The concentration of bivalent lead ions in a sample of polluted of polluted water that aslo contains nitrate ions is determined by adding solid sodium sulphate (M=142) to exactly 500mL water. Calculate the molarity of lead ions if 0.355g is sodium sulphate was nedded for complete precipitation of lead ions as sulphate.

Answer

To solve the problem of determining the molarity of bivalent lead ions in a sample of polluted water, we will follow these steps:

### Step 1: Write the Reaction
The reaction between bivalent lead ions (Pb²⁺) and sodium sulfate (Na₂SO₄) can be represented as follows:
\[ \text{Pb}^{2+} + \text{Na}_2\text{SO}_4 \rightarrow \text{PbSO}_4 (s) + 2\text{Na}^+ \]
This indicates that one mole of lead ions reacts with one mole of sulfate ions to form one mole of lead sulfate precipitate.

### Step 2: Calculate the Number of Moles of Sodium Sulfate
To find the number of moles of sodium sulfate used, we can use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of sodium sulfate (Na₂SO₄) = 0.355 g
- Molar mass of sodium sulfate (Na₂SO₄) = 142 g/mol

Calculating the number of moles:
\[ \text{Number of moles of Na}_2\text{SO}_4 = \frac{0.355 \, \text{g}}{142 \, \text{g/mol}} = 0.0025 \, \text{mol} \]

### Step 3: Relate Moles of Sodium Sulfate to Moles of Lead Ions
From the reaction, we see that the number of moles of sodium sulfate is equal to the number of moles of lead ions (Pb²⁺) because they react in a 1:1 ratio. Therefore:
\[ \text{Number of moles of Pb}^{2+} = 0.0025 \, \text{mol} \]

### Step 4: Calculate the Molarity of Lead Ions
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula for molarity is:
\[ \text{Molarity} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

Given:
- Volume of solution = 500 mL = 0.500 L

Calculating the molarity of lead ions:
\[ \text{Molarity of Pb}^{2+} = \frac{0.0025 \, \text{mol}}{0.500 \, \text{L}} = 0.005 \, \text{M} \]

### Final Answer
The molarity of lead ions (Pb²⁺) in the sample of polluted water is **0.005 M**.

---