Question

Identify the complex ion with electronic configuration \( t_{2g}^{3} e_{g}^{2} \).

• A. \([\text{Fe}(\text{H}_2\text{O})_6]^{3+}\)
• B. \([\text{Cr}(\text{H}_2\text{O})_6]^{3+}\)
• C. \([\text{Ni}(\text{H}_2\text{O})_6]^{2+}\)
• D. \([\text{Ti}(\text{H}_2\text{O})_6]^{3+}\)

Hint:

For octahedral complexes, weak field ligands (e.g., \(\text{H}_2\text{O}\)) lead to high-spin configurations, whereas strong field ligands (e.g., CN\(^-\)) lead to low-spin configurations.

Answer 1

The Correct Option is A

Step 1: Identify the oxidation state of iron - The given complex is \([\text{Fe}(\text{H}_2\text{O})_6]^{3+}\). - Since water (\(\text{H}_2\text{O}\)) is a neutral ligand, the oxidation state of iron in this complex is \(+3\). Step 2: Determine the electronic configuration - The atomic number of Fe is 26, so the electronic configuration of neutral Fe is: \[ \text{Fe}: [\text{Ar}] 3d^6 4s^2 \] - In \(\text{Fe}^{3+}\), three electrons are removed, leading to: \[ \text{Fe}^{3+}: [\text{Ar}] 3d^5 \] Step 3: Identify the crystal field splitting - The complex contains \(\text{H}_2\text{O}\), a weak field ligand, so it forms a high-spin octahedral complex.
- In an octahedral field, the \(3d\) orbitals split into two sets: - \( t_{2g} \) (lower energy, three orbitals)
- \( e_g \) (higher energy, two orbitals) - For \( d^5 \) configuration in a weak field ligand system, electrons fill according to Hund’s rule: \[ t_{2g}^{3} e_{g}^{2} \] Step 4: Verification with given configuration - The configuration \( t_{2g}^{3} e_{g}^{2} \) exactly matches the given one, confirming the correct answer.