Page 75 - Battery Reference Book

1/60 Introduction to battery technology

that is, the displacement of hydrogen ions from solu- metal higher in Table 1.2 will displace from solution,
tion by metallic cadmium, is possible theoretically Le. reduce, the ions of a metal (or of hydrogen) lower
when all the substances are in their standard states. in the table of standard oxidation potentials.
This reaction would occur in the cell These conclusions are strictly applicable only when
the ions are all at unit activity. By changing the
CdljCdz+(a = l)IIHf(a = l)IIHz(l atm.) activity it is possible for a process to be reversed,
t0.402 0 particularly if the standard potentials of the systems
the standard e.m.f. of which is the same as the oxida- involved are not far apart. For example, copper should
tion potential of the cadmium electrode, i.e. +0.402V be unable to displace hydrogen ions from solution,
at 25°C. Since E:ell is positive, AFo is negative since the Cu, Cu2+ system has a lower oxidation
and the reaction should be capable of taking place potential than the H2, H+ system; this is true in so far
spontaneously; the actual value of the standard free as copper does not normally liberate hydrogen from
energy change could be determined, if required, from acid solution. However, if the concentration of the
Equation 1.124, using n = 2 for the cell reaction as cupric ions is decreased very greatly (for example, by
written above. the formation of complex ions), the oxidation potential
An illustration of another kind is provided by the is increased until it is greater than that of hydrogen
cell against hydrogen ions in the same solution. In these
circumstances, the displacement of hydrogen ions by
AgllAgC104(a = l)I/Fe(C104)2, Fe(C104)3(a = 1)IIPt metallic copper, with the evolution of hydrogen gas,
-0.799 -(-0.771) becomes possible.
Similar observations have been made in connection
in which the reaction is
with the Ag, Ag' and Fez+, Fe3+ systems; as seen
Ag(s) + Fe3+ = Ag' + Fez+ above, if all the substances are in their standard states
of unit activity, the spontaneous reaction should be the
for the passage of 1F. The standard oxidation potential reduction of silver ions to metallic silver by ferrous
of the left-hand (Ag, Ag+) electrode is -0.799V, ions, as is actually the case. The standard oxidation
while the reduction potential of the right-hand (Fez+, potentials of the two systems are not very different,
Fe3+, Pt) electrode is -(-0.771), i.e. +0.771V although that of the Fez+, Fe3+ system is the higher.
(Table 1.2). The standard e.m.f. of the cell depicted Although the standard potentials provide some indi-
is thus -0.799 + 0.771 - 0.028V; since Eocell is cation, therefore, of the direction in which a particular
negative, AFo is positive, and the reaction as written reaction may he expected to proceed spontaneously,
will not occur spontaneously for the reactants and especially if the potentials are appreciably different for
products in their standard states. For the reverse the two systems involved, the results may sometimes
reaction, however, AF' will be negative, so that the be misleading. The real criterion, which is always sat-
process isfactory, is that the e.m.f. of the actual cell, i.e. E, with
the substances at the given activities, and not neces-
Fez' + Agf = Fe3+ + Ag(s) sarily EEel,, when the activities are all unity, should be
positive for the reaction to be spontaneous. In other
can be spontaneous if all the substances taking part are words, the actual oxidation potential of the left-hand
at unit activity. electrode must be greater algebraically than that of the
An examination of the foregoing results, or a general right-hand electrode if the reaction occurring in the
consideration of the situation, will reveal the fact that cell is to proceed spontaneously.
the standard e.m.f. of a cell is positive when the
standard oxidation potential of the left-hand electrode
is greater algebraically than the standard oxidation 1.23.3 Equilibrium constants
potential of the right-hand electrode; that is, when
the former lies above the latter in Table 1.2. When For many purposes it is more convenient to calculate
this is the case, the cell reaction will be capable of the equilibrium constant of a reaction, instead of the
occurring spontaneously, oxidation taking place at the free energy change; this constant provides the same
left-hand side and reduction at the right-hand side. It information from a slightly different viewpoint. The
follows, therefore, that any system in Table 1.2 should equilibrium constant is related to the standard free
he able, theoretically, to reduce any system lying below energy change by Equation 1.117, namely
it in the table, while it is itself oxidized, provided all
the substances concerned are in their standard states AFo = -RTlnK
of unit activity. Thus, as seen above, zinc (higher in
the table) reduces cupric ions to copper (lower in the and since AFo is equal to -nFE:e,l, by Equation 1.124
table), while it is itself oxidized to zinc ions; similarly, it follows that:
cadmium reduces hydrogen ions to hydrogen gas, and RT
is itself oxidized to cadmium ions. In general, any = - 1nK (1.125)
nF