Question

Based on the given value of the Ksp, what is the molar solubility of Mg(OH)2 in 0.160 M NaOH?

Express your answer with the appropriate units.

Calculate how many times more soluble Mg(OH)2 is in pure water Based on the given value of the Ksp, calculate the ratio of solubility of Mg(OH)2 dissolved in pure H2O to Mg(OH)2 dissolved in a 0.160 M NaOH solution. Express your answer numerically to three significant figure

Ksp, of 5.61×10−11.

Answer 1

Ans :-

Solubility of Mg(OH)₂ in pure water :-

Let solubility of Mg(OH)₂ in water = S mol/L

Partial dissociation of Mg(OH)₂ in aqueous solution is :

Mg(OH)₂ (s) <----------------> Mg²⁺ (aq) ............+...........2 OH^- (aq)

..............................................S mol/L..............................2 S mol/L

Expression of K_sp is :

K_sp = [Mg²⁺].[OH^-]²

5.61 x 10^-11 = S (2S)²

4S³ = 5.61 x 10^-11

S³ = 1.4025 x 10^-11

S = 2.41 x 10^-4 mol/L

Solubility of Mg(OH)₂ in 0.160 M NaOH :-

Let solubility of Mg(OH)₂ in 0.100 M NaOH = S' mol/L

Dissociation of NaOH is :

NaOH ----------------------> Na⁺ ..............+.................OH^-

0.160 M............................0.160 M............................0.160 M

Total concentration of Common ion i.e. OH^- = [OH^-]_Total = (2S' + 0.100 ) M

Expression of K_sp is :

K_sp = [Mg²⁺].[OH^-]²_Total

5.61 x 10^-11 = S' (2S' + 0.160)²

Neglect 2S' as compare to 0.160

5.61 x 10^-11 = 0.0256 S'

S' = 2.19 x 10^-9 mol/L

So, S/S' = 2.41 x 10^-4 mol/L / 2.19 x 10^-9 mol/L

S/S' = 1.10 x 10⁵