Consider a 0.10 M solution of a weak polyprotic acid (H₂A) with the possible values of K_a1 and K_a2 given here.
a. K_a1 = 1.0 × 10^–4; K_a2 = 5.0 × 10^–5
Calculate the contributions to [H₃O⁺] from each ionization step. At what point can the contribution of the second step be neglected?

Verified step by step guidance

1. <strong>Step 1:</strong> Understand the ionization process of the polyprotic acid H₂A. The first ionization step is: H₂A ⇌ H⁺ + HA^- with K_a1 = 1.0 × 10^-4. The second ionization step is: HA^- ⇌ H⁺ + A^2- with K_a2 = 5.0 × 10^-5. Each step contributes to the [H₃O⁺].
2. <strong>Step 2:</strong> Set up the equilibrium expression for the first ionization step: K_a1 = [H⁺][HA^-]/[H₂A]. Assume initial concentration of H₂A is 0.10 M and initial [H⁺] and [HA^-] are 0. Use an ICE table to express changes in concentration and solve for [H⁺] from the first ionization.
3. <strong>Step 3:</strong> Calculate the [H⁺] from the first ionization step using the approximation that x (the change in concentration) is small compared to the initial concentration of H₂A. This simplifies the expression to K_a1 ≈ x²/0.10.
4. <strong>Step 4:</strong> For the second ionization step, set up the equilibrium expression: K_a2 = [H⁺][A^2-]/[HA^-]. Use the [H⁺] from the first ionization as the initial concentration for the second ionization. Assume [HA^-] is approximately equal to the [H⁺] from the first ionization.
5. <strong>Step 5:</strong> Determine when the contribution of the second ionization step can be neglected. This occurs when the [H⁺] from the second ionization is significantly smaller than that from the first ionization. Compare the calculated [H⁺] from both steps to decide if the second step's contribution is negligible.

Key Concepts

Polyprotic Acids

Polyprotic acids are acids that can donate more than one proton (H+) per molecule in a solution. Each ionization step has its own dissociation constant (Ka), which indicates the strength of the acid at that step. For example, H2A can lose its first proton to form HA-, and then lose a second proton to form A2-. Understanding the sequential ionization is crucial for calculating the concentrations of hydronium ions produced.

Dissociation Constants (Ka)

The dissociation constant (Ka) quantifies the strength of an acid in solution, with lower values indicating weaker acids. For polyprotic acids, the first dissociation constant (Ka1) is typically larger than the second (Ka2), reflecting that the first proton is more easily lost. These constants are essential for determining the extent of ionization and the contributions to hydronium ion concentration from each step of the dissociation process.

Hydronium Ion Concentration ([H3O+])

The concentration of hydronium ions ([H3O+]) in a solution is a measure of its acidity. In the context of polyprotic acids, contributions to [H3O+] come from each ionization step, but as the acid dissociates further, the contribution from subsequent steps may become negligible. Identifying when this occurs is important for simplifying calculations and understanding the overall acidity of the solution.