15.3 Exercise 17

The following question is taken from a Chemistry Advanced Placement Examination and is used with the permission of the Educational Testing Service.

Solve the following problem:

$\text{MgF}_{2} \left(s\right) \rightleftharpoons \text{Mg}^{\text{2}+} \left(a q\right) + 2 \text{F}^{−} \left(a q\right)$

In a saturated solution of MgF₂ at 18 °C, the concentration of Mg²⁺ is 1.21 $\times$ 10^–3 M. The equilibrium is represented by the preceding equation.

(a) Write the expression for the solubility-product constant, K_sp, and calculate its value at 18 °C.

(b) Calculate the equilibrium concentration of Mg²⁺ in 1.000 L of saturated MgF₂ solution at 18 °C to which 0.100 mol of solid KF has been added. The KF dissolves completely. Assume the volume change is negligible.

(c) Predict whether a precipitate of MgF₂ will form when 100.0 mL of a 3.00 $\times$ 10^–3-M solution of Mg(NO₃)₂ is mixed with 200.0 mL of a 2.00 $\times$ 10^–3-M solution of NaF at 18 °C. Show the calculations to support your prediction.

(d) At 27 °C the concentration of Mg²⁺ in a saturated solution of MgF₂ is 1.17 $\times$ 10^–3 M. Is the dissolving of MgF₂ in water an endothermic or an exothermic process? Give an explanation to support your conclusion.