General Chemistry
General Chemistry
7th Edition
ISBN: 9780073402758
Author: Chang, Raymond/ Goldsby
Publisher: McGraw-Hill College
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Chapter 19, Problem 19.123SP

(a)

Interpretation Introduction

Interpretation:

The emf of the cell in the given conditions, energy density of the zinc electrode and the volume of air supplied to the cell in each second has to be calculated.

Concept Introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The standard free energy change (ΔG°rxn) is the difference in free energy of the reactants and products in their standard state.

  ΔG°rxn=nΔGf°(Products)-nΔGf°(Reactants)

Where, n is the number of moles

The relation between Gibbs free energy and cell potential: The amount of energy in a system that can be converted into useful energy is defined as free energy in thermodynamics

Free energy and the cell potential is related by the given equation.

  ΔG=-nFE

Where,

  ΔG is the change in free energy

  n is the number of electrons transferred

  F is the Faraday constant (F=96500Cmol-1)

  E is the cell potential

Nernst equation is one of the important equations in electrochemistry.  In Nernst equation the electrode potential of a cell reaction is related to the standard electrode potential, concentration or activities of the species that is involved in the chemical reaction and temperature.

  Ecell=E°cell-RT2.303nFlog[Red][Oxd]

Where,

  Ecell is the potential of the cell at a given temperature

  E°cell is the standard electrode potential

  R is the universal gas constant (R=8.314JK-1mol-1)

  T is the temperature

  n is the number of electrons involved in a reaction

  F is the Faraday constant (F=9.64853399×104Cmol-1)

  [Red] is the concentration of the reduced species

  [Oxd] is the concentration of the oxidised species

At room temperature (25°C), after substituting the values of all the constants the equation can be written as

  Ecell= E°cell-0.0591nlog[Red][Oxd]

Ideal gas equation is an equation that is describing the state of a imaginary ideal gas.

  PV=n RT

Where,

  P is the pressure of the gas

  V is the volume

  n is the number of moles of gas

  R is the universal gas constant (R=0.0821LatmK-1mol-1)

  T is the temperature

(a)

Expert Solution
Check Mark

Answer to Problem 19.123SP

The half cell reactions of the given cell,

  ZnZn2++2e-Anode12O2+2e-O2-Cathode

The standard emf of the cell is found to be 1.65V

Explanation of Solution

To record the given data

  Gf°(ZnO)=-318.2KJmol-1ΔGf°(Zn)=0ΔGf°(O2)=0

To write the half cell reactions and overall reaction

The half cell reactions are,

ZnZn2++2e-Anode12O2+2e-O2-Cathode

Overall reaction,

Zn+12O2ZnO

To find the ΔG°rxn of the given reaction

The of ΔG°rxn the given reaction is calculated by plugging in the values of standard free energy of the reactants and products in the given equation.

  ΔG°rxn=nΔGf°(Products)-nΔGf°(Reactants)

  =ΔGf°(ZnO)-[ΔGf°(Zn)+12ΔGf°(O2)]=-318.2KJmol-1-[0+0]=-318.2kJmol-1

To find the E°cell

Using the value of free energy and the number of electrons transferred the E°cell can be calculated.

  ΔG°=-nFE°

On rearranging the equation we get,

  E°=ΔG°-nF=-318.2×103Jmol-1(2)(96500)JV-1mol)=1.65V

(b)

Interpretation Introduction

Interpretation:

The emf of the cell in the given conditions, energy density of the zinc electrode and the volume of air supplied to the cell in each second has to be calculated.

Concept Introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The standard free energy change (ΔG°rxn) is the difference in free energy of the reactants and products in their standard state.

  ΔG°rxn=nΔGf°(Products)-nΔGf°(Reactants)

Where, n is the number of moles

The relation between Gibbs free energy and cell potential: The amount of energy in a system that can be converted into useful energy is defined as free energy in thermodynamics. 

Free energy and the cell potential is related by the given equation.

  ΔG=-nFE

Where,

  ΔG is the change in free energy

  n is the number of electrons transferred

  F is the Faraday constant (F=96500Cmol-1)

  E is the cell potential

Nernst equation is one of the important equations in electrochemistry.  In Nernst equation the electrode potential of a cell reaction is related to the standard electrode potential, concentration or activities of the species that is involved in the chemical reaction and temperature.

  Ecell=E°cell-RT2.303nFlog[Red][Oxd]

Where,

  Ecell is the potential of the cell at a given temperature

  E°cell is the standard electrode potential

  R is the universal gas constant (R=8.314JK-1mol-1)

  T is the temperature

  n is the number of electrons involved in a reaction

  F is the Faraday constant (F=9.64853399×104Cmol-1)

  [Red] is the concentration of the reduced species

  [Oxd] is the concentration of the oxidised species

At room temperature (25°C), after substituting the values of all the constants the equation can be written as

  Ecell= E°cell-0.0591nlog[Red][Oxd]

Ideal gas equation is an equation that is describing the state of a imaginary ideal gas.

  PV=n RT

Where,

  P is the pressure of the gas

  V is the volume

  n is the number of moles of gas

  R is the universal gas constant (R=0.0821LatmK-1mol-1)

  T is the temperature

(b)

Expert Solution
Check Mark

Answer to Problem 19.123SP

The emf of the cell when the partial pressure of oxygen is 0.21atm is found to be 1.63V

Explanation of Solution

To record the given data

Partial pressure of oxygen =0.21atm

E°cell=1.65V

To calculate the emf of the cell

The emf of the cell at the given conditions can be calculated by using the modified Nernst equation.

  Ecell= E°-0.05912VnlogPZnOPZnPO2= 1.65V-0.0591V2log1PO2=1.65V-0.0591V2log10.21=1.63V

(c)

Interpretation Introduction

Interpretation:

The emf of the cell in the given conditions, energy density of the zinc electrode and the volume of air supplied to the cell in each second has to be calculated.

