Page 39 - Battery Reference Book

1/24 Introduction to battery technology

Table 1.4 Change of e.m.f. with concentration of electrolyte
Concentration, Activity Activity Ratio of Ratio Of E2 - E1(V)
m coeficient, a = ym concentrations activities n=2
(mol44 Y

0.2 molal HzSO4 0.2 0.244 2 1.56 0.005 71
diluted two-fold 0.1 0.313 0.03 1 3
0.2 molal HzSO4 0.2 0.244 0.048 8 } 10 4.70 0.019 9
diluted ten-fold 0.02 0.519 0.01038
2 molal H2SO4 2 0.147 0.294 } 2 1.96 0.008 64
diluted two-fold 1 0.150 0.150
2 molal H2SO4 2 0.147 0.294 } 10 6.02 0.023 0
diluted ten-fold 0.2 0.244 0.048 8

From Equation 1.68, EZ-El = 0.0; 15 log (0.600)
~
~
0.393
0.059 15 log (0.842)
EZ-El = ~ __ = 0.005 43 V
n 0.436
0.059 15 From 0.01 to 0.0154 molal
-
- log 1.931 15 log ( 0.0855 )
n 0.0;
E2-El = ~ 0.006 27
if n = 2, E2 - El, the potential change accompanying
an increase in the concentration of sulphuric acid from = 0.0418 V
2.71 to 4.17 molal, is 0.008 45 V at 25°C. For relatively
concentrated solutions of sulphuric acid, as in the case That is, when more dilute solutions and stronger solu-
of the example just quoted, the ratio of the activities tions are diluted by the same amount, the e.m.f. dif-
at the two acid concentrations is similar to the ratio of ference obtained with the former is greater than that
the molal concentrations: obtained with the latter.
The greater the concentration difference of the two
Molality of H2SO4, m 2.71 4.17 solutions, the greater the e.m.f. difference E2 - El, as
Activity coefficient of H2SO4, y 0.161 0.202 shown in Table 1.4.
Activity, a = ym 0.436 0.842
4.17 1.10 Effect of sulphuric acid
2.71 concentration on e.m.f. in the
Ratio of molalities = ~ = 1.54
0.842 lead -acid battery
Ratio of activities = __ -
0.436 - 1’93 For the reaction
i.e. the two ratios are fairly similar. For less con- Pb + PbO2 + 2HzS04 = 2PbSO4 + 2Hz0
centrated sulphuric acid solutions (0.01 molal and
0.0154 molal, i.e. in the same concentrations ratio as from the free energy (Equation 1.27),
the stronger solutions) these two ratios are not as sim-
ilar, as the following example illustrates:
Molality of H2SO4, m 0.01 0.0154
Activity coefficient of HzS04, y 0.617 0.555 as, from Equation 1.23,
Activity, a = ym 0.006 17 0.0855
AF = -nFE and AFo = -nFEo
0.1
0.01 we have
Ratio of molalities = ~ = 10.00
0.0855
- 1.38
0.006 17
Ratio of activities = ~ -
Potential changes at 25°C resulting from the same two-
fold change in concentration of sulphuric acid are as where a is the activity of sulphuric acid solution (my),
follows: m the concentration in moles per kilogram, y the
activity coefficient, Eo the e.m.f. in standard state, E
From 2.71 to 4.17 molal the cell e.m.f., F = 1 F (96 500 C), n the number of