Number of Iron Carbon Bonds in Coordination Complex

To determine the total number of $\text{Fe}-\text{C}$ bonds in the complex acetylbromidodicarbonylbis(triethylphosphine)iron(II), let us write the formula and identify the donor atoms of each ligand coordinated to the central iron ($\text{Fe}$) atom:

1. Acetyl ligand ($\text{CH}_3\text{CO}^-$): The acetyl group is an anionic ligand that coordinates to the iron center through its acyl carbon atom: $\text{Fe}-\text{C}(=\text{O})\text{CH}_3 \implies 1\text{ }\text{Fe}-\text{C}\text{ bond}$

2. Bromido ligand ($\text{Br}^-$): Coordinates through the bromine atom: $\text{Fe}-\text{Br} \implies 0\text{ }\text{Fe}-\text{C}\text{ bonds}$

3. Dicarbonyl ligands ($2 \times \text{CO}$): Each carbonyl ligand coordinates to the iron center through its carbon atom: $2 \times (\text{Fe}-\text{CO}) \implies 2\text{ }\text{Fe}-\text{C}\text{ bonds}$

4. Bis(triethylphosphine) ligands ($2 \times \text{P}(\text{C}_2\text{H}_5)_3$): Each triethylphosphine ligand coordinates through its phosphorus atom: $2 \times (\text{Fe}-\text{P}) \implies 0\text{ }\text{Fe}-\text{C}\text{ bonds}$

The chemical formula of the complex is: $[\text{Fe}(\text{COCH}_3)\text{Br}(\text{CO})_2(\text{P}(\text{C}_2\text{H}_5)_3)_2]$

Summing up the $\text{Fe}-\text{C}$ bonds: $\text{Total number of }\text{Fe}-\text{C}\text{ bonds} = 1\text{ (from acetyl)} + 2\text{ (from carbonyls)} = 3$

Thus, the total number of $\text{Fe}-\text{C}$ bonds is 3.