Thorsteinn I Sigfusson
The Taming of the Proton
Appendix VIII
A few fuel cell details.
The reactions in a fuel cell will involve an electron transferred according to the equation
H2 = 2H+ + 2e at the anode
O2 + 2H+ + 2e = H2O at the cathode.
The reversible standard potential for the H2/O2 reaction is 1.23 Volts (Eo) at room temperature. If the conditions are non standards, at different temperature T and partial pressure P of the different participating gasses, we have to use the so called Nernst Equation for calculating the potential.
For the standard cell reaction H2 + 1/2O2 = H2O , the potential E is usually written:
E = E0 + RT/nF ln (PH2)P(O2) 1/2/P (H2O),
Here R is the gas constant 8.314 Joule/molK, T temperature in Kelvin, F is Faraday’s constant 96.485 coulombs/mole of electrons, n is molecules per mole H2 (n=2 for the above reaction) E0 the standard reversible potential and the P´s refer to partial pressures of the participating gasses H2, O2 and H2O.
Temperature will affect the standard reversible potential in proportion to the entropy change of the reaction for H2O by the formula
Eo2 - Eo1 = DS/nF (T2 - T1).
Eo2 and Eo1 are reversible potentials at temperatures T2 and T1 respectively. DS is the entropy change (-163.2 J/K) for the H2/O2 reaction at 25°C and unit activity for liquid water product.
The performance
of a fuel cell can best be described in terms of its efficiency h
h = electrical power output (Pw)/fuel input Fw (both in watts).
The two figures appear on page 272 of the Philosophical
Magazine and Journal of Science, 1843, with William Grove's letter
"On the Gas Voltaic Battery." Grove undertook the series of thirty
experiments described in this letter when, "after my original publication
I received a letter from Dr. Schönbein [Christian F. Schönbein (1799-1868)] ...
[who] there expresses an opinion, that in the gas battery oxygen does not
immediately contribute to the production of current, but that it is produced by
the combination of hydrogen with water."