Page 38 - Battery Reference Book

Influence of ionic concentration in the electrolyte on electrode potential 1/23

equation such as Zn”, Cd2+, Fez+, Cu2+, etc., the value of
RT n is 2, and hence the electrode potential changes by
El=EL---lna (1.63) 0.059 1512, i.e. 0.0296 V, for every ten-fold change of
nF ionic activity; a hundred-fold change, which is equiv-
As has been seen from Equation 1.54, alent to two successive ten-fold changes, would mean
an alteration of 0.059 15 V in the potential at 25°C. For
a=ym univalent ions, n is 1 and hence ten-fold and hundred-
fold changes in the activities of the reversible ions
where m is the molality of the solute (moles or gram- produce potential changes of 0.059 15 and 0.1183V,
ions per lOOOg solvent) and y is the appropriate respectively. The alteration of potential is not deter-
activity coefficient. Hence
mined by the actual ionic concentrations OI- activities,
RT but by the ratio of the two concentrations; that is, by
E1(Vj =EL -- - lnym the relative change of concentration. Thus, a change
nF
from 1 .O gram-ion to 0.1 gram-ion per litre produces
(1.64) the same change in potential as a decrease from
to 10-7gram-ions per litre; in each case the ratio of
If the solution is diluted to decrease the activity of the two concentrations is the same, namely 10 to 1.
the cations to one-tenth of its initial value, that is to An equation similar to Equation 1.67, but with a
say to O.lu, i.e. 0.1~ = y’rn’, the electrode potential negative sign, can be derived for electrodes reversible
becomes with respect to anions; for such ions, therefore, a ten-
fold decrease of concentration or activity, at 25T,
RT
Ez(Vj =EL -- - 1nO.la causes the oxidation potential to become 0.0594 151n V
nF
more negative. For reduction potentials, the changes
are of the same magnitude as for oxidation potentials,
- EL __ log 0, la (1.65)
-
n but the signs are reversed in each case.
To quote a particular example, the concentration of
i.e.
sulphuric acid in a fully charged lead-acid battery is
RT approximately 29% by weight (relative density 1.21)
E~(v) = E& - - y’m’
In
nF whilst that in a fully discharged battery is 21% by
0.059 15 weight (relative density 1.15).
n
= EL __ ~ log y’rn’ (1.66) Weight concentrations of 29% and 21 % of sulphuric
acid in water, respectively, correspond to molalities
The resulting change of potential is obtained by sub- (mol HzS04/1000 g water) of
tracting El from Ez: 21 x 1000
RT m= 98 x (100 - 21) = 2.71
Ez - E1(V) = -(lnO.la - lna)
nF
RT and
= -1n10 , 29 x 1000
nF m= 98 x (100 - 29) = 4.17
0.059 15
-~ log 10
-
n The activity coefficients (y) corresponding to m =
0.059 15 2.71 and m’ = 4.17 molal sulphuric acid are respec-
- (1.67) tively y = 0.161 and y’ = 0.202 (obtained from stand-
-
n
ard activity tables, see Table 1.3).
i.e. Hence the activities (pn) are
RT
EZ - EI(V) = -((In y’m’ - In ym) a = 0.161 x 2.71 = 0.436
nF
and
2a‘ = 0.202 x 4.17 = 0.842
(1.68) Hence, from Equation 1.64,
It can be seen, therefore, that at 25°C every ten- E~ =E;- 0‘059 l5 log 0.436
fold decrease in ionic activity or, approximately, in
the concentration of the cations results in the oxida- From Equation 1.65,
tion potential becoming more positive by 0.059 1% V,
where n is the valence of the ions. For bivalent ions, Ez=E;- 0‘059 l5 log 0.842