Physical Chemistry , 1st ed.

This means that the activity of Fe^3 is

aFe^3 0.0442 

0

1

.1

.0

0

0

0

m

m

o

o

l

l

a

a

l

l

0.00442

Similarly, we can calculate that the activity coefficient for Cu^2 is

Cu^2 0.308

Therefore, the activity for Cu^2 is

aCu^2 0.308 

0.

1

0

5

0

0

0

0

m

m

o

o

la

l

l

al

0.0154

Using activities instead of concentrations, we find that

E0.379 V ln 

(

(

0

0

.0

.0

0

1

4

5

4

4

2

)

)

3

2



E(0.379 0.00718) V 0.372 V

Surely, the difference in the two calculated Evalues is not a large difference

in voltages. But it is an easily measurable one, and for precise measurements

the difference can have a big impact on the predicted properties of the ionic

solution. For example, it is necessary to consider activity factors when using

pH and other ion-selective electrodes, because the exact voltage of the electro-

chemical cell that is made in the course of the measurement is dependent on

the activity of the ions involved, not their concentration. Activity, like fugacity,

is a more realistic measure of how real chemical species behave. For precise cal-

culations, activity must be used for ionic solutions, not concentration.

8.8 Ionic Transport and Conductance

One additional property that solutions of ionic solutes have and solutions of

non-ionic solutions don’t is that ionic solutions conduct electricity. The word

electrolyteis used to describe ionic solutes, for that reason. (The word nonelec-

trolyteis used to describe those solutes whose solutions do not conduct elec-

tricity.) This property of electrolytes had deep ramifications in the basic un-

derstanding of ionic solutions, as demonstrated by Svante Arrhenius in 1884.

Arrhenius (Figure 8.9) actually proposed in his doctoral thesis that electrolytes

are compounds composed of oppositely charged ions that separate when

they dissolve, thereby allowing them to conduct electricity. He passed with

the lowest possible grade. However, with the increasing evidence of the elec-

trical nature of atoms and matter, he was awarded the third Nobel Prize in

Chemistry, in 1903, for his work.

The conductivity of ionic solutions is due to movement of both cations and

anions. They move in opposite directions (as might be expected), and so we

can consider a current due to positive ions,I , and a current due to negative

ions,I. If we consider the current as the change in the amount of ions pass-

ing through a cross-sectional area Aper unit time, as shown in Figure 8.10,

then we can write the current as

I 

q

t

^

I 

q

t

^

(8.314 moJlK)(298 K)

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

234 CHAPTER 8 Electrochemistry and Ionic Solutions

Figure 8.9 Svante Arrhenius (1859–1927), a

Swedish chemist who laid the groundwork for the

understanding of ionic solutions. Although he

barely passed his doctoral examination, this same

work won him a Nobel Prize in Chemistry.

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