# Solubility equilibrium

Solubility equilibrium describes the chemical equilibrium between solid and dissolved states of a compound.

The substance that is dissolved can be an organic solid such as sugar or an ionic solid such as salt. The main difference is that ionic solids dissociate into constituent ions when they dissolve in water. Most commonly water is the solvent of interest, although the same basic prinicples apply with any solvent.

## Non-ionic compounds

Dissolution of an organic solid can be described as an equilibrium between the substance in its solid and dissolved forms:

[itex]sugar(s) \Leftrightarrow sugar(aq)[itex]

We can write an equilibrium expression for this reaction, as for any chemical reaction (products over reactants):

[itex]K = \frac{\left [sugar\right](aq)}{ \left \{sugar\right\}(s)}[itex]

where K is called the equilibrium (or solubility) constant and the square brackets mean molar concentration in mol/L (sometimes called molarity with symbol M). Because the concentration of a solid doesn't make sense, we use the curly brackets, which mean activity, around the solid. Luckily, the activity of a solid is amost always equal to one. So, we have a very simple expression:

[itex]K = \left [sugar\right](aq)[itex]

This statement says that water at equilibrium with solid sugar contains a concentration equal to K. For table sugar (sucrose) at 25 °C, K = 1.971 mol/L. (This solution is very concentrated; sucrose is extremely soluble in water.) This is the maximum amount of sugar that can dissolve at 25 °C; the solution is saturated. If the concentration is below saturation, more sugar dissolves until the solution reaches saturation, or all the solid is consumed. If more sugar is present than is allowed by the solubility expression then the solution is supersaturated and solid will precipitate until the saturation concentration is reached. This process can be slow; the equilibrium expression describes concentrations when the system reaches equilibrium, not how fast it gets there.

## Ionic compounds

Ionic compounds normally dissociate into their constituent ions when they dissolve in water. For example, for calcium sulfate:

[itex]\mbox{CaSO}_4(s) \Leftrightarrow \mbox{Ca}^{2+}(aq) + \mbox{SO}_4^{2-}(aq)[itex]

As for the previous example, the equilibrium expression is:

[itex]K_c = \frac{\left[\mbox{Ca} ^{2+}(aq)\right]\left[\mbox{SO}_4^{2-}(aq)\right]}{ \left\{\mbox{CaSO}_4(s)\right\}}[itex]

where K is called the equilibrium (or solubility) constant, the square brackets mean molar concentration (M, or mol/L), and curly brackets mean activity. Since the activity of a pure solid is equal to one, this expression reduces to the solubility product expression:

[itex]K_{sp} = \left[\mbox{Ca}^{2+}(aq)\right]\left[\mbox{SO}_4^{2-}(aq)\right][itex]

This expression says that an aqueous solution in equilibrium with (saturated with) solid calcium sulfate has concentrations of these two ions such that their product equals Ksp; for calcium sulfate Ksp=4.93×10-5. If the solution contains only calcium sulfate the concentration of each ion is:

[itex]\sqrt{ K_{sp}}=\sqrt{4.93\times10^{-5}}=7.02\times10^{-5}=\left[\mbox{Ca}^{2+}\right]=\left[\mbox{SO}_4^{2-}\right][itex]

Solubility constants have been experimentally determined for a large number of compounds and tables are readily available. For ionic compounds the constants are called solubility products. Concentration units are assumed to be molar (moles per liter) unless otherwise stated. Solubility is sometimes listed in mass units such as grams dissolved per liter of water.

Solubility (and equilibrium) constants themselves have are dimensionless (they may have units, however); the lack of units in the constant looks inconsistant; it comes about because the use of molar concentration in the solubility expression is only an approximation to activity, a unitless quantity that is approximately equal to molarity at low concentrations.

The common ion effect refers to the fact that solubility equilibria shift in response to Le Chatelier's Principle. In the above example, addition of sulfate ions to a saturated solution of calcium sulfate causes CaSO4 to precipitate until the ions in solution again satisfy the solubility expression. (Addition of sulfate ions could be accomplished by adding a very soluble salt, such as Na2SO4.)

Solubility is sensitive to temperature. For example, sugar is more soluble in hot water than cool water, but the solubility of calcium sulfate decreases as the solution is heated. These effects occur because solubility constants, like other types of equilibrium constant, are functions of temperature. A thermodynamic approach is required to predict how much and in what direction a particular constant changes.

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