Question

Which of the following do not obey Sidgwick’s effective atomic number?
A) $\left[ {Cr{{\left( {CO} \right)}_6}} \right]$
B) ${\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }}$
C) ${\left[ {Ni{{\left( {N{H_3}} \right)}_6}} \right]^{2 + }}$
D) ${\left[ {PtC{l_6}} \right]^{2 - }}$

Answer 1

EAN or effective atomic number is calculated by the formula EAN $=$ Atomic number $-$ Oxidation number $+$ electrons donated by Ligand. According to Sidgwick’s theory this EAN value should be equal to the atomic number of the closest noble gas. Calculate the EAN values of the given complexes.

Complete answer:
Firstly, we write the formula EAN $=$ Atomic number $-$ Oxidation number $+$ electrons donated by Ligand which should be equal to the atomic number of the nearest noble gas.
Let us calculate the EAN values of given complexes.

A) Given complex is $\left[ {Cr{{\left( {CO} \right)}_6}} \right]$
The atomic number of chromium is $24$
Since the ligand CO is a neutral compound, the oxidation state of chromium is $0$
Each CO molecule donates two electrons so the total number of electrons donated by this ligand are $6 \times 2 = 12$
Now we calculate the EAN value.
$EAN = 24 - 0 + 12 = 36$ and this is the atomic number of the nearest noble gas i.e. Krypton.
Therefore, this compound obeys Sidgwick’s rule.

B) Given complex is ${\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{3 + }}$
Atomic number of cobalt is $27$
The ligand $N{H_3}$ is a neutral compound and does not have any charge. But the total charge on the complex is $+ 3$ and hence the oxidation state of cobalt would be $+ 3$
Each $N{H_3}$ molecule donates two electrons so the total number of electrons donated by this ligand are $6 \times 2 = 12$
Now , the EAN value would be $EAN = 27 - 3 + 12 = 36$
Since $36$ is the atomic number of Krypton, this complex obeys Sidgwik’s rule.

C) Given compound is ${\left[ {Ni{{\left( {N{H_3}} \right)}_6}} \right]^{2 + }}$
Similarly, we calculate the EAN value for this complex as follows.
$EAN = 28 - 2 + 12 = 38$
Since this value is not the atomic number of a noble gas, this compound does not obey Sidgwick’s theory.

D) EAN for ${\left[ {PtC{l_6}} \right]^{2 - }}$ is $EAN = 78 - 4 + 12 = 86$ which is the atomic number of the noble gas radon. Hence this complex obeys Sidgwick’s rule.

Hence, the correct answer is option C.

Note: It is to be noted that before calculating the effective atomic number or EAN, the oxidation state of the central atom should be calculated properly. This oxidation state can be calculated as X $+$ oxidation state of the ligands $=$ the total charge. Here X is the oxidation state of the central atom that is to be calculated.