Hydroxyapatite is the primary constituent of tooth enamel and is the hardest sub

Question

Hydroxyapatite is the primary constituent of tooth enamel and is the hardest substance in the human body. Addition of F- to drinking water converts Hydroxyapatite to Fluoroapatite, (Ca5(PO4)3F. the Ksp of Hydroxyapatite, (Ca5(PO4)3F is 6.8 X 10-37 and the Ksp for Fluoroapatite is 1 X 10-60. [Other pertinent K values can be found elsewhere (i.e. online or in textbooks) if necessary]

A) Write a series of equilibrium expressions, a mass balance charge and a charge balance representing the complete reaction of the hydroxyapatite, including the solubility, and the further reaction of phosphate with water.

B) Write a series of equilibrium expressions, a mass balance charge and a charge balance representing the complete reaction of the hydroxyapatite, including the solubility, and the further reaction of phosphate and Fluoride with water.

Explanation / Answer

Ksp, from here on to be referred to just as K, is the product of the concentration of the components of the ionic compound raised to the power of their coefficients. For example, a compound AB would have K = [A+]*[B-], and the compound DX2 would have K = [D 2+]([X-]^2).

So, we take our compound, Ca5(PO4)3F. It's K should be equal to ([Ca 2+]^5)([PO4 3-]^3)([F-]).

Now, we want to solve for the solubility, x. We know that however many molar of the compound dissolves is equal to the concentration of F- in solution, because there's one F- in every one of the compound. So we let F- equal to x. We know for every molar of F-, we have 5 molar of Ca 2+ and 3 molar of PO4 3-, or 5x and 3x, respectively. Now we plug these values in.

K = ((5x)^5)((3x)^3)(x) = 84375 x^9
K = 1*(10^-60)
x = 6.109*10^-8 mol/L

Now, we convert into g/mol by multiplying by the molar mass, which is 504.422 g/mol.
(6.109*10^-8 mol/L)(504.422 g/mol) = 3.082 * 10^-5 g/L, or the third option.

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