Physical Chemistry , 1st ed.

b.If the standard change in the Gibbs free energy of the molar reaction in

part a is 1354 kJ, what is the difference between the reduction reaction’s

electric potential and the oxidation reaction’s electric potential?

Solution

a.The easiest way to determine the number of electrons transferred is to sep-

arate the individual oxidation and reduction processes. This is easily done:

2Fe^3 (aq) 6e^ →2Fe (s)

3Mg (s)→3Mg^2 (aq) 6e^

The two reactions show that 6 electrons are transferred in the course of the

balanced redox reaction. In molar units, there would be 6 moles of electrons

transferred.

b.Using equation 8.21 after converting the units on rxnG° to joules:

1,354,000 J

(6 mol e^ )96,485 

mo

C

le^

E°

E°2.339 V

The unit of volts follows from equation 8.7.

There is one thing to notice about the signs on the electromotive force.

Because Gis related to the spontaneity of an isothermal, isobaric process

(that is,Gis positive for a nonspontaneous process, negative for a sponta-

neous process, and zero for equilibrium) and because of the negative sign in

equation 8.21, we can establish another spontaneity test for an electrochemical

process. IfEis positivefor a redox process, it is spontaneous. IfEisnegative,

the process is not spontaneous. IfEis zero, the system is at (electrochemical)

equilibrium. Table 8.1 summarizes the spontaneity conditions.

Just because a redox reaction occurs doesn’t mean that anything electro-

chemically useful is happening. In order to get something useful from a redox

reaction (besides the chemical outcome), a redox reaction must be set up prop-

erly. But even if a redox reaction is set up properly, how much can we expect

to get out of the differences in the electric potentials?

The answer lies in the fact that E, the difference in electric potentials, is re-

lated to the change in the Gibbs free energy of the reaction, equation 8.21.

Furthermore, we showed in Chapter 4 that if some non-pressure-volume type

of work is performed on or by the system,Gfor that change represents a limit

to the amount of non-pVwork that can be performed:

Gwnon-pV

This was equation 4.11. Since electrical work is a type of non-pVwork, we can

state that

Gwelect (8.22)

Since work done bythe system has a negative numerical value, we can restate

equation 8.22 by saying that Gfor a redox reaction represents the maximum

amount of electrical work that the system can do on the surroundings.

How do we extract this work? Figure 8.2a shows a solution containing Cu^2

ions and some zinc metal. In Figure 8.2b, zinc has been added to the

solution. The colored Cu^2 ions have reacted to make solid Cu metal, while

8.3 Energy and Work 213

Table 8.1 A summary of spontaneity con-

ditions

IfGis IfEis Then the process is

Negative Positive Spontaneous

Zero Zero At equilibrium

Positive Negative Not spontaneous

Figure 8.2 (a) Zinc metal is added to a blue

solution containing Cu^2 ions. (b) The zinc has

reacted to make colorless Zn^2 ions and the blue

Cu^2 ions have reduced to Cu metal. Although a

redox reaction has occurred, no useful work has

been obtained from this physical system.

© Charles D. Winters