Page 31 - Battery Reference Book

1/16 Introduction to battery technology

only the e.m.f. of a cell, made by combining two elec- the electrode when all the substances concerned are in
trodes, that can be determined experimentally. How- their standard states of unit activity. The qualification
ever, by choosing an arbitrary zero of potential, it is 'oxidation' is used because it describes the process tak-
possible to express the potentials of individual elec- ing place at the electrode; the corresponding 'reduction
trodes. The arbitrary zero of potential is taken as the potentials' will be considered below.
potential of a reversible hydrogen electrode, with gas at The application of Equation 1.34 may be illustrated
1 atm. pressure, in a solution of hydrogen ions of unit by reference to a few simple cases of different types.
activity. This particular electrode, namely H2 (1 atm.) Consider, first, an electrode consisting of a metal in
H+ (a = 1), is known as the standard hydrogen elec- contact with a solution of its own cations, e.g. copper
trode. The convention, therefore, is to take the potential in copper (cupric) sulphate solution. The electrode
of the standard hydrogen electrode as zero; electrode (oxidation) reaction is
potentials based on this zero are said to refer to the
hydrogen scale. If any electrode, M, M', is combined cu = CU~' + 2e
with the standard hydrogen electrode to make a com- the Cu being the reduced state and Cu2+ the oxidized
plete cell, i.e.
state; in this case n is 2, and hence by Equation 1.34
M 11 M+(soln) H+(a = 1) 11 Hz(l atm.)
E 0
the e.m.f. of this cell, E, is equal to the potential of The activity of acu of the solid metal is unity, by
the M, M+ electrode on the hydrogen scale. convention, and hence
When any reversible electrode is combined with a
RT
standard hydrogen electrode, as indicated above, and E = E!~ - - Inacuz+ (1.35)
oxidation reaction takes place at the former, while the 2F
hydrogen ions are reduced to hydrogen gas at the latter. so that the electrode potential is dependent on the
The electrode (oxidation) process may be written in the standard (oxidation) potential E:, of the Cu, Cu2+
following general form: system, and on the activity acu2+ of the cupric ions
Reduced state = Oxidized state + ne in the copper sulphate solution. The result may be
generalized, so that for any metal M (or hydrogen) in
and the corresponding hydrogen electrode reaction is equilibrium with a solution of its ions M' of valence
n, the oxidation potential of the M, M+ electrode is
nH+ +ne = inHz(g) given by
The complete cell reaction for the passage of n fara- RT
days is consequently E = E:] - - InaM+
nF
Reduced state + nH+ = Oxidized state + $nHz(g) (1.32) At 25"C,
The e.m.f. of the cell, which is equal to the potential 0.059 15
of the reversible electrode under consideration, is then E=Eo el -~ log aM+ (1.36)
given by Equation 1.29 as where aM+ is the activity of the M+ ions in the
(Oxidized state) x a:; 1 (1.33) solution. For a univalent ion (e.g. hydrogen, silver,
cuprous), n is 1; for a bivalent ion (e.g. zinc, nickel,
(Reduced state) x a;- ferrous, cupric, mercuric), n is 2 and so on.
where parentheses have been used to represent the Similarly, the general equation for the oxidation
activities of the oxidized and reduced states as they potential of any electrode reversible to the anion A-
actually occur in the cell. In the standard hydrogen of valence n is
electrode, the pressure of the gas is 1 atm., and hence RT
the activity aH2 is unity; furthermore, by definition, the E = Efl + - lnaA-
nF
activity of the hydrogen ions UH+ in the electrode is
also unity. It can thus be seen that Equation 1.33 for At 25T,
the electrode potential can be reduced to the simple E = E:l + 0.059 15 log a*- (1.37)
form
(Oxidized state) where UA- is the activity of the A- ions in the given
E = E:~ - - I (1.34) electrode solution. It should be noted, in compar-
In
nF [ (Reduced state)
RT
ing Equations 1.36 and 1.37 that in the former, for
This is the general equation for the oxidation potential cations, the second term is preceded by a negative
of any reversible electrode; E:, is the corresponding sign, whilst in the latter, for anions, the sign is pos-
standard electrode potential; that is, the potential of itive. To make practical use of the electrode potential