General Chemistry
General Chemistry
7th Edition
ISBN: 9780073402758
Author: Chang, Raymond/ Goldsby
Publisher: McGraw-Hill College
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Chapter 19, Problem 19.129SP

a)

Interpretation Introduction

Interpretation:

Half reactions; the anode and cathode have to be labelled.

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 19.129SP

        Figure.1

For the given redox reactions,

In the galvanic cell, Oxidation occurs at anode and reduction occurs at cathode.

Therefore,

Anode (Oxidation): Co(s)Co2+(aq)+2e

Cathode (Reduction): Mg2+(aq)+2eMg(s)

b)

Interpretation Introduction

Interpretation:

The minimum voltage needed to drive the reaction 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.

b)

Expert Solution
Check Mark

Explanation of Solution

The emf values for the two given half-reactions are,

Anode (Oxidation): Co(s)Co2+(aq)+2eEanode=+0.28V

Cathode (Reduction): Mg2+(aq)+2eMg(s)Ecathode=2.37V

Calculated standard emf for galvanic cell as follows,

Ecello=Ecathodeo+Eanodeo=(-2.37)V+(0.28)V=-2.09V

The minimum voltage needed to drive the reaction is +2.09V

c)

Interpretation Introduction

Interpretation:

The emf of a given galvanic cell 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: Eocell 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.

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.

c)

Expert Solution
Check Mark

Explanation of Solution

Given: Current= 10.0 A; Time, t=2hr=2×60×60=7200sec

Convert Current into coulomb:

(Current)×(time)=no.ofCoulomb

As known, 1Ampere=1CoulombSec

(Current)=no.ofCoulombtimeno.ofCoulomb=(Current)(time)=(10.0C.Sec1)(7200sec)=72000C

Convert number of Coulombs into mole of electrons:

moleofe-=no.ofCoulombFaradayconstant=72000C96500Cmolee-=0.746molee-1

Convert mole of electrons into number of moles:

Co(s)Co2+(aq)+2eEanode=+0.28V

1 mole of Cobalt 2 mole of e-

‘X’of Cobalt = 0.746molee-1 moles of e-

Number of moles of Co=(1moleofCo)(0.746molee-1)2molofe=0.373molofCo

Therefore, no.of moles of Cobalt is 0.373molofCo

Assuming solution volumes of 1.00L, the concentration of Co2+ in solution after  2hours is 2.373 M, and the concentration of Mg2+ in solution after 2 hours is 1.627 M. we use the Nernst equation to solve for Ecell

Mg(s)+Co2+(aq)Mg2+(aq)+Co(s)

Calculation of non-standard emf value using Nernst equation:

The reaction quotient for the given reaction is, Q=[Mg2+][Co][Mg][Co2+]

The concentration of pure solids and pure liquids do not appear in the expression for Q.

Hence, the reaction quotient becomes, Q=[Mg2+][Co2+]

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

Ecell=2.09V-(0.0257V)nln[Mg2+][Co2+]

The number of electrons transferred in the given redox reaction is TWO (n=2) and Ecell0=+2.09V

Ecell(+2.09V)-(0.0257V)2ln1.6272.373=(+2.09V)-(0.01285)ln(0.686)=(+2.09V)-(0.01285)(0.377)=(+2.09V)+0.00485=+2.095V

The emf of the given cell reaction is +2.095V

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Chapter 19 Solutions

General Chemistry

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