Solubility equilibrium

Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical reaction with another constituent of the solution, such as acid or alkali. Each solubility equilibrium is characterized by a temperature-dependent solubility product which functions like an equilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.

A solubility equilibrium exists when a chemical compound in the solid state is in chemical equilibrium with a solution containing the compound. This type of equilibrium is an example of dynamic equilibrium in that some individual molecules migrate between the solid and solution phases such that the rates of dissolution and precipitation are equal to one another. When equilibrium is established and the solid has not all dissolved, the solution is said to be saturated. The concentration of the solute in a saturated solution is known as the solubility. Units of solubility may be molar (mol dm⁻³) or expressed as mass per unit volume, such as μg mL⁻¹. Solubility is temperature dependent. A solution containing a higher concentration of solute than the solubility is said to be supersaturated. A supersaturated solution may be induced to come to equilibrium by the addition of a "seed" which may be a tiny crystal of the solute, or a tiny solid particle, which initiates precipitation.^{[citation needed]}

There are three main types of solubility equilibria.

In each case an equilibrium constant can be specified as a quotient of activities. This equilibrium constant is dimensionless as activity is a dimensionless quantity. However, use of activities is very inconvenient, so the equilibrium constant is usually divided by the quotient of activity coefficients, to become a quotient of concentrations. See Equilibrium chemistry § Equilibrium constant for details. Moreover, the activity of a solid is, by definition, equal to 1 so it is omitted from the defining expression.

For a chemical equilibrium $${\displaystyle \mathrm {A} _{p}\mathrm {B} _{q}\leftrightharpoons p\mathrm {A} +q\mathrm {B} }$$ the solubility product, K_sp for the compound A_pB_q is defined as follows $${\displaystyle K_{\mathrm {sp} }=[\mathrm {A} ]^{p}[\mathrm {B} ]^{q}}$$ where [A] and [B] are the concentrations of A and B in a saturated solution. A solubility product has a similar functionality to an equilibrium constant though formally K_sp has the dimension of (concentration)^p+q.

Solubility is sensitive to changes in temperature. For example, sugar is more soluble in hot water than cool water. It occurs because solubility products, like other types of equilibrium constants, are functions of temperature. In accordance with Le Chatelier's Principle, when the dissolution process is endothermic (heat is absorbed), solubility increases with rising temperature. This effect is the basis for the process of recrystallization, which can be used to purify a chemical compound. When dissolution is exothermic (heat is released) solubility decreases with rising temperature. Sodium sulfate shows increasing solubility with temperature below about 32.4 °C, but a decreasing solubility at higher temperature. This is because the solid phase is the decahydrate (Na
₂SO
₄·10H
₂O) below the transition temperature, but a different hydrate above that temperature.^{[citation needed]}

The dependence on temperature of solubility for an ideal solution (achieved for low solubility substances) is given by the following expression containing the enthalpy of melting, Δ_mH, and the mole fraction ${\displaystyle x_{i}}$ of the solute at saturation: $${\displaystyle \left({\frac {\partial \ln x_{i}}{\partial T}}\right)_{P}={\frac {{\bar {H}}_{i,\mathrm {aq} }-H_{i,\mathrm {cr} }}{RT^{2}}}}$$ where ${\displaystyle {\bar {H}}_{i,\mathrm {aq} }}$ is the partial molar enthalpy of the solute at infinite dilution and ${\displaystyle H_{i,\mathrm {cr} }}$ the enthalpy per mole of the pure crystal.

This differential expression for a non-electrolyte can be integrated on a temperature interval to give: $${\displaystyle \ln x_{i}={\frac {\Delta _{m}H_{i}}{R}}\left({\frac {1}{T_{f}}}-{\frac {1}{T}}\right)}$$