Textbook Question
For each pair of compounds, use Ksp values to determine which has the greater molar solubility: (a) CdS or CuS (b) PbCO3 or BaCrO4 (c) Ni(OH)2 or NiCO3 (d) AgI or Ag2SO4.
Ch.17 - Additional Aspects of Aqueous Equilibria
Chapter 17, Problem 100a
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 guidance1
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.
Step 2: For hydroxyapatite, the balanced chemical equation for its dissolution in water is: Ca5(PO4)3OH(s) ⇌ 5Ca2+(aq) + 3PO43-(aq) + OH-(aq).
Step 3: The expression for the solubility product constant for hydroxyapatite is therefore: Ksp = [Ca2+]^5[PO43-]^3[OH-].
Step 4: For fluoroapatite, the balanced chemical equation for its dissolution in water is: Ca5(PO4)3F(s) ⇌ 5Ca2+(aq) + 3PO43-(aq) + F-(aq).
Step 5: The expression for the solubility product constant for fluoroapatite is therefore: Ksp = [Ca2+]^5[PO43-]^3[F-].
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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Solubility Product Constant
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.
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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.
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Related Practice
Textbook Question
The solubility of CaCO3 is pH dependent. (b) Use the Kb expression for the CO32- ion to determine the equilibrium constant for the reaction CaCO3(s) + H2O(l) ⇌ Ca2+(aq) + HCO3-(aq) + OH-(aq)
Textbook Question
Calculate the solubility of Mg1OH22 in 0.50 M NH4Cl.
Textbook Question
The solubility-product constant for barium permanganate, Ba1MnO422, is 2.5 * 10-10. Assume that solid Ba1MnO422 is in equilibrium with a solution of KMnO4. What concentration of KMnO4 is required to establish a concentration of 2.0 * 10-8 M for the Ba2 + ion in solution?