First, determine the moles of reactants available.
Moles Pb(NO₃)₂: 0.285 mol/L * 1 L/1000 mL * 320 mL = 0.0912
Moles NaIO₃: 0.512 mol/L * 1 L/1000 mL * 386 mL = 0.1976
Next, determine which reactant is limiting. The balanced reaction is:
Pb(NO₃)₂(aq) + 2 NaIO₃(aq) --> Pb(IO₃)₂(s) + 2 NaNO₃(aq)
Theoretical Amount of NaIO₃ needed for 0.0912 mol Pb(NO₃)₂: 0.0912 mol Pb(NO₃)₂* 2 mol NaIO₃/1 mol Pb(NO₃)₂ = 0.1824 moles NaIO₃
Since the theoretical amount is less than what's available, this means NaIO₃ is the excess reactant while Pb(NO₃)₂ is the limiting reactant. Thus, let;s base our answer using the amount of 0.0912 mol Pb(NO₃)₂.
Mass of Precipitate = 0.0912 mol Pb(NO₃)₂ * 1 mol Pb(IO₃)₂/1 mol Pb(NO₃)₂ * 557 g/mol = 50.8 grams of Pb(IO₃)₂ precipitate