Calculate the solubility (in grams per 1.00 times 10^2 mL of solution) of magnes

Question

Calculate the solubility (in grams per 1.00 times 10^2 mL of solution) of magnesium hydroxide in a solution buffered at pH=12. Express your answer using two significant figures. Calculate the solubility (in grams per 1.00 times 10^2 mL of solution) of magnesium hydroxide in pure water. Express your answer using two significant figures. How does the solubility of Mg(OH)_2 in a buffered solution compare to the solubility of Mg(OH)_2 in pure water? Express your answer using two significant figures.

Explanation / Answer

A) pH = 12 , pOH = 14-pH = 14-12 = 2 , [OH=] = 10^ -pOH = 10^ -2

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

Ksp = [Mg2+] [OH-]^2

2.06 x 10^ -13 = [Mg2+] ( 10^-2)^2

[Mg2+] = 2.06 x 10^ -9 moles/Liter is solubility

Mg(OH)2 solubility in g/L = moles/iter x molar mass = ( 2.06x10^-9) x 58.3197 = 1.2 x 10^ -7 g/L

per 1000 ml solubility is 1.2x10^ -7 g

solubility in g/100 ml = 1.2x10^ -8 g/100 ml

B) in pure water Ksp = [Mg2+][OH-]^2 = (S) (2S)^2 = 4S^3

2.06x10^-13 = 4S^3 ,

S = 3.72 x 10^ -5 moles/liter   is solubility

S in g/L = moles /liter x molar mass = 3.72x10^-5 x 58.3197 = 2.17 x 10^ -3 g/L

solubility in g/100 ml = 2.17x10^ -4 g/100 ml

C) S1/S = 1.28x10^ -8 / 2.17x10^ -4 = 5.9 x 10^-5

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