Tooth enamel is composed of hydroxyapatite, Ca5(PO4)3OH (Ksp = 6.8 10-37). Many water treatment plants add F- ion to drinking water, which reacts with Ca5(PO4)3OH to form the more tooth decay-resistant fluorapatite, Ca5(PO4)3F (Ksp = 1.0 10-60). Fluoridated water has resulted in a dramatic decrease in the number of cavities among children. Calculate the solubility of Ca5(PO4)3F in water.

6.1 × 10⁻⁸ M

Explanation:

Let's consider the solution of fluorapatite.

Ca₅(PO₄)₃F(s) ⇄ 5 Ca²⁺(aq) + 3 PO₄³⁻(aq) + F⁻(aq)

We can relate the solubility (S) with the solubility product constant (Ksp) using an ICE chart.

        Ca₅(PO₄)₃F(s) ⇄ 5 Ca²⁺(aq) + 3 PO₄³⁻(aq) + F⁻(aq)

I                                        0                   0                0

C                                     +5 S              +3 S            +S

E                                       5 S               3 S               S

The Ksp is:

Ksp = [Ca²⁺]⁵ × [PO₄³⁻]³ × [F⁻] = (5 S)⁵ × (3 S)³ × S = 84,375 S⁹

it is the most commonly accepted one