 Hydroxyapatite

Hydroxyapatite is a crystalline calcium phosphate whose ideal composition is $\mathrm{C}{\mathrm{a}}_{10}(\mathrm{P}{\mathrm{O}}_4{)}_6(\mathrm{OH}{)}_2$, equivalently $\mathrm{C}{\mathrm{a}}_5(\mathrm{P}{\mathrm{O}}_4{)}_3\mathrm{OH}$. The formula describes an extended ionic solid, not a discrete hydroxyapatite molecule. Its ideal calcium-to-phosphorus molar ratio is $10/6=5/3$. NIST uses hydroxyapatite reference powder to evaluate physical and chemical measurements of apatites.^[ref]

The ideal composition is electrically neutral: ten calcium ions contribute charge $+20$, six phosphate ions contribute $-18$ and two hydroxide ions contribute $-2$. Changing a subscript changes this composition; it is not the same operation as multiplying the whole chemical formula by a coefficient.

An original composition calculation uses approximate molar masses $40.078$ for calcium, $30.974$ for phosphorus, $15.999$ for oxygen and $1.008$ for hydrogen, in grams per mole. The full formula has molar mass about $1004.62\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$, with ideal calcium mass fraction about $39.89\%$ and phosphorus mass fraction about $18.50\%$. Their mass-fraction ratio is about $2.157$, whereas their mole ratio is $1.667$. An elemental mass ratio cannot be compared directly with the stoichiometric mole ratio.

Identity also needs structural evidence. NIST characterized its reference powder by elemental analysis and powder X-ray diffraction, comparing diffraction positions with the hydroxyapatite pattern. Its certificate distinguishes certified composition values from supplementary diffraction information.^[ref] A measured Ca/P ratio near $5/3$ alone does not establish that every part of a specimen is a single hydroxyapatite phase: a mixture can reproduce an overall elemental ratio. Composition, phase identification and the properties of a biological composite material answer related but different questions.