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Question

During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 to 1.139 gmL1. H2SO4 of density 1.294gmL1 is 39% and that of density 1.139gmL1 is 20% by weight.The battery holds 3.5 L of acid and the volume practically remains constant during discharge. The number of ampere hours for which the battery must have been used are........................
The discharging and charging reactions are:
Pb+SO24PbSO4+2e (charging)
PbO2+4H++SO24+2ePbSO4+2H2O (discharging)

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Solution

Assume 1 L of sulphuric acid is present.

Initial number of moles of sulphuric acid =1294×0.3998=5.15 moles

Final number of moles of sulphuric acid =1139×0.2098=2.32 moles

Number of moles of sulphuric acid consumed =5.152.32=2.83 moles.

Number of moles of sulphuric acid consumed corresponds to number of moles of electrons.

Number of moles of electrons =2.83

The number of ampere hours =2.83×965003600=76

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