Which of the following carboxylic acids will yield the least amount of protons in an aqueous solution?

2-methylbutanoic acid 

The correct answer is option 4. 2-methylbutanoic acid.

Let us delve into the factors that influence the acidity of carboxylic acids and analyze why 2-methylbutanoic acid yields the least amount of protons in an aqueous solution compared to the other acids listed.

Acidity of Carboxylic Acids:

The acidity of carboxylic acids is determined by their ability to donate protons (\( \text{H}^+ \)) in an aqueous solution. The more readily a carboxylic acid donates a proton, the stronger the acid. This ability is influenced by the stability of the carboxylate anion (RCOO\(^-\)) formed after deprotonation.

Factors Affecting Acidity:

Inductive Effect:

Electron-withdrawing groups (EWGs) stabilize the carboxylate anion by pulling electron density away from the carboxylate group, making the acid stronger. Electron-donating groups (EDGs) destabilize the carboxylate anion by pushing electron density towards the carboxylate group, making the acid weaker.

Resonance and Hybridization:

Resonance stabilization of the carboxylate anion can also affect acidity, but this is more relevant for aromatic carboxylic acids.

Analysis of Each Carboxylic Acid:

1. Butanoic Acid:

A straight-chain carboxylic acid with no substituents.

Effect: No significant electron-withdrawing or electron-donating effects.

Acidity: Moderately strong acid.

2. Propanoic Acid:

A straight-chain carboxylic acid with no substituents, but with one less carbon than butanoic acid.

Effect: Similar to butanoic acid, but the shorter chain slightly reduces the overall electron-releasing inductive effect of the alkyl chain.

Acidity: Slightly weaker than butanoic acid due to the shorter carbon chain.

3. 2-Chlorobutanoic Acid:

Contains a chlorine atom at the 2-position.

Effect: The chlorine atom is a strong electron-withdrawing group (EWG) via the inductive effect, which stabilizes the carboxylate anion.

Acidity: Significantly stronger acid due to the EWG effect of chlorine, leading to more proton release.

4. 2-Methylbutanoic Acid :

Contains a methyl group at the 2-position.

Effect: The methyl group is an electron-donating group (EDG) via the inductive effect, which destabilizes the carboxylate anion.

Acidity: Weaker acid due to the EDG effect of the methyl group, leading to less proton release.

Conclusion:

2-Chlorobutanoic Acid: Most acidic due to the electron-withdrawing chlorine.

Butanoic Acid: Moderately acidic with no significant substituent effects.

Propanoic Acid: Slightly weaker than butanoic acid due to the shorter chain.

2-Methylbutanoic Acid: Least acidic due to the electron-donating effect of the methyl group.

Therefore, 2-methylbutanoic acid will yield the least amount of protons in an aqueous solution because the electron-donating methyl group reduces its acidity by destabilizing the carboxylate anion.

The correct answer is 2-methylbutanoic acid.