Concept Introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The standard free energy change (ΔG°rxn) is the difference in free energy of the reactants and products in their standard state.

  ΔG°rxn=nΔGf°(Products)-nΔGf°(Reactants)

Where, n is the number of moles

The relation between Gibbs free energy and cell potential: The amount of energy in a system that can be converted into useful energy is defined as free energy in thermodynamics. 

Free energy and the cell potential is related by the given equation.

  ΔG=-nFE

Where,

  ΔG is the change in free energy

  n is the number of electrons transferred

  F is the Faraday constant (F=96500Cmol-1)

  E is the cell potential

Nernst equation is one of the important equations in electrochemistry.  In Nernst equation the electrode potential of a cell reaction is related to the standard electrode potential, concentration or activities of the species that is involved in the chemical reaction and temperature.

  Ecell=E°cell-RT2.303nFlog[Red][Oxd]

Where,

  Ecell is the potential of the cell at a given temperature

  E°cell is the standard electrode potential

  R is the universal gas constant (R=8.314JK-1mol-1)

  T is the temperature

  n is the number of electrons involved in a reaction

  F is the Faraday constant (F=9.64853399×104Cmol-1)

  [Red] is the concentration of the reduced species

  [Oxd] is the concentration of the oxidised species

At room temperature (25°C), after substituting the values of all the constants the equation can be written as

  Ecell= E°cell-0.0591nlog[Red][Oxd]

Ideal gas equation is an equation that is describing the state of a imaginary ideal gas.

  PV=n RT

Where,

  P is the pressure of the gas

  V is the volume

  n is the number of moles of gas

  R is the universal gas constant (R=0.0821LatmK-1mol-1)

  T is the temperature

(c)

Expert Solution
Check Mark

Answer to Problem 19.123SP

The energy density of the zinc electrode is found to be 4.86×103kJ/kg

Explanation of Solution

To record the given data

Amount of zinc =1kg

Molecular weight of zinc =65.41gmol1

To calculate the number of moles of zinc

Number of moles of zinc in 1kg zinc can be calculated as given below.

  Numberofmolesofzinc=1000g65.41gmol-1=15.28mol

To calculate the energy density of zinc electrode

Free energy is the maximum amount of energy in the system that can be converted into useful work.  Energy density can be obtained by multiplying the free energy value with the number of moles of zinc.

  Energy density =318.2kJ1molZn×1molZn65.41gZn×1000gZn1kgZn  =4.86×103kJ/kgZn

(d)

Interpretation Introduction

Interpretation:

The emf of the cell in the given conditions, energy density of the zinc electrode and the volume of air supplied to the cell in each second has to be calculated.

Concept Introduction:

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The standard free energy change (ΔG°rxn) is the difference in free energy of the reactants and products in their standard state.

  ΔG°rxn=nΔGf°(Products)-nΔGf°(Reactants)

Where, n is the number of moles

The relation between Gibbs free energy and cell potential: The amount of energy in a system that can be converted into useful energy is defined as free energy in thermodynamics. 

Free energy and the cell potential is related by the given equation.

  ΔG=-nFE

Where,

  ΔG is the change in free energy

  n is the number of electrons transferred

  F is the Faraday constant (F=96500Cmol-1)

  E is the cell potential

Nernst equation is one of the important equations in electrochemistry.  In Nernst equation the electrode potential of a cell reaction is related to the standard electrode potential, concentration or activities of the species that is involved in the chemical reaction and temperature.

  Ecell=E°cell-RT2.303nFlog[Red][Oxd]

Where,

  Ecell is the potential of the cell at a given temperature

  E°cell is the standard electrode potential

  R is the universal gas constant (R=8.314JK-1mol-1)

  T is the temperature

  n is the number of electrons involved in a reaction

  F is the Faraday constant (F=9.64853399×104Cmol-1)

  [Red] is the concentration of the reduced species

  [Oxd] is the concentration of the oxidised species

At room temperature (25°C), after substituting the values of all the constants the equation can be written as

  Ecell= E°cell-0.0591nlog[Red][Oxd]

Ideal gas equation is an equation that is describing the state of a imaginary ideal gas.

  PV=n RT

Where,

  P is the pressure of the gas

  V is the volume

  n is the number of moles of gas

  R is the universal gas constant (R=0.0821LatmK-1mol-1)

  T is the temperature

(d)

Expert Solution
Check Mark

Answer to Problem 19.123SP

The amount of air supplied to the battery in each second is found to be 64L

Explanation of Solution

To record the given data

Amount of current derived from the cell =2.1×105A

To calculate the number of moles of electrons required for producing given amount of charge

Charge produced and the numbers of moles of electrons transferred are related by the following equation.

  Charge=nF

The number of moles of electrons transferred,

  n=CF=2.1×105C96,500Cmol-1=2.2mol

To calculate the number of moles of oxygen gas reduced by 2.2mol of electrons.

From the equation for the cell reaction we have seen that 4moles of electrons are required to reduce one mole of oxygen gas.  Hence, the number of moles of oxygen reduced by 2.2mol of electrons can be calculated as given below.

  Number of moles of O2=2.2 mol e×1molO24mole-=0.55molO2

To calculate the volume of oxygen when the partial pressure is 1atm.

The volume of oxygen at 1atm partial pressure can be calculated using ideal gas equation.

  VO2=n RTP=(0.55molO2)[0.0821LatmK-1mol-1](298K)1atm=13.5L

To calculate the volume of air required at each second.

The volume of air required at each second is found as given below.

  Vair=13.5L×100%air21%O2=64L

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Chapter 19 Solutions

General Chemistry

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