During the discharge of a lead storage battery the density of sulphuric acid fell from 1.294 to 1.139 g.ml^-1. H₂SO₄ of density 1.294 g.ml ^-1 is 39% and that of density 1.139 g.ml ^-1  is 20% by weight. The battery holds 3.5 L of acid and the volume practically remains constant during discharge. Calculate the number of ampere hours for which the battery must have been used. The discharging and charging reactions are
$$\begin{gathered} \mathrm{Pb}+{\mathrm{SO}}_4^{-2}\to {\mathrm{PbSO}}_4+2{\mathrm{e}}^{-} [\mathrm{Anodic} \mathrm{reaction}] \\ {\mathrm{PbO}}_2+4{\mathrm{H}}^{+}+{\mathrm{SO}}_4^2+2{\mathrm{e}}^{-}\to {\mathrm{PbSO}}_4+2{\mathrm{H}}_2\mathrm{O} [\mathrm{Cathode} \mathrm{reaction}] \end{gathered}$$