Indicate the steps in the preparation of:
$(i)$ $K_2Cr_2O_7$ from chromite ore.
$(ii)$ $KMnO_4$ from pyrolusite ore.

(N/A) $(i)$ Potassium dichromate $(K_2Cr_2O_7)$ is prepared from chromite ore $(FeCr_2O_4)$ in the following steps.
Step $(1):$ Preparation of sodium chromate
$4 FeCr_2O_4 + 16 NaOH + 7 O_2 \longrightarrow 8 Na_2CrO_4 + 2 Fe_2O_3 + 8 H_2O$
Step $(2):$ Conversion of sodium chromate into sodium dichromate
$2 Na_2CrO_4 + 2 H^+ \longrightarrow Na_2Cr_2O_7 + 2 Na^+ + H_2O$
Step $(3):$ Conversion of sodium dichromate to potassium dichromate
$Na_2Cr_2O_7 + 2 KCl \longrightarrow K_2Cr_2O_7 + 2 NaCl$
$(ii)$ Potassium permanganate $(KMnO_4)$ is prepared from pyrolusite $(MnO_2)$. The ore is fused with $KOH$ in the presence of air or an oxidizing agent like $KNO_3$ to give $K_2MnO_4$.
$2 MnO_2 + 4 KOH + O_2 \longrightarrow 2 K_2MnO_4 + 2 H_2O$
The green mass is extracted with water and oxidized either electrolytically or by passing chlorine/ozone.
Electrolytic oxidation:
$2 MnO_4^{2-} + H_2O + [O] \longrightarrow 2 MnO_4^- + 2 OH^-$
Oxidation by chlorine:
$2 MnO_4^{2-} + Cl_2 \longrightarrow 2 MnO_4^- + 2 Cl^-$
Oxidation by ozone:
$2 MnO_4^{2-} + O_3 + H_2O \longrightarrow 2 MnO_4^- + 2 OH^- + O_2$