# 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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Adding the charging and discharging reactions
Pb+PbO_(2)+4H^(+)+2SO_(4)^(2-) rarr 2PbSO_(4)+2H_(2)O
N_(H_(2)SO_(4)) = M_(H_(2)SO_(4)) (Since 2SO_(4)^(2-) requires 2 electrons)
i.e., Normality = Molarity
{:("Now before electrolysis",|,"after electrolysis"),(M_(H_(2)SO_(4_(I))) = (39 xx 1.294 xx 1000)/(98 xx 100) = 5.15,M_(H_(2)SO_(4_(II))) = (20 xx 1.139 xx 1000)/(98 xx 100) = 2.325,),("Now mole of" H_(2)SO_(4),"Mole of" H_(2)SO_(4),),( = 5.15 xx 3.5 = 18.025,= 2.325 xx 3.5 = 8.1375,):}
:. Mole or equivalents of H_(2)SO_(4) used = 18.025-8.1375 = 9.8875
because (w)/(E) = (i.t)/(96500)
:. i.t = 9.8875 xx 96500 = 954143.75 ampere sec
= 265.04 ampere hr