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When an oxide of manganese (A) is fused with KOH in the presence of an oxidising agent and dissolved in water, it gives a dark green solution of compound (B). Compound (B) disproportionates in neutral or acidic (C ) oxidises potassium iodide solution to a compound (D) and compound (A) is also formed. Identify compounds A to D and also explain the reactions involved.

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The available data suggests the compound (A) is `MnO_(2)`. It participates in the following reaction to account for the different products.
` underset("Manganese dioxide (A)")(2MnO_(2))+4KOH+O_(2) overset("Fuse")to underset("(dark green)(B)") underset(" Pot. manganate ")(2K_(2)MnO_(4))+2H_(2)O`
`3MnO_(4)^(2-)+4H^(+) to underset(" Purple (C)") (2MnO_(4)^(-))+MnO_(2)+2H_(2)O`
`overset((A))(2MnO_(4)^(-))+H_(2)O+KO to underset((A))(2MnO_(2))+2OH^(-)+ underset((D))(KIO_(3))`

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