Page 49 - Handbook of Battery Materials

1.3 Thermodynamics 15

For the Daniell element under standard conditions T = 298 K
Zn + CuSO 4 −→ ZnSO 4 + Cu

Reaction enthalpy H =−210.1kJ mol −1
Entropy S =−7.2JK −1 mol −1
Reaction free energy G = H − T · S
−1
G =−208 kJ mol
−1
Faraday constant F = 96 485 C mol
Number of exchanged electrons z = 2
−1
G kJ mol
Cell voltage ε 00 =−
z·F −1
Cmol
ε 00 = 1.1V

1.3.3
Concentration Dependence of the Equilibrium Cell Voltage

It is established from the chemical thermodynamics that the sum of the chemical
potentials µ i of the substances ν i involved in the gross reaction is equal to the
reaction free energy.

G = ν i · µ i (1.9)
Here ν i are the stoichiometric factors of the compounds used in the equation for
the cell reaction, having a plus sign for the substances formed and a negative sign
for the consumed compounds.
As a result of the combination of Equations 1.8 and 1.9, the free reaction enthalpy
G and the equilibrium cell voltage ε 00 under standard conditions are related to
the sum of the chemical potentials µ i of the involved substances.
G 1
− = ε 00 = ν i · µ i (1.10)
z · F z · F
Earlier it was shown that the equilibrium cell voltage ε 00 is equal to the difference
of the equilibrium potentials of its half cells, for example, for the Daniell element:
2+
ε 00 = ε 00, Cu/Cu 2+ − ε 00, Zn/Zn (1.11)
The chemical potential of one half cell depends on the concentrations c i of the
compounds, which react at the electrode:

(1.12)
µ i = µ i,0 + R · T · ln c i
−1
−1
R = universal gas constant: 8.3 J·mol ·K .
As a consequence, the equilibrium potential of the single half cell also depends
on the concentrations of the compounds. The NERNST equation (Equation 1.13),