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A saturated solution of the sparingly soluble strong electrolyte AgIO3 is in equilibrium with its solid phase as AgIO3(s) ⇌ Ag+(aq) + IO3−(aq). If the solubility product constant of AgIO3 at a certain temperature is 1.0 × 10⁻⁸, what mass of AgIO3 is present in 100 mL of the saturated solution?
- 1.0 × 10⁻⁴ g
- 28.3 × 10⁻² g
- 2.83 × 10⁻³ g
- 1.0 × 10⁻⁷ g
Correct answer: 2.83 × 10⁻³ g
Solution
The solubility product constant (Ksp) relates the concentrations of the ions in a saturated solution. Given Ksp = 1.0 × 10⁻⁸, we can set up the equation Ksp = [Ag+][IO3−]. Since the stoichiometry is 1:1, if 's' is the solubility in mol/L, then Ksp = s². Solving for 's' gives s = 1.0 × 10⁻⁴ mol/L. In 100 mL, this corresponds to 1.0 × 10⁻⁴ mol, which converts to 2.83 × 10⁻³ g of AgIO3, confirming option C as correct.
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