Chromium, with atomic number 24, and manganese, with atomic number 25, are transition elements that sit next to each other in period 4 of the periodic table. Starting from the K shell, chromium has 2, 8, 13 and 1 electrons, and manganese has 2, 8, 13 and 2.
Both can use electrons from the inner M shell in reactions, so they take many different oxidation numbers.
The chromate ion, \mathrm{CrO_4^{2-}}, is yellow, and the dichromate ion, \mathrm{Cr_2O_7^{2-}}, is orange; in both, the oxidation number of chromium is +6.
When acid is added to a solution of potassium chromate, it changes to orange dichromate ions.
2\mathrm{CrO_4^{2-}} + 2\mathrm{H^+} \longrightarrow \mathrm{Cr_2O_7^{2-}} + \mathrm{H_2O}
When a base is then added, the solution turns back to yellow chromate ions.
\mathrm{Cr_2O_7^{2-}} + 2\mathrm{OH^-} \longrightarrow 2\mathrm{CrO_4^{2-}} + \mathrm{H_2O}
The permanganate ion, \mathrm{MnO_4^{-}}, is purple, and the oxidation number of manganese in it is +7. In a solution acidified with sulfuric acid, it takes electrons from other substances and changes into \mathrm{Mn}^{2+}, which is almost colourless.
\mathrm{MnO_4^{-}} + 8\mathrm{H^+} + 5\mathrm{e^-} \longrightarrow \mathrm{Mn^{2+}} + 4\mathrm{H_2O}
So as long as some of the substance it reacts with is left, the purple colour of each added drop disappears at once. When all of that substance has reacted, the purple colour stays, so the end of the reaction can be seen from the colour.
Potassium dichromate solution acidified with sulfuric acid is also a strong oxidizing agent, and when it oxidizes another substance, the chromium changes into green \mathrm{Cr}^{3+}.
\mathrm{Cr_2O_7^{2-}} + 14\mathrm{H^+} + 6\mathrm{e^-} \longrightarrow 2\mathrm{Cr^{3+}} + 7\mathrm{H_2O}
This colour change was once used to test for ethanol in a person's breath.
The name chromium comes from the Greek word for colour. The colour of chromium compounds depends on the oxidation number: green at +3, and yellow or orange at +6. Manganese, too, is almost colourless at +2, black as manganese(IV) oxide at +4, and purple as the permanganate ion at +7.
Chromium resists corrosion and is hard, so it is used for plating and in stainless steel, and manganese(IV) oxide is used as the positive electrode of zinc-carbon dry cells.