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Potassium manganate (\[{K_2}Mn{O_4}\]) is formed when:
(This question has multiple correct options)
A. Chlorine is passed through aqueous \[KMn{O_4}\] solution
B. Manganese dioxide is fused with potassium hydroxide in air
C. Formaldehyde reacts with potassium permanganate in presence of a strong alkali
D. Potassium permanganate reacts with sulphuric acid.

Answer
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Hint: Manganese is a group 7 transition metal. Manganese is present in +6 oxidation state in potassium manganate. Potassium manganate is a green coloured salt.

Complete step by step answer:
Potassium manganate is an inorganic compound with the molecular formula \[{K_2}Mn{O_4}\]. It is a green coloured salt which is an intermediate in the industrial synthesis of potassium permanganate (\[KMn{O_4}\]). Occasionally, potassium manganate and potassium permanganate are confused, but they are different compounds with distinctly different properties.
Potassium manganate consists of two \[{K^ + }\] cations and one \[Mn{O_4}^{ - 2}\] anion. X-ray crystallography shows that the anion is tetrahedral, with Mn-O distances of 1.66 Å, 0.03 Å longer than the Mn-O distances in \[KMn{O_4}\]. It is isostructural with potassium sulphate.
In the given question, potassium manganate is formed when:
Manganese dioxide is fused with potassium hydroxide in air.
When manganese dioxide is reacted with potassium hydroxide in the presence of oxygen, it forms potassium manganate according to the reaction:
\[4KOH + 2Mn{O_2} + {O_2} \to 2{K_2}Mn{O_4} + 2{H_2}O\]

Formaldehyde reacts with potassium permanganate in presence of a strong alkali.
When Formaldehyde reacts with potassium permanganate in presence of a strong alkali, it forms potassium manganate according to the reaction:
\[HCHO + 2KMn{O_4} + 2KOH \to {K_2}Mn{O_4} + {H_2}O + HCOOH\]

Hence, the correct answers are (B) and (C).

Note: Remember that potassium permanganate is formed when chlorine is passed through a solution of potassium manganate and not the opposite.