Calculate the minimum concentration of Mg²⁺ that must be added to 0.10 M NaF in order to initiate a precipitate of magnesium fluoride.(For MgF₂ , K_sp = 6.9 × 10^-9.)

Question

Quizplus · Accepted Answer

The balanced chemical equation for the precipitation reaction between Mg²⁺ and NaF is: Mg²⁺ + 2 NaF → MgF2 + Na2²⁺ The solubility product constant (Ksp) for MgF₂ is given as 6.9 × 10^-9. The equilibrium expression for the dissolution of MgF₂ is: Ksp = [Mg2+] [F-]2 At equilibrium, the concentration of Mg2+ ions and F- ions in the solution will be equal to the solubility of MgF₂: [Mg2+] = [F-] = s Substituting these values in the equation for Ksp, we get: Ksp = s (2s)2 = 4s3 Rearranging the equation, we can calculate the solubility (s) of MgF₂: s3 = Ksp/4 = 6.9 × 10^-9/4 s ≈ 1.09 × 10^-3 M To initiate precipitation of MgF2, we need to increase the concentration of Mg2+ ions and F- ions in the solution to a value greater than their solubility. Let x be the concentration of Mg²⁺ that must be added to the solution. After the reaction, the concentration of Mg2+ ions in the solution will be x M, and the concentration of F- ions will be (2x + 0.10) M (due to the presence of 0.10 M NaF initially). The concentration of Mg2+ ions and F- ions in the solution should be equal to the solubility of MgF2 to initiate precipitation. Therefore, we can write the following equation: s = [Mg2+] = [F-] = 2x + 0.10 Substituting the value of solubility (s), we get: 1.09 × 10^-3 = 2x + 0.10 x ≈ 6.95 × 10^-4 M Therefore, the minimum concentration of Mg²⁺ that must be added to 0.10 M NaF in order to initiate a precipitate of MgF2 is approximately 6.95 × 10^-4 M. This closest to answer E: 6.9 × 10^-7 M.

Calculate the Minimum Concentration of Mg2+ That Must Be Added

Calculate the Minimum Concentration of Mg²⁺ That Must Be Added