Question

The number of unpaired electron(s) of chromium in [($\eta^6$-C$_6$H$_6$)Cr(CO)$_3$] is _ _ _. (answer in integer)

Hint:

Metal carbonyl complexes usually follow the 18-electron rule and are generally diamagnetic due to strong field CO ligands

Answer 1

Correct Answer: 0

Step 1: Identify the ligands.
The complex contains one $\eta^6$-benzene ligand and three carbonyl ligandsCO is a neutral strong field ligand and benzene is also neutral

Step 2: Determine oxidation state of chromium.
Since all ligands are neutral, the oxidation state of chromium is
\[ x + 0 = 0 \]
\[ x = 0 \]

Step 3: Determine d-electron count.
Chromium has atomic number 24 and electronic configuration $[Ar]3d^54s^1$In zero oxidation state, chromium has 6 valence electrons
\[ \text{Cr}^0 = d^6 \]

Step 4: Apply 18-electron rule.
$\eta^6$-benzene donates 6 electrons and three CO ligands donate 6 electrons in total
\[ 6(\text{Cr}) + 6(\text{benzene}) + 6(3CO) = 18 \]

Step 5: Effect of strong field ligands.
CO is a strong field ligand and causes pairing of electronsTherefore, the complex is low spin

Step 6: Magnetic nature.
Since all electrons are paired in this 18-electron complex, chromium has no unpaired electrons

Step 7: Conclusion.
\[ \boxed{0} \]