing the electron density around it, making the carboxylate ion less stable. Benzylacetic acid is the least acidic among the listed acids because the phenyl group does not withdraw electron density as effectively as the nitro, cyano, or fluoro groups.

Summary of Acidity Order:

1. Nitroacetic Acid (\(O_2NCH_2COOH\)): Strongest acid due to the very strong electron-withdrawing effects of the nitro group. It has the smallest \( pK_a \) value.

2. Cyanacetic Acid (\(NCCH_2COOH\)): Stronger acid than simple acetic acid but less acidic than nitroacetic acid due to the weaker electron-withdrawing nature of the cyano group.

3. Fluoroacetic Acid (\(FCH_2COOH\)): More acidic than simple acetic acid but less acidic than cyanacetic acid and nitroacetic acid.

4. Benzylacetic Acid (\(C_6H_5CH_2COOH\)): Least acidic due to the electron-donating effects of the phenyl group.

Conclusion: The compound with the smallest \( pK_a \) value, indicating the strongest acid, is: 1. Nitroacetic Acid (\(O_2NCH_2COOH\))