Reduction of Permanganate Ion Metal Centre in Different Media

To determine the number of electrons involved in the reduction of the metal centre in the aqueous permanganate ion ($\text{MnO}_4^-$), we examine the redox half-reactions in different reaction media:

1. In Acidic Medium:
   Permanganate ion ($\text{Mn}$ in $+7$ oxidation state) is reduced to manganese(II) ion ($\text{Mn}^{2+}$, in $+2$ oxidation state):
   $\text{MnO}_4^- + 8\text{H}^+ + 5e^- \longrightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O}$

   • The change in oxidation state is from $+7$ to $+2$.
   • This process involves the transfer of $5$ electrons.
   • Therefore, Option (D) is correct.

2. In Neutral Medium:
   Permanganate ion is reduced to manganese dioxide ($\text{MnO}_2$, where $\text{Mn}$ is in $+4$ oxidation state):
   $\text{MnO}_4^- + 2\text{H}_2\text{O} + 3e^- \longrightarrow \text{MnO}_2 + 4\text{OH}^-$

   • The change in oxidation state is from $+7$ to $+4$.
   • This process involves the transfer of $3$ electrons.
   • Therefore, Option (A) is correct, and Option (B) is incorrect.

3. In Alkaline Medium (faintly alkaline / dilute alkaline):
   In faintly alkaline solutions, the permanganate ion similarly undergoes reduction to manganese dioxide ($\text{MnO}_2$):
   $\text{MnO}_4^- + 2\text{H}_2\text{O} + 3e^- \longrightarrow \text{MnO}_2 + 4\text{OH}^-$

   • The change in oxidation state is from $+7$ to $+4$.
   • This process involves the transfer of $3$ electrons.
   • Therefore, Option (C) is correct.

Hence, the correct options are A, C, and D.