In exactly of a saturated aqueous solution of (), of solid () is thoroughly added. The resultant con — Ionic Equilibrium Chemistry Question
Question
In exactly $1 \text{ L}$ of a saturated aqueous solution of $AgCl$ ($K_{sp} = 1.6 \times 10^{-10}$), $0.1 \text{ mol}$ of solid $CuCl$ ($K_{sp} = 1.0 \times 10^{-6}$) is thoroughly added. The resultant concentration of $Ag^+$ in the solution is experimentally found to be $1.6 \times 10^{-x} \text{ M}$. What is the integer value of '$x$'?
💡 Solution & Explanation
$CuCl$ is more soluble than $AgCl$. Its dissolution $CuCl \rightleftharpoons Cu^+ + Cl^-$ dominates the $[Cl^-]$. Let its solubility be $y$. $y^2 \approx 10^{-6} \Rightarrow y = 10^{-3} \text{ M}$. Since $0.1 \text{ mol}$ was added to $1 \text{ L}$, it won't dissolve completely, creating a saturated solution of $CuCl$ where $[Cl^-] = 10^{-3} \text{ M}$. For the simultaneous equilibrium, the $Ag^+$ concentration is determined by the $Cl^-$ from $CuCl$: $[Ag^+] = K_{sp}(AgCl) / [Cl^-] = 1.6 \times 10^{-10} / 10^{-3} = 1.6 \times 10^{-7} \text{ M}$. Thus, $x = 7$.