Arrange the following acids in increasing order of their acidic strengths:

\(HCOOH,\) \(FCH_2COOH,\) \(NO_2CH_2COOH,\) \(ClCH_2COOH\)

\(HCOOH < ClCH_2COOH < FCH_2COOH < NO_2CH_2COOH\)

The correct answer is option 4. \(HCOOH < ClCH_2COOH < FCH_2COOH < NO_2CH_2COOH\).

To understand the increasing order of acidic strengths of the given acids \(HCOOH\), \(FCH_2COOH\), \(NO_2CH_2COOH\), and \(ClCH_2COOH\), let us delve into how substituents influence the acidity of carboxylic acids.

Electron-Withdrawing Groups (EWGs): These groups increase the acidity of carboxylic acids by stabilizing the negative charge on the conjugate base (carboxylate ion) through inductive or resonance effects. The more effective the electron withdrawal, the stronger the acid.

Inductive Effect: This is the transmission of charge through a chain of atoms in a molecule by electrostatic induction. The effect decreases with distance from the substituent.

Analysis of each of the given acids:

Formic Acid (\(HCOOH\)):

No Substituent Effect: Formic acid has no additional substituents on the carbon chain, so its acidity is purely based on the carboxyl group itself.

Baseline Acidity: It serves as a reference for comparing other substituted acids.

Fluoroacetic Acid (\(FCH_2COOH\)):

Fluorine Substituent: Fluorine is highly electronegative and an effective electron-withdrawing group via the inductive effect.

Acidity Increase: The presence of fluorine significantly increases the acidity compared to formic acid.

Nitroacetic Acid (\(NO_2CH_2COOH\)):

Nitro Group Substituent: The nitro group (\(NO_2\)) is one of the strongest electron-withdrawing groups due to both inductive and resonance effects.

Strongest Acidity Increase: This results in a very high increase in acidity, making nitroacetic acid more acidic than fluoroacetic acid.

Chloroacetic Acid (\(ClCH_2COOH\):

Chlorine Substituent: Chlorine is less electronegative than fluorine but still an effective electron-withdrawing group via the inductive effect.

Moderate Acidity Increase: Chlorine increases the acidity, but less so than fluorine and the nitro group.

Order of Acidic Strength: Based on the electron-withdrawing capabilities of the substituents:

The nitro group (\(NO_2\)) is the most powerful, leading to the highest acidity.

Fluorine (\(F\)) comes next due to its strong electronegativity.

Chlorine (\(Cl\)) follows, being less effective than fluorine but still significant.

Formic acid (\(HCOOH\)) is the least acidic as it has no additional electron-withdrawing groups.

Thus, the increasing order of acidic strengths is \( HCOOH < ClCH_2COOH < FCH_2COOH < NO_2CH_2COOH\)

Therefore, the correct answer is: 4. \(HCOOH < ClCH_2COOH < FCH_2COOH < NO_2CH_2COOH\)