Number of M-M bonds in Co4(CO)12

Co4(CO)12 is a tetrahedral complex of cobalt. Each cobalt atom is surrounded by three carbonyl (CO) ligands.

Step 1: Determine the oxidation state of Co in Co4(CO)12.
We know that each CO ligand has a formal charge of -1. Therefore, the oxidation state of Co can be calculated as follows:

4Co + 12CO = 0
4Co = -12
Co = -3

Therefore, the oxidation state of Co in Co4(CO)12 is -3.

Step 2: Determine the number of valence electrons in Co.
The atomic number of Co is 27. Therefore, the number of valence electrons in Co is 9 (2+7).

Step 3: Calculate the total number of valence electrons in the complex.
The total number of valence electrons in the complex can be calculated as follows:

4Co = 4 x 9 = 36
12CO = 12 x (4 + 6) = 120
Total = 36 + 120 = 156

Step 4: Determine the number of electrons required for the complex to achieve an octet configuration.
Each Co atom in Co4(CO)12 has 6 valence electrons from the CO ligands. Therefore, each Co atom needs 2 more electrons to achieve an octet configuration.

2 x 4 = 8

Therefore, the complex requires a total of 8 electrons to achieve an octet configuration.

Step 5: Calculate the number of M-M bonds.
The number of M-M bonds can be calculated using the following formula:

Number of M-M bonds = (Total number of valence electrons - Number of electrons required for octet configuration) / 2

Number of M-M bonds = (156 - 8) / 2 = 74

However, we need to divide this number by 12 (the number of bonds per Co atom in a tetrahedral geometry) to get the number of M-M bonds per Co atom.

Number of M-M bonds per Co atom = 74 / 12 = 6.17

Therefore, the number of M-M bonds in Co4(CO)12 is 6.