how do I figure out the molecular formula for The concentration of lead (II) ions in a sample of polluted water that also contains nitrate ions is determined by adding solid sodium sulfate.

You don't have a question as much as a statement. No data, no numbers.

Adding Na2SO4 to a sample of water containing Pb^+2 will ppt PbSO4. You measure the amount of water, ppt PbSO4, filter, dry, weigh the dry PbSO4 collected, then mass Pb = mass PbSO4 x (molar mass Pb/molar mass PbSO4).
Finally %Pb = (mass Pb/mass sample)*100 = ??

To figure out the molecular formula for the concentration of lead (II) ions in a sample of polluted water that also contains nitrate ions, you'll need to consider the reaction between lead (II) ions and sodium sulfate.

The chemical equation for this reaction is:
Pb2+ (aq) + SO4 2- (aq) → PbSO4 (s)

Here's how to determine the molecular formula:

1. Begin by writing the balanced chemical equation for the reaction between lead (II) ions and sodium sulfate, as shown above.

2. Determine the number of lead (II) ions present. This can be calculated using the concentration and volume of the sample of polluted water that is being tested. For example, if the concentration of lead (II) ions is given as 0.05 mol/L and the volume of the sample is 250 mL, you can use the following formula:

Number of moles of lead (II) ions = Concentration × Volume
Number of moles of lead (II) ions = 0.05 mol/L × 0.250 L
Number of moles of lead (II) ions = 0.0125 mol

3. Using the balanced chemical equation, we see that 1 mole of lead (II) ions reacts with 1 mole of sodium sulfate to produce 1 mole of lead sulfate. Therefore, the number of moles of lead (II) ions is the same as the number of moles of lead sulfate formed.

4. Finally, convert the number of moles of lead sulfate to grams by multiplying it by its molar mass. The molar mass of lead sulfate (PbSO4) is the sum of the atomic masses of its constituent elements (Pb + S + 4O). Look up the atomic masses in the periodic table.

5. Once you have the mass of lead sulfate, divide it by the total mass of the sample (given by the concentration and volume of the sample) and multiply by 100 to determine the percentage of lead (II) ions in the sample.

Using these steps, you can calculate the concentration of lead (II) ions in the sample of polluted water in terms of its molecular formula (PbSO4).