   Chapter 17, Problem 69PS

Chapter
Section
Textbook Problem

If the concentration of Mg2+ ion in seawater is 1350 mg/L, what OH− concentration is required to precipitate Mg(OH)2?

Interpretation Introduction

Interpretation:

The minimum concentration of hydroxide (OH) ion required to start the precipitation of Mg(OH)2 in sea water has to be calculated.

Concept introduction:

Solubility product constant, Ksp, is an equilibrium constant and is defined as the product of the equilibrium concentration of the ions of the salt raised to the power of their coefficients in the balanced chemical equation.

The expression for Ksp of a salt is given as,

AxBy(s)xAy+(aq)+yBx(aq)Ksp=[Ay+]x[Bx]y

Here,

• [Ay+] and [Bx] are equilibrium concentration.

Reaction quotient, Q, for a reaction is defined as the product of the concentration of the ions at any time of the reaction (other than equilibrium time ) of the salt raised to the power of their coefficients in the balanced chemical equation.

The expression for Q of a salt is given as,

AxBy(s)xAy+(aq)+yBx(aq)Q=[Ay+]x[Bx]y

Here,

• [Ay+] and [Bx] are the concentration at any time except equilibrium.
1. 1. If Q=Ksp, this implies that the solution is saturated solution and the concentration of the ions have reached their maximum limit.
2. 2. If Q<Ksp, this implies that the solution is not saturated and more salt can be added to the solution or the salt present in the solution already will dissolve more until the precipitation starts.
3. 3. If Q>Ksp, this implies that the solution is oversaturated and precipitation of salt will occur.
Explanation

The minimum concentration required to cause the precipitation of Mg(OH)2 is calculated below.

Given:

Refer to the Appendix J in the textbook for the value of Ksp

The value of solubility product constant,Ksp, for Mg(OH)2 is 5.6×1012.

Mass of Mg2+ present is 1350 mg.

Volume of solution is 1 L.

Mg(OH)2 is dissociated as follows in water,

Mg(OH)2(s)Mg2+(aq)+2OH(aq)

The expression of Ksp for Mg(OH)2 is,

Ksp=[Mg2+][OH1]2 (1)

The concentration of Mg2+ ions is calculated as follows,

[Mg2+]=wMV  (2)

Here,

• w is the given mass of Magnesium.
• M is the gram molecular mass of the Magnesium.
• is the volume of the solution in liter.

Gram molecular mass of Magnesium is 24 gmol.

Substitute 1350 mg for w, 24 gmol for M and 1 L for in equation (2)

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