Solubility Equilibria

Solubility equilibrium forms when the rate of dissolution equals the rate of precipitation. For example, when lead chloride is added to water, some solid dissolves while dissolved ions recombine to form precipitate. When these opposing processes occur at equal rates, the system reaches equilibrium, with undissolved solid coexisting with dissolved ions in solution.

The solubility product constant, or Ksp, is the equilibrium constant for dissolution reactions of sparingly soluble salts. For lead chloride, Ksp equals the molar concentration of lead ions multiplied by the square of chloride ion concentration. The solid's concentration is excluded because it remains constant. At 25°C, lead chloride's Ksp is 1.17 × 10⁻⁵, representing the extent to which the compound dissolves.

Molar solubility is calculated using an ICE table and the Ksp expression. For lead chloride, if x represents molar solubility, then lead ion concentration is x and chloride concentration is 2x. Substituting into Ksp = x(2x)² = 4x³ = 1.17 × 10⁻⁵ gives x = 1.43 × 10⁻² molar, the compound's solubility in moles per liter.

When mixing solutions containing Ca²⁺ and CO₃²⁻ ions, compare the reaction quotient Q to Ksp. If Q < Ksp, no precipitation occurs because the solution is unsaturated. If Q > Ksp, the solution is supersaturated and precipitation will occur, lowering ion concentrations until Q equals Ksp and equilibrium is established.

Solids have constant concentration and do not participate in equilibrium expressions. Only dissolved ions and aqueous species are included in Ksp calculations. For lead chloride, the solid's concentration remains constant regardless of how much dissolves, so only the molar concentrations of lead and chloride ions appear in the Ksp equation.

Compound solubility varies depending on solution pH and the presence of other ions. At a given temperature, Ksp remains constant, but the molar solubility can change based on these factors. Understanding how pH and ion concentration influence solubility is essential for managing natural and technological processes like water purification and tooth decay prevention.

For compounds with identical dissociation stoichiometry, such as lead chloride and calcium fluoride, where one mole produces three moles of dissolved ions, their Ksp values can be directly compared to determine relative solubilities. The compound with the larger Ksp value is more soluble under the same conditions.