Consider the solubility of solid magnesium hydroxide, Mg(OH)2, in water, for whi
ID: 927224 • Letter: C
Question
Consider the solubility of solid magnesium hydroxide, Mg(OH)2, in water, for which the solubility equilibrium is: Mg(OH)2 (s) <> Mg^2+ (aq) + 2OH^- (aq) A saturated solution of Mg(OH)2 is prepared and allowed to equilibrate at 25 degrees C. A 25.00 Ml sample of the 25 degrees C solution is titrated with .00508 M HCL solution. 1.38 ml of the HCL solution are required to fully react the solution sample. A) Determine the molar solubility of Mg(OH)2 at 25 degrees C B) Calculate Ksp for Mg(OH)2 in water at 25 degrees C C) Calculate delta G for Mg(OH)2 dissolving in water at 25 degrees C D) What additional experimental measurements would be required in order to determine detla H and delta S for Mg(OH)2 dissolving in water.
Explanation / Answer
Suppose the solubility of Mg(OH)2 is S
Mg(OH)2 ---> Mg2+ + 2OH-
.......................S...........2S
Concentration of OH- at equilibrium = 2S M
Given,
Molarity of HCl = 0.00508 M
Volume of HCl added = 1.38 mL = 1.38 x 10^-3 L
=> Moles of HCl added = 0.00508 x 1.38 x 10^-3 = 7.0104 x 10^-6
The reaction is,
HCl + OH- ----> H2O + Cl-
According to the stoichiometry of the reaction 1 mole of HCl reacts with 1 mole of OH-
=> Moles of OH- present in the solution = Moles of HCl added
=> Moles of OH- present in the solution = 7.0104 x 10^-6
Volume of Mg(OH)2 solution =25 mL = 0.025 L
=> [OH-] = 7.0104 x 10^-6 / 0.025 = 2.8042 x 10^-4 M
=> 2S = 2.8042 x 10^-4 M
=> S = 1.4021 x 10^-4 M = Molar solubility of Mg(OH)2
B)
Mg(OH)2 ---> Mg2+ + 2OH-
.......................S...........2S
Ksp = [Mg2+] [OH-]^2
=> Ksp = S x (2S)^2 = 4S^3
=> Ksp = 4 x (1.4021 x 10^-4 )^3 = 1.1 x 10^-11
C) delta G = - RT ln K
=> delta G = - 8.314 x 298 x ln (1.1 x 10^-11) = 62511.3 J / mol = 62.5 kJ / mol
D) To calculate delta H, we need the heat of dissolution of Mg(OH)2 in water.