Page 50 - Handbook of Battery Materials

16 1 Thermodynamics and Mechanistics

which is one of the most important electrochemical relations, expresses this [10]. It
results if Equation 1.12 is inserted into Equation 1.10 with regard to one half cell:
R · T
ε 0 = ε 00 + · ν i · ln c i (1.13)
z · F
For a metal-ion electrode the NERNST equation is
R · T c Me z+
ε 0 = ε 00 + · ln (1.14)
z · F c Me
and this is used in the following example for the calculation of the concentration
dependence of the zinc electrode.

For one half cell of the Daniell element at a temperature of T = 298 K
Zn −→ Zn 2+ + 2e −

−1
with the concentration c Zn 2+ = 0.1mol L
−1 −1
universal gas constant R = 8.3J · mol · K
Faraday constant F = 96 485 C · mol −1
number of exchanged electrons z = 2
standard potential vs NHE, ε 00 (Zn/Zn ) =−0.76 V
2+
c
R·T Zn 2+
ε 0 = ε 00 + · ln
z·F c Zn
ε 0 =−0.79 V
The variation of the concentration from 1 mol L −1 (standard condition) to
0.1 mol L −1 is related to a change in the potential of −0.03 V.

If the concentrations of the copper and zinc ions within a Daniell element are
known, the following cell voltage ε 0 results:

ε 00 = ε 0, Cu/Cu 2+ − ε 0, Zn/Zn 2+ (1.15)

1.3.4
Temperature Dependence of the Equilibrium Cell Voltage

The temperature dependence of the equilibrium cell voltage forms the basis to
determine the thermodynamic variables G, H, and S. The values of the
equilibrium cell voltage ε 00 and the temperature coefficient d ε 00 /dT, which are
necessary for the calculation, can be measured exactly in experiments.
The temperature dependence of the cell voltage ε 0 results from Equation 1.10
by partial differentiation at a constant cell pressure.

∂ ε 0 1 ∂ G
=− · (1.16)
∂T z · F ∂T
p p