Solubility equilibria

Some salts, like silver chloride, dissolve only very slightly (they are sparingly soluble). In a saturated solution, the tiny dissolved amount is in equilibrium with the solid. For a salt MₓXᵧ ⇌ xMᵖ⁺ + yX^q⁻, the solubility product is:

Ksp = [Mᵖ⁺]ˣ[X^q⁻]ʸ

If S is the molar solubility (moles dissolved per litre), each ion's concentration is its coefficient times S, so Ksp = xˣyʸ S^(x+y):

• AgCl ⇌ Ag⁺ + Cl⁻: Ksp = S × S = S².
• A salt of type MX₂ (such as CaF₂): Ksp = S × (2S)² = 4S³.
• Fe(OH)₃: Ksp = S × (3S)³ = 27S⁴.
• A₂X₃: Ksp = (2S)² × (3S)³ = 108S⁵.

When salts have different formula types, compare their solubilities (S), not their Ksp values, to see which dissolves more.

Will a precipitate form? Calculate the ionic product, Q, from the actual concentrations, and compare it with Ksp:

• Q > Ksp: the solution has more than it can hold: a precipitate forms.
• Q < Ksp: no precipitate.
• Q = Ksp: the solution is just saturated.

The common ion effect lowers solubility. Nickel hydroxide dissolves far less in sodium hydroxide solution (which supplies OH⁻) than in pure water. Passing HCl gas into a saturated solution of common salt adds Cl⁻ ions, and pure NaCl crystallises out. This is used to purify salt.

Salts of weak acids dissolve more at lower pH: the acid's H⁺ ions take up the anion (turning it into the weak acid), so more of the salt dissolves to replace it. S = √(Ksp([H⁺] + Ka)/Ka).