Page 46 - Battery Reference Book

Calculation of initial volume of sulphuric acid 1/31
i.e. 1553.4ml and the final acid concentration will be 21%
by weight sulphuric acid. Two faradays (193000C)
= 11.472ml __ - 87.176ml and AH(-93 458 cal) will have been evolved for the
loo
-
1.8035 1.1471
consumption of 2mol (196g) of sulphuric acid. If
(where 1.8035 and 1.1471, respectively, are the spe- when a battery of unknown capacity, C, is discharged
cific quantities of 100% and 21% by weight sulphuric from V1 ml of A% by weight to V2 ml of B% by weight
acid). Therefore sulphuric acid, and it is observed calorimetrically that
X calories are evolved, corrected for any ohmic (Joule
Volume or weight of water present heating) contribution (X has negative value as heat is
= 75.704mi or g per 87.176ml solution evolved), then if E, T and dEldT are known from
Equation 1.76:
= 86.840% W/V
c=- 4.18 x X
and r
L
3600 E-T (J
-
29 g 100% H2S04/100 ml solution
21 x 100 V1 and A will be known, so it is possible to calculate
- ~- = 24.089% W/V
-
87.176 V2 and B and hence the weights of sulphuric acid, lead
and lead dioxide consumed during the discharge.
If VI and VF, respectively, are the volumes (in ml) A more generalized approach to the calculation
of 29% by weight and 21% by weight sulphuric acid of the volume of sulphuric acid to introduce into a
present in the battery at the start and end of the lead-acid battery to optimize performance character-
discharge, istics is given in Section 1.16.
At start of discharge
1 .16 Calculation of initial volume of
100% by wt H2SO4 H20/100ml29% by wt H2S04 sulphuric acid
35.102g 80.824 g
The following calculation determines the initial vol-
Therefore ume of sulphuric acid of known weight concentration,
VI x 35.102 VI x 80.824 required at the start of discharge, to provide a pre-
100 100 determined final acid weight concentration after the
consumption in the cell reaction (i.e. at end of dis-
At end of discharge charge) of a predetermined weight of sulphuric acid. If
H20/100ml21% by wt H2S04 c - initial concentration (% wlw) sulphuric acid (at
24.089 g 86.840g
start qf discharge)
Therefore Cz = final concentration (% wlw) of sulphuric acid
(at end of discharge)
VF x 24.089 VF x 86.840 SI = relative density of sulphuric acid of
100 100 concentration C1
It is known that S2 = relative density of sulphuric acid of
concentration C2
VI x 35.012 __ VF x 24.089 = 96 glOO% H2S04 (2mol) S3 = relative density of concentrated (100% wlw)
100 100 sulphuric acid (= 1.8305)
and at the start of discharge we have Cl% H2SO4, Le.
VF x 86.8408 VI x 80.824
- = 36g water (2 mol) C1 g 100% H2SO4 per lOOg C1% HzS04
100 100
Solving for VI and VF, i.e.
VI = 1624.5ml
VF = 1553.4d
comprising
VI - VF = 71.1 ml volume reduction (theoretical)
mi
We can now completely define the battery. When A 100% H~SO~
1.8305
lmol of each of lead and lead dioxide in contact
with 1624.5ml 29% by weight sulphuric acid is dis- and
charged, then when the lead and lead dioxide are com-
'1
pletely reacted the final volume will have reduced to loo 1.8305 ml water
Si