Page 40 - Battery Reference Book

Effect of sulphuric acid concentration on e.m.f. in the lead-acid battery 1/25

electrons involved in the net chemical reaction, T the (3
temperature in kelvins, and R the gas constant (8.312 = 2 x 0.029 57 log
international ,joules).
By definitison, apbso4 = aH20 = apb = apb02 = 1. = 0.059 15 log (E)

(1.70) = 0.0169 V at 25°C
or, in general,
at 25°C 2 x 8.312 x (273 + T) x 2.303log(a,,/u,,)
E,, -E,, =
8.312 (273 + 25) x 2.203 2 x 96500
E=EO-
2 x 96500 = 0.000 1984(273 + T)log(a,,/a,)
= Eo - 0.029 57 log (7) where E,, is the e.m.f. at T"C when the acid has
1
(1.71) activity acl at the start of discharge, E,, is the e.m.f. at
H2S04 T"C when acid has activity a,, at the end of discharge,
and T is the cell temperature in "C. That is,
Consider the previously discussed case of a lead-acid
battery at the start and the end of discharge. At the start
of discharge the electrolyte contains 29% by weight
of sdphuric acid, i.e. molality = 4.17 and activity
coefficient = 0.202 (Table 1.3). Therefore, the activ- To ascertain the value of the standard potential Eo
ity is 0.202 x 4.17 = 0.842. Similarly, at the end of
discharge, the acid strength is 21% by weight, i.e. According to the literature, the e.m.f. of a cell contain-
m = 2.71 and y = 0.161, i.e. a = 0.436. ing 21% by weight (2.71 molal) sulphuric acid at 15°C
If the cell potentials at the start and end of discharge is 2.0100V.
are respectively by E29 and Ezl, then 2.303 x 8.312 x 288 1
E=EO- 2 x 96500
1
E29 = Eo - 0.029 57 log -
((0.842)') = Eo - 0.02856 x log (-) 1
= Eo - 0.004 40 V (0.436)'
1
-
and Eo = E + 0.02856 x log ( (0.436y )
0.029 57 log (-) 1 = 2.0100 + 0.02856 = 2.03059V
E21 =EO-
(0.436)2
E29(25"C) = 2.030 59 - 0.00440 = 2.0262 V
=Eo - 0.021 32V
and
Therefore the potential decrease (E29 - E211 during E21 (25°C) = 2.03059 - 0.021 32 = 2.0093 V
discharge is given by
These equations can be used to calculate the effect
E29 - E21 = -.0.00440 + 0.021 52V of sulphuric acid concentration (expressed as activity)
= 0.0169V at 25°C and cell temperature on cell e.m.f. If, for example,
the electrolyte consists of 29% by weight sulpharic
Alternatively acid at the start of discharge (i.e. activity a29 = 0.842)
decreasing to 21% by weight sulphuric acid @e. activ-
(2) ity a21 = 0.436) at the end of discharge, and if the tem-
E29 = Eo - 0.029 57 log perature at the start of discharge, TI, is 15°C increasing
M to 40"C(TF) during discharge, then from Equation 1.71
E21 = Eo - 0.029 57 log E29 = Eo - 8.312 x (273 + 15) x 2.303 log (&)
2 x 96500
where E29 is c.he cell e.m.f. at 25°C when the sulphuric and
acid concentration is 29% by weight, i.e. activity 8.312 x (273 + 40) x 2.303
a29 = 0.842, and E21 is the cell e.m.f. at 25°C when E21 = Eo -
the sulphuric acid concentration is 21% by weight, i.e. 2 x 96500
activity ~2~ = 0.436. If Eo = 2.0359 V,
E29 = 2.0263 V
E21 = 2.0082V