Physical Chemistry Third Edition

358 8 The Thermodynamics of Electrochemical Systems

We can now write

2 FE◦−∆G◦−RTln(Q) (8.2-11)

where

∆G◦ 2 μ◦(HCl)+ 2 μ◦(Ag)+μ◦(H 2 )+ 2 μ◦(AgCl) (8.2-12)

and whereQis theactivity quotient:

Qa(HCl)^2 a(Ag)^2 a(H 2 )−^1 a(AgCl)−^2 

a(HCl)^2 a(Ag)^2

a(H 2 )a(AgCl)^2

(8.2-13)

This quantity is the same as the activity quotient of Chapter 7. If the reaction takes

place outside of an electrochemical cell,Qwill tend toward its equilibrium value.

If the reaction takes place in an electrochemical cell,Qcan take on other values at

equilibrium. If a passive circuit is connected, the reaction will tend toward the same

equilibrium that would occur outside of the cell. If a counter voltage is applied by an

external circuit, the equilibrium state will depend on the value of the counter e.m.f.,

and at equilibriumEwill be equal to the counter e.m.f. If all substances are in their

standard states, all activities are equal to unity, andQis equal to unity. In this case we

obtain the important equation

E◦−

∆G◦

2 F

(for the example cell) (8.2-14a)

whereE◦is thestandard-state cell voltage. The version of Eq. (8.2-14a) that applies

to a general cell is

E◦−

∆G◦

nF

(for a general cell) (8.2-14b)

wherenis the number of electrons in the cell reaction equation. With this relation,

Eq. (8.2-11) becomes theNernst equationfor this cell:

EE◦−

RT

2 F

ln(Q)

(Nernst equation for

the example cell)

(8.2-15)

The Nernst equation is named for
Walther Hermann Nernst, 1864–1941,
the German physical chemist who was
mentioned in Chapter 3 for his work on
the third law of thermodynamics.
Since Ag and AgCl are both pure solids, their activities are nearly equal to unity
and can be omitted from the productQ. Treating hydrogen as an ideal gas and using
Eq. (6.3-37) for the activity of HCl in terms of molalities,

EE◦−

RT

2 F

ln

[(

γ(H+)^2 m(H+)^2 γ(C1−)^2 m(C1−)^2

m◦^4

)(

P(H 2 )

P◦

)− 1 ]

(8.2-16)

E◦−

RT

2 F

ln

(

γ±^4 (m/m◦)^4

P(H 2 )/P◦

)

(8.2-17)

where we assume thatm(H+) andm(Cl−) are both equal tom.