Calculate the molar solubility in waterPart complete Mg(OH)2 is a sparingly solu

Question

Calculate the molar solubility in waterPart complete Mg(OH)2 is a sparingly soluble compound, in this case a base, with a solubility product, Ksp, of 5.61×10?11. It is used to control the pH and provide nutrients in the biological (microbial) treatment of municipal wastewater streams. Based on the given value of the Ksp, what is the molar solubility of Mg(OH)2 in pure H2O? ANSWER=2.41 x 10^-4 Calculate the molar solubility in NaOH Based on the given value of the Ksp, what is the molar solubility of Mg(OH)2 in 0.150 M NaOH?

Explanation / Answer

Mg(OH)2(s) ------------------> Mg^2+ (aq) + 2OH^- (aq)

                                       s                    2s

   Ksp    = [Mg^2+][OH^-]^2

5.61*10^-11   = s*(2s)^2

4s^3             = 5.61*10^-11

s^3             = 1.4025*10^-11

s                 = 2.41*10^-4

solubility of Mg(OH)2 = 2.41*10^-4M

NaOH ---------------> Na^+ (aq) + OH^- (aq)

0.15M                                   0.15M

Mg(OH)2(s) ------------------> Mg^2+ (aq) + 2OH^- (aq)

                                       s                    2s+0.15

   Ksp    = [Mg^2+][OH^-]^2

5.61*10^-11   = s*(2s+0.15)^2                             [ 2s+ 0.15 = 0.15 , compare to 0.15M 2s is neglisible]

5.61*10^-11   = s*(0.15)^2

s*0.0225            = 5.61*10^-11

s             =     5.61*10^-11/0.0225   = 2.5*10^-9 M

solubility of Mg(OH)2 in NaOH = 2.5*10^-9 M

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