Question

Benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\right)\) has \(K_{\mathrm{a}}=6.5 \times 10^{-5}\) and citric acid \(\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\right)\) has \(K_{\mathrm{a}}=7.2 \times 10^{-4}\). Which is the stronger conjugate base, benzoate \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}\right)\) or citrate \(\left(\mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{7}^{-}\right) ?\)

Short answer

Benzoate is the stronger conjugate base.

Step-by-step solution

Identify the relationship between the strength of acids and conjugate bases

The strength of a conjugate base is inversely related to the strength of its acid. The weaker the acid, the stronger its conjugate base.

Analyze given data

We have two acids: benzoic acid with \(K_{a}=6.5 \times 10^{-5}\) and citric acid with \(K_{a}=7.2 \times 10^{-4}\). Higher \(K_a\) values indicate stronger acids.

Determine acid strength

Compare the \(K_a\) values: citric acid (\(7.2 \times 10^{-4}\)) is stronger than benzoic acid (\(6.5 \times 10^{-5}\)).

Infer conjugate base strength

Based on the acid strength, benzoic acid is weaker, so its conjugate base, benzoate \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}\), is stronger than the conjugate base of citric acid, citrate \(\mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{7}^{-}\).

Key concepts

Conjugate Base Strength

In acid-base chemistry, the concept of conjugate base strength is essential to understanding how acids and bases interact. Every acid has a corresponding conjugate base that forms when the acid donates a proton ( H^{+} ). The strength of a conjugate base is directly related to the ability of its parent acid to release a proton.

• If an acid dissociates easily, it is considered a strong acid, and its corresponding conjugate base is weaker. This is because the strong acid has already lost its proton and doesn't readily gain it back.
• On the other hand, if an acid is weak and does not dissociate easily, its conjugate base is stronger, illustrating a greater tendency to re-accept a proton.

The inverse relationship between an acid's strength and the strength of its conjugate base is a pivotal concept to grasp in acid-base chemistry.

Acid Dissociation Constant (Ka)

The acid dissociation constant, represented as \(K_{a}\), is a measure of the strength of an acid in solution. It quantifies how easily an acid donates protons to the surrounding water molecules when dissolved.

• A large \(K_{a}\) value indicates a stronger acid. This means that the acid dissociates more fully in solution, producing more hydrogen ions (\(H^{+}\)).
• Conversely, a smaller \(K_{a}\) signifies a weaker acid, which partially dissociates, producing fewer hydrogen ions.

Understanding \(K_{a}\) is crucial because it allows us to compare different acids and predict the behavior of their conjugate bases. For example, in the comparison between benzoic acid and citric acid, the \(K_{a}\) values reveal that citric acid is the stronger acid, while benzoic acid is weaker.

Benzoic Acid and Citric Acid Comparison

When comparing benzoic acid and citric acid, one must consider their acid dissociation constants (\(K_{a}\)). Benzoic acid has a \(K_{a}\) of \(6.5 \times 10^{-5}\), whereas citric acid has a \(K_{a}\) of \(7.2 \times 10^{-4}\). This comparison tells us:

• Citric acid, with its higher \(K_{a}\) value, is a stronger acid than benzoic acid.
• Since benzoic acid is weaker, its conjugate base, the benzoate ion \((\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-})\), is stronger than the conjugate base of citric acid, the citrate ion \((\mathrm{C}_{6} \mathrm{H}_{7} \mathrm{O}_{7}^{-})\).

This understanding helps us determine which conjugate base will dominate under different conditions, a critical consideration in chemical reactions and buffering systems.