Question

The effective atomic number of cobalt in the complex ${\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }}$ is:
A.36
B.33
C.24
D.30

Answer 1

To solve this question, you must recall the formula for calculating the effective atomic number of a metal. It represents the total number of electrons surrounding the nucleus of the metal.
Formula used: ${\text{EAN}} = \left( {{\text{Z}} - {\text{O}}{\text{.S}}{\text{.}}} \right) + \left( {{\text{C}}{\text{.N}}{\text{.}} \times {\text{2}}} \right)$
Where, ${\text{EAN}}$ is the effective atomic number of the central metal atom/ ion
${\text{Z}}$ is the atomic number of the metal whose EAN is to be found
${\text{O}}{\text{.S}}{\text{.}}$ is the oxidation state of the central metal atom/ ion in the complex.
And, ${\text{C}}{\text{.N}}{\text{.}}$ is the coordination number of the central metal in the complex.

Complete step by step answer:
The effective atomic number rule was proposed in order to explain the stability of coordination compounds. It was suggested that metal ion will continue accepting electron pairs till the total number of electrons in the metal ion (after gaining electrons from the donor atoms of the ligands) becomes equal to those present in the next noble gas. This total number of electrons is termed as the effective atomic number.
Effective atomic number can be given as, (Atomic number of metal) – (number of electrons lost in ion formation) + (number of electrons gained from ligands)
Or, ${\text{EAN}} = \left( {{\text{Z}} - {\text{O}}{\text{.S}}{\text{.}}} \right) + \left( {{\text{C}}{\text{.N}}{\text{.}} \times {\text{2}}} \right)$
In the given complex, the oxidation of cobalt is $+ 3$ and it is attached to six ligands and thus the coordination number is $6$
Substituting the values for the given complex in the formula, we get
$EAN = \left( {27 - 3} \right) + \left( {2 \times 6} \right) = 24 + 12$
$EAN = 36$

Thus, the correct answer is A.

Note:
By using the EAN rule, it is possible to predict the number of ligands present in these types of complexes and also in the products of their reactions. Although, it is not necessary that this rule must be followed in all coordination.