$A$ sparingly soluble salt having general formula $A_{x}B_{y}$ and molar solubility $S$ is in equilibrium with its saturated solution. Derive a relationship between solubility and the solubility product for such salt.

(N/A) sparingly soluble salt has the general formula $A_{x}B_{y}$. Its molar solubility is $S \ mol \ L^{-1}$.
The dissociation equilibrium is:
$A_{x}B_{y} (s) \rightleftharpoons x A^{p+} (aq) + y B^{q-} (aq)$
When $S$ moles of $A_{x}B_{y}$ dissolve,it produces $xS$ moles of $A^{p+}$ and $yS$ moles of $B^{q-}$ ions in the solution.
The solubility product constant $(K_{sp})$ is defined as:
$K_{sp} = [A^{p+}]^{x} [B^{q-}]^{y}$
Substituting the concentrations:
$K_{sp} = (xS)^{x} (yS)^{y}$
$K_{sp} = x^{x} \cdot S^{x} \cdot y^{y} \cdot S^{y}$
$K_{sp} = x^{x} y^{y} S^{x+y}$