Chemistry
Chemistry
9th Edition
ISBN: 9781133611097
Author: Steven S. Zumdahl
Publisher: Cengage Learning
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Chapter 16, Problem 37E

Calculate the solubility (in moles per liter) of Fe(OH)3 (Ksp = 4 × 10−38) in each of the following.

a. water

b. a solution buffered at pH = 5.0

c. a solution buffered at pH = 11.0

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The solubility product of Fe(OH)3 is given. The solubility (in mol/L ) of Fe(OH)3 is to be calculated for each given conditions.

Concept introduction: Solubility is defined as the maximum amount of solute that can dissolve at a certain amount of solvent at certain temperature. The solubility product, Ksp is the equilibrium constant that is applied when salt partially dissolve in a solvent. The solubility product of dissociation of AxBy is calculated as,

Ksp=[A]x[B]y

The ion product of water is calculated using the formula,

Kw=[H+][OH]

Answer to Problem 37E

Answer

The solubility of Fe(OH)3 in water is 4×1017mol/L_ .

Explanation of Solution

Explanation

To determine: The solubility of Fe(OH)3 in water.

The solubility of Fe(OH)3 in water is 4×1017mol/L_ .

Given

Solubility product of Fe(OH)3 is 4×1038 .

Since, solid Fe(OH)3 is placed in contact with water. Therefore, compound present before the reaction is Fe(OH)3 and H2O . The dissociation reaction of Fe(OH)3 is,

Fe(OH)3(s)Fe3+(aq)+3OH(aq)

Since, Fe3+ does not dissolved initially, hence,

[Fe3+]initial=0

The solubility of Fe(OH)3 can be calculated from the concentration of ions at equilibrium.

It is assumed that smol/L of solid is dissolved to reach the equilibrium. The meaning of 1:3 stoichiometry of salt is,

smol/LFe(OH)3smol/LFe3++3smol/LOH

Since, in a neutral solution, the initial concentration of OH is 1×107 . Hence, in a saturated solution, the concentration of OH is 1×107+3s . But the value of s is expected to be very small, therefore, the concentration of OH is approximated to,

1×107+3s1×107

Make the ICE table for the dissociation reaction of Fe(OH)3 .

Fe(OH)3(s)Fe3+(aq)3OH(aq)Initial(M):01×107Chang(M):s3sEquilibrium(M):s1×107+3s1×107

Formula

The solubility product of Fe(OH)3 is calculated as,

Ksp=[Fe3+][OH]3=(s)(1×107)3

Where,

  • Ksp is solubility product.
  • [Co3+] is concentration of Co3+ .
  • [OH] is concentration of OH .
  • s is the solubility.

Substitute the value of Ksp in the above expression.

Ksp=(s)(1×107)34×1038=s(1×107)3s=4×1017mol/L_

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The solubility product of Fe(OH)3 is given. The solubility (in mol/L ) of Fe(OH)3 is to be calculated for each given conditions.

Concept introduction: Solubility is defined as the maximum amount of solute that can dissolve at a certain amount of solvent at certain temperature. The solubility product, Ksp is the equilibrium constant that is applied when salt partially dissolve in a solvent. The solubility product of dissociation of AxBy is calculated as,

Ksp=[A]x[B]y

The ion product of water is calculated using the formula,

Kw=[H+][OH]

Answer to Problem 37E

Answer

The solubility of Fe(OH)3 in a buffered solution at pH=5.0 is 4×1011mol/L_ .

Explanation of Solution

Explanation

To determine: The solubility of Fe(OH)3 in a buffered solution at pH=5.0 .

The concentration of H+ is 1×105M_ .

Given

Solubility product of Fe(OH)3 is 4×1038 .

The pH value of buffered solution is 5.0 .

Formula

The pH is calculated using the formula,

pH=log10[H+]

Substitute the value of pH in the above equation.

pH=log10[H+]5.0=log10[H+][H+]=1×105M_

The concentration of OH is 1×109M_ .

The concentration of H+ is 1×105M .

Formula

The ion product of water is calculated using the formula,

Kw=[H+][OH]

Where,

  • Kw is ion product of water (1×1014) .

Substitute the values of [H+] and Kw in the above equation.

