A certain lead ore contains the compound \(\mathrm{PbCO}_{3} .\) A sample of the
ore weighing \(1.526 \mathrm{~g}\) was treated with nitric acid, which dissolved
the \(\mathrm{PbCO}_{3}\). The resulting solution was filtered from undissolved
rock and required \(29.22 \mathrm{~mL}\) of \(0.122 \mathrm{M} \mathrm{Na}_{2}
\mathrm{SO}_{4}\) to completely precipitate all of the lead as
\(\mathrm{PbSO}_{4}\). (a) How many moles of lead were in the ore sample? (b)
How many grams of lead were in the ore sample? (c) What is the percentage by
mass of lead in the ore? (d) Would you expect the same results if the solid
\(\mathrm{PbSO}_{4}\) was collected, washed, dried, and weighed and the final
mass was used to answer this question?