Calculate the solubility of Mn1OH22 in grams per liter when buffered at pH (b) 9.5.

Verified step by step guidance

1. Identify the chemical formula of the compound, which is Mn(OH)2, and recognize that it dissociates into Mn2+ and OH- ions in solution.
2. Write the solubility product expression (Ksp) for Mn(OH)2, which is Ksp = [Mn2+][OH-]^2.
3. Use the given pH to calculate the concentration of OH- ions. pH + pOH = 14, so pOH = 14 - 9.5. Then, calculate [OH-] using [OH-] = 10^{-pOH}.
4. Substitute the [OH-] value back into the Ksp expression and solve for [Mn2+], assuming that the solubility of Mn(OH)2, s, is equal to [Mn2+] and that [OH-] = 2s due to the stoichiometry of the dissociation.
5. Calculate the solubility in grams per liter by converting the molarity of Mn(OH)2 (which is equal to [Mn2+]) to grams per liter using the molar mass of Mn(OH)2.

Key Concepts

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 Mn(OH)2, Ksp can be used to determine the solubility in a specific pH environment, as the concentration of hydroxide ions affects the equilibrium.

pH and Hydroxide Ion Concentration

pH is a measure of the acidity or basicity of a solution, with lower values indicating higher acidity and higher values indicating higher basicity. At a pH of 9.5, the concentration of hydroxide ions (OH-) is significant, which can shift the equilibrium of the dissolution of Mn(OH)2. Understanding how pH influences the solubility of metal hydroxides is crucial for calculating their solubility in buffered solutions.

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH upon the addition of small amounts of acids or bases. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, the buffer at pH 9.5 helps maintain a stable hydroxide ion concentration, which is essential for accurately calculating the solubility of Mn(OH)2 in the solution.