Write the expression for the solubility product constant of MgF2 (see Problem 4.139). If [Mg2+] = 2.6 * 10-4 mol/L in a solution, what is the value of Ksp?

Verified step by step guidance

1. Identify the dissociation reaction of MgF2 in water. The reaction can be written as: \( MgF_2(s) \rightarrow Mg^{2+}(aq) + 2F^{-}(aq) \).
2. Write the expression for the solubility product constant (Ksp) based on the dissociation reaction. The expression is: \( K_{sp} = [Mg^{2+}][F^{-}]^2 \).
3. Substitute the given concentration of \( Mg^{2+} \) into the Ksp expression. Since \( [Mg^{2+}] = 2.6 \times 10^{-4} \, mol/L \), you can substitute this value directly.
4. Determine the concentration of \( F^{-} \) from the stoichiometry of the reaction. For every mole of \( Mg^{2+} \), there are two moles of \( F^{-} \). Therefore, \( [F^{-}] = 2 \times [Mg^{2+}] \).
5. Calculate the value of \( K_{sp} \) by substituting the concentrations of \( Mg^{2+} \) and \( F^{-} \) into the Ksp expression and simplifying.

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 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 MgF2, the dissolution can be represented as MgF2(s) ⇌ Mg2+(aq) + 2F-(aq), leading to the expression Ksp = [Mg2+][F-]^2.

Dissociation of Ionic Compounds

Ionic compounds, such as MgF2, dissociate into their constituent ions when dissolved in water. This dissociation is crucial for calculating Ksp, as it determines the concentrations of the ions in solution. For MgF2, one formula unit produces one Mg2+ ion and two F- ions, which must be accounted for when substituting into the Ksp expression.

Calculating Ion Concentrations

To find the Ksp value, it is essential to know the concentrations of the ions in solution. Given that [Mg2+] = 2.6 * 10^-4 mol/L, the concentration of F- can be derived from the stoichiometry of the dissociation. Since two F- ions are produced for every Mg2+ ion, [F-] will be twice that of [Mg2+], which is necessary for accurately calculating Ksp.