Physical Chemistry , 1st ed.

Applying Hess’s law, the overall Gvalue for the process is

G°overallG° (Rxn 1) G° (Rxn 2) 10,400 75,600 J

G°overall

68,500 J

Converting this into an equivalent Egives

68,500 J

(1 mol e^ )96,485 

mo

C

le^

E°overall

E°overall0.783 V

which is much closer to the number from the standard reduction potential
table. (The difference is related to the differing activities of the iron ions in the
solutions.) The key point is that electric potentials are strictly additive only if
the electrons cancel completely. However, energies are alwaysadditive.

Example 8.3

a.What is E° for the following unbalanced reaction?

Fe (s) O 2 (g) 2H 2 O () →Fe^3 4OH^

(The ultimate products are FeO(OH) and H 2 O, but they are formed by a

nonredox reaction. The hydrated FeO(OH) is what we know as rust.)

b.Balance the reaction.

c.What are the conditions of the above process?

Solution

a.With the help of Table 8.2, we find that the above reaction can be separated

into the two half-reactions

Fe (s) →Fe^3 3e^ E°0.037 V

O 2 (g) 2H 2 O () 4e^ →4OH^ E°0.401 V

We do not have to balance the reaction yet, since we can determine the over-

all E° value by combining the two E° values above. We get

E°0.438 V

The reaction is spontaneous, and actually represents a summary reaction for

the corrosion of iron.

b.Electrons must cancel in a balanced electrochemical (that is, redox) reac-

tion. Since the oxidation reaction involves three electrons and the reduction

reaction involves four, the lowest common multiple is 12 and we get

4Fe (s) 3O 2 (g) 6H 2 O () →4Fe^3 (aq) 12OH^ (aq)

as the balanced chemical reaction.

c.Because of the ° superscript on the E, we must assume that the following

conditions apply to the reaction: 25°C, a fugacity of 1 for O 2 and an activity

of 1 for Fe (s), H 2 O (), Fe^3 (aq), and OH^ (aq). [Again, these conditions

are usually approximated by 1 bar (or atm) pressure for the gaseous reactants,

and 1 M concentration for the aqueous, dissolved ions.]

As you might suspect, in real life the corrosion of iron does not occur at
standard conditions, especially standard conditions of concentration. We

8.4 Standard Potentials 217