When an electrochemical cell is operated under standard state conditions,
the free energy change of the reaction will be 
. Corresponding to
this will be a standard state cell potential, 
, related to by
Recall that the standard state condition for a solution is 1 M concentration, assuming ideal solution behavior.
Rather than tabulate standard cell potentials for all possible electrochemical
cells (a huge number), potentials for half cells (anode or cathode)
are tabulated. By combining these, all possible complete cells
can be constructed. We only need a rule for combining the
half-cell potentials. Consider the cell Cu|Cu 
||Ag 
|Ag.
We adopt the convention that each half cell reaction is written
as if it were a reduction reaction. Thus, for this cell, the
two half cell reactions are written as
Using this convention, there is a standard state half-cell potential
corresponding to each reaction: 
| 
and 
| 
. The free energy change for the
overall reaction would be obtained by adding twice the first reaction to
the reverse of the second reaction. The first reaction is the cathode
reaction, while the second is the anode reaction:
Since the above pertains to 2 moles of electrons, we can express this in terms of half-cell potentials:
Canceling the common factor of 
, the overall cell potential is
That is, the net cell potential is the difference between the cathode and anode half cell potentials, when each is written as a reduction reaction. Also, note that the cell potentials are not multiplied by the number of moles like the free energies are.
Since is related to the Gibbs free energy, absolute cell potentials
cannot be determined, only differences in cell potentials. Thus, we
need to define a reference cell potential, with respect to which all
other cell potentials are measured. The choice is that the half-cell reaction
Thus, for the Cu|Cu ||Ag |Ag cell, the cell potential is
where the half-cell potentials for the two half reactions are taken from the list in Appendix E of the book.
It is also possible to derive standard half cell potentials for half-cell reactions not tabulated. The relation is derived by adding the free energies, according to the usual rules. Suppose we wish to add the half-cell reactions:
to produce the overall half-cell reaction:
where it is assumed that m;SPMgt;n. The overall free energy change is
which can be rewritten as
But the free energy for the overall half-cell reaction is
Equating the two expressions shows that
Thus, for the half-cell reactions
which are combined to give the overall half-cell reaction
The half-cell potential for this reaction is, according to the formula
