Physical Chemistry , 1st ed.

Solution

The expression for Qis

Q 

[

[

C

Zn

u

2

2

]

]



which is 0.00444/0.0333 0.133. Given that the voltage under standard con-

ditions,E°, is 1.104 V, we have

E1.104 V ln (0.133)

All of the units cancel except for the expression J/C, which equals the unit

volt. Solving:

E1.104 V ( 0.0259 V)

E1.130 V

This is slightly greater than the standard voltage.

The Nernst equation is very useful for estimating the voltage of electro-
chemical cells at nonstandard conditions of concentration or pressure. But
despite the fact that the Nernst equation contains temperature,T, as a variable,
it has limited use at temperatures other than 25°C, the common reference tem-
perature. That’s because E° itself varies with temperature. We can estimate how
E° varies with temperature by considering the following two expressions:

G°

nFE°



G

T



p


S or 

(



T

G)



p



S

Combining them, we find that



(

T

G°)



p


nF

E

T

°



p



S°

where we have now included the ° symbol on G,E, and S. Solving for the change
in E° with respect to the change in temperature (that is, E°/ T), we get



E

T

°



p





n

S

F

°

 (8.26)

The derivative ( E°/ T)pis called the temperature coefficientof the reaction.
Equation 8.26 can be rearranged and approximated as

E°



n

S

F

°

T (8.27)

where Tis the change in temperature from the reference temperature (usu-
ally 25°C). Keep in mind that this is the change in the EMF of a process, so the
new EMF at the nonreference temperature is

EE°E° (8.28)

These equations are approximations, but fairly good ones. We aren’t even consid-
ering the change in S° as the temperature changes—those can be substantial, as
we saw in previous chapters. But equations 8.26 and 8.27 do provide a rough

(8.314 moJlK)(298 K)



(2 mol e^ )(96,485 moCle^ )

m

m

Zn

°

2





m

m

Cu

°

2



8.5 Nonstandard Potentials and Equilibrium Constants 219