Environmental Engineering Reference
In-Depth Information
This equation permits the calculation of the equilibrium cell potential E
eq
from
the change of free energy associated with a redox reaction for a given temperature.
If the pair oxygen-water in acidic solution is considered against the reference
pair, the following semi-reactions can be written:oxidation of hydrogen at the
anode:
H
2
2H
þ
þ
2e
E
a
¼
0V
ð
3
:
11
Þ
reduction of oxygen at the cathode:
1
2
O
2
þ
2H
þ
þ
2e
H
2
O
E
c
¼
1
:
23 V
ð
3
:
12
Þ
therefore the over all redox reaction is:
H
2
þ
1
E
¼
1
:
23 V
2
O
2
H
2
O
ð
3
:
13
Þ
which is the spontaneous reaction occurring in fuel cells using hydrogen as fuel.
The value of E = 1.23 V for the cell of the reaction (
3.13
) can be calculated from
Eq.
3.10
, with the change in free energy at 25C and 1 atm DG =-237.2 kJ/mol,
n = 2, F = 96.485 Coulombs/electron-mol. It represents the theoretical potential
for the electrochemical cell based on reaction (
3.13
), or also the reversible open-
circuit voltage of the cell, at 25C and atmospheric pressure.
Equation
3.8
gives the maximum amount of useful work (electricity) obtainable
at the outlet of the electrochemical converter, whereas the amount of energy
entering the converter is given by the chemical energy contained in chemical
substances providing the electron flow. For hydrogen fuel cells this energy corre-
sponds to the enthalpy variation of the reaction (
3.13
)(DH), also called the
hydrogen's heating value, defined as the difference between the heats of formation
of products and reactants. At 25C and atmospheric pressure, water is in liquid
form, and in these conditions its heat of formation is -286 kJ/mol, whereas for
vapor water is 242 kJ/mol, the difference being the heat of evaporation of water at
25C (44 kJ/mol). As heat of formation of elements is by definition equal to zero,
the enthalpy of reaction (
3.13
) results to be -286 kJ/mol if the produced water is
considered in the liquid state (higher heating value of hydrogen, DH
HHV
), and -
242 kJ/mol if vapor water is obtained as product at 25C(lower heating value of
hydrogen, DH
LHV
). The negative sign for DH means, by convention, that heat is
released by the reaction (exothermic reaction).
While hydrogen heating value can be used as a measure of energy input in a
fuel cell, the creation of entropy, which accompanies every spontaneous chemical
reaction, is regarded as a measure of irreversible losses which limit the amount of
useful work obtainable from the fuel cell, according to the second principle of
Thermodynamics. The fraction of hydrogen enthalpy which can be transformed
into electric work in a fuel cell is then given by the following equation:
DG
¼
DH
TDS
ð
3
:
14
Þ
