   # A cell is constructed using the following half-reactions: Ag + (aq) + e − → Ag(s) Ag 2 SO 4 (s) + 2 e − → 2 Ag(s) + SO 4 2− (aq) E ° = 0.653 V (a) What reactions should be observed at the anode and cathode? (b) Calculate the solubility product constant, K sp , for Ag 2 SO 4 . ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 19, Problem 64GQ
Textbook Problem
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## A cell is constructed using the following half-reactions:Ag+(aq) + e− → Ag(s)Ag2SO4(s) + 2 e− → 2 Ag(s) + SO42− (aq)E° = 0.653 V (a) What reactions should be observed at the anode and cathode? (b) Calculate the solubility product constant, Ksp, for Ag2SO4.

(a)

Interpretation Introduction

Interpretation:

The reactions observed at the anode and cathode has to be identified.

Concept introduction:

According to the first law of thermodynamics, the change in internal energy of a system is equal ti the heat added to the sysytem minus the work done by the system.

The equation is as follows.

ΔU = Q - WΔU = Change in internal energyQ = Heat added to the systemW=Work done by the system

In voltaic cell, the maximum cell potential is directly related to the free energy difference between the reactants and products in the cell.

ΔG0= -nFE0n = Number of moles transferred per mole of reactant and productsF = Faradayconstant=96485C/mol  E0= Volts = Work(J)/Charge(C)

The relation between standard cell potential and equilibrium constant is as follows.

lnK = nE00.0257 at 298K

The relation between solubility product Ksp and equilibrium constant is as follows.

Ksp= e+lnK

### Explanation of Solution

The given reactions are as follows.

Ag+(aq) + e- Ag(s)Ag2SO4(s) + 2e- 2Ag(s) + SO42-(aq)  ; E0= 0.653 V

Let’s write the reduction potential values of each reaction.

Ag+(aq) + e- Ag(s) ; E0=0.799 VAg2SO4(s) + 2e- 2Ag(s) + SO42-(aq)  ; E0= 0

(b)

Interpretation Introduction

Interpretation:

The solubility product constant , Ksp for Ag2SO4 has to be calculated.

Concept introduction:

According to the first law of thermodynamics, the change in internal energy of a system is equal ti the heat added to the sysytem minus the work done by the system.

The equation is as follows.

ΔU = Q - WΔU = Change in internal energyQ = Heat added to the systemW=Work done by the system

In voltaic cell, the maximum cell potential is directly related to the free energy difference between the reactants and products in the cell.

ΔG0= -nFE0n = Number of moles transferred per mole of reactant and productsF = Faradayconstant=96485C/mol  E0= Volts = Work(J)/Charge(C)

The relation between standard cell potential and equilibrium constant is as follows.

lnK = nE00.0257 at 298K

The relation between solubility product Ksp and equilibrium constant is as follows.

Ksp= e+lnK

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