The of . What concentration ion in aqueous solution will just fail to give a precipitate of with a s — Ionic Equilibrium Chemistry Question
Question
The $K_{sp}$ of $\text{Ag}_2\text{CrO}_4 = 1.2 \times 10^{-11}$. What concentration $\text{Ag}^+$ ion in aqueous solution will just fail to give a precipitate of $\text{Ag}_2\text{CrO}_4$ with a solution in which $[\text{CrO}_4^{2-}] = 3 \times 10^{-4}\text{ M}$?
💡 Solution & Explanation
A precipitate will just fail to form when the ionic product is exactly equal to the solubility product. $K_{sp} = [\text{Ag}^+]^2[\text{CrO}_4^{2-}] \implies 1.2 \times 10^{-11} = [\text{Ag}^+]^2 (3 \times 10^{-4})$. Solving for $[\text{Ag}^+]^2 = \frac{1.2 \times 10^{-11}}{3 \times 10^{-4}} = 4 \times 10^{-8}$. Therefore, $[\text{Ag}^+] = \sqrt{4 \times 10^{-8}} = 2 \times 10^{-4}\text{ M}$.