   Chapter 17, Problem 70PS

Chapter
Section
Textbook Problem

Will a precipitate of Mg(OH)2 form when 25.0 mL of 0.010 M NaOH is combined with 75.0 mL of a 0.10 M solution of magnesium chloride?

Interpretation Introduction

Interpretation:

Whether precipitation of Mg(OH)2 occurs or not on addition of 25 ml 0.01 MNaOH to 75ml 0.1 M MgCl solution has to be predicted.

Concept introduction:

Solubility product constant,Ksp is 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)Ksp=[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

Value of reaction quotient,Q, is calculated and compared with the value of Ksp for Mg(OH)2.

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.

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

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

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

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

millimoles of Mg2+=75×0.1=7.5millimoles of OH=25×0.01=0.25

Total volume of the solution is 100 ml.

Concentration of Magnesium ions in the solution is,

[Mg2+]=7.5100=7.5×102 M

Concentration of hydroxide ions in the solution is,

[OH1]=0

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