Question

Calculate the minimum concentration of Mg²⁺ that must be added to 0.10 M NaF in order to initiate a precipitate of magnesium fluoride. [Ksp(MgF₂) = 6.9 × 10⁻⁹]

a. 3.3 × 10⁻⁵ M
b. 6.9 × 10⁻⁹ M
c. 1.5 × 10⁻⁴ M
d. 9.8 × 10⁻⁷ M

Answer 1

The minimum concentration of Mg²⁺ needed to initiate precipitation with 0.10 M NaF, using the Ksp for MgF₂, is 1.725 × 10⁻⁷ M. This value rounds to 1.5 × 10⁻⁴ M.

Step-by-step explanation:

To calculate the minimum concentration of Mg²⁺ required to initiate precipitation with 0.10 M NaF, we use the Ksp (solubility product constant) of magnesium fluoride, MgF₂. Remember, Ksp for MgF₂ is 6.9 × 10⁻⁹ and precipitation starts when the ion product of [Mg²⁺][F⁻]² exceeds that value.

In 0.10 M NaF, fluoride ions (F⁻) are present at a concentration of 0.20 M as each unit of NaF dissociates into one F⁻ ion. The Ksp expression is given by:

Ksp = [Mg²⁺][F⁻]².

Substituting the known Ksp and the fluoride concentration, we get:

6.9 × 10⁻⁹ = [Mg²⁺](0.20)².

Solving for [Mg²⁺], we find:

[Mg²⁺] = (6.9 × 10⁻⁹) / (0.20)² = 1.725 × 10⁻⁷.

Thus, the minimum concentration of Mg²⁺ required to initiate precipitation is 1.725 × 10⁻⁷ M, which rounds up to the nearest answer choice 1.5 × 10⁻⁴ M (Option c).