Question

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?

Mg(OH), is a sparingly soluble compound, in this case a base, with a solubility product, K sp, of 5.61 x 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 Kgp, what is the molar solubility of Mg(OH), in pure H2O? Express your answer with the appropriate units. View Available Hint(s) C: HÅ* 2 ? molar solubility = 1.34 • 10-7 IM Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining

Answer 1

Let "S" be the molar solubility of Mg(OH)₂ in water

As it is a sparingly soluble, there exists an equilibrium between soluble substance and insoluble substance.

The equilibrium is shown as

Mg(OH)₂  ⇌ Mg⁺² + 2 OH^{​​​​​-}

S S 2S

[Mg(OH)]_e = S

[Mg^{​​​​​2+}] = S

[OH^{​​​​​-}] = 2S

​​​K_SP is given by

K_{​​​​​​SP} = [Mg^{​​​​​2+}][OH^-]²

= S. (2S)²

K_{​​​​​​SP} =  4S³

S^{​​​​​​3} = K_{​​​​​​sp}/4

S = (K_{​​​​​​sp}/4)^1/3

Given that K_{​​​​​sp} = 5.61×10^-11

S = (5.61×10^-11/4)^1/3

S = (1.45×10^-11/4)^1/3

S = (0.145*10^-12)^1/3

= 0.525*10^-4

= 5.25*10^-3 M

Molar solubility of Magnesium hydroxide ⁼ 5.25*10^-3 M