Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
9th Edition
ISBN: 9781133949640
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
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Chapter 17, Problem 100GQ

(a)

Interpretation Introduction

Interpretation:

The value of the equilibrium constant Knet has to be calculated for the given reaction.

  AgBr(s)+2S2O32(aq)Knet[Ag(S2O3)2]3(aq)+Br(aq)

Concept introduction:

Some metal ions when present in an aqueous solution containing anions or neutral species called Lewis base or ligands having a tendency to donate electron pairs to metal ions then complex ion formation will take place.

Example of metal ions that form complex ions includes,Cd2+,Fe2+,Zn2+,Ni2+ etc.

Example of Lewis bases includes,NH3,OH etc.

The complex ion remains in equilibrium with the metal ion and the ligand called complex ion formation equilibrium and the equilibrium constant is called as formation constant Kf.

A larger value of Kf implies that the complex ion formed is more stable. Kf is the measure of the strength of the interaction between the metal ions and the Lewis base to form the complex ion.

For example for general complex ion formation reaction,

xM+yL[MxLy]

Kf can be given as

Kf=[MxLy][M]x[L]y

 Here,

  • [MxLy] is the equilibrium concentration of complex ion.
  • [M] is the equilibrium concentration of metal ion.
  • [L] is the equilibrium concentration of the ligand.
  • x and y are the coefficients of metal ion and ligand respectively.

Complex ions are stable and thus formation of these increase the solubility of the salt containing the metal ions same as in complex ions. Effect of complex ion formation on the solubility of salt can be explained as below,

AgBr when dissolved in water does not dissolve completely and dissociates as follows,

  AgBr(s)KspAg+(aq)+Br(aq) (1)

For this reaction Ksp expression is,

Ksp=[Ag+][Br]

Ag+ ions are capable of forming complex with ligand so when aqueous ammonia solution (strong ligand) is added to the saturated solution of AgBr, Ag+ ions present in the solution form complex with NH3.

  Ag+(aq)+2NH3(aq)Kf[Ag(NH3)2]+(aq) (2)

The expression for formation constant Kf is given as,

Kf=[[Ag(NH3)2]+][Ag+][NH3]2

Complex formation leads to the decrease in the concentration of the Ag+ ions in the solution, as a result, according to Le Chatelier’s principle the equilibrium in equation (1) move in the forward direction producing more of the Ag+ ions and the solubility of the slightly soluble salt AgBr increases.

Adding two equilibrium equation (1) and (2) new overall equilibrium constant can be defined.

Net chemical equation:

  Ag+(aq)+2NH3(aq)Knet[Ag(NH3)2]+(aq)+Br(aq) (3)

Net equilibrium constant can be given as,

Knet=(Ksp)(Kf) (4)

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.

For example, general salt AxBy when dissolved in water dissociates as,

AxBy(s)xAy+(aq)+yBx(aq)

The expression for Ksp of a salt is,

Ksp=[Ay+]x[Bx]y

(a)

Expert Solution
Check Mark

Explanation of Solution

The value of equilibrium constant, Knet for the given reaction 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 AgBr is 5.4×1013 .

The value of formation constant, Kf for [Ag(S2O3)2]3 is 2.9×1013 .

AgBr dissociates as follows in water,

  AgBr(s)KspAg+(aq)+Br(aq) (5)

Ag+ ions present in solution react with the thio ions added to the solution to form [Ag(S2O3)2]3.

  Ag+(aq)+2S2O32(aq)Kf[Ag(S2O3)2]3(aq) (6)

Net chemical equation is,

  AgBr(s)+2S2O32(aq)Knet[Ag(S2O3)2]3(aq)+Br(aq)                   (7)

The net equilibrium constant, Knet for equation (7) is given as,

Knet=Ksp×Kf

Substitute 5.4×1013 for Ksp and 2.9×1013 for Kf.

Knet=(5.4×1013)(2.9×1013)=1.56×101

The equilibrium constant, Knet for the given reaction is 1.56×101.

(b)

Interpretation Introduction

Interpretation:

For the given reaction,

  AgBr(s)+2S2O32(aq)Knet[Ag(S2O3)2]3(aq)+Br(aq)

The mass of Na2S2O3 that must be added to dissolve 1.00 g of AgBr suspended in 1.00 L of water has to be calculated.

