Question

The EAN of metal atoms in $[Fe{(CO)_2}{(N{O^ + })_2}]$ and $[Co{(CO)_8}]$ respectively are
A.$34,35$
B.$34,36$
C.$36,36$
D.$36,35$

Answer 1

$\,EAN\,$ consists of the electrons of the metal atom and the bonding electrons of the atoms and molecules accompanying electron-donation. It represents the total number of electrons in a metal complex containing the nucleus of a metal atom.
Formula used: The $EAN$ or effective atomic number can be calculated using the formula,
$EAN = Z - X + Y$ where,
$Z =$ Atomic number of central metal atom
$X =$ Oxidation state of central metal atom or the number of electrons lost by central metal atom
$Y =$ Total number of electrons donated by ligands

Complete step by step answer:
$EAN$ is the effective atomic number. By name itself we can say that it is the actual atomic number a metal finally owned.
We know that atomic number is the number of electrons in an atom, so the effective atomic number is the total number of electrons around an atom in a complex.
Now let’s solve the question,
For substituting the formula mentioned above, we need $Z,X,Y$ values.
First consider with $[Fe{(CO)_2}(N{O^ + })]$
Atomic number of $Fe$ is $26$, that is $Z = 26$
To calculate oxidation state let’s assume $x$ is the charge on $Fe$. Charge on $CO$ is $0$ and on $N{O^ + }$is $+ 1$
So, $x + 0 + (1 \times 2) = 0$
$x + 2 = 0$
$x = - 2$
So $X = - 2$
The number of electrons donated by each ligand through one bond will be two , there are $4$ ligands, so the total number of electrons donated by $4$ ligands will be $4 \times 2 = 8$. That is $Y = 8$.

Substitute these values in formula given in hint
$EAN = Z - X + Y$
$= 26 - ( - 2) + 8$
EAN of iron = $36$
Next complex is $[C{o_2}{(CO)_8}]$
Atomic number of $Co$ is $27$,$Z = 27$
Let’s calculate oxidation state,
$2x + (8 \times 0) = 0$
$x = 0$
That is $X = 0$
The total number of electrons donated by ligand is $Y = 8 \times 2 = 16$
But while calculating here , note that there are two $Co$ atoms here, so total contribution of electron by it will be $27 \times 2 = 54$
Here one more additional bond occur by two metal atom $(Co - Co)$ bond, in that bond there will be $2$ atom ,
So $EAN$ will be
$= 54 + 0 + 16 + 2 = 72$ this is for two $Co$,for one $Co$ it will be $\frac{{72}}{2} = 36$
So the right option is C, $36,36$.

Note:
$EAN$ should always be calculated by a general logic, that is the total number of electrons in a metal atom is surrounded by a metal complex. Using just the formula may lead to wrong answers as we know the case of $[C{o_2}{(CO)_8}]$.