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

\

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.