Ch.17 - Additional Aspects of Aqueous Equilibria

Problem 102

Chapter 17, Problem 102

Calculate the solubility of Mg1OH22 in 0.50 M NH4Cl.

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Identify the chemical formula of the compound. The correct formula for Magnesium hydroxide is Mg(OH)2, not Mg1OH22.

Write the solubility product expression (Ksp) for Mg(OH)2. It dissociates in water according to the equation: Mg(OH)2(s) ⇌ Mg2+(aq) + 2 OH-(aq). The expression for Ksp is: Ksp = [Mg2+][OH-]^2.

Recognize the common ion effect due to NH4Cl. NH4Cl dissociates into NH4+ and Cl-. NH4+ can slightly increase the concentration of H+ in solution through its reaction with water, which affects the concentration of OH- by the relationship [H+][OH-] = 1 x 10^-14 at 25°C.

Calculate the new equilibrium concentration of OH- considering the presence of NH4+. Use the expression [H+][OH-] = 1 x 10^-14 to find [OH-] when [H+] is altered by NH4+.

Substitute the new [OH-] back into the Ksp expression to solve for the new [Mg2+], and hence find the solubility of Mg(OH)2 in the presence of 0.50 M NH4Cl.

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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 represents the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For Mg(OH)2, Ksp can be used to determine how much of the compound can dissolve in a solution, which is essential for calculating its solubility in the presence of other ions.

Common Ion Effect

The common ion effect refers to the decrease in solubility of an ionic compound when a common ion is added to the solution. In this case, NH4Cl provides NH4+ ions, which can shift the equilibrium of Mg(OH)2 dissolution, reducing its solubility. Understanding this effect is crucial for calculating the solubility of Mg(OH)2 in the presence of NH4Cl.

Ionic Equilibrium

Ionic equilibrium involves the balance between the dissolved ions in a solution and the undissolved solid phase of an ionic compound. For Mg(OH)2, the equilibrium can be expressed as the dissolution of the solid into Mg2+ and OH- ions. Analyzing this equilibrium is key to determining how the addition of NH4Cl affects the concentrations of these ions and, consequently, the solubility of Mg(OH)2.

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