Solubility Product of a 1:1 Salt

Drop silver chloride into water and a little dissolves until the solution is saturated: AgCl(s) ⇌ Ag⁺ + Cl⁻. The solid's concentration never appears in an equilibrium expression, so Ksp is simply [Ag⁺][Cl⁻], and because each formula unit hands over one of each ion, both equal the molar solubility s. Hence Ksp = s². AgCl dissolves to about 1.3 × 10⁻⁵ M, giving Ksp = 1.7 × 10⁻¹⁰ — a number small enough that gravimetric chloride analysis can assume essentially all the silver precipitates.

Running it backwards is just as useful: barium sulfate's Ksp of 1.1 × 10⁻¹⁰ gives s = √(1.1 × 10⁻¹⁰) = 1.05 × 10⁻⁵ M, which is why patients can safely swallow a barium meal of a compound whose free Ba²⁺ ion is highly toxic — almost none of it ever enters solution. The trap is the common-ion effect: this s = √Ksp shortcut assumes pure water. Add 0.10 M NaCl and AgCl's solubility collapses to Ksp/[Cl⁻] ≈ 1.7 × 10⁻⁹ M, a hundredfold drop, which is exactly how analysts force a precipitation to completion.