Step 1: Begin with the raw ore. Pyrolusite is manganese dioxide, \( MnO_2 \), where manganese sits in the +4 state. To reach the +7 of permanganate the manganese must be oxidised twice over, so the preparation is naturally a two-stage climb in oxidation number.
Step 2: First stage, \( +4 \rightarrow +6 \). Powdered ore is heated (fused) with caustic potash and air (or with \( KNO_3 \) as oxidant). The product is potassium manganate \( K_2MnO_4 \), a green compound: \( 2MnO_2 + 4KOH + O_2 \rightarrow 2K_2MnO_4 + 2H_2O \).
Step 3: Second stage, \( +6 \rightarrow +7 \). The green manganate solution is subjected to electrolytic oxidation at the anode, converting \( MnO_4^{2-} \) into the deep purple \( MnO_4^{-} \) of potassium permanganate. (Alternatively, in acid the manganate disproportionates to give permanganate plus \( MnO_2 \).)
Step 4: Structure. Draw manganese at the centre bonded to four oxygen atoms pointing to the four corners of a tetrahedron. This tetrahedral \( MnO_4^{-} \) has \( sp^3 \) manganese in the +7 state, four identical Mn to O bonds with double-bond character, and a net charge of \( -1 \).