The value of K sp for Cd(OH) 2 is 2.5 × 10 -14 . (a) What is the molar solubility of Cd(OH) 2 ?

Identify the dissolution equation for Cd(OH)_{2}: Cd(OH)_{2}(s) ⇌ $$Cd^{2+}(aq$$) + $$2OH^{-}(aq).. $$Write the expression for the solubility product constant (K_{sp}): K_{sp} = [$$Cd^{2+}$$][$$OH^{-}$$]^{2}.. Let the molar solubility of Cd(OH)_{2} be 's'. Then, [$$Cd^{2+}$$] = s and [$$OH^{-}$$] = 2s.. Substitute the expressions for the ion concentrations into the K_{sp} expression: K_{sp} = $$(s)(2s)^{2}$$ = $$4s^{3}.. $$Set the K_{sp} expression equal to the given K_{sp} value and solve for 's': $$4s^{3} = 2.5$$ × $$10^{-14}.$$

The value of Ksp for Cd(OH)2 is 2.5 × 10-14. (a) What is the molar solubility of Cd(OH)2?

Identify the dissolution equation for Cd(OH)_{2}: Cd(OH)_{2}(s) ⇌ $$Cd^{2+}(aq$$) + $$2OH^{-}(aq). $$Write the expression for the solubility product constant (K_{sp}): K_{sp} = [$$Cd^{2+}$$][$$OH^{-}$$]^{2}. Let the molar solubility of Cd(OH)_{2} be 's'. Then, [$$Cd^{2+}$$] = s and [$$OH^{-}$$] = 2s. Substitute the expressions for the ion concentrations into the K_{sp} expression: K_{sp} = $$(s)(2s)^{2}$$ = $$4s^{3}. $$Set the K_{sp} expression equal to the given K_{sp} value and solve for 's': $$4s^{3} = 2.5$$ × $$10^{-14}.$$

Ch.17 - Additional Aspects of Aqueous Equilibria

Brown - Chemistry: The Central Science 15th Edition

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Ch.17 - Additional Aspects of Aqueous Equilibria

Problem 109a

Chapter 17, Problem 109a

The value of K_sp for Cd(OH)₂ is 2.5 × 10^-14. (a) What is the molar solubility of Cd(OH)₂?

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Identify the dissolution equation for Cd(OH)₂: Cd(OH)₂(s) ⇌ Cd²⁺(aq) + 2OH^-(aq).

Write the expression for the solubility product constant (K_sp): K_sp = [Cd²⁺][OH^-]².

Let the molar solubility of Cd(OH)₂ be 's'. Then, [Cd²⁺] = s and [OH^-] = 2s.

Substitute the expressions for the ion concentrations into the K_sp expression: K_sp = (s)(2s)² = 4s³.

Set the K_sp expression equal to the given K_sp value and solve for 's': 4s³ = 2.5 × 10^-14.

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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 Cd(OH)2, Ksp = [Cd^2+][OH^-]^2, which helps determine how much of the compound can dissolve in water.

Molar Solubility

Molar solubility refers to the maximum concentration of a solute that can dissolve in a given volume of solvent at equilibrium. It is typically expressed in moles per liter (mol/L). In the case of Cd(OH)2, calculating the molar solubility involves determining the concentration of Cd^2+ and OH^- ions that can exist in solution when the compound is at its saturation point.

Stoichiometry of Dissolution

The stoichiometry of dissolution describes the ratio in which ions are produced when a compound dissolves. For Cd(OH)2, the dissolution can be represented as Cd(OH)2(s) ⇌ Cd^2+(aq) + 2OH^-(aq). This indicates that one mole of Cd(OH)2 produces one mole of Cd^2+ and two moles of OH^-, which is essential for relating Ksp to molar solubility.