Final answer:
The oxidation number of manganese in KMnO₄ is +7, as it balances out the -8 from the four oxygen atoms and the +1 from the potassium atom, resulting in a neutral compound.
Step-by-step explanation:
The oxidation number of manganese in KMnO₄ (potassium permanganate) can be determined by knowing the oxidation number of each element and the fact that the sum of the oxidation numbers in a compound must equal zero. Oxygen generally has an oxidation number of -2, and since there are four oxygen atoms in KMnO₄, their total contributes -8 to the sum.
Potassium, being an alkali metal, has an oxidation number of +1. To balance the overall charge to zero, manganese must have an oxidation number that will counteract the negative eight from the oxygen atoms and the positive one from potassium. The total charge to be counteracted is -7 (since 4x(-2) + 1 = -7), therefore the oxidation number of manganese must be +7 to balance this and make the compound neutral.