Kw=[H+][OH](1×1014)=(1×105M)[OH][OH]=1×109M_

The solubility of Fe(OH)3 in a buffered solution at pH=5.0 is 4×1011mol/L_ .

The solubility of Fe(OH)3 can be calculated from the concentration of ions at equilibrium.

It is assumed that smol/L of solid is dissolved to reach the equilibrium. The meaning of 1:3 stoichiometry of salt is,

smol/LFe(OH)3smol/LFe3++3smol/LOH

Make the ICE table for the dissociation reaction of Fe(OH)3 .

Fe(OH)3(s)Fe3+(aq)3OH(aq)Initial(M):01×109Chang(M):s3sEquilibrium(M):s1×109+3s

Formula

The solubility product of Fe(OH)3 is calculated as,

Ksp=[Fe3+][OH]3=(s)(1×109+3s)3

Where,

  • Ksp is solubility product.
  • [Al3+] is concentration of Al3+ .
  • [OH] is concentration of OH .
  • s is the solubility.

Since, the value of s is expected to be very small value, hence, it is assumed that,

1×109+3s1×109

Substitute this value in the solubility product expression.

Ksp=(s)(1×109+3s)3=(s)(1×109)3

Substitute the value of Ksp in the above expression.

Ksp=(s)(1×109)34×1038=(s)(1×109)3s=4×1011mol/L_

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: The solubility product of Fe(OH)3 is given. The solubility (in mol/L ) of Fe(OH)3 is to be calculated for each given conditions.

Concept introduction: Solubility is defined as the maximum amount of solute that can dissolve at a certain amount of solvent at certain temperature. The solubility product, Ksp is the equilibrium constant that is applied when salt partially dissolve in a solvent. The solubility product of dissociation of AxBy is calculated as,

Ksp=[A]x[B]y

The ion product of water is calculated using the formula,

Kw=[H+][OH]

Answer to Problem 37E

Answer

The solubility of Fe(OH)3 in a buffered solution at pH=11.0 is 4×1029mol/L_ .

Explanation of Solution

Explanation

To determine: The solubility of Fe(OH)3 in a buffered solution at pH=11.0 .

The concentration of H+ is 1×1011M_ .

Given

Solubility product of Fe(OH)3 is 4×1038 .

The pH value of buffered solution is 11.0 .

Formula

The pH is calculated using the formula,

pH=log10[H+]

Substitute the value of pH in the above equation.

pH=log10[H+]11.0=log10[H+][H+]=1×1011M_

The concentration of OH is 1×103M_ .

The concentration of H+ is 1×1011M .

Formula

The ion product of water is calculated using the formula,

Kw=[H+][OH]

Where,

  • Kw is ion product of water (1×1014) .

Substitute the values of [H+] and Kw in the above equation.

Kw=[H+][OH](1×1014)=(1×1011M)[OH][OH]=1×103M_

The solubility of Fe(OH)3 in a buffered solution at pH=11.0 is 4×1029mol/L_ .

The solubility of Fe(OH)3 can be calculated from the concentration of ions at equilibrium.

It is assumed that smol/L of solid is dissolved to reach the equilibrium. The meaning of 1:3 stoichiometry of salt is,

smol/LFe(OH)3smol/LFe3++3smol/LOH

Make the ICE table for the dissociation reaction of Fe(OH)3 .

Fe(OH)3(s)Fe3+(aq)3OH(aq)Initial(M):01×103Chang(M):s3sEquilibrium(M):s1×103+3s

Formula

The solubility product of Fe(OH)3 is calculated as,

Ksp=[Fe3+][OH]3=(s)(1×103+3s)3

Where,

  • Ksp is solubility product.
  • [Fe3+] is concentration of Fe3+ .
  • [OH] is concentration of OH .
  • s is the solubility.

Since, the value of s is expected to be very small value, hence, it is assumed that,

1×103+3s1×103

Substitute this value in the solubility product expression.

Ksp=(s)(1×103+3s)3=(s)(1×103)3

Substitute the value of Ksp in the above expression.

Ksp=(s)(1×103)34×1038=(s)(1×103)3s=4×1029mol/L_

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Chapter 16 Solutions

Chemistry

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