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

Explanation

(i)
Potassium dichromate (`K_(2)Cr_(2)O_(7)`) is prepared from chromite ore (`FeCr_(2)O_(4)`)in the following steps.
Step (1): Preparation of sodium chromate
`4FeCr_(2)O_(4)+16NaOH+7O_(2) rarr 8Na_(2)CrO_(4)+2Fe_(2)O_(3)+8H_(2)O`
Step (2): Conversion of sodium chromate into sodium dichromate
`2Na_(2)CrO_(4)+conc.H_(2)SO_(4) rarr Na_(2)Cr_(2)O_(7)+Na_(2)SO_(4)+H_(2)O`
Step(3): Conversion of sodium dichromate to potassium dichromate
`Na_(2)Cr_(2)O_(7)+2KCl rarr K_(2)Cr_(2)O_(7)+2NaCl`
Potassium chloride being less soluble than sodium chloride is obtained in the form of orange coloured crystals and can be removed by filtration.
The dichromate ion (`Cr_(2)O_(7)^(2-)`) exists in equilibrium with chromate (`CrO_(4)^(2-)`) ion at pH 4. However, by changing the pH, they can be interconverted.
`{:underset(("Yellow"))underset("Chromate")(2CrO_(4)^(2-))underset("Alkali")overset("Acid") harr underset("chromate")underset("Hydrogen")(2HCrO_(4)^(-))underset("Alkali")overset("Acid")harrunderset(("Orange"))underset("Dichromate")(Cr_(2)O_(7)^(3-))`
(ii)
Potassium permanganate (`KMnO_(4)`) can be prepared from pyrolusite (`MnO_(2)`). The ore is fused with KOH in the presence of either atmospheric oxygen or an oxidising agent, such as `KNO_(3)` or `KClO_(4)`, to give `K_(2)MnO_(4)`.
`2MnO_(2)+4KOH+O_(2) overset(heat)rarr underset((Green))(2K_(2)MnO_(4))+2H_(2)O`
The green mass can be extracted with water and then oxidized either electrolytically or by passing chlorine/ozone into the solution.
Electrolytic oxidation
`{:(K_(2)MnO_(4) hArr 2K^(+)+MnO_(4)^(2-)),(H_(2)O hArr H^(+)+OH^(-)):}`
At anode, manganate ions are oxidized to permanganate ions.
`{:(MNO_(4)^(2-) hArr MnO_(4)^(-)+e^(-)),("Green"" Purple"):}`
Oxidation by chlorine
`{:(2K_(2)MnO_(4)+Cl_(2) rarr2KMnO_(4)+2KCl),(2MNC_(4)^(2-)+Cl_(2)rarr2MnO_(4)^(-)+2Cl^(-)):}`
Oxidation by ozone
`{:(2K_(2)MnO_(4)+O_(3)+H_(2)Oto 2KMnO_(4)+2KOH+O_(2)),(2MNO_(4)^(2-)+O_(3)+H_(2)Orarr 2MNO_(4)^(2-)+2OH^(-)+O_(2)):}`