= Solution
A \b[<lead-acid battery>] is suitable. Its positive <electrode> reduces PbO2 to PbSO4 and its negative <electrode> oxidizes Pb to PbSO4. The net discharge reaction is
$$
\mathrm{Pb}+\mathrm{PbO}_2+4\mathrm H^++2\mathrm{SO}_4^{2-}\to2\mathrm{PbSO}_4+2\mathrm H_2\mathrm O.
$$
Using the supplied rounded potentials gives $E^\circ=1.70-(-0.35)=2.05\,\mathrm V$. The <Nernst equation>, taking solid and water activities as unity, gives
$$
E=2.05+\frac{RT}{2F}\ln\left(a_{\mathrm H^+}^4a_{\mathrm{SO}_4^{2-}}^2\right).
$$
At $\mathrm{pH}=1$ and $298\,\mathrm K$,
$$
\boxed{E\simeq1.932+0.0591\log_{10}a_{\mathrm{SO}_4^{2-}}\;\mathrm V.}
$$
Thus \b[$1.93\,\mathrm V$ if <sulfate> activity is assumed unity]. The pH alone does not specify <sulfate> activity, particularly where bisulfate formation and nonideal concentrated acid matter; without that assumption the numerical <voltage> is underdetermined.
For recharge, reverse both <electrode> reactions without irreversible loss of active material. Use porous, electronically connected Pb and PbO2 on acid-compatible conducting grids, with enough pore volume for PbSO4 formation and <electrolyte> transport. Fine, reversible <sulfate> deposits are desirable; coarse persistent crystals cause <sulfation>. The separator must remain acid-resistant, electronically insulating and permeable to <electrolyte> <ions> while preventing shorts; selective <ion> exchange is not intrinsically required. A compatible lead-alloy grid is preferable to assuming any metallic substrate survives the positive <electrode>'s oxidizing acidic environment. Control current and charging <voltage> to limit hydrogen evolution, oxygen evolution, water loss, corrosion, heating and active-material shedding. Nickel hydroxide-based alkaline <electrodes> are poor choices in this acidic <electrolyte> because their phase stability and reaction conditions differ from those of their tabulated alkaline half-reactions.
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