Thermodynamics and Chemistry

CHAPTER 14 GALVANIC CELLS

14.3 MOLARREACTIONQUANTITIES OF THECELLREACTION 461

Note that the cell has reaction equilibrium only ifÅrGis zero. The cell has thermal,
mechanical, and transfer equilibrium when the electric current is zero and the cell potential
is the zero-current cell potentialEcell, eq. Equations14.3.13and14.3.14show that in order
for the cell to also have reaction equilibrium,Ecell, eqmust equal the liquid junction potential
if there is a liquid junction, or be zero otherwise. These are the conditions of an exhausted,
“dead” cell that can no longer do electrical work.

14.3.3 Standard molar reaction quantities

Consider a hypothetical galvanic cell in which each reactant and product of the cell reac-
tion is in its standard state at unit activity, and in which a liquid junction if present has
a negligible liquid junction potential. The equilibrium cell potential of this cell is called
thestandard cell potentialof the cell reaction,Ecell, eq. An experimental procedure for
evaluatingEcell, eqwill be described in Sec.14.5.
In this hypothetical cell,ÅrGcellis equal to the standard molar reaction Gibbs energy
ÅrG. From Eq.14.3.13, or Eq.14.3.14withEjassumed equal to zero, we have

ÅrGDzFEcell, eq (14.3.15)

ÅrGis the molar reaction Gibbs energy when each reactant and product is at unit activity
and, if it is an ion, is in a phase of zero electric potential. SinceÅrGis equal toRTlnK
(Eq.11.8.10), we can write

lnKD

zF

RT

Ecell, eq (14.3.16)
Equation14.3.16allows us to evaluate the thermodynamic equilibrium constantKof
the cell reaction by a noncalorimetric method. Consider for example the cell

Ag AgC.aq/ Cl.aq/ AgCl.s/ Ag

in which the pair of dashed vertical bars indicates a liquid junction of negligible liquid
junction potential. The electrode reactions are

Ag(s)!AgC(aq)Ce

AgCl(s)Ce !Ag(s)CCl(aq)

and the cell reaction is
AgCl.s/!AgC.aq/CCl.aq/

The equilibrium constant of this reaction is the solubility productKsof silver chloride (Sec.
12.5.5). At298:15K, the standard cell potential is found to beEcell, eq D 0:5770V. We
can use this value in Eq.14.3.16to evaluateKsat298:15K (see Prob. 14. 5 ).
Equation14.3.16also allows us to evaluate the standard molar reaction enthalpy by
substitution in Eq.12.1.13on page 368 :

ÅrHDRT^2

d lnK

dT

DzF

T

dEcell, eq

dT

Ecell, eq

!

(14.3.17)

(no solute standard states

based on concentration)