Physical Chemistry Third Edition

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:

μiμi,chem+ziFφ

whereziis the valence of the charged speciesi,Fis Faraday’s constant, andφis the

electric potential.

The Nernst equation is

EE◦−

RT

nF

ln(Q)

whereQis the activity quotient for the reaction and whereE◦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)

whereE◦(R) andE◦(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◦

KQeqe−∆G

◦

chem/RTenFE

◦/RT

where∆G◦chemrefers to the reaction outside of the cell.

ADDITIONAL PROBLEMS

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 ofE◦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 itsE◦.

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 constantPP◦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