Question

The EAN of \[{\text{Fe}}\] in ${\left( {{\text{CO}}} \right)_3}{\text{Fe}}{\left( {{\text{CO}}} \right)_3}{\text{Fe}}{\left( {{\text{CO}}} \right)_3}$ is:
A. $34$
B. $35$
C. $36$
D. $37$

Answer 1

Hint: Effective atomic number is abbreviated as EAN. It is also called the $18$ electron rule. It explains that the sum of d electrons of metal and the electrons of ligand is $18$. It denotes the total number of electrons surrounding the nucleus of a metal in a metal complex. This was introduced by Sidgwick.

Complete step by step answer:
Sidgwick’s electronic theory states that the ligands donate the electron pair to the central metal ion and thus form a number of coordinate bonds. EAN rule states that a stable organometallic compound has $18$ valence electrons. This rule is mostly applicable for carbonyl complexes. Other complexes can also use this method to calculate the total number of electrons.
Now consider the molecule ${\left( {{\text{CO}}} \right)_3}{\text{Fe}}{\left( {{\text{CO}}} \right)_3}{\text{Fe}}{\left( {{\text{CO}}} \right)_3}$.

In this molecule, three carbonyl groups are terminal, i.e. the carbonyl compounds on the side. It provides two electrons for each carbonyl. So a total of six electrons are contributed.
Three carbonyl groups are bridged, i.e. which are common for both iron. It donates one electron each for each carbonyl. So a total of three electrons are contributed.
There is a bond between ${\text{Fe - Fe}}$ which donates one electron. And the atomic number of iron is also considered, i.e. $26$
Adding all these values we get
EAN$ = $ Number of electrons in terminal carbonyl $ + $ Number of electrons contributed in bridged carbonyl $ + $Number of electrons for ${\text{Fe - Fe}}$ bond $ + $ atomic number of ${\text{Fe}}$
i.e. ${\text{EAN = 6 + 3 + 1 + 26 = 36}}$, which is a multiple of $18$.
Hence it satisfies the effective atomic number of $18$ electron rule.

So the correct option is C.

Note:
The table shows the number of electrons donated for particular ligands.

Ligands	Number of electrons donated
${\text{CO,P}}{{\text{R}}_3}$	$2$
${\text{N}}{{\text{H}}_3}{\text{,}}{{\text{H}}_2}{\text{O}}$	$2$
${\text{CNR}}$	$2$
Ethylene	$2$
butadiene	$4$
cyclopentadienyl	$5$