Identify the reactants and products in the given chemical reaction. The reactants are aluminum (Al) and permanganate ions (MnO4⁻) in an aqueous solution, and the products include manganese dioxide (MnO2) and aluminum hydroxide species.
Determine the oxidation states of the elements involved in the reaction. Aluminum (Al) starts in the 0 oxidation state and is oxidized, while manganese in permanganate (MnO4⁻) is reduced from +7 to +4 in MnO2.
Write the half-reactions for oxidation and reduction. The oxidation half-reaction involves Al being oxidized to Al(OH)4⁻, and the reduction half-reaction involves MnO4⁻ being reduced to MnO2.
Balance each half-reaction for mass and charge. For the oxidation half-reaction, balance aluminum and hydroxide ions. For the reduction half-reaction, balance manganese, oxygen, and hydrogen ions, using water molecules and hydrogen ions as needed.
Combine the balanced half-reactions, ensuring that the electrons lost in the oxidation half-reaction equal the electrons gained in the reduction half-reaction. This will give you the balanced overall equation for the reaction.