Ch.17 - Additional Aspects of Aqueous Equilibria

Problem 103

Chapter 17, Problem 103

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?

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Write the dissolution equation for barium permanganate, BaMnO4, which dissociates into Ba2+ and MnO4- ions in solution: BaMnO4(s) ⇌ Ba2+(aq) + MnO4-(aq).

Express the solubility-product constant (Ksp) for this reaction. Given that Ksp = [Ba2+][MnO4-], substitute the given Ksp value: 2.5 * 10^-10 = [Ba2+][MnO4-].

Substitute the given concentration of Ba2+ ions into the Ksp expression: 2.5 * 10^-10 = (2.0 * 10^-8)[MnO4-].

Solve for the concentration of MnO4- by isolating [MnO4-] on one side of the equation: [MnO4-] = (2.5 * 10^-10) / (2.0 * 10^-8).

Calculate the concentration of MnO4- using the values provided to find the required concentration of KMnO4 in the solution.

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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 barium permanganate, Ksp helps determine the maximum concentration of Ba2+ ions that can exist in solution at equilibrium.

Equilibrium in Chemical Reactions

Equilibrium in chemical reactions refers to the state where the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In the context of solubility, this means that the dissolution of solid barium permanganate and the precipitation of Ba2+ ions occur at the same rate, allowing us to use Ksp to find the concentration of ions in solution.

Common Ion Effect

The common ion effect describes the decrease in solubility of a salt when a common ion is added to the solution. In this case, adding KMnO4 introduces MnO4- ions, which affects the solubility of Ba1MnO422 by shifting the equilibrium position. Understanding this effect is crucial for calculating the required concentration of KMnO4 to achieve a specific concentration of Ba2+ ions in solution.

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