# 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

First, let me state the standard formula of hydroxyapaptite:

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.

Reference

1. Hydroxyapatite-Based Materials: Synthesis and Characterization By Eric M. Rivera-Muñoz, 2011, DOI: 10.5772/19123
2. http://calcium.atomistry.com/basic_calcium_phosphates.html
• Oh thank you, this is exactly what I needed. I always use (more) brackets (than typically needed) to make calculations clear for me, so the way it was written here confused me. Thank you so much. Jul 19, 2020 at 10:11