Concise Physical Chemistry

c14 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

FINDINGE◦ 227

The Nernst equation for this cell is

E=E◦−

RT

F

ln

aAgaH+aCl−

aAgClaH 2

(^12)
We can set three of these five activities equal to 1.0 because two of them refer to solids
AgCl(s)and Ag(s) and the other has an activityaH 2 = 1 .0 at a hydrogen pressure
of 1.0 atm (or 1.0 bar). The remaining activities areaH+aCl−=γ±mH+γ±mCl−=
γ±^2 mHCl^2 , provided that HCl is completely ionized (which it is) and there are no
other sources of H+or Cl−. Now the Nernst equation reads

E=E◦−

RT

F

lnaH+aCl−=E◦−

RT

F

lnγ±^2 mHCl^2

=E◦−

2 RT

F

lnγ±−

2 RT

F

lnmHCl

or

E+

2 RT

F

lnmHCl=E◦−

2 RT

F

lnγ±

The right-hand side of this equation approachesE◦asmapproaches zero because

γ±→ 1 .0. PlottingE+(2RT/F)lnmHClas a function ofmand extrapolating to

m=0 is appealing, but it is not quite the way the problem is solved. Debye–Huckel ̈

theory (Section 13.9) says that lnγ±=− 1. 171

√

μ ̃where, in this case, ̃μ=mnear

infinite dilution. Let us call the term on the leftE′for convenience in plotting, so that

E′=

(

E+

2 RT

F

lnmHCl

)

whereupon

E′=E◦−

2 RT(1.171)

F

m^1 /^2

Now we need only plotE′as a function ofm^1 /^2 to obtain an intercept ofE◦(Fig. 14.2).

The plot will yield a straight line with a slope of− 2 RT(1.171)/Fbut only in

the limit of infinite dilution. The extrapolation has been carried out with consid-

erable precision. It yields 0.22239 volts for the silver chloride–hydrogen cell and,

since the standard hydrogen electrode has a half-cell potential of zero by definition,

this is equal to the half-cell potential of the silver–silver chloride half-cell listed in

Table 14.1.