Mg(OH)2 is a sparingly soluble salt with a solubility product, Ksp, of 5.61Ã—10âˆ’11. It is used...

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Mg(OH)2 is a sparingly soluble salt with a solubility product,Ksp, of 5.61Ã—10âˆ’11. It is used to control the pH andprovide nutrients in the biological (microbial) treatment ofmunicipal wastewater streams. What is the ratio of solubility ofMg(OH)2 dissolved in pure H2O to Mg(OH)2dissolved in a 0.160M NaOH solution?
Express your answer numerically as the ratio of molarsolubility in H2O to the molarsolubility in NaOH.

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4.1 Ratings (841 Votes)

In pure water:

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Mg (OH)2Â Â ----> Mg2+ + 2OH-

initiak:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0Â Â Â Â Â Â Â Â Â Â Â Â Â 0

at equilibrium:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SÂ Â Â Â Â Â Â Â Â Â Â Â Â 2S

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

5.61*10^-11 = S* (2S)^2

5.61*10^-11 = 4S^3

S = 2.4*10^-4

In NaOH:

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Mg (OH)2Â Â ----> Mg2+ + 2OH-

initiak:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0Â Â Â Â Â Â Â Â Â Â Â Â Â 0.16

at equilibrium:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SÂ Â Â Â Â Â Â Â Â Â Â Â Â 0.16+2S

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

5.61*10^-11 = S* (0.16+2S)^2

Since Ksp is very small, S will be very small and it can ignored as compared to 0.16

5.61*10^-11 = S* (0.16)^2

S = 2.2*10^-9

molar solubility in H2O to the molar solubility in NaOH = 2.4*10^-4 / (2.2*10^-9)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =1.1*10^5

Answer: Â Â 1.1*10^5

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