At \(25^{\circ} \mathrm{C}\), the solubility of iron(III) hydroxide in water is \(4.49 \times 10^{-10} \mathrm{M}\). (a) What is the solubility in grams per liter? (b) What is the molar equilibrium concentration of each ion? (c) How many grams of iron(III) hydroxide could you dissolve in a 20,000-gallon swimming pool?

To find the solubility of iron(III) hydroxide in g/L, we can use the given solubility in M (mol/L) and calculate its mass in grams by using the molar mass of iron(III) hydroxide. When we have this value, we can convert it to g/L. Molar mass of Fe(OH)₃: \(1 \times 55.85 (Fe) + 3 \times 16.00 (O) + 3 \times 1.008 (H) = 106.87\, g/mol\) Now we can find the solubility in g/L: Solubility (g/L) = solubility (M) × molar mass (g/mol) Solubility (g/L) = \(4.49 \times 10^{-10}\,M \times 106.87\,g/mol = 4.799\times 10^{-8}\, g/L\)

To find the molar equilibrium concentration of each ion, we can use the solubility product constant expression for iron(III) hydroxide: \(K_{sp} = [Fe^{3+}] [OH^-]^3\) Since the solubility of iron(III) hydroxide is given in M, we can use this value for both [Fe³⁺] and [OH⁻] concentrations: \(4.49 \times 10^{-10}M = [Fe^{3+}] [OH^-]^3\) Assuming equal concentrations of Fe³⁺ and OH⁻ ions: [Fe⁺³] = solubility = \(4.49\times 10^{-10}M\) To find [OH⁻], we can use the formula: [OH⁻] = \(\sqrt[3]{\frac{K_{sp}}{[Fe^{3+}]}}\) [OH⁻] = \(\sqrt[3]{\frac{4.49\times 10^{-10}}{4.49\times 10^{-10}}}\) [OH⁻] = 1 M

To find the amount of iron(III) hydroxide that can dissolve in a 20,000-gallon swimming pool, we need first to convert gallons to liters and then multiply the resulting volume by the solubility in g/L. 1 gallon = 3.78541 L Total volume of swimming pool in liters: \(20000 \times 3.78541 = 75708.2\,L\) Now, by using the solubility in g/L and the total volume of the swimming pool, we can find the total mass in grams: Mass of iron(III) hydroxide = solubility (g/L) × volume (L) Mass of iron(III) hydroxide = \(4.799 \times 10^{-8}\,g/L \times 75708.2\,L = 3.634\times 10^{-3}\,g\) Therefore, the amount of iron(III) hydroxide that can dissolve in a 20,000-gallon swimming pool is approximately \(3.634\times 10^{-3}\,g\).