The oxidation and reduction electric potential terms do notcancel from
equation 8.16. The electric potential of An^ is not going to be the same as the
electric potential from Bn^. (Consider the following comparison. Will the elec-
tric potential of an Li^ ion be the same as that for a Cs^ ion only because they
have the same charge? Of course not. Li^ has completely different properties
from Cs^ .)
Rearranging equation 8.16:nF (^) ox nF (^) redAn^ B
A
Bn^
nF( (^) ox (^) red) An^ B
A
Bn^
By convention, we rewrite the left side of the equation by substituting
( (^) red (^) ox) for ( (^) ox (^) red):
nF( (^) red (^) ox) An^ B
A
Bn^ (8.17)
All of the terms on the right side of equation 8.17 are constant for a given
state (pressure, temperature, and so on) of a system. Therefore, the entire right
side of equation 8.17 is a constant. This means that the left side of equation
8.17 must be constant, also. The variables nand Fare constants for the chem-
ical reaction. Therefore, the expression ( (^) red (^) ox) must also be a constant
for the reaction.
We define the electromotive force, E, as the difference between the reduction
reaction’s electric potential and the oxidation’s electric potential:
E (^) red (^) ox (8.18)
Because values are expressed in units of volts, electromotive forces are ex-
pressed in units of volts. The letters EMF are sometimes used to stand for
electromotive force. EMFs are not true “forces” in the scientific sense. Rather,
they are changes in electric potential.
Equation 8.17 becomes
nFEAn^ B
A
Bn^ (8.19)
Now consider the right side of equation 8.19. It is the chemical potential of
the products minus the chemical potential of the reactants. This equals the
change in the Gibbs free energy of the reaction,rxnG. Equation 8.19 can be
rewritten as
rxnG
nFE (8.20)
Under standard conditions of pressure and concentration, this is
rxnG°
nFE° (8.21)
This is the basic equation for relating changes in electric potential with changes
in energy. This equation also takes advantage of the definition that 1 J 1 VC.
The variable nrepresents the number of moles of electrons that are transferred
in the balanced redox reaction. Because completed redox reactions do not usu-
ally show the balanced number of electrons explicitly, we might have to figure
this out from the redox reaction itself.
Example 8.2
a.What is the number of electrons transferred in the course of the following
simple redox reaction?
2Fe^3 (aq) 3Mg (s) →2Fe (s) 3Mg^2 (aq)
212 CHAPTER 8 Electrochemistry and Ionic Solutions