1. Write the balanced chemical equation:

BaCl₂(aq) + Na₂SO₄(aq) → BaSO₄(s) + 2NaCl(aq)

2. Calculate moles of Na₂SO₄:

* Molar mass of Na₂SO₄ = (2 * 22.99 g/mol) + (32.07 g/mol) + (4 * 16.00 g/mol) = 142.04 g/mol

* Moles of Na₂SO₄ = (742 mg / 1000 mg/g) / 142.04 g/mol = 0.00522 mol

3. Determine moles of BaCl₂ needed:

* From the balanced equation, 1 mole of BaCl₂ reacts with 1 mole of Na₂SO₄.

* Therefore, 0.00522 mol of BaCl₂ is needed.

4. Calculate the molarity of the BaCl₂ solution:

* Molarity = moles of solute / volume of solution (in liters)

* Volume of BaCl₂ solution = 57.0 mL = 0.0570 L

* Molarity of BaCl₂ = 0.00522 mol / 0.0570 L = 0.0916 M

Therefore, the molarity of the BaCl₂ solution is 0.0916 M.