During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 to 1.139g`//`mL. Sulphuric acid of density 1.294 g `//`mL is 39% `H_(2)SO_(4)` by weight and that of density 1.139g`//`mL is 20% `H_(2)SO_(4)` by weight. The battery holds 3.5 L of the acid and the volume remained practically constant during the discharge. Calculate the number of ampere-hours for which the battery must have been used. The discharging reactions are
`Pb+ SO_(4)^(2-) rarr PbSO_(4) + 2e^(-)` ( chargining)
`PbO_(2) + 4H^(+) + SO_(4)^(2-) + 2e^(-) rarr PbSO_(4) + 2H_(2) O ` ( dischargining)

Explanation

For 1.0 L `H_(2) SO_(4)`,
Initial mass of `H_(2) SO_(4) = 1294 xx ( 39)/( 100) = 504 .66g`
Final mass of `H_(2) SO_(4)`
`= 1139 xx ( 20)/( 100) = 227.80 g`
`:. H_(2) SO_(4)` consumed `//` litre
`= 504.66-227.80 = 276.86g`
`:.` Total `H_(2) SO_(4)` used up
`= 276 . 86 xx 3.5 = 969.01g`
`:.` 1 mole of `H_(2) SO_(4)` is associated with transfer of 1.0 mole of electrons, total 9.888 moles of electron transfer has occurred Coulomb produced `= 9.888 xx 96500`
`= ( 9.888xx96500) /( 3600) = 265`