Properties and Reactions of Manganese Compounds

To determine the correct statements, let us first identify the salts $\mathbf{W}$ and $\mathbf{X}$, and their corresponding manganese-containing ions $\mathbf{Y}$ and $\mathbf{Z}$.

1. Identification of Species

• Formation of Salt $\mathbf{W}$: Fusing manganese dioxide ($\text{MnO}_2$) with potassium hydroxide ($\text{KOH}$) in the presence of atmospheric oxygen ($\text{O}_2$) yields potassium manganate ($\text{K}_2\text{MnO}_4$): $2\text{MnO}_2 + 4\text{KOH} + \text{O}_2 \xrightarrow{\Delta} 2\text{K}_2\text{MnO}_4 + 2\text{H}_2\text{O}$ Thus, salt $\mathbf{W} = \text{K}_2\text{MnO}_4$ and the manganese-containing ion present in $\mathbf{W}$ is the manganate ion, $\mathbf{Y} = \text{MnO}_4^{2-}$.

• Formation of Salt $\mathbf{X}$: Electrolytic oxidation of an alkaline solution of potassium manganate ($\text{K}_2\text{MnO}_4$) yields potassium permanganate ($\text{KMnO}_4$): $\text{MnO}_4^{2-} \xrightarrow{\text{electrolytic oxidation}} \text{MnO}_4^- + e^-$ Thus, salt $\mathbf{X} = \text{KMnO}_4$ and the manganese-containing ion present in $\mathbf{X}$ is the permanganate ion, $\mathbf{Z} = \text{MnO}_4^-$.

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2. Evaluation of Options

• Option (A): In an acidic medium, the manganate ion ($\mathbf{Y} = \text{MnO}_4^{2-}$) is unstable and undergoes a disproportionation reaction to form the permanganate ion ($\mathbf{Z} = \text{MnO}_4^-$) and manganese dioxide ($\text{MnO}_2$): $3\text{MnO}_4^{2-} + 4\text{H}^+ \rightarrow 2\text{MnO}_4^- + \text{MnO}_2 + 2\text{H}_2\text{O}$ Hence, Statement (A) is correct.

• Option (B):

  • Manganate ion ($\text{MnO}_4^{2-}$) has a green color and possesses a tetrahedral geometry.
  • Permanganate ion ($\text{MnO}_4^-$) has an intense dark purple/violet color (due to ligand-to-metal charge transfer) and also possesses a tetrahedral geometry. Hence, Statement (B) is correct.

• Option (C):

  • Oxidation state of $\text{Mn}$ in $\mathbf{Y}$ ($\text{MnO}_4^{2-}$) is $+6$ with an electronic configuration of $[\text{Ar}]\,3d^1$. Due to the presence of one unpaired electron, $\mathbf{Y}$ is paramagnetic.
  • Oxidation state of $\text{Mn}$ in $\mathbf{Z}$ ($\text{MnO}_4^-$) is $+7$ with an electronic configuration of $[\text{Ar}]\,3d^0$. With zero unpaired electrons, $\mathbf{Z}$ is diamagnetic. The given statement asserts the reverse, so Statement (C) is incorrect.

• Option (D): In both oxoanions ($\text{MnO}_4^{2-}$ and $\text{MnO}_4^-$), the multiple bonds between manganese and oxygen consist of $\sigma$-bonds and $\pi$-bonds. The $\pi$-bonds are formed via overlap of the filled $2p$-orbitals of oxygen with the vacant $3d$-orbitals of manganese ($d\pi-p\pi$ bonding). Hence, Statement (D) is correct.

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Conclusion

The correct options are A, B, and D.