Ionic Product and Solubility Product
   
What is Ionic Product

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.

 
The importance in dentistry

Ionic and Solubility Products are the basic chemical phenomena behind tooth mineralisation, demineralisation and stability. In other words they are critical to:

1.

the processes which form teeth (odontogenesis, amelogenesis and cementogenesis)

2.

those which contribute to their loss (caries and tooth erosion)

3.

the functions of saliva which are aimed at tooth preservation, including the concept of "Critical pH"

Silver chloride, a simple salt

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.

 
Calcium fluoride is more complex

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

The common ion effect

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.

 

 
Common ion in the mouth

The common ion effect is an important phenomenon and has great significance in tooth decay.

The reason for this is that the fluid bathing teeth, whether saliva or plaque fluid, contains calcium and phosphate ions which are not just derived from teeth. In other words, the fluid is not the result of an equilibrium between the aqueous and the mineral phases. It is, rather, an exogenously supplied fluid, supersaturated with respect to tooth mineral, in which the calcium and phosphate ion concentrations can be greatly altered by, for example, elements of the diet.

Furthermore, in plaque fluid, calcium ion activity is affected by pH-sensitive calcium-binding components which cause the calcium activity to increase if the pH drops. Both these will significantly affect the ionic product of the fluid and, thus, the dissociation equilibrium of the tooth mineral.

In the case of fluoride, this ion can replace hydroxyl ions in the hydroxyapatite crystal. It could, therefore, be considered to be a common ion of hydroxyl. In fluoride-containing toothpastes the fluoride concentration is about 1500 ppm which is equivalent to 0.08M. This is 800,000 times more concentrated than hydroxyl ions at neutral pH so there is significant pressure for fluoride ions to precipitate with calcium and phosphate as fluor-hydroxyapatite. In fact, this is what happens in plaque fluid during a cariogenic challenge to the tooth. This re-mineralisation with fluor-hydroxyapatite is one of the major ways that fluoride works to protect teeth.

Solubility products of some calcium phosphate salts

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.

 

 

Ksp of Hydroxyapatite and Fluorapatite

Reported values for the solubility products of these salts scatter over quite large ranges. The reasons for this are complex and not fully understood. There is, however, general agreement that the value for fluorapatite is lower than that of hydroxyapatite.

The values cited below are those of McDowell et al (1977) J Res Natl Bur Standards:81A:273 (HA) and Moreno et al (1974) Nature:247:64 (FA)

   
Solubility of Hydroxyapatite and Fluorapatite

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.

 

 
Question:
If hydroxyapatite is allowed to reach equilibrium in water, what is the concentration of calcium in solution?

 

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.

 
Solubility Products of some
calcium phosphate salts
 
Biological Apatite

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 in biological apatite
 

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.

Structures of the apatites in enamel, dentine and bone
   

SUMMARY

1.

Ionic and solubility products are important basic chemical phenomena underpinning tooth mineralisation, demineralisation and stability.

2.

The product of the soluble ions of a salt in solution is called the ionic product

3.

At equilibrium the ionic product of a salt is called the solubility product.

4.

The solubility product is not a measure of the solubility of a salt but can be used to calculate it.

5.

Addition of a common ion affects the ionic product. This has important implications in the mouth since the concentration of calcium and phosphate ions in saliva and plaque fluid can be influenced by external factors.

6.

A variety of calcium phosphate salts are found in mineralised tissue but the major salt is an imperfect hydroxyapatite called biological apatite or, sometimes, apatite. Biological apatite is much more soluble than hydroxyapatite.

7.

Reliable solubility products for hydroxyapatite and fluorapatite are not available but fluorapatite is less soluble and has a lower solubility product. The variabilty of biological apatite means that there is no meaningfull solubility product.

8.

The major contaminating ions in biological apatite are strontium, barium, potassium, lead, sodium, magnesium, mono-hydrogenphosphate and carbonate.

9.

Carbonate is of major importance in apatite because it very significantly increases solubility.

 

 

 

 

 

 

 

 

 

 

   

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