# What is the chemical formula for the synthesis of Hydroxyapatite (Ca10(PO4)6(OH)2)?

This might be a basic question but I am a little confused.

I have some lecture notes that says calcium phosphate ($$\ce{Ca3(PO4)2}$$) reacts with calcium hydroxide ($$\ce{Ca(OH)2}$$) to form Hydroxyapatite ($$\ce{Ca10(PO4)6(OH)2}$$).

So, the chemical formula (even when unbalanced) should be:

$$\ce{Ca3(PO4)2 + Ca(OH)2 -> Ca10(PO4)6(OH)2}$$

I can't figure out why $$\ce{Ca10(PO4)6(OH)2}$$ is the product of $$\ce{Ca3(PO4)2}$$ and $$\ce{Ca(OH)2}$$ and I am having trouble balancing it (see below). On Sigma Aldrich's website, it says the linear Formula for hydroxyapatite is $$\ce{3Ca3(PO4)2·Ca(OH)2}$$. I copied and pasted this directly. I assume the dot between the calcium phosphate and calcium hydroxide means 'plus'.

On the Sigma Aldrich's website, the calcium phosphate is written/balanced as $$\ce{3Ca3(PO4)2}$$, whereas the lecture notes I have are just $$\ce{Ca3(PO4)2}$$. Even with the three in front as the coefficient, I get $$\ce{9Ca + Ca -> Ca10}$$, $$\ce{(PO4)2}$$ and $$\ce{(OH)2}$$ which is $$\ce{Ca10(PO4)2(OH)2}$$, instead of $$\ce{Ca10(PO4)6(OH)2}$$. If I use the formula in my lecture notes, I get $$\ce{Ca3(PO4)2 + Ca(OH)2 -> Ca4(PO4)2(OH)2}$$, which is even more off.

Should it be $$\ce{3(Ca3(PO4)2)}$$ instead of $$\ce{3Ca3(PO4)2}$$ so the coefficient 3 can be applied to the subscript 2 on the $$\ce{PO4}$$ to give $$\ce{(PO4)6}$$?

What am I missing?

• Well, it seems that before studying chemistry you must know the notation which is passed around through a word of mouth. In 3Ca3(PO4)2, the "4" refers to O and nothing else, the "2" refers to PO4, the second "3" refers to Ca, but the first "3" refers to everything after it. Pretty obvious, huh? Jul 18, 2020 at 6:12
• Stephanie's last question show that she does not master the basic convention for writing chemical formulas. I repeat her question here : "Should it be "3(Ca3(PO4)2)" instead of "3Ca3(PO4)2" ? " Well. Stephanie should absolutely be convinced that these two formulas are identical, before going ahead with apatite structures. Jul 18, 2020 at 9:17
• @IvanNeretin I know this. But in my working out, I always (to make it clear to myself) always, always put everything in as many brackets as needed to separate the items (maths or otherwise) so I thought the 3 without the brackets was only for the Ca. Got it now. Thanks Jul 19, 2020 at 10:09

The term "apatite" applies to a group of compounds with a general formula in the form $$\ce{M10(XO4)6Z2}$$, where $$\ce{M^2+}$$ is a metal and species $$\ce{XO4^3-}$$ and $$\ce{Z-}$$ are anions. The particular name of each apatite depends on the elements or radicals M, X and Z. In these terms, hydroxyapatite (HAp) has the molecular structure of apatite, where M is calcium ($$\ce{Ca^2+}$$), X is phosphorus ($$\ce{P^5+}$$) and Z is the hydroxyl radical ($$\ce{OH-}$$). This is known as stoichiometric hydroxyapatite and its atomic ratio Ca/P is $${1.67}$$. Its chemical formula is $$\ce{Ca10(PO4)6(OH)2}$$, with $$\ce{39 {%}}$$ by weight of $$\ce{Ca}$$, $$\ce{18.5 {%} P}$$ and $$\ce{3.38 {%}}$$ of $$\ce{OH}$$.
The anion radical can be replaced with fluorine/chlorine to become fluoroapatite/chloroapatite. This formula can also be written as $$\ce{3[Ca3(PO4)2]· Ca(OH)2}$$ which indicates three moles of calcium phosphate and one mole of calcium hydroxide which is basically the same as the Sigma-Aldrich's formula. The confusion arises since they have omitted the brackets, you didn't considered calcium phosphate as single entity for which you had a wrong formula. Brackets are generally not given but you have consider them as a single entity or you can even use brackets conveniently for your purpose. But do note that this formula doesn't prove that it is a basic salt but is actually a product of polymerisation:
According to Bassett, the solid existing in stable equilibrium at $$\pu{25 °C}$$., with solutions of a range from faintly acid to nearly pure lime-water, is oxy- or hydroxyapatite, but, although its composition may be indicated by the formula $$\ce{3Ca3(PO4)2.Ca(OH)2}$$, it is not to be regarded as a basic salt, but rather as the salt of a polymeride of phosphoric acid, $$\ce{H11P3O13}$$ (or $$\ce{3H3PO4.H2O}$$), with one hydrogen atom un-neutralised (like orthophosphoric acid or pyrophosphoric acid). The slowness of formation of hydroxyapatite favours the view that it is produced by polymerisation.