Final answer:
Balancing a redox reaction involving MnO₄⁻ and SO₃²⁻ in a basic medium involves several steps to ensure conservation of mass and charge, and hydroxide ions are added to reflect the basic conditions.
Step-by-step explanation:
To balance the redox reaction MnO₄⁻ + SO₃²⁻ in a basic medium, we follow a series of steps that include separating the two half reactions, balancing the atoms other than oxygen and hydrogen, adding water molecules to balance oxygen atoms, adding hydroxide ions to balance hydrogen atoms, and then balancing the charges with electrons. The balanced reaction will also reflect the conditions of the basic medium by including additional hydroxide ions to neutralize any hydrogen ions and to ensure that the products and reactants are in their proper oxidation states.
Once the separate half-reactions are balanced, they can be combined to give the final balanced redox equation, ensuring that the number of electrons lost in the oxidation half is equal to the number of electrons gained in the reduction half. This process demonstrates the conservation of mass and charge.