Question

The terminal and bridged ${\text{CO}}$ ligands in the compound $\left[ {{\text{C}}{{\text{o}}_{\text{2}}}{{\left( {{\text{CO}}} \right)}_{\text{8}}}} \right]$ are respectively:
A. ${\text{0,2}}$
B. ${\text{6,1}}$
C. ${\text{5,2}}$
D. ${\text{6,2}}$

Answer 1

Hint: Calculate the total electrons for the complex. Place the bonds in such a way that the total electron count is satisfied.
The metal atom ${\text{Co}}$ contributes nine electrons each.
The ${\text{CO}}$ ligand at terminal position donates two electrons to each metal and one electron to each metal when bridged.

Complete step by step answer:
Step 1:
Calculate the total electrons for the complex $\left[ {{\text{C}}{{\text{o}}_{\text{2}}}{{\left( {{\text{CO}}} \right)}_{\text{8}}}} \right]$.
The metal ${\text{Co}}$ contributes nine electrons each while the ligand ${\text{CO}}$ contributes two electrons each. Thus,
Total electron count for $\left[ {{\text{C}}{{\text{o}}_{\text{2}}}{{\left( {{\text{CO}}} \right)}_{\text{8}}}} \right]$ $ = \left( {2 \times {\text{Electrons of Co}}} \right) + \left( {8 \times {\text{Electrons of CO}}} \right)$
                                                                       $ = \left( {2 \times 9} \right) + \left( {8 \times 2} \right)$
                                                                       $ = 18 + 16$
Total electron count for $\left[ {{\text{C}}{{\text{o}}_{\text{2}}}{{\left( {{\text{CO}}} \right)}_{\text{8}}}} \right]$ $ = 34$
Step 2:
Calculate the number of metal – metal bonds per metal:
Number of metal - metal bonds per metal $ = \dfrac{{\left( {{\text{Number of metal atoms}} \times 18} \right) - {\text{Total electron count}}}}{2}$
The complex $\left[ {{\text{C}}{{\text{o}}_{\text{2}}}{{\left( {{\text{CO}}} \right)}_{\text{8}}}} \right]$ has $2$ ${\text{Co}}$metal atoms. Thus, substitute $2$ for the number of metal atoms and ${\text{34}}$ for the total electron count. Thus,
Number of metal - metal bonds per metal $ = \dfrac{{\left( {2 \times 18} \right) - {\text{34}}}}{2}$
                                                                            $ = \dfrac{{36 - {\text{34}}}}{2}$
                                                                            $ = \dfrac{2}{2}$
Number of metal - metal bonds per metal $ = 1$
Step 3:
Draw the structure for the complex $\left[ {{\text{C}}{{\text{o}}_{\text{2}}}{{\left( {{\text{CO}}} \right)}_{\text{8}}}} \right]$:
There is one metal – metal bond i.e. there is one bond between ${\text{Co}} - {\text{Co}}$.
Each ${\text{Co}}$ atom contributes nine electrons.
The ${\text{CO}}$ ligand at terminal position donates two electrons to each metal and one electron to each metal when bridged. Thus, the structure for the complex is,

Step 4:
Calculate the number of terminal and bridged ${\text{CO}}$ ligands.
From the structure,
There are $6$ terminal ${\text{CO}}$ ligands and $2$ bridged ${\text{CO}}$ ligands.
Thus, the terminal and bridged ${\text{CO}}$ ligands in the compound $\left[ {{\text{C}}{{\text{o}}_{\text{2}}}{{\left( {{\text{CO}}} \right)}_{\text{8}}}} \right]$ are $6{\text{ and 2}}$ respectively.
Thus, the correct option is option (D).

Note: The metal atom ${\text{Co}}$ contributes nine electrons each. The ${\text{CO}}$ ligand at terminal position donates two electrons to each metal and one electron to each metal when bridged. Placing the bonds accurately to satisfy the total electron count gives the exact number of terminal and bridged ligands.