Identify the correct coefficients (a), (b), (c) and (d) in the following equations i) x MnO ₄⁻+ (a) SO ₃ ²⁻+ (b) H ⁺ x Mn ²⁺+ (a) SO ₄ ²⁻+ (c) H ₂ O ii) (c) S ₂ O ₃ ²⁻+ (d) MnO ₄ ⁻+ H ₂ O (d) MnO ₂+ (b) SO ₄ ²⁻+ x OH ⁻

Step-by-step solution

For reaction (i): x MnO₄⁻ + a SO₃²⁻ + b H⁺ x Mn²⁺ + a SO₄²⁻ + c H₂O . The oxidation half-reaction is SO₃²⁻ + H₂O SO₄²⁻ + 2H⁺ + 2e⁻ . The reduction half-reaction is MnO₄⁻ + 8H⁺ + 5e⁻ Mn²⁺ + 4H₂O . To balance electrons, multiply the oxidation half-reaction by 5 and the reduction half-reaction by 2. This gives x=2 and a=5 . The balanced equation is 2 MnO₄⁻ + 5 SO₃²⁻ + 6 H⁺ 2 Mn²⁺ + 5 SO₄²⁻ + 3 H₂O . Comparing coefficients, a=5 , b=6 , c=3 . For reaction (ii): c S₂O₃²⁻ + d MnO₄⁻ + H₂O d MnO₂ + b SO₄²⁻ + x OH⁻ . The oxi