To determine the oxidation number of iron in the complex ion \( \text{Fe(CN)}_6^{3-} \), we first need to recognize the charge and nature of the ligands involved.
Cyanide (\( \text{CN}^- \)) is a ligand with a charge of -1. In the complex \( \text{Fe(CN)}_6^{3-} \), there are 6 cyanide ligands. Therefore, the total contribution of the cyanide ligands to the charge is:
\[ 6 \times (-1) = -6 \]
Let the oxidation number of iron (\( \text{Fe} \)) be \( x \). The overall charge of the complex ion is -3. We can set up the following equation based on the sum of the oxidation states:
\[ x + (-6) = -3 \]
Solving for \( x \):
\[ x - 6 = -3 \ x = -3 + 6 \ x = +3 \]
Thus, the oxidation number of iron in \( \text{Fe(CN)}_6^{3-} \) is \( +3 \).