For the simultaneous solubility of two sparingly soluble binary salts (with solubility product ) and — Ionic Equilibrium Chemistry Question

💡 Solution & Explanation

Let the solubility of $AgSCN$ be $s_1$ and $AgBr$ be $s_2$. $[Ag^+] = s_1 + s_2$, $[SCN^-] = s_1$, $[Br^-] = s_2$. $K_{sp1} = (s_1+s_2)s_1 = x$; $K_{sp2} = (s_1+s_2)s_2 = y$. Adding them gives $(s_1+s_2)(s_1+s_2) = x+y$, so $[Ag^+] = s_1+s_2 = \sqrt{x+y}$. Substituting this back, $s_1 = \frac{x}{\sqrt{x+y}}$ and $s_2 = \frac{y}{\sqrt{x+y}}$. The ratio $s_1/s_2 = x/y$. All statements are mathematically valid.