Question

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:

MgF₂ (S) ⇌ Mg²⁺(aq) + 2F^- (aq)

In a saturated solution of MgF₂ at 18 °C, the concentration ofMg²⁺is 1.21×10^-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 MgF₂solution 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 MgF^­₂ will form whensolution of 100.0mL of a 3.00 ×10^-3 -M Mg(NO3)₂ is mixed with 200.0 mL of a 2.00 × 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 1.17×10^-3 M. Is the dissolving of MgF₂ in water an endothermic or an exothermic process? Give an explanation to support your conclusion.

Short answer

a) The value at 18 ̊ C is 7.09×10^-9

b) The equilibrium concentration ofMg2+ is7.09×10^-7M.

c) The precipitate will not form

d) It is exothermic

Step-by-step solution

Define Saturated solution

A saturated solutionis a solution in which there is so muchsolute that if there was any more, it would notdissolve

Express the solubility product

a) The value at 18̊C is

From the solubility product formula

K_sp = [Mg²⁺] ×[F^-]²

= (1.21 ×10^-3) × (2.42×10^-3)²

⁼ 7.09×10^-9

Determining equilibrium concentration

b) The equilibrium concentration of Mg²⁺ in 1.000L is

7.09×10^-9 = s × (0.100)²

S = 7.09×10^-7

[Mg²⁺] = s = 7.09×10^-7M.

Predicting the precipitate

c) Predicting the precipitate of MgF₂

[Mg²⁺] × [F^-]²=1×10^-3× (1.33 × (10^-3)²

= 1.78 ×10^-9

Determining exothermic reaction

d) The dissolving of MgF₂

MgF₂ (S) ⇌ Mg²⁺(aq) + 2F^- (aq) + heat

Therefore, it is an exothermic reaction