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My textbook says the formula for fluoroapatite is $\ce{CaF2 * 3Ca3(PO4)2}$, whereas according to Wikipedia it's $\ce{Ca5(PO4)3F}$.

What is the correct chemical formula of fluoroapatite and why there are different representation of the same compound?

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    $\begingroup$ Both are correct; moreover, to a chemist both are identical. $\endgroup$ – Ivan Neretin Feb 19 at 13:14
  • $\begingroup$ It will be helpful if I get an exlplanation of them being identical. $\endgroup$ – Sayemun Rahman Tasin Feb 19 at 13:18
  • $\begingroup$ If I'd see my name written like "Ivan Neretin", I'd instantly recognize it as such. If I'd see it written like "Neretin Ivan", I'd still recognize it right away. But their equivalence might be less obvious to a person who knows only the letters of the script, and still less obvious to someone who does not even know those. Same thing here. $\endgroup$ – Ivan Neretin Feb 19 at 13:50
  • $\begingroup$ @ToddMinehardt ionic minerals do not have “molecules”. There is no fluorite in fluorapatite. Fluorapatite can be taken as containing CaF2 (not fluorite!!) as a chemical/thermodynamic component, but this is only a convenient mathematical or stoichiometric construct by people which has little relation to reality. $\endgroup$ – Gimelist Aug 4 at 1:21
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All comments on the subject in this page (vide supra) explain why those two formulas are identical. Since you insist that you need an explanation for them being identical, I'll try my best (I'm not an expert on mineral but getting interested):

According to Wikipedia, apatite is a group of phosphate minerals, usually referring to hydroxylapatite, fluorapatite, and chlorapatite, with high concentrations of $\ce{OH−}$, $\ce{F−}$, and $\ce{Cl−}$ ions, respectively, in the crystal matrix. The crystal unit cell formulas of the individual stoichiometric minerals are usually written as $\ce{Ca10(PO4)6(OH)2}$, $\ce{Ca10(PO4)6F2}$, and $\ce{Ca10(PO4)6Cl2}$, to denote that the crystal unit cell comprises two entities of $\ce{Ca5(PO4)3X}$ (where $\ce{X}$ is $\ce{OH}$, $\ce{F}$, or $\ce{Cl}$, respectively).

Calcium phosphate formula is $\ce{Ca3(PO4)2}$. The crystal unit cell formula of fluorapatite, $\ce{Ca10(PO4)6F2}$ can also be written in $\ce{Ca3(PO4)2}$ such that it'd show its calcium phosphate entity, $\ce{CaF2\cdot 3[Ca3(PO4)2]}$, or simply $\ce{CaF2 3Ca3(PO4)2}$. In this way, it shows it contain both $\ce{CaF2}$ and $\ce{Ca3(PO4)2}$ in 1:3 ratio. Thus, both formulas, $\ce{CaF2 3Ca3(PO4)2}$ and $\ce{Ca5(PO4)3F}$, represent identical mineral.

Footnote: Solid solutions between carbonated hydroxylapatite and fluorapatite occur naturally in the body, in bone and teeth. The solubility product of stoichiometric fluorapatite and hydroxylapatite at $\pu{37°C}$ are $\pu{3.19 \times 10^{−61}mol\cdot l^{−1}}$ and $\pu{7.36 \times 10^{−60}mol\cdot l^{−1}}$, respectively.

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As it's been stated in the comments, both formulas are equivalent, however, I'd like to clarify the terminology and use cases for both.

$\ce{CaF2 * 3Ca3(PO4)2}$ is a formula of a formal addition compound (often used for clathrates, crystallohydrates and multiple salts). Widely used several decades ago when crystal structure of a given compound hasn't been elucidated enough to speak of exact atomic positions, hence it's often been attempted to present it as a ratio of simpler compounds packed in a crystal lattice.

$\ce{Ca5(PO4)3F}$ is a formula unit. Constituents are ordered from the most electropositive to the most electronegative groups; the ratio between them is denoted with numerical indices. By multiplying the formula unit $\ce{Ca5(PO4)3F}$ by $Z = 2$ ($Z$ is the number of chemical formula units per unit cell), you get $\ce{Ca10(PO4)6F2}$ — the content of the entire unit cell. $\ce{Ca10(PO4)6F2}$ is equal to $\ce{CaF2 * 3Ca3(PO4)2}$ in terms of stoichiometry, but the use of latter middle-dot-notation is deprecated for multiple salts as it doesn't carry additional structural information and often leads to confusion.

I think it's important to mention that not only $\ce{Ca5(PO4)3F}$, but $\ce{CaF2}$ and $\ce{Ca3(PO4)2}$ are also formula units, and not molecules!

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