Final answer:
The solubility product (Ksp) for AB3 is calculated by taking the stoichiometry of the dissolution reaction into account. It involves finding the molarity of A3+ (1/3 of B− concentration) and then using these concentrations to calculate Ksp.
Step-by-step explanation:
To find the solubility product (Ksp) for AB3 when the concentration of B⁻ is 9.3×10⁻⁷ M, we use the stoichiometry of the dissolution reaction AB3(s) ⇔ A³⁺(aq) + 3B⁻(aq). The solubility (s) of AB3 represents the molarity of A³⁺ in solution, and in this equilibrium, it is 1/3 of the concentration of B⁻. Therefore, s is 3.1×10⁻⁷ M (9.3×10⁻⁷ M / 3). Since each formula unit of AB3 produces three ions of B⁻, we raise the concentration of B⁻ to the third power and multiply by the concentration of A³⁺ to get the Ksp. Thus, Ksp for AB3 is (s)(s×3)³ = (3.1×10⁻⁷)(9.3×10⁻⁷)³.