In a saturated aqueous solution of the sparingly soluble strong electrolyte (molar mass = ), the equ — Ionic Equilibrium Chemistry Question
Question
In a saturated aqueous solution of the sparingly soluble strong electrolyte $AgIO_3$ (molar mass = $283 \text{ g/mol}$), the equilibrium $AgIO_3 (s) \rightleftharpoons Ag^+ (aq) + IO_3^- (aq)$ is established. If the solubility product constant $K_{sp}$ of $AgIO_3$ at a given temperature is strictly $1.0 \times 10^{-8}$, what is the exact mass of $AgIO_3$ contained in $100 \text{ mL}$ of its saturated solution?
💡 Solution & Explanation
For a strict 1:1 electrolyte like $AgIO_3$, $K_{sp} = s^2$, where $s$ is the molar solubility. Thus, $s = \sqrt{1.0 \times 10^{-8}} = 1.0 \times 10^{-4} \text{ mol/L}$. The number of moles contained within $100 \text{ mL}$ ($0.1 \text{ L}$) of the solution is $1.0 \times 10^{-4} \times 0.1 = 1.0 \times 10^{-5} \text{ moles}$. To determine the mass, multiply by the molar mass: Mass = $1.0 \times 10^{-5} \text{ mol} \times 283 \text{ g/mol} = 283 \times 10^{-5} \text{ g} = 2.83 \times 10^{-3} \text{ g}$.