(a) Will Co(OH)2 precipitate from solution if the pH of a 0.020 M solution of Co(NO3)2 is adjusted to 8.5? (b) Will AgIO3 precipitate when 20 mL of 0.010 M AgNO3 is mixed with 10 mL of 0.015 M NaIO3? The Ksp of AgIO3 is 3.1 * 10^-8.

Verified step by step guidance

1. Step 1: For part (a), write the dissolution equation for Co(OH)_2: Co(OH)_2 (s) ⇌ Co^{2+} (aq) + 2OH^- (aq).
2. Step 2: Calculate the concentration of OH^- ions at pH 8.5 using the formula: [OH^-] = 10^{-(14 - pH)}.
3. Step 3: Determine the solubility product expression for Co(OH)_2: K_{sp} = [Co^{2+}][OH^-]^2.
4. Step 4: Compare the calculated ion product [Co^{2+}][OH^-]^2 with the known K_{sp} value for Co(OH)_2 to determine if precipitation occurs.
5. Step 5: For part (b), calculate the initial concentrations of Ag^+ and IO_3^- ions after mixing the solutions using the dilution formula: C_1V_1 = C_2V_2.

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It quantifies the extent to which a compound can dissolve in water, expressed as the product of the molar concentrations of its ions, each raised to the power of their coefficients in the balanced equation. For example, for AgIO3, Ksp = [Ag+][IO3-]. If the product of the ion concentrations exceeds Ksp, precipitation occurs.

pH and Precipitation

pH is a measure of the acidity or basicity of a solution, which can significantly influence the solubility of metal hydroxides. In the case of Co(OH)2, increasing the pH to 8.5 shifts the equilibrium towards the formation of the solid precipitate, as higher pH levels increase the concentration of hydroxide ions (OH-) in solution. This can lead to the precipitation of metal hydroxides when their solubility limits are exceeded.

Stoichiometry of Mixing Solutions

Stoichiometry involves calculating the concentrations of reactants and products in a chemical reaction. When mixing two solutions, the final concentrations of the ions must be determined to assess whether a precipitate will form. For AgIO3, the total moles of Ag+ and IO3- from the mixed solutions must be calculated to see if their product exceeds the Ksp, indicating precipitation.