Which of the following represents the correct order of the acidity in the given compound?

\(FCH_2COOH > ClCH_2COOH > BrCH_2COOH > CH_3COOH\)

The correct answer is option 2. \(FCH_2COOH > ClCH_2COOH > BrCH_2COOH > CH_3COOH\).

Let us delve into the acidity trends among the substituted acetic acids provided in the options.

Understanding Acidity in Carboxylic Acids:

Acidity in carboxylic acids is influenced by the stability of the carboxylate anion (conjugate base) formed after the loss of a proton (H⁺). This stability is affected by the electron-withdrawing or donating effects of substituents attached to the carboxyl group.

Electron-Withdrawing Effects of Substituents:

Fluorine (F): Fluorine is highly electronegative. It withdraws electron density through the inductive effect (through bonds) and resonance effects (through conjugation), making the carboxyl group more electron-deficient and stabilizing the conjugate base. This increases the acidity of the carboxylic acid.

Chlorine (Cl): Chlorine is moderately electronegative and also withdraws electron density through the inductive effect. It stabilizes the conjugate base to a lesser extent than fluorine but still increases acidity compared to unsubstituted acetic acid.

Bromine (Br): Bromine is less electronegative than chlorine and fluorine but still withdraws electron density through the inductive effect. It has a weaker effect on increasing acidity compared to fluorine and chlorine.

Methyl Group (CH₃): Methyl groups are electron-donating through hyperconjugation and destabilize the carboxylate anion. This electron donation reduces the acidity of the carboxylic acid compared to halogen-substituted acetic acids.

Evaluating the Options: Now, let us analyze the provided options in detail:

1. \( BrCH_2COOH > ClCH_2COOH > FCH_2COOH > CH_3COOH \)

Bromoacetic acid (BrCH₂COOH): Bromine is less electronegative than chlorine and fluorine, making bromoacetic acid less acidic than the others.

Chloroacetic acid (ClCH₂COOH): Chlorine is more electronegative than bromine but less than fluorine, making chloroacetic acid more acidic than bromoacetic acid but less than fluoroacetic acid.

Fluoroacetic acid (FCH₂COOH): Fluorine is highly electronegative, making fluoroacetic acid the most acidic among the substituted acetic acids due to strong electron-withdrawing effects.

Acetic acid (CH₃COOH): Methyl group is electron-donating and decreases the acidity compared to halogen-substituted acetic acids.

2. \( FCH_2COOH > ClCH_2COOH > BrCH_2COOH > CH_3COOH \)

This order correctly reflects the increasing acidity due to the electron-withdrawing effects of the substituents:

Fluoroacetic acid (FCH₂COOH) is most acidic due to the strong electron-withdrawing effect of fluorine.

Chloroacetic acid (ClCH₂COOH) is next, followed by bromoacetic acid (BrCH₂COOH), and acetic acid (CH₃COOH) is the least acidic due to the electron-donating effect of the methyl group.

Conclusion: Based on the electron-withdrawing effects discussed, option (2) \( FCH_2COOH > ClCH_2COOH > BrCH_2COOH > CH_3COOH \) represents the correct order of acidity among the given compounds. Fluoroacetic acid is the most acidic, followed by chloroacetic acid, bromoacetic acid, and then acetic acid (unsubstituted).

Understanding these acidity trends is crucial in organic chemistry for predicting reactivity and understanding the stability of carboxylic acids and their derivatives in various chemical reactions.