378
8 The Thermodynamics of Electrochemical Systems
Summary of the Chapter
An electrochemical cell can function as an electrolytic cell, in which case an externally
imposed voltage produces a chemical reaction, or as a galvanic cell, in which case a
spontaneous chemical reaction produces a current in an external circuit. An equilibrium
electrochemical cell is at the state between these two conditions.
The chemical potential of a charged species was separated into two contributions:
µ i µ i,chem + z i F ϕ
where z i is the valence of the charged species i, F is Faraday’s constant, and ϕ is the
electric potential.
The Nernst equation is
E E
◦
−
RT
nF
ln(Q)
where Q is the activity quotient for the reaction and where E ◦ is the reversible standard
state cell voltage.
Standard-state half-cell reduction potentials can be used to obtain the standard-state
voltage for any cell that can be made from two half-cells in the table, using the relation
E
◦
E
◦ (R) − E
◦ (L)
where E ◦ (R) and E ◦ (L) are the half-cell potentials for the right and left electrodes in
their standard states.
Thermodynamic functions can be determined electrochemically, using the relations
∆G
◦
chem −nFE
◦
K Q eq e
−∆G ◦
chem /RT
e
nFE ◦ /RT
where ∆G ◦
chem refers to the reaction outside of the cell.
A D D I T I O N A L P R O B L E M S
8.37 A fuel cell is a galvanic cell into which reactants are
brought into the cell continuously, so that no recharging or
replacement of the cell is necessary. A hydrogen–oxygen
fuel cell can have either an acidic or a basic electrolyte
solution.
a. Write the half-reaction equations and the cell equation
for a hydrogen–oxygen fuel cell with an aqueous KOH
electrolyte.
b. Calculate the value of E ◦ for the fuel cell of part a and
write its Nernst equation. To what circumstance does
the standard state correspond?
c. Write the half-cell reaction equations and the cell
reaction for a hydrogen fuel cell with an acidic
electrolyte. Find its E ◦ .
d. Find the reversible cell voltage of a hydrogen–oxygen
fuel cell at 298.15 K if the hydrogen and oxygen are
both at a pressure of 150 torr (roughly the total pressure
maintained in a manned space vehicle with a pure
oxygen atmosphere) and if the electrolyte solution is an
HCl solution at 2.50 mol kg −1 .
8.38 a. A hydrogen–oxygen fuel cell is operating reversibly
at constant P P ◦ and with unit activity of all
substances. Using data from Appendix A, calculate
the maximum amount of work that could be done if
2.000 mol of hydrogen gas and 1.000 mol of oxygen
gas are consumed at 298.15 K to form liquid
water.
b. Using the Carnot efficiency formula, Eq. (3.1-22), find
the maximum work that can be done with a heat engine
8 The Thermodynamics of Electrochemical Systems
Summary of the Chapter
An electrochemical cell can function as an electrolytic cell, in which case an externally
imposed voltage produces a chemical reaction, or as a galvanic cell, in which case a
spontaneous chemical reaction produces a current in an external circuit. An equilibrium
electrochemical cell is at the state between these two conditions.
The chemical potential of a charged species was separated into two contributions:
µ i µ i,chem + z i F ϕ
where z i is the valence of the charged species i, F is Faraday’s constant, and ϕ is the
electric potential.
The Nernst equation is
E E
◦
−
RT
nF
ln(Q)
where Q is the activity quotient for the reaction and where E ◦ is the reversible standard
state cell voltage.
Standard-state half-cell reduction potentials can be used to obtain the standard-state
voltage for any cell that can be made from two half-cells in the table, using the relation
E
◦
E
◦ (R) − E
◦ (L)
where E ◦ (R) and E ◦ (L) are the half-cell potentials for the right and left electrodes in
their standard states.
Thermodynamic functions can be determined electrochemically, using the relations
∆G
◦
chem −nFE
◦
K Q eq e
−∆G ◦
chem /RT
e
nFE ◦ /RT
where ∆G ◦
chem refers to the reaction outside of the cell.
A D D I T I O N A L P R O B L E M S
8.37 A fuel cell is a galvanic cell into which reactants are
brought into the cell continuously, so that no recharging or
replacement of the cell is necessary. A hydrogen–oxygen
fuel cell can have either an acidic or a basic electrolyte
solution.
a. Write the half-reaction equations and the cell equation
for a hydrogen–oxygen fuel cell with an aqueous KOH
electrolyte.
b. Calculate the value of E ◦ for the fuel cell of part a and
write its Nernst equation. To what circumstance does
the standard state correspond?
c. Write the half-cell reaction equations and the cell
reaction for a hydrogen fuel cell with an acidic
electrolyte. Find its E ◦ .
d. Find the reversible cell voltage of a hydrogen–oxygen
fuel cell at 298.15 K if the hydrogen and oxygen are
both at a pressure of 150 torr (roughly the total pressure
maintained in a manned space vehicle with a pure
oxygen atmosphere) and if the electrolyte solution is an
HCl solution at 2.50 mol kg −1 .
8.38 a. A hydrogen–oxygen fuel cell is operating reversibly
at constant P P ◦ and with unit activity of all
substances. Using data from Appendix A, calculate
the maximum amount of work that could be done if
2.000 mol of hydrogen gas and 1.000 mol of oxygen
gas are consumed at 298.15 K to form liquid
water.
b. Using the Carnot efficiency formula, Eq. (3.1-22), find
the maximum work that can be done with a heat engine