   Chapter 17, Problem 67PS

Chapter
Section
Textbook Problem

If the concentration of Zn2+ in 10.0 mL of water is 1.63 × 10−4 M, will zinc hydroxide, Zn(OH)2, precipitate when 4.0 mg of NaOH is added?

Interpretation Introduction

Interpretation:

Whether the precipitation of Zn(OH)2 occurs or not on addition of 4 mg NaOH to 40ml  water containing 1.63×104 M zinc ions 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 Zn(OH)2.

Given:

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

The value of solubility product constant,Ksp, for Zn(OH)2 is 3.0×1017.

The concentration of Zn2+ ions present in the solution is 1.63×104molL1.

The volume of solution is 10.0 ml

Given mass of added NaOH is 4.0 mg.

When Zn(OH)2 is dissolved in water it undergoes dissociation in as follows,

Zn(OH)2(s)Zn2+(aq)+2OH(aq)

The Q expression for Zn(OH)2 is,

Q=[Zn2+][OH]2 (1)

NaOH is strong electrolyte and when dissolved in water dissociates completely into its constituent ions. Therefore the concentration of the hydroxide ions and sodium ions coming from NaOH is equal to the initial concentration of NaOH.

NaOH(s)Na+(aq)+OH(aq)

The concentration of sodium hydroxide (NaOH) is calculated as follows,

[NaOH]=wMV  (2)

Here,

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

The volume of the solution is,

V =(10.0 ml)(1.00 L1000 ml)=102L

Gram molecular mass of sodium hydroxide is 40.0 gmol.

Substitute 4.0 mg for w, 40

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