Which of the following acid has the smallest dissociation constant?

BrCH₂CH₂COOH

The correct answer is option 3. BrCH₂CH₂COOH.

Let us explain why BrCH₂CH₂COOH has the smallest dissociation constant among the given acids by analyzing the effects of the substituents on the carboxylic acid group.

Factors Affecting Acid Strength:

Inductive Effect: Electronegative substituents (like halogens) withdraw electron density through the sigma bonds, stabilizing the conjugate base and increasing the acid strength.

Position of Substituents: The closer the electronegative substituent to the carboxyl group, the stronger the inductive effect.

Given Acids:

1. CH₃CHFCOOH (2-fluoropropanoic acid):

Substituent: Fluorine on the α-carbon.

Effect: Strong inductive electron-withdrawing effect due to fluorine being very electronegative and close to the carboxyl group. This makes the acid quite strong.

2. FCH₂CH₂COOH (3-fluoropropanoic acid):

Substituent: Fluorine on the β-carbon.

Effect: Fluorine still withdraws electron density but less effectively because it is farther from the carboxyl group compared to CH₃CHFCOOH. Thus, the acid is weaker than CH₃CHFCOOH.

3. BrCH₂CH₂COOH (3-bromopropanoic acid):

Substituent: Bromine on the β-carbon.

Effect: Bromine is less electronegative than fluorine and is on the β-carbon. The inductive effect is weaker than fluorine’s and less effective due to the position, making the acid weaker.

4. CH₃CHBrCOOH (2-bromopropanoic acid):

Substituent: Bromine on the α-carbon.

Effect: Bromine’s inductive effect is stronger when closer to the carboxyl group (α-carbon), making this acid stronger than BrCH₂CH₂COOH but weaker than CH₃CHFCOOH due to bromine being less electronegative than fluorine.

Comparison:

CH₃CHFCOOH: Strongest acid due to the strong inductive effect of fluorine on the α-carbon.

FCH₂CH₂COOH: Weaker than CH₃CHFCOOH but still relatively strong due to fluorine on the β-carbon.

CH₃CHBrCOOH: Weaker than both fluorine-containing acids because bromine is less electronegative but still stronger than BrCH₂CH₂COOH due to the α-position.

BrCH₂CH₂COOH: Weakest acid due to bromine’s weak inductive effect from the β-position.

Conclusion: BrCH₂CH₂COOH has the smallest dissociation constant because the bromine atom's inductive effect is weaker and less effective due to its position on the β-carbon. Therefore, it stabilizes the conjugate base the least, making the acid the weakest among the given options.