Fuel Cell Systems Explained, Second Edition

30 Fuel Cell Systems Explained
2.2 The Open Circuit Voltage of Other Fuel Cells and Batteries
The equation that we have derived for the OCV of the hydrogen fuel cell
E = −�g f
2F
can be applied to other reactions too. The only step in the derivation that was specific to
the hydrogen fuel cell was the ‘2’ electrons for each molecule of fuel, which led to the
2 in the equation. If we generalise it to any number of electrons per molecule, we have
the formula
E = −�gf [2.2]
zF
where z is the number of electrons transferred for each molecule of fuel.
The derivation was also not specific to fuel cells and applies just as well to other
electrochemical power sources, particularly primary and secondary batteries. For example,
the reaction in the familiar alkali battery used in radios and other portable appliances can
be expressed (Bockris, 1981) by the equation
2MnO2 + Zn → ZnO + Mn2O3
for which �g f is −277 kJ mol −1 . At the anode the reaction is
And at the cathode we have
Zn + 2OH − → ZnO + H 2 O + 2e −
2MnO 2 + H 2 O + 2e − → Mn 2 O 3 + 2OH −
Electrons flow from anode to
cathode
Thus, two electrons are passed round the circuit, and so the equation for the OCV is
exactly the same as equation 2.1. This gives
E =
2.77 × 105
2 × 96485
= 1.44 V
Another useful example is the methanol fuel cell, which we will look at later in Chapter
5. The overall reaction is
2CH3OH + 3O2 → 4H2O + 2CO2
with 12 electrons passing from anode to cathode, that is, 6 electrons for each molecule of
methanol. For the methanol reaction, �g f is −698.2 kJ mol −1 . Substituting these numbers
into equation 2.2 gives
E =
6.98 × 105
6 × 96485
= 1.21 V