Question

Using Crystal Field Theory (CFT), what is the correct electronic configuration and magnetic behavior of the high-spin complex \[ [\text{Fe}(\text{H}_2\text{O})_6]^{2+} \, ? \] 

• A. \(t_{2g}^4 e_g^2\), Paramagnetic
• B. \(t_{2g}^6 e_g^0\), Diamagnetic
• C. \(t_{2g}^3 e_g^3\), Paramagnetic
• D. \(t_{2g}^5 e_g^1\), Paramagnetic

Hint:

For \(d^4\) through \(d^7\) metals, look at the ligand field strength: Weak-field ligands keep systems in a high-spin state (\(\Delta_o & Lt; P\)), while strong-field ligands force low-spin configurations (\(\Delta_o > P\)).

Answer 1

The Correct Option is A

Concept: In an octahedral coordination field, \(d\)-orbitals split into lower energy \(t_{2g}\) and higher energy \(e_g\) levels. Weak-field ligands have a splitting energy smaller than the pairing energy (\(\Delta_o & Lt; P\)), which creates a high-spin configuration.

Step 1: Find the oxidation state and valence electrons.
Water is a neutral ligand, meaning \(\text{Fe}\) has an oxidation state of \(+2\). The electron configuration of an \(\text{Fe}^{2+}\) ion is \([\text{Ar}]3d^6\).

Step 2: Distribute electrons based on weak-field rules.
Because \(\text{H}_2\text{O}\) is a weak-field ligand, electrons fill all five orbital sub-levels singly before any pairing occurs:
• Place the first 3 electrons singly in the lower tier: \(t_{2g}^3\)
• Place the next 2 electrons singly in the upper tier: \(e_g^2\)
• Place the final 6th electron in the lower tier to pair up: \(t_{2g}^4 e_g^2\) This arrangement results in 4 unpaired electrons, making the complex paramagnetic.