Industrial wastewater contains Pb^{2+}, Na^{+}, and NO_{3}^{-} ions, each at an initial concentration of 0.020 M. To remove lead(II) ions, engineers plan to treat the water with solid sodium sulfate decahydrate, Na_{2}SO_{4}\cdot10H_{2}O, until the equilibrium concentration of Pb^{2+} falls below 1.0×10^{-4}\,\text{M}. Assume the final solution volume remains 1.00 L and that precipitation is complete and stoichiometric.
(a) Write the balanced net ionic equation for the reaction that removes Pb^{2+} from solution.
(b) Determine the minimum mass (in grams) of Na_{2}SO_{4}\cdot10H_{2}O that must be added to each liter of wastewater to achieve the required Pb^{2+} concentration. Clearly state any assumptions and show all calculations.
(c) Explain why the concentrations of Na^{+} and NO_{3}^{-} are expected to remain essentially unchanged during the treatment process.
(d) Propose one alternative aqueous reagent that could be added to precipitate Pb^{2+} without removing Na^{+}. Write the balanced net ionic equation for the precipitation that would occur with your chosen reagent and justify its effectiveness based on solubility considerations.