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Question

During the discharge of a lead storage battery, density of H2SO4 fell from 1.294 to 1.139\ g/mL.Sulphuricacidofdensity1.294is39H_{2}SO_{4}byweightandthatofdensity1.139\ g/mLis20H_{2}SO_{4}byweight.Thebatteryhold3.5\ litreoftheacidandvolumeremainspracticallyconstantduringdischarge.Calculateamperehourofwhichthebatterymusthavebeenused.Thecharginganddischargingreactionsare:Pb + SO_{4}^{2-} \rightarrow PbSO_{4} + 2e^{-}(charging)PbO_{2} + 4H^{+} + SO_{4}^{2-} + 2e^{-}\rightarrow PbSO_{4} + 2H_{2}O$ (discharging).

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Solution

Weight of solution before discharge =3500×1.294
=4529 g
Weight of H2SO4 before discharge =39100×4529
=1766.31 g
Weight of solution after discharge =3500×1.139
=3986.5 g
Weight of H2SO4 after discharge =20100×3986.5
=797.3 g
Loss in mass of H2SO4 during discharge
=1766.31797.3=969.01 g
Now from first law of electrolysis,
W=Q×E96500
969.01=Q×9896500
Q=954178.21 coulomb
Amperehour=Coulomb3600=954178.213600
=265.04 amperehour.

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