to include the change in work due to the electric charges. We get
dG
S dT V dp (^)
0
i
idni (^)
0
i
(^) iziFdni (8.11)
Under conditions of constant temperature and pressure, this equation becomes
dG
0
i
idni (^)
0
i
(^) iziFdni
which can be rearranged algebraically because both of the sums are summing
over the same index (the component i) and the same variable (the change in
amount,dni):
dG
0
i
(i (^) iziF) dni (8.12)
If we redefine the quantity inside the parentheses in equation 8.12 as i,el:
i,eli (^) iziF (8.13)
then we have
dG
0
i
i,eldni (8.14)
i,elis called the electrochemical potential,rather than the chemical potential.
For electrochemical equilibrium, the equation analogous to equation 5.4
(ii0) is
0
i
nii,el 0 (8.15)
This is the basic equation for electrochemical equilibrium.
Any reaction that involves a transfer of charge (that is, electrons) is an
oxidation-reduction reaction, or redoxreaction. Since an oxidation process
and a reduction process always occur together, let us adopt a Hess’s-law ap-
proach by considering each individual process independently, and then con-
sider the overall process as the sum of the two individual reactions. Species
A is being oxidized; the general chemical reaction can be represented as
A →An^ ne^
where species A has lost nelectrons, symbolized ne^. Species B is being re-
duced. The general chemical reaction for this can be represented as
Bn^ ne^ →B
The overall chemical reaction is
A Bn^ →An^ B
Keeping in mind that the nivalues are positive for the reactants and negative
for products, equation 8.15 becomes
0 An^ ,el B,el
A,el
Bn^ ,el
Using equation 8.13, and recognizing that we are requiring the same charge n
on the ionic species, we have
0 An^ B nF (^) red
A
Bn^ nF (^) ox (8.16)
where we are now labeling each as the potential from either the oxidation
reaction (“ox”) or the reduction reaction (“red”). Since the species A and B
have no charge, there is no electrical work term (that is, equation 8.10) on their
chemical potentials.
8.3 Energy and Work 211