Exercises: Calculating oxidation numbers in compounds

The mineral hematite, from which iron is extracted, is iron(III) oxide, Fe₂O₃. Calculate the oxidation number of iron by setting up the condition that the sum of the oxidation numbers in the whole compound must be 0 (oxygen is $-2$).

The nitrate ion, NO₃⁻, is present in fertilizers. Since it is an ion with charge $-1$, the sum of the oxidation numbers must be $-1$. Calculate the oxidation number of nitrogen, showing the equation you set up.

Potassium permanganate (KMnO₄) is a violet disinfectant sold in pharmacies. Calculate the oxidation number of manganese knowing that potassium is $+1$ and oxygen is $-2$, and that the compound is neutral. Compare your result with the oxidation number of manganese in MnO₂ ($+4$) and state in which one it is more oxidized.