Problem 18 - Chemistry and Chemical Reactivity

Question

Which of the following compounds or ions has the strongest conjugate acid? Briefly explain your choice. (a) \(\mathrm{CN}^{-}\) (b) \(\mathrm{NH}_{3}\) (c) \(\mathrm{SO}_{4}^{2-}\)

Step-by-Step Solution

Answer

\(\mathrm{HSO}_{4}^{-}\) has the strongest conjugate acid.

Step 1: Identify Conjugate Acids

The conjugate acid of a base is formed by adding a proton (H\(^+\)) to the base. Let's identify the conjugate acids:(a) \/ \(\mathrm{CN}^{-}\) becomes \(\mathrm{HCN}\) when it gains a proton.(b) \/ \(\mathrm{NH}_{3}\) becomes \(\mathrm{NH}_{4}^{+}\) when it gains a proton.(c) \/ \(\mathrm{SO}_{4}^{2-}\) becomes \(\mathrm{HSO}_{4}^{-}\) when it gains a proton.

Step 2: Analyze the Strength of Conjugate Acids

The strength of a conjugate acid is inversely related to the strength of its conjugate base. A weaker base forms a stronger conjugate acid.(a) \/ \(\mathrm{CN}^{-}\) is a relatively strong base, so \(\mathrm{HCN}\) is a weak acid.(b) \/ \(\mathrm{NH}_{3}\) is a weak base, so \(\mathrm{NH}_{4}^{+}\) is a relatively strong acid.(c) \/ \(\mathrm{SO}_{4}^{2-}\) is a very weak base, so \(\mathrm{HSO}_{4}^{-}\) is a strong acid.

Step 3: Compare and Conclude

Compare the strengths of the conjugate acids formed to determine which is the strongest.Among \(\mathrm{HCN}\), \(\mathrm{NH}_{4}^{+}\), and \(\mathrm{HSO}_{4}^{-}\), \(\mathrm{HSO}_{4}^{-}\) is recognized as the strongest conjugate acid due to \(\mathrm{SO}_{4}^{2-}\) being the weakest base.

Key Concepts

Conjugate Acids

In acid-base chemistry, a conjugate acid is formed when a base gains a proton (H\(^+\)). This process is like a handoff during a relay race, where the proton is passed from the acid to the base. Understanding conjugate acids is crucial because it helps predict how substances will behave in different chemical reactions.
To illustrate, let's consider the examples from our original exercise:

• The ion \(\mathrm{CN}^{-}\) becomes the conjugate acid \(\mathrm{HCN}\) by gaining a proton.
• Ammonia \(\mathrm{NH}_{3}\) gains a proton to form ammonium \(\mathrm{NH}_{4}^{+}\).
• Sulfate \(\mathrm{SO}_{4}^{2-}\) turns into hydrogen sulfate \(\mathrm{HSO}_{4}^{-}\).

The transformation reveals how bases can become acids by accepting protons, thus forming conjugate acids.

Strength of Acids

Acid strength refers to an acid's ability to donate a proton, which is a fundamental aspect of acid-base chemistry. A stronger acid releases more protons into a solution. Thus, it affects the acidity of a solution significantly. The strength of an acid is often depicted through its dissociation in water, where it splits into ions.
Based on the examples:

• \(\mathrm{HCN}\) is a weaker acid because \(\mathrm{CN}^{-}\) holds onto protons tightly, releasing less in solutions.
• \(\mathrm{NH}_{4}^{+}\) is stronger compared to \(\mathrm{HCN}\), as it's more willing to donate protons.
• \(\mathrm{HSO}_{4}^{-}\), being the strongest among the given examples, dissociates more readily, increasing its effectiveness in lowering pH.

Each acid's strength is inversely related to its conjugate base's strength, with stronger acids having weaker conjugate bases.

Conjugate Base-Strength Relationship

In acid-base equilibria, the relationship between conjugate acids and bases is like a seesaw. Their strengths balance each other with one being strong if the other is weak. This seesaw relationship plays a critical role in predicting reactions and understanding chemical stability.
For the compounds in the exercise:

• \(\mathrm{CN}^{-}\) is a strong base, resulting in a weaker conjugate acid \(\mathrm{HCN}\).
• \(\mathrm{NH}_{3}\) is a weak base, producing a stronger conjugate acid \(\mathrm{NH}_{4}^{+}\).
• \(\mathrm{SO}_{4}^{2-}\) is very weak as a base, so its conjugate acid \(\mathrm{HSO}_{4}^{-}\) is quite strong.

Understanding this relationship allows us to predict the behavior of substances when mixed in solutions and how they will influence the overall acidity or basicity.