Page 77 - Battery Reference Book

1/62 Introduction to battery technology
of the solution. With other electrodes, e.g. lead, a According to the Tafel relationship:
more negative potential is required to secure its lib-
eration. The difference between the reversible hydro- i = Ke-* (1.128)
gen potential and the actual decomposition potential where i is the current (A), b a constant characteristic
in the same solution is known as the hydrogen over- of the electrode, E the potential (V) of the cathode or
voltage of the metal. Approximate determinations of the anode, and a is a constant identified as
the hydrogen overvoltage can be made by observ-
ing the potential of the lead cathode when the cur- F
~
rent-voltage curve shows that appreciable electrolysis 2RT
is taking place, or by making the cathode very small where F = 96 500 C, R is the gas constant (1.987) and
and observing its potential when the first visible bub- T is the temperature (K).
bles of hydrogen occur. Hydrogen overvoltages in the Hence
range 0.36-0.64 V have been obtained by these meth-
ods at a lead cathode. i = kexp(-FE/2RT) (1.129)
Similar considerations apply in the case of liberation
of oxygen at the lead dioxide anode. The reversible Taking logarithms of Equation 1.129,
anode oxygen potential for the liberation of oxygen at FE
the lead dioxide anode is considerably more positive In i = constant - __ (1.130)
2xRT
than the value calculated from free energy data and is,
in fact, in the region 0.4-0.5 V. or
Although the decomposition potential of an aqueous FE
solution of sulphuric acid to produce hydrogen and log i = constant - 2 x 2.303 x RT (1.131)
oxygen is constant at about 1.7V with smooth plat- or
inum electrodes, due to the overvoltage phenomenon,
the value is different if other materials are employed as dE - 2 x 2.203 x RT (1.132)
electrode materials. If the cathode is lead and the anode d log i F
is platinum, for example, the decomposition potential
increases to about 2.2 V. Inserting values in Equation 1.132, at 18°C (291 K):
The decomposition voltage for the electrolysis of dE 2 x 2.303 x 1.987 x 291
sulphuric acid to hydrogen and oxygen is about 1.7 V - = 0.116V
and the hydrogen overvoltage at the cathode is 0.6 V; d log i 96 500
thus hydrogen does not start to be evolved in a Le. the cathode potential becomes 0.116V more neg-
lead-acid battery until the charging potential reaches ative for each ten-fold increase in the current and the
2.3 V. Similarly, the oxygen overvoltage at the anode anode potential becomes 0.116V more positive for
is 0.5 V; thus oxygen does not start to be evolved until each ten-fold increase in the current.
the charging potential reaches 2.2 V. In this sense, in a If E, denotes the e.m.f. of the cathode and i, the
lead-acid battery, the anode and cathode behave inde- current flowing, and E, denotes the e.m.f. of the anode
pendently of each other, each releasing oxygen and and i, the current flowing, then from Equation 1.1 3 1 :
hydrogen, respectively, as dictated by the electrode
e.m.f. log i, = c - FEC
During the discharge of a lead-acid battery the 2 x 2.303 x RT
following reactions occur: and
H2S04 = 2H' + SO:- logi, = C - FE,
2 x 2.303 x RT
1 At the positive electrode (anode):
then
PbOz + H2S04 + 2H' + 2e = PhS04 + 2H20
(1.133)
above 2.2 V (oxygen evolution):
At 18°C
PbOz + 2H' + 2e + SO:- = PhS04 + H20 + $02
ia
2. At the negative electrode (cathode): log 7 = 36.233(Ec - E,)
1,
Pb + SO:- = PbS04 + 2e Assume that E,, the e.m.f. of the cathode, is 2.3V
(hydrogen liberation) and assume a range of values of
above 2.3 V (hydrogen evolution): 2.2-2.35V for E,, the e.m.f. of the anode (oxygen
Pb + SO% + 2H' = PbS04 + HZ liberation), Le. the anode e.m.f. starts off being less
than and finishes up being greater than the cathode
During charge the above reactions occur in reverse. e.m.f.