Page 53 - Handbook of Battery Materials

1.3 Thermodynamics 19

For a hydrogen/oxygen fuel cell at standard conditions, T = 298 K and
p = 101.3 kPa, where

cell reaction is 2 H 2 + O 2 → 2H 2 O
standard potential (oxygen) ε 00 =+1.23 V
standard potential (hydrogen) ε 00 = 0V
standard cell voltage ε 00 =+1.23 V vs NHE
For the anode ε 0 = ε 00 + R·T = 1.23 + 0.03 V
n·F ln p O 2
ε 0 = 1.26 V
For the cathode ε 0 = ε 00 − R·T ln p 2 = 0 − 0.06 V
n·F H 2
ε 0 =−0.06 V
ε 0 = 1.26 V − (−0.06 V) = 1.32 V
an increase in the pressure to 1013 kPa results in an increase in the standard
cell voltage of 0.09 V.

1.3.6
Overpotential of Half Cells and Internal Resistance

The potential of the electrode surface is determined using the Nernst equation
introduced in Section 1.3.3. In equilibrium, the currents in anodic and cathodic
direction are equal. If they are related to an electrode area, they are called exchange
current densities j 0 .

(1.27)
j a = j c = j 0

−2
j a,c represents anodic, cathodic current density (A cm ).
If a current flows, for example, while discharging a battery, a shift in the potential
of the single half cell is measured. This deviation is called overpotential, η [12].
Thus, the real potential ε real has to be calculated using the following
equation:

ε real = ε 0 − |η| (1.28)
It is obvious that for a half cell the sum of the overpotentials should be as
low as possible. Depending on their origin, a distinction has to be made be-
tween:
• Charge transfer overpotential: The charge transfer overpotential is caused by
the fact that the speed of the charge transfer through the phase-boundary
electrode/electrolyte is limited. It generally depends on the kind of substances
that are reacting, the conditions in the electrolyte, and the characteristic of the
electrode (for example, what kind of metal). The formulae which deal with
this form of overpotential are called the Butler–Volmer equation and the Tafel
equation [10].