Determination of Solubility Product from Molar Solubility

$K_{sp}$ can be calculated from the molar solubility -- the maximum number of moles of solute dissolving per litre. For $X_mY_n(s) \rightleftharpoons mX^{n+}(aq)+nY^{m-}(aq)$, one mole of $X_mY_n$ furnishes $m$ moles of $X^{n+}$ and $n$ moles of $Y^{m-}$; if $s$ is the molar solubility, $[X^{n+}]=ms$ and $[Y^{m-}]=ns$, so $K_{sp}=[X^{n+}]^m[Y^{m-}]^n=(ms)^m(ns)^n=m^m\,n^n\,s^{m+n}$ -- a single formula relating $K_{sp}$ and $s$ for any salt stoichiometry once $m$ and $n$ are known. …