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Chapter 16: Problem 2

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) \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Short Answer

Expert verified
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 by step solution

01

(a) Equilibrium Equation for AgCl

To write the equilibrium equation for the dissolution of \(\mathrm{AgCl}\) in water, the solid dissociates into ions: $$\mathrm{AgCl(s)} \rightleftharpoons \mathrm{Ag^{+}(aq)} + \mathrm{Cl^{-}(aq)}$$
02

(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: $$K_{sp} = [\mathrm{Ag^{+}}][\mathrm{Cl^{-}}]$$
03

(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: $$ \mathrm{Al}_{2}(\mathrm{CO}_{3})_{3}(s) \rightleftharpoons 2\mathrm{Al^{3+}(aq)} + 3\mathrm{CO^{2-}_{3}(aq)} $$
04

(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: $$K_{sp} = [\mathrm{Al^{3+}}]^{2}[\mathrm{CO^{2-}_{3}]^{3}$$
05

(c) Equilibrium Equation for MnS2

To write the equilibrium equation for the dissolution of \(\mathrm{MnS}_{2}\) in water: $$ \mathrm{MnS}_{2}(s) \rightleftharpoons \mathrm{Mn^{2+}(aq)} + 2\mathrm{S^{-}(aq)} $$
06

(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: $$K_{sp} = [\mathrm{Mn^{2+}}][\mathrm{S^{-}}]^{2}$$
07

(d) Equilibrium Equation for Mg(OH)2

To write the equilibrium equation for the dissolution of \(\mathrm{Mg}(\mathrm{OH})_{2}\) in water: $$ \mathrm{Mg}(\mathrm{OH})_{2}\mathrm{(s)} \rightleftharpoons \mathrm{Mg^{2+}(aq)} + 2\mathrm{OH^{-}(aq)} $$
08

(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: $$K_{sp} = [\mathrm{Mg^{2+}}][\mathrm{OH^{-}}]^{2}$$

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Write an overall net ionic equation and calculate \(K\) for the reaction where \(\mathrm{CuCl}\left(K_{s p}=1.9 \times 10^{-7}\right)\) is dissolved by \(\mathrm{NaCN}\) to form \(\left[\mathrm{Cu}(\mathrm{CN})_{2}\right]^{-}\) \(\left(K_{f}=1.0 \times 10^{16}\right)\).

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