(Solved): The lead-acid storage battery is the oldest rechargeable battery in existence. It was invented in 1 ...

The lead-acid storage battery is the oldest rechargeable battery in existence. It was invented in 1859 by French physician Gaston Plante and still retains application today, more than 150 years later. There are two reactions that take place during discharge of the lead-acid storape battery. In one step, sulfuric acid decomposes to form sulfur trioxide and watert \[ \mathrm{H}_{2} \mathrm{SO}_{4}(l) \rightarrow \mathrm{SO}_{3}(9)+\mathrm{H}_{2} \mathrm{O}(0) \quad \Delta H=+113 . \mathrm{kJ} \] In another step, lead, lead(IV) oxide, and sulfur trioxide react to form lead(II) sulfote: \[ \mathrm{Pb}(\mathrm{s})+\mathrm{PbO}_{2}(\mathrm{~s})+2 \mathrm{SO}_{3}(\mathrm{~g})+2 \mathrm{PbSO}_{4}(5) \quad \Delta H=-775, \mathrm{~kJ} \] Calculate the net change in enthalpy for the formation of one mole of lead(II) sulfate from lead, leod(IV) oxide, and sulfuric acid from these reactions.