Problem 21 - Chemistry and Chemical Reactivity

Question

Which of the following compounds or ions has the weakest conjugate acid? Briefly explain your choice. (a) \(\mathrm{HCO}_{3}^{-}\) (b) \(\mathrm{F}^{-}\) (c) \(\mathrm{NO}_{2}^{-}\)

Step-by-Step Solution

Answer

\( \mathrm{F}^{-} \) corresponds to the weakest conjugate acid, \( \mathrm{HF} \).

Step 1: Understanding the Conjugate Acid-Base Pair

Each given ion is a base that can accept a proton (H⁺) to form its conjugate acid such as: - \( \mathrm{HCO}_{3}^{-} \) forms \( \mathrm{H}_{2}\mathrm{CO}_{3} \)- \( \mathrm{F}^{-} \) forms \( \mathrm{HF} \)- \( \mathrm{NO}_{2}^{-} \) forms \( \mathrm{HNO}_{2} \). To find the weakest conjugate acid, we need to identify which of these acids is the weakest.

Step 2: Assessing Acid Strength

A weaker acid has a lower tendency to donate a proton. Among the given conjugate acids, - \( \mathrm{H}_{2}\mathrm{CO}_{3} \), - \( \mathrm{HF} \), and - \( \mathrm{HNO}_{2} \),the acid dissociation constant (\( K_a \)) values help us determine acid strength. The smaller the \( K_a \), the weaker the acid. Generally, \( \mathrm{HF} \) is a weak acid with relatively low \( K_a \),\( \mathrm{H}_{2}\mathrm{CO}_{3} \) is a weak acid but dissociates more than \( \mathrm{HF} \), and \( \mathrm{HNO}_{2} \) is also weak.

Step 3: Identifying the Weakest Conjugate Acid's Base

The weakest conjugate acid corresponds to the strongest base because it accepts protons less readily. Given the weak acid examples, \( \mathrm{HF} \) tends to retain its proton more than \( \mathrm{H}_{2}\mathrm{CO}_{3} \) and \( \mathrm{HNO}_{2} \). Thus, the strongest base is \( \mathrm{F}^{-} \). Therefore, \( \mathrm{F}^{-} \) corresponds to the weakest conjugate acid.

Key Concepts

Conjugate Acids

In acid-base chemistry, a conjugate acid is the species formed when a base accepts a proton (H⁺). Consider the concept of a conjugate acid-base pair: they are like two sides of a reversible reaction. For instance, if you have a base like F⁻ (fluoride ion), it can accept a proton to become its conjugate acid, HF (hydrofluoric acid).

• Conjugate Acid of a Base: When a base accepts a proton, it transforms into its conjugate acid. For example, e.g., HCO₃⁻ becomes H₂CO₃.
• Conjugate acids have distinct properties from their base forms. Typically, the conjugate acid is more willing to donate that proton back into the environment.

Remember, the strength of a conjugate acid inversely relates to how strong the original base was. A strong base forms a weaker conjugate acid. Understanding this relationship helps in predicting the behavior of substances in various chemical reactions and environments.

Acid Strength

When discussing acid strength, we are primarily talking about an acid’s ability to donate a proton. A stronger acid will more readily part with its proton compared to a weaker acid.
For the acids formed from the given bases ( HCO₃⁻, F⁻, NO₂⁻), these acid counterparts ( H₂CO₃, HF, HNO₂) vary in their ability to donate protons.

• Factors affecting Acid Strength: The primary influencer is the atom bonded to hydrogen. Electronegativity and atomic size play a huge role.
• For instance, HF is weak because the fluorine atom is highly electronegative, strongly holding onto its hydrogen atom.
• In contrast, other variables can include the stability of the conjugate base.

Understanding acid strength allows us to rank acids and predict reaction outcomes, which is crucial in fields ranging from chemical synthesis to biological systems.

Acid Dissociation Constant

The acid dissociation constant, K_a , is a quantitative measure of an acid’s strength in solution. It represents the equilibrium constant for the dissociation of the acid into its constituent ions.
The higher the value of K_a , the stronger the acid, because it shows a greater tendency for the acid to donate its proton.

• How to Interpret K_a values: If K_a is large, the acid readily dissociates, indicating it’s a strong acid. Conversely, a small K_a implies a weak acid.
• Examples: Among H₂CO₃, HF, and HNO₂, values of K_a help determine that HF is particularly weak compared to the others due to its lower dissociation.

Understanding K_a provides insight into not only the intrinsic strengths of acids but also how they will react in different environments, which is fundamental for students tackling various problems in chemistry.