Final answer:
The equilibrium concentrations of species in a diprotic acid solution depend on the acid's two dissociation steps and their respective Ka values. Specific values for these constants and initial concentration are needed to calculate concentrations of H₂A, HA⁻, A²⁻, and H₃O⁺ at equilibrium.
Step-by-step explanation:
To determine the concentrations in the original unknown solution of diprotic acid H₂A, we must consider the dissociation steps of the acid and their respective equilibrium constants, Ka₁ and Ka₂. For a diprotic acid, there are two dissociation steps:
- H₂A → HA⁻ + H₃O⁺ (with equilibrium constant Ka₁)
- HA⁻ → A²⁻ + H₃O⁺ (with equilibrium constant Ka₂)
Initially, we have the concentration of H₂A [H₂A]₀ and none of HA⁻, A²⁻, or H₃O⁺, which would correspond to option (a). As the acid starts dissociating at equilibrium, we will have a lessened concentration of H₂A, and some concentration of HA⁻ and H₃O⁺ generated, but the second dissociation is generally much less pronounced, hence A²⁻ concentration is typically low after the first dissociation step.
Given the complexity of calculating exact concentrations, an ICE (initial, change, equilibrium) table and approximations using the given Ka values are often employed to find the concentrations at equilibrium. The correct answer will depend on the specific Ka values and the initial concentration of H₂A. Without specific values for the Ka's or the initial concentration [H₂A]₀, it is not possible to definitively choose which of the given options (a, b, c, or d) will reflect the equilibrium state of the solution. Therefore, a step-by-step calculation using the specific values for Ka₁, Ka₂, and [H₂A]₀ is required to accurately find the concentrations of all species at equilibrium