Problem 66 - Chemistry: An Atoms-Focused Approach

Question

In calculating the pH of \(1.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{3},\) we can ignore the \(\mathrm{H}^{+}\) ions produced by the ionization of the bisulfite \(\left(\mathrm{HSO}_{3}^{-}\right)\) ion; however, in calculating the pH of \(1.0 \mathrm{M}\) sulfuric acid, we cannot ignore the \(\mathrm{H}^{+}\) ions produced by the ionization of the bisulfate ion. Why?

Step-by-Step Solution

Answer

Question: Explain why we can ignore H+ ions produced by the ionization of the bisulfite ion (HSO3-) in calculating the pH of 1.0M H2SO3 solution, but cannot ignore H+ ions produced by the ionization of the bisulfate ion in calculating the pH of 1.0M sulfuric acid solution. Answer: We can ignore the H+ ions produced by the ionization of HSO3- ions in 1.0M H2SO3 solution because H2SO3 is a weak dibasic acid that does not ionize completely, making the second ionization's contribution to the overall H+ ion concentration negligible. However, for 1.0M sulfuric acid, the acid is strong and ionizes completely, resulting in significant contributions from both ionizations in determining the H+ ion concentration. Thus, we cannot ignore the H+ ions produced by the ionization of the HSO4- ion when calculating the pH of 1.0M sulfuric acid solution.

Step 1: Ionization of H2SO3 and H2SO4

H2SO3 is a weak dibasic acid that partially ionizes in water to produce H+ ions and HSO3- ions. The weak ionization of H2SO3 means that the concentration of H+ ions produced by the ionization of the HSO3- ions will be negligible compared to the concentration of H+ ions produced by the ionization of H2SO3 itself. H2SO4, on the other hand, is a strong dibasic acid that ionizes completely in water to produce 2H+ ions and SO4^2- ions. Since it is a strong acid, both its ionizations are significant. Therefore, the H+ ion concentration produced by the ionization of the HSO4- ion is also significant and cannot be ignored when calculating the pH.

Step 2: Ionization constants

To better explain this, let's consider the ionization constants of H2SO3 and H2SO4. For H2SO3, we have: First ionization: \(H_2SO_3 \rightleftharpoons H^+ + HSO_3^-\) with the equilibrium constant \(K_{a1}\) Second ionization: \(HSO_3^- \rightleftharpoons H^+ + SO_3^{2-}\) with the equilibrium constant \(K_{a2}\) For H2SO4, we have: First ionization: \(H_2SO_4 \rightleftharpoons H^+ + HSO_4^-\) with the equilibrium constant \(K_{a1}\) being very large (indicating complete ionization) Second ionization: \(HSO_4^- \rightleftharpoons H^+ + SO_4^{2-}\) with the equilibrium constant \(K_{a2}\) The first ionization constant of H2SO3 (\(K_{a1}\)) is much smaller than the first ionization constant of H2SO4, and the second ionization constants of both the acids are of the order of \(10^{-2}\), which gives a significant contribution of H+ ions in H2SO4 solution on second ionization but not as significant in H2SO3 solution.

Step 3: Conclusion

In conclusion, we can ignore the H+ ions produced by the ionization of HSO3- ions in calculating the pH of 1.0M H2SO3 as this acid is weak and does not ionize completely; thus, the second ionization has a negligible effect on the overall H+ ion concentration. However, for 1.0M sulfuric acid, as it is a strong acid and ionizes completely, the contribution of H+ ions from both the ionizations is significant, and so we cannot ignore the H+ ions produced by the ionization of the HSO4- ion while calculating the pH.

Key Concepts

Ionization Constants

Ionization constants are vital when understanding how acids behave in solution. An ionization constant, often denoted as \( K_a \), is a measure of the strength of an acid in solution. It indicates how well an acid dissociates into its ions. Higher \( K_a \) values mean stronger acids, as they dissociate more completely, releasing more hydrogen ions \( (H^+) \).
Sulfuric acid \((H_2SO_4)\), for instance, has a large \( K_a1 \), indicating complete dissociation in its first ionization. This means it almost entirely produces \( H^+ \) ions from the first ionization step.

• The first ionization reaction is: \( H_2SO_4 \rightleftharpoons H^+ + HSO_4^- \)
• With a high \( K_a1 \), nearly all \( H_2SO_4 \) molecules ionize, showing it's a strong acid.
• For the weak acid \((H_2SO_3)\), the first ionization constant \( K_{a1} \) is much smaller, showing that only a small fraction of molecules ionize, making it less effective at releasing \( H^+ \) ions.

This difference in ionization constants helps predict how an acid will affect the pH of a solution.

Strong and Weak Acids

Acids are categorized as strong or weak based on their ability to ionize in solution. Strong acids fully dissociate into their ions, meaning almost every acid molecule breaks into \( H^+ \) ions and the accompanying anion. Because of this complete ionization, strong acids produce a high concentration of \( H^+ \) ions, significantly affecting the solution's pH.

• Sulfuric acid \( (H_2SO_4) \) is a strong acid. It ionizes almost completely in water, creating a lot of \( H^+ \) ions from both stages of its dissociation.
• Weak acids, like sulfurous acid \( (H_2SO_3) \), only partially dissociate in water.
• Because weak acids don't fully ionize, they have a much less dramatic impact on pH.

Recognizing whether an acid is strong or weak is crucial for understanding how it will behave in aqueous solutions and how it will affect pH levels.

Sulfuric Acid Ionization

Sulfuric acid's ionization process is unique due to its two-step nature. It undergoes a complete and highly effective first ionization, followed by a second incomplete but still significant ionization.
The first step of sulfuric acid ionization is as follows:

• \( H_2SO_4 \rightleftharpoons H^+ + HSO_4^- \).
• Here, sulfuric acid dissociates entirely, producing hydrogen and bisulfate ions, effectively making it a strong acid at this stage.

The second ionization stage is characterized by its partial disassociation:

• \( HSO_4^- \rightleftharpoons H^+ + SO_4^{2-} \).
• Though not complete, this step is significant enough that it must be considered when calculating the concentration of \( H^+ \) ions in sulfuric acid solutions.

Understanding both stages helps in accurately determining pH levels of sulfuric acid solutions and recognizing the importance of each ionization phase in contributing to overall acidity.