Step 1: Determine the Oxidation State of the Central Metal.
In the complex \( [Fe(H_2O)_6]^{3+} \), water molecules (\(H_2O\)) are neutral ligands and do not contribute to the charge. The overall charge of the complex is \( +3 \), so the charge on the iron ion must be \( +3 \) to balance the charge.
Therefore, the oxidation state of iron (Fe) in this complex is \( +3 \).
Step 2: Determine the Hybridization of the Central Metal.
The central metal ion is \( \text{Fe}^{3+} \), and it is surrounded by six water molecules, forming an octahedral geometry. In octahedral geometry, the metal ion uses six hybrid orbitals to form bonds with the ligands.
Therefore, the hybridization of the iron ion in this complex is sp³d².
Conclusion.
The oxidation state of iron in \( [Fe(H_2O)_6]^{3+} \) is \( +3 \), and its hybridization is sp³d².