Solution

Preparation of potassium dichromate $$\displaystyle K_2Cr_2O_7$$ from chromite ore $$\displaystyle FeO \cdot Cr_2O_3 (FeCr_2O_4) $$:
(i) Chromite ore is fused with $$NaOH$$ or sodium carbonate in air to form sodium chromate.
$$\displaystyle 4FeCr_2O_4 + 16NaOH + 7O_2 \rightarrow 8Na_2CrO_4 + 2Fe_2O_3 +8H_2O$$

(ii) Sodium chromate solution is filtered and acidified to form sodium dichromate
$$\displaystyle 2Na_2CrO_4 + H_2SO_4 \rightarrow Na_2Cr_2O_7 + Na_2SO_4 +H_2O$$
The solution is cooled to remove crystallized sodium sulphate. Sodium dichromate remains soluble.

(iii) Equimolar proportions of a hot solution of sodium dichromate and KCl are mixed to form potassium dichromate.
$$\displaystyle Na_2Cr_2O_7 + 2KCl \rightarrow K_2Cr_2O_7 + 2 NaCl$$

Sodium chloride precipitates out in hot solution and is removed by filtration. On cooling, potassium dichromate separates out from the mother liquor.
At pH 4, there is an equilibrium between chromate ions and dichromate ions

$$\displaystyle \underset {\displaystyle \text {Dichromate ion (orange red)} }{Cr_2O_7^{2-}} + H_2O \rightleftharpoons \underset {\displaystyle \text {Chromate ion (yellow)} }{2CrO_4^{2-}} +2H^+$$

By adding alkali, pH can be increased and the equilibrium reaction will shift in the forward direction to produce more chromate ions (yellow color). This is in accordance with Le chatelier's principle. By adding an acid, pH can be decreased and the equilibrium reaction will shift in the backward direction to produce more dichromate ions (orange-red color).