7.11 Introduction to Solubility Equilibria

Ksp defines solubility equilibrium

The solubility-product constant (Ksp) describes the equilibrium between a slightly soluble ionic solid and its dissolved ions in a saturated solution. For a salt A_xB_y(s) ⇌ xA^y+ + yB^x-, Ksp = [A]^x[B]^y, with the solid omitted since it's a pure condensed phase. A larger Ksp generally indicates greater solubility, though stoichiometry must be considered when comparing different salts.

Molar solubility from Ksp

Molar solubility (s) is the moles of solid that dissolve per liter to reach saturation. Using a reaction table (ICE), express equilibrium ion concentrations in terms of s, substitute into the Ksp expression, and solve. For example, for CaF2 ⇌ Ca^2+ + 2F-, Ksp = (s)(2s)^2 = 4s^3, so solving for s gives molar solubility.

Comparing Ksp values carefully

You cannot directly compare Ksp values to rank solubility unless the salts produce the same number of ions. A salt with a smaller Ksp but a 1:2 ion ratio can be more soluble than a 1:1 salt with a larger Ksp, because the exponents affect the algebra differently. Always solve for molar solubility to make valid comparisons.

Key terms

Ksp

Solubility-product constant; equilibrium constant for the dissolution of a slightly soluble ionic solid into its ions.

Molar solubility (s)

Moles of solid that dissolve per liter of solution to form a saturated solution.

Ksp expression for AxBy(s) ⇌ xA + yB

Ksp = [A]^x[B]^y, with the solid omitted from the expression.

Why can't you always compare Ksp values directly?

Different stoichiometries (ion ratios) mean equal Ksp values can correspond to different molar solubilities.

Example: CaF2 ⇌ Ca^2+ + 2F-

Ksp = [Ca^2+][F-]^2 = (s)(2s)^2 = 4s^3, used to solve for molar solubility s.

Try an AP-style question

Ksp for AgCl is 1.8 × 10⁻¹⁰. What is its molar solubility?

1. 1.3 × 10⁻⁵ M
2. 1.8 × 10⁻¹⁰ M
3. 9.0 × 10⁻¹¹ M
4. 3.6 × 10⁻¹⁰ M