20 Electrocatalysis and the splitting of water
This is formulated in equation 2.1 50.
Ucell =
��Gf
nF
(2.1)
where Ucell is the equilibrium potential also called reversible open circuit potential
of the cell, F is the Faraday constant (96485 C/mol) and n the number
of electrons transferred in the reaction. While this equation holds at standard
conditions, the change in Gibbs free energy for a reaction vary with temperature
and pressure. This variation can be calculated for the general reaction
jJ + kK ! mM as
Gf = G0f
�� RT ln(
aj
J ak
K
am
M
) (2.2)
where G0f
is the change in Gibbs free energy at standard conditions, R the
gas constant, T the temperature and a denotes reactant activity; a = P
P0
. P
is partial pressure and P0 the standard pressure, 1 atm. Combining equation
2.1 and 2.2 gives the Nernst equation which relates the reversible open circuit
potential to temperature and pressure (equation 2.3).
Ucell = U0
cell ��
RT
nF
ln(
aj
J ak
K
am
M
) (2.3)
With these equations it is possible to evaluate the minimum potential dierence
needed to run a non-spontaneous reaction in an electrochemical cell, or similarly
the maximum potential dierence generated by a spontaneous reaction. However,
the actual operating potentials, U of such cells are typically signicantly
dierent from Ucell. The components of the operating voltage are the following:
U = Ucell U
Ut (2.4)
In equation 2.4 "" should be "+" for power consuming cells where nonspontaneous
reactions are driven, whereas "��" should be used for power generating
cells. denotes the overpotential needed to drive the reaction when
current is owing due to non-ideal kinetics at the electrode interface. U
is
the loss of potential dierence due to resistance losses in the system and nally
Ut is the potential increase or decrease over time. Electrocatalysis deals with
decreasing by nding the best suited electrode material. The theoretical relation
between overpotential and current j is described in the Butler-Volmer
equation:
j = j0
h
exp
(1 �� )nF
RT
�� exp
nF
RT
i
(2.5)
In equation 2.5 j0 is the exchange current density and is a symmetry factor.
The exchange current density is a quantity that denes the current owing