General Chemistry
General Chemistry
7th Edition
ISBN: 9780073402758
Author: Chang, Raymond/ Goldsby
Publisher: McGraw-Hill College
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Chapter 19, Problem 19.121SP

a)

Interpretation Introduction

Interpretation:

A Ecell value has to be calculated.

Concept introduction:

Standard reduction potential: The voltage associated with a reduction reaction at an electrode when all solutes are 1M and all gases are at 1 atm. The hydrogen electrode is called the standard hydrogen electrode (SHE).

Standard emf: Ecell0 is composed of a contribution from the anode and a contribution from the cathode is given by,

Ecello=EcathodeoEanodeo

Where both Ecathodeo and Eanodeo are the standard reduction potentials of the electrodes.

Thermodynamics of redox reactions:

The change in free-energy represents the maximum amount of useful work that can be obtained in a reaction: ΔG0=-nFEcell0

Relation between Ecell0 and equilibrium constant (K) of a redox reaction:

Ecell0=RTnFlnKwhereRisgasconstant(8.314J/K.mol)TisTemperatureinKelvinnisno.ofelectronstransferredinredoxreactionFisFaradayconstant(96500J/V.mol)Kisequilibriumconstant

Relation between ΔG0 and K:ΔG0=-RTlnK

Effect of concentration on cell Emf:

The mathematical relationship between the emf of galvanic cell and the concentration of reactants and products in a redox reaction under nonstandard-state conditions is,

ΔG=ΔG0+RTlnQwhere, ΔG0isstandardGibb'sfreeenergy            Qisreactionquotient.

As known ΔG0=-nFEcell0 and ΔG=-nFEcell, above expression can be written as,

ΔG=ΔG0+RTlnQ-nFEcell=-nFEcell0+RTlnQ

Dividing by –nF, the above equation becomes,

-nFEcellnF=-nFEcell0nF+RTlnQnFEcell=Ecell0RTnFlnQNernst equation

Nernst equation: The Nernst equation is used to calculate the cell voltage under nonstandard-state conditions.

a)

Expert Solution
Check Mark

Explanation of Solution

General Chemistry, Chapter 19, Problem 19.121SP

        Figure.1

A galvanic concentration cell, each compartment consists of Co electrode in Co(NO3)2 solution. The concentrations in the compartments are 2.0M and 0.10M, respectively. The anode and cathode are labelled as shown above. The electron flows from anode to cathode compartments.

Nernst equation of the concentration cell and Substitute known constant values of R, T and F into Nernst equation becomes as follows,

Ecell=Ecell0-(0.0257V)nln[Co2+]dil[Co2+]conc

The number of electrons transferred in the given redox reaction is TWO (n=2) and Ecell0=0.0V as the electrodes on two compartments are same.

Ecell(+0.0V)-(0.0257V)2ln0.102.0=(+0.0V)-(0.01285)ln(0.05)=(+0.0V)-(0.01285)(2.996)=(+0.0V)+0.023549=+0.0385 V

The emf of the given galvanic cell reaction is +0.0385 V

b)

Interpretation Introduction

Interpretation:

The concentrations in the compartments when Ecell drops to 0.020 V has to be calculated.

Concept introduction:

Standard reduction potential: The voltage associated with a reduction reaction at an electrode when all solutes are 1M and all gases are at 1 atm. The hydrogen electrode is called the standard hydrogen electrode (SHE).

Standard emf: Ecell0 is composed of a contribution from the anode and a contribution from the cathode is given by,

Ecello=EcathodeoEanodeo

Where both Ecathodeo and Eanodeo are the standard reduction potentials of the electrodes.

Thermodynamics of redox reactions:

The change in free-energy represents the maximum amount of useful work that can be obtained in a reaction: ΔG0=-nFEcell0

Relation between Ecell0 and equilibrium constant (K) of a redox reaction:

Ecell0=RTnFlnKwhereRisgasconstant(8.314J/K.mol)TisTemperatureinKelvinnisno.ofelectronstransferredinredoxreactionFisFaradayconstant(96500J/V.mol)Kisequilibriumconstant

Relation between ΔG0 and K:ΔG0=-RTlnK

Effect of concentration on cell Emf:

The mathematical relationship between the emf of galvanic cell and the concentration of reactants and products in a redox reaction under nonstandard-state conditions is,

ΔG=ΔG0+RTlnQwhere, ΔG0isstandardGibb'sfreeenergy            Qisreactionquotient.

As known ΔG0=-nFEcell0 and ΔG=-nFEcell, above expression can be written as,

ΔG=ΔG0+RTlnQ-nFEcell=-nFEcell0+RTlnQ

Dividing by –nF, the above equation becomes,

-nFEcellnF=-nFEcell0nF+RTlnQnFEcell=Ecell0RTnFlnQNernst equation

Nernst equation: The Nernst equation is used to calculate the cell voltage under nonstandard-state conditions.

b)

Expert Solution
Check Mark

Explanation of Solution

As a concentration cell runs, the concentration of the two solutions approaches each other. Let concentration of the dilute solution equal (0.10+x) and the concentration of the concentrated solution equal (0.10+x)

Ecell=Ecell0-(0.0257V)nln[Co2+]dil[Co2+]conc

The number of electrons transferred in the given redox reaction is TWO (n=2) and Ecell0=0.0V as the electrodes on two compartments are same.

Ecell(+0.0V)-(0.0257V)2ln0.10+x2.0-x0.020V=-(0.01285)ln0.10+x2.0-x0.020V-(0.01285)=ln0.10+x2.0-xe1.56=0.10+x2.0-x

Solve for x as follows,

0.210(2.0-x)=(0.10+x)0.420.10=0.210x+x0.32=(0.210+1)x0.321.210=xx=0.26M

At anode compartment: 0.10M+0.26M = 0.36 M

At cathode compartment: 2.0M0.26M = 1.74 M

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Chapter 19 Solutions

General Chemistry

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