Page 32 - Battery Reference Book

Single electrode potentials 1/17
equations it is necessary to insert values for R and is occurring. The situation is, fortunately, quite sim-
F in the factor RTInF which appears in all such ple; the reduction potential of any electrode is equal
equations. The potential is always expressed in volts, to the oxidation potential for the same electrode but
and since F is known to be 96 500 C, the value of R with the sign reversed. It is quite unnecessary, and
(R = 1.998 cal) must be in volt coulombs, i.e. in inter- in fact undesirable, to write out separate formulae for
national joules; thus R(1.998 x 4.18) is 8.314 absolute reduction potentials. The recommended procedure is to
joules or 8.312 international joules per degree per derive the oxidation potential for the given electrode
mole. Taking Equation 1.36 for the oxidation poten- and then merely to reverse the sign. For example, the
tial of an electrode reversible with respect to cations, reduction potential of the copper-cupric ion electrode,
that is for which the reaction is
cu2+ + 2e = cu

would be given by an equation identical to Equation
inserting the values of R and F given above, and intro- 1.35 but with the sign reversed.
ducing the factor 2.303 to convert natural logarithms To facilitate the representation of electrodes, a sirn-
TO common logarithms, i.e. to the base 10, the result is ple convention is adopted; when the electrode is a
metal M, and the process is oxidation to M+ ions,
2.303 x 8.312 T
E=E0---- log aMT the reduced state of the system is written to the left
96500 n and the oxidized state to the right. namely M, M', as
(1.38) in the electrochemical equation M + M+ + electrons.
Examples of oxidation electrodes are thus
At 25"C, i.e. T = 298.16K, which is the temperature CU, CU'+ (or CU, CUSO~ (solnj)
most frequently employed for accurate electrochemical
measurements, this equation becomes Zn, zn2+ (or Zn, ZnSo4 (soln))
0.059 15 The potentials of such electrodes are given by
E = E:l - ~ log aMt (1.39) Equation 1.34 or 1.36. On the other hand, if the elec-
Kl
trodes are represented in the reverse manner; i.e. ha',
Similarly, for the oxidation potential of an anion elec- M, with the oxidized state to the left and the reduced
trode at 25T, state to the right, e.g.
0.059 15
logq
E =E;, + ~- (1.40) cu2+, cu (or CUSO~ (solnj, CU)
Zn2+, Zn (or Z~SO~ (solnj, zn)
The general form of the equation at 25"C, which
is applicable to all reversible electrodes (see the electrode process is reduction, and the potentials
Equation 1.34) is are opposite in sign to those of the corresponding
0.059 15 (Oxidized state) oxidation electrodes.
E = E:l - ~ I (1.41) If two reversible electrodes are combined to form
n log [(Reduced state) such cells as
where the parentheses are used to indicate activities. ~n I ~n~04(solnj CuSO4 (soh) 1 Cu
It should be evident from the foregoing examples
that it is not a difficult matter to derive the equation then, in accordance with the convention given above,
for the oxidation potential of any electrode; all that is the reaction at the left-hand electrode is oxidation,
necessary is to write down the electrode reaction, and while at the right-hand electrode a reduction process
then to insert the appropriate activities of the oxidized is taking place when the cell operates spontaneously
and reduced states in Equation 1.34. The result is to produce current upon closing the external circuit.
then simplified by using the convention concerning the Thus, the e.m.f. of the complete cell is equal to the
standard states of unit activity. Thus, for any metal algebraic sum of the potentials of the two electrodes,
present in the pure state, for any pure solid compound, one being an oxidation potential and the other a reduc-
for a gas at 1 atm. pressure, and for water forming tion potential. An important point to which attention
part of a dilute solution, the activity is taken as unity. may be called is that since the e.m.f. of a cell is equal
The corresponding activity factors may then be omitted to the sum of an oxidation and a reduction electrode
from the electrode potential equation. potential, it is equivalent to the difference of two oxi-
It has been seen that, in every galvanic cell, oxida- dation potentials. As a consequence, the e.m.f. of a cell
tion occurs at one electrode, but a reduction process is independent of the arbitrary notential chosen as the
takes place at the other electrode. The equations just zero of the potential scale; the actual value; whatever
derived give the potential of the electrode at which it may be, cancels out when taking the difference of
oxidation occurs, and now reference must be made the two oxidation potentials based on the same (e&
to the potential of the electrode at which reduction hydrogen) scale.