Thermodynamics and Chemistry

CHAPTER 14 GALVANIC CELLS

14.4 THENERNSTEQUATION 463

The term.RT=zF /lnKis equal toEcell, eq(Eq.14.3.16), soEcell, eqbecomes zero—the
cell is “dead” and is incapable of performing electrical work on the surroundings.
AtTD298:15K (25:00C), the value ofRT=F is0:02569V, and we can write the
Nernst equation in the compact form

Ecell, eqDEcell, eq 

0:02569V

z

lnQrxn (14.4.2)

(TD298:15K)

As an illustration of an application of the Nernst equation, consider the reaction equation

H 2 .g/C2 AgCl.s/!2 HC.aq/C2 Cl.aq/C2 Ag.s/

This reaction takes place in a cell without liquid junction (Fig.14.1), and the electrolyte
solution can be aqueous HCl. The expression for the reaction quotient is

QrxnD

a^2 Ca^2 a^2 Ag

aH 2 aAgCl^2

(14.4.3)

We may usually with negligible error approximate the pressure factors of the solids and
solutes by unity. The activities of the solids are then 1, the solute activities areaC D

(^) CmC=mandaD (^) m=m, and the hydrogen activity isaH 2 DfH 2 =p. The ion
molalitiesmCandmare equal to the HCl molalitymB. The expression forQrxnbecomes
QrxnD
(^) C^2 ^2 .mB=m/^4
fH 2 =p

D

(^) ^4 .mB=m/^4
fH 2 =p

(14.4.4)

and the Nernst equation for this cell is

Ecell, eqDEcell, eq 

RT

2F

ln

(^) ^4 .mB=m/^4
fH 2 =p
DEcell, eq

2RT

F

ln (^) 

2RT

F

ln

mB

m

C

RT

2F

ln

fH 2

p

(14.4.5)

By measuringEcell, eqfor a cell with known values ofmBandfH 2 , and with a derived value

ofEcell, eq, we can use this equation to find the mean ionic activity coefficient (^) of the HCl
solute. This is how the experimental curve for aqueous HCl in Fig.10.3on page 296 was
obtained.
We can always multiply each of the stoichiometric coefficients of a reaction equation
by the same positive constant without changing the meaning of the reaction. How does
this affect the Nernst equation for the reaction equation above? Suppose we decide to
multiply the stoichiometric coefficients by one-half:
1
2 H^2 .g/CAgCl.s/!H
C.aq/CCl.aq/CAg(s)
With this changed reaction equation, the value ofzis changed from 2 to 1 and the
Nernst equation becomes
Ecell, eqDEcell, eq
RT
F
ln
(^) ^2 .mB=m/^2
.fH 2 =p/1=2
(14.4.6)