Calculation of Percentage Composition of Hydroxyapatite in Tooth Enamel Sample

[QuarkCharmer]

Homework Statement

Tooth enamel is mainly hydroxyapatite,
$$Ca_{10}(PO_{4})_{6}(OH)_{2}$$
If 1.117g of tooth enamel reacts with acid to give 1.111g of Calcium Chloride, what is the percentage of hydroxyapatite in the tooth enamel sample?

Homework Equations

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$$Ca_{10}(PO_{4})_{6}(OH)_{2}_{(s)} + 20HCl_{(aq)} \rightarrow 10CaCl_{2}_{(aq)} + 6H_{3}PO_{4}_{(aq)} + 2H_{2}O_{(l)}$$

The Attempt at a Solution

I don't know why, these questions always cause me problems. Writing out my work now...

$$1.111g CaCl2 * \frac{1 mol CaCl2}{110.9834g CaCl2} * \frac{1 mol Hydroxyapatite}{1 mol CaCl2} * \frac{1004.6228g Hydroxyapatite}{1 mol Hydroxyapatite} = Xg Hydroxyapatite$$

$$X = 10.05678 g Hydroxyapatite$$

How can that be?

That number (X) over the initial mass of the tooth enamel (1.117) should give me the percentage. But there is no way that this is correct..

$$\frac{10.05678}{1.117} *100\% = 900.33\%$$

Edit: Now that I look at it, it appears I used the wrong unit factor for converting moles... I'm working on it again.

Okay here it is:
$$1.111g CaCl2 * \frac{1 mol CaCl2}{110.9834g CaCl2} * \frac{1 mol Hydroxyapatite}{10 mol CaCl2} * \frac{1004.6228g Hydroxyapatite}{1 mol Hydroxyapatite} = 1.005678g Hydroxyapatite$$

and then:

$$\frac{1.005678}{1.117} * 100\% = 90.034\%$$

How does that look?

 

[Borek]

Much better now.