Tooth enamel is composed of hydroxyapatite, whose simplest formula is Ca51PO423OH, and whose corresponding Ksp = 6.8 * 10-27. As discussed in the Chemistry and Life box on page 746, fluoride in fluorinated water or in toothpaste reacts with hydroxyapatite to form fluoroapatite, Ca51PO423F, whose Ksp = 1.0 * 10-60. (a) Write the expression for the solubility-constant for hydroxyapatite and for fluoroapatite.

Verified step by step guidance

1. Step 1: The solubility product constant, Ksp, is the product of the concentrations of the ions each raised to the power of its stoichiometric coefficient in the balanced chemical equation. It is used to describe the equilibrium between a solid and its ions in a solution. The general form of the expression for Ksp is: Ksp = [A+]^m[B-]^n, where A and B are ions, and m and n are their stoichiometric coefficients.
2. Step 2: For hydroxyapatite, the balanced chemical equation for its dissolution in water is: Ca5(PO4)3OH(s) ⇌ 5Ca2+(aq) + 3PO43-(aq) + OH-(aq).
3. Step 3: The expression for the solubility product constant for hydroxyapatite is therefore: Ksp = [Ca2+]^5[PO43-]^3[OH-].
4. Step 4: For fluoroapatite, the balanced chemical equation for its dissolution in water is: Ca5(PO4)3F(s) ⇌ 5Ca2+(aq) + 3PO43-(aq) + F-(aq).
5. Step 5: The expression for the solubility product constant for fluoroapatite is therefore: Ksp = [Ca2+]^5[PO43-]^3[F-].

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For example, for a salt that dissociates into ions, Ksp = [A^n+][B^m-], where A and B are the ions and n and m are their respective stoichiometric coefficients.

Dissociation of Hydroxyapatite and Fluoroapatite

Hydroxyapatite (Ca5(PO4)3OH) and fluoroapatite (Ca5(PO4)3F) dissociate in water to release calcium and phosphate ions. The dissociation reactions can be represented as: Ca5(PO4)3OH ⇌ 5Ca^2+ + 3PO4^3- + OH^- for hydroxyapatite, and Ca5(PO4)3F ⇌ 5Ca^2+ + 3PO4^3- + F^- for fluoroapatite. Understanding these dissociation processes is crucial for writing the Ksp expressions for each compound.

Writing Ksp Expressions

To write the Ksp expression for a compound, one must identify the ions produced upon dissociation and their stoichiometric coefficients. For hydroxyapatite, the Ksp expression would be Ksp = [Ca^2+]^5[PO4^3-]^3[OH^-] for hydroxyapatite, and Ksp = [Ca^2+]^5[PO4^3-]^3[F^-] for fluoroapatite. These expressions allow for the calculation of solubility and the comparison of the solubility of different compounds.