Page 21 - Battery Reference Book

1/6 Introduction to battery technology

this objection does not apply has been obtained by or the potential difference is
thermodynamic processes.
nF (2)
RT
In an alternative approach to the calculation of V=V1-V2=-ln (1.9)
electrode potentials and of potential differences in
cells, based on concentrations, it is supposed that two i.e.
pieces of the same metal are dipping into solutions
RT
RT
in which the metal ion concentrations are rnl and m2 V1 = -1nml and V2 = -1nm2 (1.10)
respectively (Figure 1.3). nF nF
Let the equilibrium potential differences between the i.e.
metal and the solutions be V1 and V2. Suppose that the
RT
two solutions are at zero potential, so that the electrical V=-ln- ml (1.11)
potentials of the two pieces of metal are V1 and V2. nF m2
We may now carry out the following process:
Inserting values for R, T(25"C) and F and
1. Cause one gram-atom of silver ions to pass into converting from napierian to ordinary logarithms,
the solution from metal 1. Since the equilibrium 2.303 x 1.988 x 298.1 x 4.182
potential is established at the surface of the metal, V= n x 96490
the net work of this change is zero.
2. Transfer the same amount (lmol) of silver ions (1.12)
reversibly from solution 1 to solution 2. The net
work obtained is
From Equation 1.5 the electrical potential (V) of a
w' = RT In m1Imz (1.6) metal with respect to the solution is given by
provided that Henry's law is obeyed. v = nF1n ($)
-RT
3. Cause the gram-atom of silver ions to deposit (1.5)
on electrode 2. Since the equilibrium potential is
established, the net work of this change is zero. where P is the electrolytic solution pressure of the
4. Finally, to complete the process, transfer the metal and p is the osmotic pressure of metal ions.
equivalent quantity of electrons (charge nF) from For two different metal solution systems, 1 and 2, the
electrode 1 to electrode 2. The electrical work electrical potentials VI and V2 are given by
obtained in the transfer of charge -nF from
potential V1 to potential V2 (i.e. potential difference
= V1 - V2), for metal ions of valency n when
each gram-atom is associated with nF units of
electricity, is

- nF(V1 - Vz) (1.7)
Therefore
The system is now in the same state as at the
beginning (a certain amount of metallic silver has been V1 - Vz = potential difference (V)
moved from electrode 1 to electrode 2, but a change
of position is immaterial). =Eln($)
nF
The total work obtained in the process is therefore
0.059
zero, i.e. = __ log (2) at 25°C (1.13)
n
-AF(V1 - V2) + RTln(ml/mz) = 0 (1.8)
Comparing Equations 1.12 and 1.13 it is seen that,
as would be expected, rnl 0: PI and m2 0: P2, i.e. the
V
concentrations of metal ions in solution (m) are directly
proportional to the electolytic solution pressures of the
metal (P).
Kinetic theories of the electrode process
A more definite physical picture of the process at
a metal electrode was given by Butler in 1924.
According to current physical theories of the nature
of metals, the valency electrons of a metal have
I I1 considerable freedom of movement. The metal may be
Figure 1.3 Calculation of electrode potential and potential supposed to consist of a lattice structure of metal ions,
difference together with free electrons either moving haphazardly