Thermodynamics and Chemistry

CHAPTER 14 GALVANIC CELLS

14.5 EVALUATION OF THESTANDARDCELLPOTENTIAL 464

which yields the same value ofEcell, eqfor given cell conditions as Eq.14.4.5. This

value must of course be unchanged, because physically the cell is the same no matter

how we write its cell reaction, and measurable physical quantities such asEcell, eqare

unaffected. However, molar reaction quantities such asÅrGandÅrGdodepend on

how we write the cell reaction, because they are changes per extent of reaction.

14.5 Evaluation of the Standard Cell Potential

As we have seen, the value of the standard cell potentialEcell, eq of a cell reaction has useful
thermodynamic applications. The value ofEcell, eqfor a given cell reaction depends only on
temperature. To evaluate it, we can extrapolate an appropriate function to infinite dilution
where ionic activity coefficients are unity.
To see how this procedure works, consider again the cell reaction H 2 .g/C2 AgCl.s/!
2 HC.aq/C2 Cl.aq/C2 Ag.s/. The cell potential depends on the molalitymBof the HCl
solute according to Eq.14.4.5. We can rearrange the equation to

Ecell, eq DEcell, eqC

2RT

F

ln (^) C

2RT

F

ln

mB

m

RT

2F

ln

fH 2

p

(14.5.1)

For given conditions of the cell, we can measure all quantities on the right side of Eq.14.5.1

except the mean ionic activity coefficient (^) of the electrolyte. We cannot know the exact
value of ln (^) for any given molality until we have evaluatedEcell, eq. We do know that
asmBapproaches zero, (^) approaches unity and ln (^) must approach zero. The Debye–
Huckel formula of Eq. ̈ 10.4.7on page 296 is a theoretical expression for ln (^) that more
closely approximates the actual value the lower is the ionic strength. Accordingly, we define
the quantity
Ecell^0 DEcell, eqC

2RT

F



A

p

mB

1 CBa

p

mB



C

2RT

F

ln

mB

m

RT

2F

ln

fH 2

p

(14.5.2)

The expression in parentheses is the Debye–Huckel formula for ln ̈ (^) withImreplaced by
mB. The constantsAandBhave known values at any temperature (Sec.10.4), andais an
ion-size parameter for which we can choose a reasonable value. At a given temperature, we
can evaluateEcell^0 experimentally as a function ofmB.
The expression on the right side of Eq.14.5.1differs from that of Eq.14.5.2by con-
tributions to.2RT=F /ln (^) not accounted for by the Debye–Huckel formula. Since these ̈
contributions approach zero in the limit of infinite dilution, the extrapolation of measured
values ofEcell^0 tomBD 0 yields the value ofEcell, eq.
Figure14.5on the next page shows this extrapolation using data from the literature. The
extrapolated value indicated by the filled circle isEcell, eq D0:2222V, and the uncertainty
is on the order of only0:1mV.

14.6 Standard Electrode Potentials

Section14.5explained how, by measuring the equilibrium cell potential of a galvanic cell
at different electrolyte molalities, we can evaluate the standard cell potentialEcell, eq of the
cell reaction. It is not necessary to carry out this involved experimental procedure for each