Question

Apatite is a mineral that is found in tooth enamel. When fluoride toothpastes are used, this mineral is converted to fluorapatite, which is more resistant to tooth decay. The formula of apatite is $C{a_5}{(P{O_4})_x}F$ . What is the value of $x$ , if the compound contains $18.45\%$ by weight of phosphorus ?
(Atomic weight of phosphorus= $31$ , calcium= $40$ , fluorine= $19$ and oxygen= $16$ )

Answer 1

Fluorapatite is a phosphate mineral and a hard crystalline solid. In order to find the value of $x$, we have to go through a simple mathematical concept that is percentage composition. Generally, fluorapatite has a chemical formula as $Ca{(P{O_4})_3}F$ that is the value of $x$ is $3$ .

Complete step by step answer:
Given formula of fluorapatite is $C{a_5}{(P{O_4})_x}F$ , so molecular mass will be:
$\Rightarrow 40 \times 5 + (31 + 16 \times 4)x + 19 \\\ \Rightarrow 200 + 95x + 19 \\\ \Rightarrow 219 + 95x \\\$
Now, individually the weight of phosphorus present in it : $31x$
So, according to the question: phosphorus present in fluorapatite by weight is $18.45\%$
That means $18.45\%$ of $(219 + 95x)$ is equal to $31x$
So,
$\Rightarrow 18.45 \times \dfrac{{(219 + 95x)}}{{100}} = 31x \\\ \Rightarrow 0.1845 \times 219 + 0.1845 \times 95x = 31x \\\ \Rightarrow x = 2.999 \\\ \Rightarrow x \simeq 3 \\\$

Hence, the value of $x$ is $3$.

Additional information:
Fluorapatite is generally found in the teeth of sharks and other fishes in different concentrations. It is also present in human teeth that have been exposed to fluoride ions, for example, by using fluoride-containing toothpaste. The presence of fluorapatite prevents tooth decay or dental caries. It has a critical $pH$ of $4.5$ , thus it makes tooth structure more resistant to additional caries attack. It has a mild bacteriostatic property as well, which helps decrease the proliferation of Streptococcus mutans, the predominant bacterium related to dental caries.

Note:
Mass of a substance is the amount of matter present in it but weight is a different concept as weight is the force exerted by gravity on an object. The mass of a substance is constant but due to change in gravity from one place to another weight of an object may vary. We must be careful in using these terms. The mass of a substance can be determined very accurately in the laboratory by using an analytical balance. The SI unit of mass is kilogram. However, its draction gram is used in laboratories due to the smaller amounts of chemicals used in chemical reactions. There also comes a law that is the law of conservation of mass, It states that matter can neither be created nor destroyed.