Thermodynamics and Chemistry

CHAPTER 14 GALVANIC CELLS

14.6 STANDARDELECTRODEPOTENTIALS 466

 Cell 3 has the hydrogen electrode at the left and electrode R at the right; its standard

cell potential is the standard electrode potentialERof electrode R.

We wish to calculate the standard cell potentialEcell, eq of cell 1 from the standard electrode
potentialsELandER.
If we write the cell reactions of cells 1 and 2 using the same value of the electron number
zfor both, we find that their sum is the cell reaction for cell 3 with the same value ofz. Call
these reactions 1, 2, and 3, respectively:

(reaction 1)C(reaction 2)D(reaction 3) (14.6.1)

The relation of Eq.14.6.1shows that an infinitesimal advancement dof reaction 1
combined with an equal advancement of reaction 2 causes the same changes in amounts as
the advancement dof reaction 3. BecauseÅrGfor each reaction is the rate at whichG
changes withat constantTwhen the reactants and products are in their standard states,
the following relation applies when the reactions take place at the same temperature:

ÅrG(reaction 1)CÅrG(reaction 2)DÅrG(reaction 3) (14.6.2)

Making the substitutionÅrGD zFEcell, eq (Eq.14.3.15), with the same value ofzfor
each reaction, gives usEcell, eq CELDER, or

Ecell, eq DEREL (14.6.3)

whereEcell, eq ,ER, andELall refer to cell 1.
Equation14.6.3is a general relation applicable to any galvanic cell. It should be appar-
ent that we can use the relation to calculate the standard electrode potential of an electrode
from the standard electrode potential of a different electrode and the standard cell potential
of a cell that contains both electrodes. Neither electrode has to be a hydrogen electrode,
which is difficult to work with experimentally.
Using Eq.14.6.3to calculate standard cell potentials from standard electrode potentials
saves a lot of experimental work. For example, measurement ofEcell, eq for ten different
cells, only one of which needs to include a hydrogen electrode, provides values ofEfor
ten electrodes other thanED 0 for the hydrogen electrode. From these ten values ofE,
values ofEcell, eq can be calculated for 35 other cells without hydrogen electrodes.