When a salt dissolves in a solvent, usually water, the dissociated ions are present in the solvent phase in the same proportion as they are found in the solid phase. In other words, the stoichiometry of the dissociation is preserved just like it is in any chemical reaction.

The ionic product (IP) is simply a measure of the ions present in the solvent. This may sound trivial but, in fact, it is not always straightforward and the concept opens up a number of interesting features of how salts behave in solution. The solubility product (Ksp) is the ionic product when the system is in equilibrium.

The mineral found in teeth and bone is a salt formed from calcium phosphate. The major, and therefore most important, salt is an impure form of calcium hydroxyapatite, sometimes referred to as "biological apatite", but a solution of calcium phosphate can give rise to a number of different salts differing in their calcium to phosphate ratio (Ca:P). Some, most, or all of these may also be present in hard tissue but to a much lesser and varying degree.

Understanding "solubility product" using calcium phosphate as an example is made more difficult than it should be because salts with different stoichiometries can be formed from solutions of the same ions . It is much easier to consider a simple salt and then apply the principles to calcium phosphate.

Like hydroxyapatite, silver chloride is a sparingly soluble salt but it has only one form in which the silver and chloride ions are present in a 1:1 ratio. In water a small amount of silver chloride dissolves to produce an equal number of silver and chloride ions. Over time an equilibrium is established in which the amount of silver chloride dissolving from the solid phase is balanced by exactly the same amount precipitating. When this point is reached the solution is said to be saturated with respect to silver chloride.

At saturation the product of the amount of soluble silver and chloride ions (normally measured in Moles) is called the "solubility product".

Note:
It is important to understand that the ion concentrations which are being multiplied represent the ion activities in solution. In some cases, eg in calcium phosphate salts, the dissolved ions can form complexes with other ions or with other components of the system. These ions do not contribute to the ion activity and, therefore, are not counted. Simply measuring the total concentration of a specific ion in the aqueous phase can be very misleading and lead to erroneous results.

In this case the number of dissolved cations is different from the number of dissolved anions.

The amount of free calcium in solution was measured. Square brackets [ ] normally denote concentration.

The important point to note here is that if more complex salts are under consideration it is possible to calculate the concentration of any ion from a knowledge of the concentration of any other provided the relative proportions are taken into account.

Since 2 fluoride ions are produced for each calcium when calcium fluoride dissociates then:

The solubility product can now be calculated

Therefore

In the example of silver chloride the solution was at equilibrium and the product of the ions in solution (IP) was equal to the solubility product (Ksp)

What would happen if some sodium chloride, which is very soluble, was added. Let's suppose that enough sodium chloride was added so that it's final concentration in the aqueous phase was 1 mMol/L

The ionic product (IP) of the supernatant is now

Therefore

In this case the ionic product is greater than the solubility product. The dissociation equilibrium of the system will move to the left according to Le Chatelier's Principle and some silver chloride will precipitate. The concentration of silver ions in the aqueous phase will, therefore, reduce.

The equilibrium readjusts when a common ion is added to the system. In this case the common ion was chloride. Note that sodium does not enter the equation.

So far only relatively simple salts have been considered. In the mouth the situation is very much more complex because calcium and phosphate can combine to form several quite distinct salts which differ in the Ca:P ratio and solubility product. Furthermore, these salts form within a biological system which contains a great number of different ions capable of being substituted into the forming crystal.

These impurities greatly alter the physical characteristics of the solid especially their solubility.

The table below shows the ideal forms of the calcium phosphate salts relevant to oral hard tissues.

Care must be taken in interpreting solubility products. It is tempting to think that they are a direct measure of a salt's solubility. This is not always the case.

However, knowledge of the solubility product and the ionic composition of a salt enables one to calculate solubilities. See the table opposite.

Similar calculations can be done for other calcium phosphate salts. Again, see the table opposite.

Note that quite large differences in Ksp are not always reflected in the solubilities of the various ions concerned. Compare the values for octacalcium phosphate and tricalcium phosphate.

The only time a comparison is fair is when the relative proportions of the ions constituting the salt are the same. This is the case with hydroxyapatite and fluorapatite even though a fluoride ion has been substituted for hydroxyl.

These data show that calcium fluorapatite is about 20% less soluble than hydroxyaptite when the solubilities, measured as the concentration of calcium, are compared. It would be wrong to use the Ksp values to compare solubility. When this is done the difference is 86% which is misleadingly high.

It is, actually, quite difficult to make pure calcium hydroxyapatite in the laboratory because of the presence of contaminating ions of many different species even at very low concentrations. It is not surprising, therefore, that the mineral of teeth and bones behaves quite differently from the ideal when it is formed in an environment bathed in biological fluids.

Contaminating ions are such an important feature of hydroxyapatite made in biological systems that the product is distinguished from the ideal crystal form by referring to it as biological apatite or, sometimes, just apatite.

Impurities in biological apatite introduce significant stresses into the crystal structure which make it much less stable. Biological apatite composition varies so widely that any measure of solubility product is largely meaningless. It is, however, generally accepted to be very much more soluble than hydroxyapatite.

From a dental perspective, the most important contaminant is carbonate which has a major effect on increasing apatite solubility.

Fluoride may substitute for some hydroxyl ions in hydroxyapatite and thus may also be considered a contaminant, although it is not usually listed as such. The salt is referred to as fluor-hydroxyapatite.