To determine the volume of 0.100 M lead nitrate needed to completely precipitate 25.0 mL of 0.0832 M nickel(II) sulfate, start by calculating the moles of sulfate ions (SO4(-2)) in the nickel sulfate solution. The reaction between lead ions (Pb(+2)) and sulfate occurs on a one-to-one mole basis, meaning the moles of Pb(+2) required will equal the moles of SO4(-2) present. After finding the required moles of lead, calculate the corresponding volume of the lead nitrate solution needed to provide that amount. It's important to note that lead sulfate (PbSO4) is not completely insoluble, indicating that not all sulfate ions will precipitate out.