Concept introduction:

Some metal ions when present in an aqueous solution containing anions or neutral species called Lewis base or ligands having a tendency to donate electron pairs to metal ions then complex ion formation will take place.

Example of metal ions that form complex ions includes,Cd2+,Fe2+,Zn2+,Ni2+ etc.

Example of Lewis bases includes,NH3,OH etc.

The complex ion remains in equilibrium with the metal ion and the ligand called complex ion formation equilibrium and the equilibrium constant is called as formation constant Kf.

A larger value of Kf implies that the complex ion formed is more stable. Kf is the measure of the strength of the interaction between the metal ions and the Lewis base to form the complex ion.

For example for general complex ion formation reaction,

xM+yL[MxLy]

Kf can be given as

Kf=[MxLy][M]x[L]y

 Here,

  • [MxLy] is the equilibrium concentration of complex ion.
  • [M] is the equilibrium concentration of metal ion.
  • [L] is the equilibrium concentration of the ligand.
  • x and y are the coefficients of metal ion and ligand respectively.

Complex ions are stable and thus formation of these increase the solubility of the salt containing the metal ions same as in complex ions. Effect of complex ion formation on the solubility of salt can be explained as below,

AgBr when dissolved in water does not dissolve completely and dissociates as follows,

  AgBr(s)KspAg+(aq)+Br(aq) (1)

For this reaction Ksp expression is,

Ksp=[Ag+][Br]

Ag+ ions are capable of forming complex with ligand so when aqueous ammonia solution (strong ligand) is added to the saturated solution of AgBr, Ag+ ions present in the solution form complex with NH3.

  Ag+(aq)+2NH3(aq)Kf[Ag(NH3)2]+(aq) (2)

The expression for formation constant Kf is given as,

Kf=[[Ag(NH3)2]+][Ag+][NH3]2

Complex formation leads to the decrease in the concentration of the Ag+ ions in the solution, as a result, according to Le Chatelier’s principle the equilibrium in equation (1) move in the forward direction producing more of the Ag+ ions and the solubility of the slightly soluble salt AgBr increases.

Adding two equilibrium equation (1) and (2) new overall equilibrium constant can be defined.

Net chemical equation:

  Ag+(aq)+2NH3(aq)Knet[Ag(NH3)2]+(aq)+Br(aq) (3)

Net equilibrium constant can be given as,

Knet=(Ksp)(Kf) (4)

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.

For example, general salt AxBy when dissolved in water dissociates as,

AxBy(s)xAy+(aq)+yBx(aq)

The expression for Ksp of a salt is,

Ksp=[Ay+]x[Bx]y

The mass of Na2S2O3 that must be added to dissolve 1.00 g of AgBr is calculated below.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

Mass of AgBr is 1.00 L.

Volume of solution is 1.00 L.

The equilibrium constant, Knet for the given reaction is 1.56×101.

Molar mass of Na2S2O3 is 158 gmol1.

In water AgBr dissociates as,

  AgBr(s)Ag+(aq)+Br(aq)

Concentration of AgBr is,

[AgBr]=1 g(188 gmol1)(1 L)=5.33×103 molL1

If all the AgBr dissolves and all Ag+ ions produce undergoes complex formation with thio ions then the concentration of Br and [Ag(S2O3)2]3 is equal to 5.33×103 molL1.

Each Ag+ ions requires 2 moles of S2O32 ions therefore concentration of S2O32 is,

[S2O32]=2(5.33×103 molL1)=0.01064molL1

Additional concentration of S2O32 is required for maintaining equilibrium. From equation (7),

Knet=[[Ag(S2O3)2]3][Br1][S2O32]2

Substitute the values.

[S2O32]=(5.32×103)2(1.56×101)=1.34×103 molL1

Total moles of S2O32 required to dissolve 1.00 g of AgBr per liter of water is,

n=(0.01064mol)+(1.34×103 mol)=0.0119 mol

Mass of Na2S2O3 is,

m= (0.0119 mol)(158 gmol1)=1.89 g

The mass of Na2S2O3 that must be added to dissolve 1.00 g of AgBr suspended in 1.00 L of water is 1.89 g.

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Chapter 17 Solutions

Chemistry & Chemical Reactivity

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