In acidic medium which of the following does not change its colour?
A. $\text{MnO}_{4}^{-}$
B. $\text{MnO}_{4}^{2-}$
C. $\text{CrO}_{4}^{2-}$
D. $\text{FeO}_{4}^{2-}$

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Hint: The colour does not change means that a colourless compound is formed. In order to find that, we need to write the reaction of compounds in acidic medium to find whether the colour changes or not. Acidic medium means reaction with acids or $\left[ {{\text{H}}^{+}} \right]$ ions.

Complete answer:
Let us write the reactions of the compounds
A. $\text{MnO}_{4}^{-}$: The compound is permanganate ion or manganate$\left( \text{VII} \right)$ ion. This ion contains manganese which has +7 oxidation state and is a strong oxidising agent. It has tetrahedral geometry. It reaction in acidic medium is $\text{MnO}_{4}^{-}+8{{\text{H}}^{+}}+5{{\text{e}}^{-}}\to \text{M}{{\text{n}}^{+2}}+4{{\text{H}}_{2}}\text{O}$. Here, $\text{MnO}_{4}^{-}$ has purple colour and $\text{M}{{\text{n}}^{+2}}$ is colourless. So, the reaction does not change.

B. $\text{MnO}_{4}^{2-}$: The compound is tetraoxomanganate anion or manganate$\left( \text{VI} \right)$ ion. This ion contains manganese which has +6 oxidation state. It has tetrahedral geometry. It reaction is acidic medium is $\text{3MnO}_{4}^{2-}+2{{\text{H}}_{2}}\text{O}\to \text{Mn}{{\text{O}}_{2}}+2\text{MnO}_{4}^{-}+4\text{O}{{\text{H}}^{-}}$. Here, $\text{MnO}_{4}^{2-}$ has dark green colour and $\text{MnO}_{4}^{-}$ formed is of purple colour. So, the reaction does change its colour.

C. $\text{CrO}_{4}^{2-}$: The compound is a chromium oxoanion. This ion contains chromium which has +6 oxidation state. It has tetrahedral geometry. It acts as a strong oxidising agent. It reaction is acidic medium is $\text{2CrO}_{4}^{2-}\left( \text{aq}\text{.} \right)+2{{\text{H}}^{+}}\rightleftharpoons \text{C}{{\text{r}}_{2}}\text{O}_{7}^{2-}\left( \text{aq}\text{.} \right)+{{\text{H}}_{2}}\text{O}\left( \text{l} \right)$. Here, $\text{CrO}_{4}^{2-}$ has yellow colour and $\text{C}{{\text{r}}_{2}}\text{O}_{7}^{2-}$ formed is of orange colour. So, the reaction does change its colour.

D. $\text{FeO}_{4}^{2-}$: This ferrate$\left( \text{VI} \right)$ ion is isostructural with chromate and permanganate ions. It is one of the strongest water-stable oxidizing agents. The oxidation state of iron is +6 in $\text{FeO}_{4}^{2-}$. The reaction of $\text{FeO}_{4}^{2-}$ in acidic medium is ${{\left[ \text{Fe}{{\text{O}}_{4}} \right]}^{2-}}+8{{\text{H}}^{+}}+3{{\text{e}}^{-}}\to \text{F}{{\text{e}}^{+3}}+4{{\text{H}}_{2}}\text{O}$. As, $\text{FeO}_{4}^{2-}$ is unstable in an acidic and neutral medium. The colour of $\text{FeO}_{4}^{2-}$ is pink which is changed to $\text{F}{{\text{e}}^{+3}}$ which is of yellow or green in colour. So, the reaction does change its colour.
So, the correct answer is “Option A”.

Note: The colour of compound is determined by writing its electronic configuration. If there are unpaired electrons present in any compound, then it is paramagnetic or coloured. If all the electrons are paired up, then it is diamagnetic or colourless.