Problem 4 - Chemistry in 30 days

Question

trinitrophenol Which of the following acids has smallest dissociation constant? (a) \(\mathrm{CH}_{3} \mathrm{CHICOOH}\) (b) \(\mathrm{FCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\) (c) \(\mathrm{BrCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\) (d) \(\mathrm{CH}_{3} \mathrm{CHBrCOOH}\).

Step-by-Step Solution

Answer

The acid with the smallest dissociation constant is (a) \\mathrm{CH}_{3}\mathrm{CHICOOH}\\.

Step 1: Understand Acid Dissociation Constant

The acid dissociation constant \( K_a \) quantifies the strength of an acid in solution. A lower \( K_a \) value indicates a weaker acid. We are looking for the acid with the smallest \( K_a \).

Step 2: Consider Electron Withdrawing Groups

Acids are stronger when they have electron-withdrawing groups because they stabilize the negative charge on the ion formed after dissociation. Compare the strength of these groups in each formula.

Step 3: Analyze Substituents for Each Option

(a) \(\mathrm{CH}_{3}\mathrm{CHICOOH}\): Iodine is a weak electron-withdrawing group. (b) \(\mathrm{FCH}_{2}\mathrm{CH}_{2}\mathrm{COOH}\): Fluorine is a strong electron-withdrawing group. (c) \(\mathrm{BrCH}_{2}\mathrm{CH}_{2}\mathrm{COOH}\): Bromine is moderately strong as an electron-withdrawing group. (d) \(\mathrm{CH}_{3}\mathrm{CHBrCOOH}\): Bromine is close to the carboxyl group, making it more effective than option (c).

Step 4: Determine the Weakest Acid

The weakest acid would have the least effective electron-withdrawing group near the carboxyl group. Option (a) \(\mathrm{CH}_{3}\mathrm{CHICOOH}\), with iodine far from the carboxyl group, is least influenced by its substituent compared to others.

Key Concepts

Electronegativity and Acid Strength

Electronegativity is a crucial factor in determining the strength of an acid. It measures an atom's ability to attract and hold onto electrons. In the context of acids, highly electronegative atoms can stabilize the conjugate base formed after the acid donates a proton (H⁺).
When an acid releases its proton, the remaining anion (conjugate base) must be stable enough to exist in solution. Electronegative elements can help stabilize this anion by holding onto the extra electrons more tightly. This stabilization is what makes the acid stronger.
Highly electronegative atoms such as fluorine, oxygen, or nitrogen enhance the acid's strength by making the conjugate base more stable. In the original exercise, fluorine in  \(\mathrm{FCH}_{2}\mathrm{CH}_{2}\mathrm{COOH}\) is highly electronegative, which contributes to its strong acidic nature.

Electron Withdrawing Groups

Electron-withdrawing groups (EWGs) enhance an acid's strength by stabilizing the negative charge on the conjugate base. Essentially, these groups "pull" electron density away from the acidic proton, making it easier for the proton to dissociate.
Let's break down the role of such groups:

• EWGs, such as halogens (fluorine, chlorine, bromine, and iodine), or nitro groups, are pivotal for good acidity.


• These groups can stabilize the conjugate base through inductive effects, where electron density is relocated along sigma bonds.

In our consideration for the original exercise, we observed the positioning and type of substituents:

• Iodine in \(\mathrm{CH}_{3}\mathrm{CHICOOH}\) is less effective due to its weak electron-withdrawing ability.


• Fluorine in \(\mathrm{FCH}_{2}\mathrm{CH}_{2}\mathrm{COOH}\) is very strong due to its higher electronegativity.


• Bromine in \(\mathrm{BrCH}_{2}\mathrm{CH}_{2}\mathrm{COOH}\) and \(\mathrm{CH}_{3}\mathrm{CHBrCOOH}\) has a moderate effect, but positioning close to the carboxyl group increases its ability to stabilize the conjugate base.

Carboxylic Acids

Carboxylic acids are a common class of organic acids, characterized by the presence of the carboxyl group \((-COOH)\). The acidic nature of carboxylic acids comes from the ability to release a proton (H⁺) from the hydroxyl \((-OH)\) part of the group.
For carboxylic acids, the stability of the resulting carboxylate ion \((-COO^{-})\) is key to their acidity. However:

• The presence of electron-withdrawing groups can dramatically change the strength of the carboxylic acid by stabilizing the carboxylate ion.


• The position of these groups relative to the carboxyl group further influences the dissociation ability, with groups closer to the carboxyl group having a greater effect.

In the exercise provided, the different halogen-substituted carboxylic acids show varying acid strengths due to differences in their electron-withdrawing capabilities and their positions, illustrating how these factors influence carboxylic acids.