Use the values of Ksp in Appendix C to calculate the molar solubility of the following compounds: (b) Mg(OH)2

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Identify the dissolution equation for Mg(OH)_2: Mg(OH)_2 (s) \(\rightleftharpoons\) Mg^{2+} (aq) + 2OH^- (aq).

Write the expression for the solubility product constant (K_{sp}): K_{sp} = [Mg^{2+}][OH^-]^2.

Let the molar solubility of Mg(OH)_2 be 's'. Then, [Mg^{2+}] = s and [OH^-] = 2s.

Substitute the expressions for [Mg^{2+}] and [OH^-] into the K_{sp} expression: K_{sp} = (s)(2s)^2.

Solve the equation K_{sp} = 4s^3 for 's' to find the molar solubility of Mg(OH)_2.

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주요 개념

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Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced dissolution equation. For example, for Mg(OH)2, Ksp = [Mg^2+][OH^-]^2, where [Mg^2+] and [OH^-] are the molar concentrations of magnesium and hydroxide ions, respectively.

Molar Solubility

Molar solubility refers to the number of moles of a solute that can dissolve in a liter of solution at equilibrium. It is a specific measure of how much of a compound can dissolve to form a saturated solution. To find the molar solubility of Mg(OH)2, one must relate the concentrations of the ions produced upon dissolution to the Ksp value, allowing for the calculation of how many moles of Mg(OH)2 can dissolve in water.

Dissociation of Ionic Compounds

Dissociation is the process by which an ionic compound separates into its constituent ions when dissolved in a solvent. For Mg(OH)2, the dissociation can be represented as Mg(OH)2 (s) ⇌ Mg^2+ (aq) + 2OH^- (aq). Understanding this process is crucial for calculating molar solubility, as it provides the stoichiometric relationships needed to express the concentrations of the ions in terms of the solubility of the compound.