The balanced equation is
Cl₂ + SO₂ +2H₂O ⟶ 2Cl⁻ +SO₄²⁻ + 4H⁺
This is a redox reaction, so I will balance it using the ion-electron method.
Step 1. Write the skeleton equation.
Strip the equation of H⁺ and H₂O (these come back in during the balancing procedure). We get
Cl₂ + SO₂ ⟶ Cl⁻ +SO₄²⁻
Step 2: Separate the skeleton equation into two half-reactions.
Cl₂ ⟶ Cl⁻
SO₂ ⟶ SO₄²⁻
Step 3: Balance all atoms other than H and O.
Cl₂ ⟶ 2Cl⁻
SO₂ ⟶ SO₄²⁻
Step 4: Balance O.
Add enough H₂O molecules to balance O,
Cl₂ ⟶ 2Cl⁻
SO₂ + 2H₂O ⟶ SO₄²⁻
Step 5: Balance H.
Add enough H⁺ ions to balance H.
Cl₂ ⟶ 2Cl⁻
SO₂ + 2H₂O ⟶ SO₄²⁻ + 4H⁺
Step 6: Balance charge.
Add electrons to the side that needs more negative charge.
Cl₂ + 2e⁻ ⟶ 2Cl⁻
SO₂ + 2H₂O ⟶ SO₄²⁻ + 4H⁺ + 2e⁻
Step 7: Add the two half-reactions.
The balanced equation is
Cl₂ + SO₂ + 2H₂O ⟶ 2Cl⁻ + SO₄²⁻ + 4H⁺
