# During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 g mL^(-1) to 1.139 g mL^(-). Sulphuric acid of densi

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During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 g mL^(-1) to 1.139 g mL^(-). Sulphuric acid of density 1.294 g mL^(-1) is 39% by weight and that of density 1.139 g mL^(-1) is 20% by weight. The battery hold 3.5 litre of acied and discharge. Calculate the no. of ampere hour for which the battery must have been used. The charging and discharging reactions are:
Pb+SO_(4)^(2-) rarr PbSO_(4)+2e (charging)
PbO_(2)+4H^(+)+SO_(4)^(2-)+2e rarr PbSO_(4)+2H_(2)O (discharging)

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Weight of solution before discharge = 3500 xx 1.294
= 4529g
Weight of H_(2)SO_(4) before discharge = (39)/(100) xx 4529
= 1766.31 g
Weight of solution after discharge = 3500 xx 1.139
= 3986.5 g
Weight of H_(2)SO_(4) after discharge = (20)/(100) xx 3986.5
= 797.3 g
Loss in mass of H_(2)SO_(4) during discharge
= 1766.31 - 797.3 = 969.01 g
Now from first law of electrolysis,
W = (Q xx E)/(96500)
969.01 = (Q xx 98)/(96500)
Q = 954178.21 coulomb
Ampere-hour = ("Coulomb")/(3600) = (954178.21)/(3600)
= 265.04 ampere-hour