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 \(K_4[Fe(CN)_6]\) based on crystal field theory, we need to follow these steps:

1. Identify the oxidation state of the central metal atom, iron (Fe), in the complex.
2. Determine the electron configuration of Fe in its oxidation state.
3. Apply crystal field theory to determine the electron arrangement in the d-orbitals.

Step 1: Determine the oxidation state of Fe in \([Fe(CN)_6]^{4-}\).

The complex ion is \([Fe(CN)_6]^{4-}\). With each CN ligand having a charge of -1, the total charge contributed by the 6 CN ligands is -6.

The charge on the complex is -4, so the oxidation state of Fe must be:

x + 6(-1) = -4

Simplifying gives:

x - 6 = -4

Thus, \(x = +2\). Iron is in the +2 oxidation state.

Step 2: Determine the electron configuration of Fe²⁺.

The electron configuration of Fe in its ground state (atomic number 26) is:

[Ar] \,3d^6 \,4s^2

For Fe²⁺, it loses two electrons, which are removed from the 4s and 3d orbitals:

[Ar] \,3d^6

Step 3: Apply crystal field theory.

The CN ligand is a strong field ligand that leads to pairing of electrons in the lower energy \(t_{2g}\) orbitals before occupying the higher energy \(e_g\) orbitals.

So, in a strong field, the \(d\) electrons of Fe²⁺ in octahedral coordination will be distributed as:

• The 6 electrons will fill the \(t_{2g}\) orbitals first due to lower energy.
• This results in the configuration \(t_{2g}^6e^0_g\).

Conclusion: The correct electronic configuration of the central atom Fe in the complex \(K_4[Fe(CN)_6]\) is t_{2g}^6e^0_g. However, the given answer option \(t_{2g}^6e^2_g\) seems incorrect as it contradicts with these principles. The correct configuration recognizing the scenario should be \(t_{2g}^6e^0_g\)