Question

What is the correct electronic configuration of the central atom in \(K_4[Fe(CN)_6]\) based on crystal field theory?

• A. \(t_{2g}^4e^2_g\)
• B. span class="math-tex">\(t_{2g}^6e^2_g\)
• C. \(e^3t_{2}^3\)
• D. \(e^4t_{2}^2\)

Answer 1

The Correct Option is B

To determine the correct electronic configuration of the central atom in \(K_4[Fe(CN)_6]\), we need to understand the following concepts based on crystal field theory:

1. The central atom in the complex is Iron (\(Fe\)). In this complex, \(Fe\) is in the +2 oxidation state because the 4 \(K^+\) ions compensate for a total charge of +4, leaving the complex ion \([Fe(CN)_6]^{4-}\) with a -4 charge.
2. Iron in the elemental state is \(Fe\) with the electronic configuration \([Ar] 3d^6 4s^2\). In the \(Fe^{2+}\) state, it loses 2 electrons, one from the 4s subshell and one from the 3d subshell, resulting in \([Ar] 3d^6\).
3. \(CN^-\) is a strong field ligand, which causes pairing of electrons in the 3d orbital of the \(Fe^{2+}\) ion, leading to a low-spin configuration.

With \(CN^-\) as a strong field ligand, it causes the 3d electrons to pair up due to the large crystal field splitting energy (\(\Delta\)). As a result, all six \(3d\) electrons pair up in the \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\) orbitals, which correspond to the \(t_{2g}\) set.

Hence, the electronic configuration of the central atom \(Fe^{2+}\) in the presence of the ligand \(CN^-\) based on crystal field theory is given by:

t_{2g}^6e^2_g

This configuration corresponds to all six electrons being paired and filled in the lower energy \(t_{2g}\) orbitals with none in the higher energy \(e_g\) orbitals. This explains why the correct option is \(t_{2g}^6e^2_g\).

Other options can be ruled out because:

• t_{2g}^4e^2_g would apply if there were two unpaired electrons in the \(e_g\) set, which is not possible with a strong field ligand like \(CN^-\).
• e^3t_2^3 and e^4t_2^2 suggest configurations with more electrons in the \(e_g\) than \(t_{2g}\), representing a high spin scenario, not applicable with \(CN^-\).