Page 30 - Battery Reference Book

Single electrode potentials 1/15
In a reversible, isothermal process, w is the maxi- reaction as written occurs for the passage of n fara-
mum work that can be obtained from the system in the days, it follows from Equation 1.26 that AF, as given
given change. by Equation 1.27 or 1.28, is also equal to -nFE. Fur-
The quantity PAV is the work of expansion done thermore, if the e.m.f. of the reversible cell is Eo when
against the external pressure, and so -AF repre- all the substances involved are in their standard states,
sents the maximum work at constant temperature and the AFo is equal to -nFEo. Substituting these val-
pressure, other than that due to volume change. The ues for AF and AFo into Equation 1.28 and dividing
quantity w - PAV is called the net work and so the through by -nF, the result is
decrease -AF in the free energy of a system is equal
to the net work obtainable (at constant temperature RT
nF
and pressure) from the system under reversible con- E=E0--hQ, (1.29)
ditions. An important form of net work, since it does
not involve external work due to a volume change, is This expression is seen to relate the e.m.f. of a cell
electrical work; consequently, a valuable method for to the activities of the substances taking part; Eo, the
determining the free energy change of a process is standard e.m.f., is a constant for the given cell reaction,
to carry it out electrically, in a reversible manner, at varying only with the temperature, at 1 atmosphere
constant temperature and pressure. pressure.
By Equation 1.23, The foregoing results may be illustrated by reference
to the cell
AF == -nFE
iHz(g) + AgCl(s) = H+ t C1- t Ag(s)
where AF is the free energy increase, E the e.m.f. of a
reversible cell, nF the number of faradays associated for the passage of 1 F. The reaction quotient in terms
with the process occurring (F = 1 F), and of activities is

-AF
E=- (1.26)
nF
The free energy change accompanying a given reac- but since the silver and the silver chloride are present
tion depends on the concentrations or, more accurately, in the solid state, their activities are unity; hence
the activities, of the reactants and the products. It is
evident, therefore, that the e.m.f. of a reversible cell, in
which a particular reaction takes place when producing
current, will vary with the activities of the substances
present in the (cell. The exact connection can be readily Inserting this expression into Equation 1.29, with n
derived in the following manner. Suppose the general equal to unity, the e.m.f. of the cell is given by
reaction
(1.30)
aA + bB + . . . -+ 1L + mM + . . . F
occurs in a reversibie cell; the corresponding free The e.m.f. is thus seen to be dependent upon the
energy change is then given by the following equation activities of the hydrogen and chloride ions in the
solution of hydrochloric acid, and of the hydrogen gas
a'L x amM x . . . in the cell. If the substances taking part in the cell
AF = AFO + RTIn (1.27) behaved ideally, the activities in Equation 1.30 could
aaA x abB x . . .
be replaced by the corresponding concentrations of the
where aA, aB, . . . , aL, aM, ... now represent the hydrogen and chloride ions. and by the pressure of the
activities of A9 €3. . . . , L, M, . . .as they occur in the hydrogen gas. The resulting form of Equation 1.30.
reversible cell. If the arbitrary reaction quotient, in namely
terms of activities, is represented by the symbol Qa,
Equation 1.27 may be written as E=EO--II~ RT cH+ x cCI- (1.31)
F ( PHzR
AF = AFo + XT In Qa (1.28)
could be used if the solution of hydrochloric acid were
As before, AFo is the free energy change when all dilute and the pressure of the hydrogen gas low.
the substances taking part in the cell reaction are in
their standard states. 1.7 Single electrode potentials
If E is the e.m.f. of the cell under consideration
when the various substances have the arbitrary activi- There is at present no known method whereby the
ties aA, aB, . . . ~ aL, aM. . . . , as given above, and the potential of a single electrode can be measured; it is