Page 52 - Handbook of Battery Materials

18 1 Thermodynamics and Mechanistics

From experiments it is possible to obtain the temperature coefficient for the
−1
Daniell element, ε 0 /T =−3.6 × 10 −5 VK :
temperature T = 298 K
equilibrium cell voltage ε 00 = 1.1V
Faraday constant F = 96 485 C mol −1
number of exchanged electrons z = 2

reaction enthalpy H = z · F · ε 00 + T · ∂ ε 0
∂T
p
H = 212.2kJmol −1

reaction entropy S = z · F · ∂ ε 0
∂ T
p
S =−2.1kJ K −1
free reaction enthalpy G =−z · F · ε 0
G =−208 kJ mol −1

The calculation of the free reaction enthalpy is possible with Equation 1.8, and
the determination of the reaction entropy S follows from Equation 1.22.

1.3.5
Pressure Dependence of the Equilibrium Cell Voltage

It is obvious that the cell voltage is nearly independent of the pressure if the
reaction takes place between solid and liquid phases where the change in volume
is negligibly low. On the other hand, in reactions involving the evolution or
disappearance of gases, this effect has to be considered [11].
The pressure dependence of the reaction free energy is equal to the volume
change associated with one formula conversion.

∂ G

= V (1.24)
∂p T
With G =−n × F × ε 0 and V =−RT/p we have

∂ ε 0 R · T 1
=− · (1.25)
∂p n · F p
T
By integration, the equilibrium cell voltage as a function of the partial pressure of
the solved gas (with the integration constant K equivalent to ε 00 [10]) is obtained:
R · T
ε 0 = K − ln p (1.26)
n · F
The following example of a hydrogen/oxygen fuel cell illustrates this relationship.