Using the Ksp for calcium iodate hexahydrate, calculate the molarity of calcium ions in a saturated solution if the Ksp is 6.47 x 10^-6.

• A. 3.23 x 10^-3 M
• B. 2.54 x 10^-3 M
• C. 6.47 x 10^-6 M
• D. 1.27 x 10^-2 M

Answer: (D)

Verified step by step guidance

1. First, understand the dissolution process of calcium iodate hexahydrate, which can be represented by the chemical equation: Ca(IO3)2·6H2O(s) ⇌ Ca²⁺(aq) + 2 IO3⁻(aq).
2. The solubility product constant (Ksp) expression for this equilibrium is given by: $K_{\mathrm{sp}}=\; [Ca²⁺][IO3⁻]²$. This expression relates the concentrations of the ions in a saturated solution.
3. Let the molarity of calcium ions, [Ca²⁺], be represented by x. Since the stoichiometry of the dissolution shows that for every mole of Ca²⁺ produced, 2 moles of IO3⁻ are produced, the concentration of iodate ions, [IO3⁻], will be 2x.
4. Substitute these expressions into the Ksp expression: $K_{\mathrm{sp}}=\; x(2x)²\; =\; 4x³$. Set this equal to the given Ksp value, 6.47 x 10⁻⁶.
5. Solve the equation $4x³\; =\; 6.47\; imes\; 10^\{-6\}$ for x to find the molarity of calcium ions in the saturated solution.