Calculating the Number of M-M Bond in Co4(CO)12

Co4(CO)12 is a compound that contains four cobalt atoms and twelve carbon monoxide ligands. Each cobalt atom is bonded to three carbon monoxide ligands, and each carbon monoxide ligand is bonded to one cobalt atom. The number of M-M bonds in Co4(CO)12 can be calculated using the following steps:

1. Determine the total number of electrons contributed by the ligands:

Since each CO ligand donates two electrons to the metal center, the total number of electrons contributed by the twelve CO ligands is:

12 ligands x 2 electrons/ligand = 24 electrons

2. Calculate the total number of valence electrons in the metal atoms:

The valence electron configuration of cobalt is [Ar] 3d7 4s2. Each cobalt atom in Co4(CO)12 contributes five valence electrons, which gives a total of:

4 atoms x 5 electrons/atom = 20 electrons

3. Add the total number of electrons contributed by the ligands and the metal atoms:

24 electrons (ligands) + 20 electrons (metal atoms) = 44 electrons

4. Determine the electron count for each metal atom:

The electron count for each metal atom is calculated by dividing the total number of electrons by the number of metal atoms in the molecule:

44 electrons / 4 atoms = 11 electrons per metal atom

5. Determine the number of M-M bonds:

The number of M-M bonds is equal to half the difference between the electron count for each metal atom and the number of valence electrons in the metal atom.

For cobalt, the number of valence electrons is 9 (7 from the d orbitals and 2 from the s orbitals).

Number of M-M bonds = 0.5 x (11 electrons – 9 valence electrons) = 1 bond

Therefore, there is one M-M bond in Co4(CO)12.