Question

Rank the following species in order of decreasing acid strength: \(\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{H}_{2} \mathrm{SO}_{3}, \mathrm{HSO}_{3}^{-}\)

Short answer

\( \mathrm{H}_{2} \mathrm{SO}_{4} > \mathrm{H}_{2} \mathrm{SO}_{3} > \mathrm{HSO}_{3}^{-} \).

Step-by-step solution

Identify Acid Strength Factors

Consider the number of oxygen atoms and the oxidation state of sulfur in each species. More oxygen atoms typically increase acid strength due to the inductive effect and stabilization of the conjugate base.

Analyze \( \mathrm{H}_{2} \mathrm{SO}_{4} \)

\( \mathrm{H}_{2} \mathrm{SO}_{4} \) has four oxygen atoms and sulfur is in the +6 oxidation state. It is a strong acid because the high number of oxygen atoms stabilizes the conjugate base \( \mathrm{HSO}_{4}^{-} \).

Analyze \( \mathrm{H}_{2} \mathrm{SO}_{3} \)

\( \mathrm{H}_{2} \mathrm{SO}_{3} \) has three oxygen atoms and sulfur is in the +4 oxidation state. It is weaker than \( \mathrm{H}_{2} \mathrm{SO}_{4} \) because it has fewer oxygen atoms.

Analyze \( \mathrm{HSO}_{3}^{-} \)

\( \mathrm{HSO}_{3}^{-} \) is the conjugate base of \( \mathrm{H}_{2} \mathrm{SO}_{3} \). As a conjugate base of a weak acid, it is even weaker in terms of acid strength compared to \( \mathrm{H}_{2} \mathrm{SO}_{3} \).

Rank the Species

Based on the analysis, rank the species in order of decreasing acid strength: \( \mathrm{H}_{2} \mathrm{SO}_{4} \), \( \mathrm{H}_{2} \mathrm{SO}_{3} \), \( \mathrm{HSO}_{3}^{-} \).

Key concepts

Acid Strength Factors

Understanding what makes an acid strong or weak is crucial for ranking acids correctly. Several factors influence acid strength:

• Number of Oxygen Atoms: More oxygen atoms typically increase acid strength. Oxygen's high electronegativity pulls electron density away, enhancing the polarity of the O-H bond and making it easier to donate a proton (H⁺).
• Oxidation State: A higher oxidation state on the central atom (like sulfur in our example) increases acid strength. This is because higher oxidation states mean the central atom pulls electron density more effectively, weakening the O-H bond.
• Inductive Effect: Electronegative atoms like oxygen create an inductive effect. This effect stabilizes the conjugate base by distributing the negative charge more effectively.

By considering these factors, you can systematically determine acid strength and properly rank different species.

Conjugate Base Stability

The stability of a conjugate base is directly linked to the acid's strength. Strong acids have very stable conjugate bases, while weak acids have less stable conjugate bases.

• Resonance Stabilization: If a conjugate base can delocalize its negative charge over several atoms through resonance, it becomes more stable.
• Electronegative Atoms: Having electronegative atoms like oxygen in the conjugate base can increase stability. These atoms pull electron density away from the charged site, spreading out the negative charge.

For example, in sulfuric acid (\textbf{H}\(_2\textbf{SO}_4\)), the conjugate base (\textbf{HSO}_4\(^-$$) is highly stabilized due to resonance and the presence of multiple oxygen atoms. This stabilization makes \)\textbf{H}\(_2\textbf{SO}_4\)) a strong acid. In contrast, \(\textbf{HSO}_3\)^-$$, the conjugate base of sulfurous acid (\(\textbf{H}_2\textbf{SO}_3\))), is less stabilized, making $$\textbf{H}\(_2\textbf{SO}_3\)) a weaker acid.

Oxidation State

The oxidation state of the central atom in an acid influences its strength.

• Definition: The oxidation state is the charge of the central atom if all bonds were considered 100% ionic.
• Impact on Acid Strength: A higher oxidation state increases the electron-withdrawing power of the central atom. This, in turn, weakens the O-H bond, making it easier to donate a proton (H⁺).
  For example:


• Sulfuric Acid (\textbf{H}\(_2\textbf{SO}_4\))): In \(\textbf{H}_2\textbf{SO}_4\))), sulfur is in the +6 oxidation state. This high oxidation state significantly increases the acid strength.
• Sulfurous Acid (\(\textbf{H}_2\textbf{SO}_3\))): In $$\textbf{H}$$_2\textbf{SO}_3\(), sulfur is in the +4 oxidation state. Although still moderately strong, it is weaker than \)\textbf{H}\()\)_2\textbf{SO}_4\() due to the lower oxidation state.
• Conjugate Base (\)\textbf{HSO}\(_3\)^-$$): The conjugate base of \({H}$$_2\textbf{SO}_3\)), has sulfur in a +4 oxidation state. As the conjugate base of a weaker acid, it is even weaker in acid strength.
Understanding the oxidation state helps you predict and explain the acid strength of different species.