Slightly soluble ionic solids establish an equilibrium between undissolved solid and dissolved ions. If you can measure the ion concentrations in a saturated solution, you can determine $K_{sp}$ quantitatively from stoichiometry.

Core idea: saturation links concentration to equilibrium

A saturated solution contains the maximum dissolved amount of a salt at a given temperature, with undissolved solid present.

Sequence of beakers illustrating a sparingly soluble salt as more solid is added: the solution concentration increases until the saturation point is reached. Beyond saturation, additional solid accumulates at the bottom while the dissolved ion concentrations remain constant—evidence of equilibrium between solid and ions in solution. Source

This ensures the dissolution reaction is truly at equilibrium, so the equilibrium-constant expression applies.

Key term used in calculations

Molar solubility is often not measured directly; instead, you may measure equilibrium ion concentrations (for example, via conductivity, titration, or spectroscopy) and relate them to $s$ using the balanced dissolution equation.

Writing the dissolution reaction correctly

To calculate $K_{sp}$, first write the balanced dissolution equilibrium for the salt. For a generic salt $M_aX_b$:

• Include the solid as a reactant: $M_aX_b(s)$

• Write aqueous ions with correct stoichiometric coefficients and charges

• Ensure the equation is balanced for both atoms and charge

The stoichiometric coefficients determine how ion concentrations depend on $s$ (or on each other if $s$ is not explicitly used).

From measured ion concentrations to $K_{sp}$

For slightly soluble salts, AP Chemistry typically treats dilute aqueous solutions as ideal enough that concentrations can be used in place of activities. Solids are omitted from the equilibrium expression.

Plot showing combinations of ion concentrations that satisfy the equilibrium condition for a sparingly soluble salt (example shown for a 1:1 salt like AgCl). Points on the curve represent states where the ion product equals $K_{sp}$; points off the curve correspond to $Q<K_{sp}$ (unsaturated) or $Q>K_{sp}$ (supersaturated/precipitation until equilibrium is restored). Source

To use measured data, connect the measured equilibrium concentrations to the dissolution stoichiometry:

• If $M_aX_b(s) \rightleftharpoons aM^{n+}+bX^{m-}$ and the molar solubility is $s$, then ideally:

  • $[M^{n+}] = a s$

  • $[X^{m-}] = b s$

• If ion concentrations are measured directly, you may not need $s$ at all; substitute the measured equilibrium ion concentrations into the $K_{sp}$ expression.

• If only one ion concentration is measured:

  • Use stoichiometric ratios to infer the other ion concentration (e.g., if $[M^{n+}]$ is known, then $[X^{m-}] = \frac{b}{a}[M^{n+}]$).

Practical checklist for “find $K_{sp}$ from molar solubility”

• Confirm the solution is saturated (equilibrium established with excess solid).

• Write the balanced dissolution equation.

• Translate molar solubility ($s$) into equilibrium ion concentrations using coefficients.

• Substitute equilibrium ion concentrations into the $K_{sp}$ expression.

• Report $K_{sp}$ to a reasonable number of significant figures consistent with the measured data.