Page 48 - Handbook of Battery Materials

14 1 Thermodynamics and Mechanistics

membrane potential. Well-known examples are the sodium/potassium ion
pumps in human cells.

1.3.2
Reaction Free Energy ∆G and Equilibrium Cell Voltage ∆ε 00

Instead of measuring the equilibrium cell voltage ε 00 at standard conditions
directly, this can be calculated from the reaction free energy G for one
formula conversion. In this context one of the fundamental equations is the
GIBBS–HELMHOLTZ relation [7].

G = H − T · S (1.5)

For the electrochemical cell reaction, the reaction free energy G is the utilizable
electric energy. The reaction enthalpy H is the theoretical available energy, which
is increased or reduced by T · S. The product of the temperature and the entropy
describes the reversible amount of heat consumed or released during the reaction.
With tabular values for the enthalpy and the entropy it is possible to obtain G.
Using the reaction free energy, G, the cell voltage ε 0 can be calculated. First,
the number n of exchanged moles of electrons during an electrode reaction must
be determined from the cell reaction. For the Daniell element (see example below),
2 mol of electrons are released or received, respectively.

1mol Zn → 1 mol Zn 2+ + 2 mol e −
1 mol Cu → 1 mol Cu 2+ + 2mol e −

With the definition of the Faraday constant (Equation 1.3), the amount of charge
of the cell reaction for one formula conversion is given by the following equation:

Q = I · t = n · F (1.6)

With this quantity of charge, the electrical energy is

ε 00 · Q = ε 00 · n · F (1.7)
The thermodynamic treatment requires that during one formula conversion the
cell reaction is reversible. This means that all partial processes in a cell must
remain in equilibrium. The current is kept infinitely small, so that the cell voltage
ε and the equilibrium cell voltage ε 00 are equal. Furthermore, inside the cell no
concentration gradient should exist in the electrolyte; that is, the zinc and copper
ion concentrations must be constant in the whole Daniell element. Under these
conditions, the utilizable electric energy, ε 00 × z × F per mol, corresponds to the
reaction free energy G of the Galvanic cell, which is therefore given by

G =−z · F · ε 00 (1.8)