Problem 2 - Chemistry: Principles and Reactions

Question

Write the equilibrium equation and the \(K_{s p}\) expression for each of the following. (a) \(\mathrm{AgCl}\) (b) \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\) (c) \(\mathrm{MnS}_{2}\) (d) \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Step-by-Step Solution

Answer

Question: Write the equilibrium equations and solubility product constant expressions for the following compounds: (a) AgCl (b) Al2(CO3)3 (c) MnS2 (d) Mg(OH)2 Answer: (a) Equilibrium Equation: AgCl(s) ⇌ Ag+(aq) + Cl-(aq) , Ksp = [Ag+][Cl-] (b) Equilibrium Equation: Al2(CO3)3(s) ⇌ 2Al3+(aq) + 3CO32-(aq) , Ksp = [Al3+]^2[CO32-]^3 (c) Equilibrium Equation: MnS2(s) ⇌ Mn2+(aq) + 2S-(aq) , Ksp = [Mn2+][S-]^2 (d) Equilibrium Equation: Mg(OH)2(s) ⇌ Mg2+(aq) + 2OH-(aq) , Ksp = [Mg2+][OH-]^2

Step 1: (a) Equilibrium Equation for AgCl

To write the equilibrium equation for the dissolution of \(\mathrm{AgCl}\) in water, the solid dissociates into ions: $$\mathrm{AgCl(s)} \rightleftharpoons \mathrm{Ag^{+}(aq)} + \mathrm{Cl^{-}(aq)}$$

Step 2: (a) Solubility Product Constant Expression for AgCl

For \(\mathrm{AgCl}\), the \(K_{sp}\) expression will be the product of the concentrations of the ions at equilibrium: $$K_{sp} = [\mathrm{Ag^{+}}][\mathrm{Cl^{-}}]$$

Step 3: (b) Equilibrium Equation for Al2(CO3)3

To write the equilibrium equation for the dissolution of \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\) in water: $$ \mathrm{Al}_{2}(\mathrm{CO}_{3})_{3}(s) \rightleftharpoons 2\mathrm{Al^{3+}(aq)} + 3\mathrm{CO^{2-}_{3}(aq)} $$

Step 4: (b) Solubility Product Constant Expression for Al2(CO3)3

For \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{3}\), the \(K_{sp}\) expression will be the product of the concentrations of the ions raised to appropriate powers at equilibrium: $$K_{sp} = [\mathrm{Al^{3+}}]^{2}[\mathrm{CO^{2-}_{3}]^{3}$$

Step 5: (c) Equilibrium Equation for MnS2

To write the equilibrium equation for the dissolution of \(\mathrm{MnS}_{2}\) in water: $$ \mathrm{MnS}_{2}(s) \rightleftharpoons \mathrm{Mn^{2+}(aq)} + 2\mathrm{S^{-}(aq)} $$

Step 6: (c) Solubility Product Constant Expression for MnS2

For \(\mathrm{MnS}_{2}\), the \(K_{sp}\) expression will be the product of the concentrations of the ions raised to appropriate powers at equilibrium: $$K_{sp} = [\mathrm{Mn^{2+}}][\mathrm{S^{-}}]^{2}$$

Step 7: (d) Equilibrium Equation for Mg(OH)2

To write the equilibrium equation for the dissolution of \(\mathrm{Mg}(\mathrm{OH})_{2}\) in water: $$ \mathrm{Mg}(\mathrm{OH})_{2}\mathrm{(s)} \rightleftharpoons \mathrm{Mg^{2+}(aq)} + 2\mathrm{OH^{-}(aq)} $$

Step 8: (d) Solubility Product Constant Expression for Mg(OH)2

For \(\mathrm{Mg}(\mathrm{OH})_{2}\), the \(K_{sp}\) expression will be the product of the concentrations of the ions raised to appropriate powers at equilibrium: $$K_{sp} = [\mathrm{Mg^{2+}}][\mathrm{OH^{-}}]^{2}$$

Key Concepts

Equilibrium Equation

An equilibrium equation is essential when dealing with the solubility of ionic compounds in solution. It represents the dissolving process of a solid, denoting the balance when the solid goes into solution as it forms ions. Understanding this helps us predict how much of a substance can dissolve in water before it precipitates or crystallizes back. When

• For AgCl, the equilibrium equation is: \[\mathrm{AgCl(s)} \rightleftharpoons \mathrm{Ag^{+}(aq)} + \mathrm{Cl^{-}(aq)}\]
• For Al₂(CO₃)₃: \[\mathrm{Al}_{2}(\mathrm{CO}_{3})_{3}(s) \rightleftharpoons 2\mathrm{Al^{3+}(aq)} + 3\mathrm{CO^{2-}_{3}(aq)}\]
• For MnS₂: \[\mathrm{MnS}_{2}(s) \rightleftharpoons \mathrm{Mn^{2+}(aq)} + 2\mathrm{S^{-}(aq)}\]
• For Mg(OH)₂: \[\mathrm{Mg(OH)}_{2}\mathrm{(s)} \rightleftharpoons \mathrm{Mg^{2+}(aq)} + 2\mathrm{OH^{-}(aq)}\]

Each equation provides insight into how a specific compound will interact when introduced to a solution. It's a vital first step in calculating the solubility product constant (Ksp).

Dissolution Process

The dissolution process involves a solid substance dissolving in a solvent, leading to the formation of ions in solution. It is the key event that sets the stage for establishing an equilibrium between the dissolved ions and undissolved solid. This process depends on various factors including temperature, pressure, and the nature of the solvent. Solubility increases when more of the solid is capable of dissolving, contributing to a higher concentration of ions.

• In the dissolution of AgCl, the solid silver chloride dissociates into silver ions (Ag⁺) and chloride ions (Cl⁻).
• Similarly, dissolving Mg(OH)₂ will produce magnesium ions (Mg²⁺) and hydroxide ions (OH⁻).

A balance is sought where the rate of dissolution equals the rate of precipitation, yielding a dynamic equilibrium. Understanding this process facilitates the calculation of Ksp values, allowing prediction of solubility under various conditions.

Ionic Concentrations

Ionic concentrations are crucial in determining the extent of a compound's solubility in a solution, as described by the solubility product constant, Ksp. This constant is a measure of the equilibrium between the insoluble solid and the ions it releases upon dissolving. For each dissolved ionic compound, the Ksp expression reflects the concentrations of the resulting ions raised to the power of their stoichiometric coefficients in the balanced equilibrium equation.

• For AgCl, its Ksp formula is \(K_{sp} = [Ag^{+}][Cl^{-}]\)
• For Al₂(CO₃)₃, the expression expands to \(K_{sp} = [Al^{3+}]^2[CO₃^{2-}]^3\)
• In the case of Mg(OH)₂, it is \(K_{sp} = [Mg^{2+}][OH^{-}]^2\)

These expressions reveal how each compound dissociates and emphasizes the deep connection between solubility and ionic concentration. A higher Ksp indicates greater solubility, whereas a lower Ksp suggests limited ion dissolution.