Physical Chemistry Third Edition

360 8 The Thermodynamics of Electrochemical Systems

The Nernst equation is

EE◦−

RT

2 F

ln(Q)

where

Q

1

P(Cl 2 )/P◦



P◦

P(Cl 2 )



100000 Pa

(0.965 atm)(101325 Pa atm−^1 )

 1. 0227

Exercise 8.3

FindEfor the cell at 298.15 K ifP(Cl 2 ) 0 .965 atm anda(Cl−) 0 .250. The value ofE◦is

1 .091 V.

If the cell reaction equation is modified by multiplying all of the stoichiometric

coefficients by the same constant, sayC, the Nernst equation is unchanged, becauseQ

will be raised to the powerC, while thendivisor in front of ln(Q) will be increased

by the same factorC, canceling the effect of the exponentC.

Exercise 8.4

Multiply the cell reaction equation in Eq. (8.2-4) by 1/2. Write the Nernst equation for the new

reaction equation and show that it is the same as Eq. (8.2-17).

Determination ofE◦Values

Using the Nernst equation,E◦for a cell can be calculated from a measured value

ofEif the activity coefficients are known. If the activity coefficients are not known

we can measureEat different concentrations and carry out an extrapolation to zero

concentration, since the activity coefficients approach unity in this limit. Consider the

cell of Figure 8.2. We keep the pressure of the hydrogen equal toP◦, and measure

Eat various molalities. We will use the augmented Debye–Hückel formula forγ±

in Eq. (6.4-30) to guide our extrapolation. For HCl, the ionic strength is equal to

the molalitymif no other electrolytes are present. If Eq. (6.4-30) is substituted into

Eq. (8.2-17) we obtain

EE◦+

2 RT

F

(

αm^1 /^2

1 +(m/m◦)^1 /^2

+bm−ln

(m

m◦

))

which can be rewritten

E+

2 RT

F

(

−

αm^1 /^2

1 +(m/m◦)^1 /^2

−ln

(m

m◦

))

E◦−

2 RT

F

bm (8.2-21)

The left-hand side of Eq. (8.2-21) contains only measurable quantities and known

constants. If this function is plotted as a function ofmthe plot should be linear in the

region nearm0, and extrapolation tom0 gives the value ofE◦. The slope of

the tangent line near the axis can be used to obtain a value of the parameterbsince

the slope is equal to 2RTb/F.