The given question pertains to the molecular geometry and bonding in manganate and permanganate ions. We need to understand why these ions adopt a tetrahedral shape.
The correct option is: The \(\pi\) bonding involves overlap of p-orbitals of oxygen with d-orbitals of manganese.
Here’s a breakdown of the reasoning:
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Geometry of the Ions: Both manganate (\( \text{MnO}_4^{2-} \)) and permanganate (\( \text{MnO}_4^- \)) ions have a tetrahedral geometry. In tetrahedral structures, the central metal atom, manganese in this case, is surrounded symmetrically by four oxygen atoms.
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Bonding Explanation:
- The manganese in these ions is in a high oxidation state (\(+6\) in manganate and \(+7\) in permanganate), which allows it to participate in extensive \(\pi\)-bonding with oxygen atoms.
- Oxygen, being a highly electronegative element, tends to form strong bonds with metals through sigma (\(\sigma\)) and pi (\(\pi\)) bonding. In these ions, the p-orbitals of the oxygen overlap with the d-orbitals of manganese to form \(\pi\)-bonds.
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Electronic Configuration: Manganese in its high oxidation states makes use of its available vacant d-orbitals for forming \(\pi\)-bonds with the filled p-orbitals of oxygen, leading to the overlap required for \(\pi\)-bonding.
This \(\pi\)-bonding is crucial for the stability and shape of these ions. Explaining the incorrect options:
- There is no \(\pi\) bonding: This is incorrect because \(\pi\)-bonding is essential for the molecular stability and tetrahedral geometry.
- The \(\pi\)-bonding involves overlap of p-orbitals of oxygen with p-orbitals of manganese: Manganese in these compounds favors d-orbital participation for \(\pi\)-bonding due to its electronic configuration.
- The \(\pi\)-bonding involves overlap of d-orbitals of oxygen with d-orbitals of manganese: Oxygen does not have d-orbitals in its ground state; hence this option is incorrect.
In summary, the tetrahedral shape arises due to the effective \(\pi\)-bonding through the overlap of p-orbitals of oxygen with d-orbitals of manganese.