If a saturated solution of Ag₂CO₃ contains 2.56 × 10⁻⁴ M of Ag⁺ ions, determine its solubility product constant.

• A. 4.30 × 10⁻¹⁵
• B. 8.39 × 10⁻¹²
• C. 1.68 × 10⁻¹¹
• D. 6.55 × 10⁻⁸

Answer: (B)

Verified step by step guidance

1. Understand the dissolution of Ag2CO3 in water: Ag2CO3(s) ⇌ 2Ag+(aq) + CO3^(2−)(aq). This equation shows that one mole of Ag2CO3 produces two moles of Ag+ ions and one mole of CO3^(2−) ions.
2. Identify the concentration of Ag+ ions in the saturated solution, which is given as 2.56 × 10^−4 M. Since the stoichiometry of the dissolution reaction shows that two moles of Ag+ are produced for every mole of Ag2CO3, the concentration of CO3^(2−) ions will be half of the Ag+ concentration.
3. Calculate the concentration of CO3^(2−) ions using the stoichiometry: [CO3^(2−)] = [Ag+] / 2 = 2.56 × 10^−4 M / 2.
4. Write the expression for the solubility product constant (Ksp) for Ag2CO3: Ksp = [Ag+]^2 × [CO3^(2−)]. Substitute the known concentrations into this expression.
5. Perform the calculation using the concentrations: Ksp = (2.56 × 10^−4 M)^2 × (2.56 × 10^−4 M / 2). This will give you the solubility product constant for Ag2CO3.