Question: What is ‘effective atomic number’(EAN)? Calculate the effective atomic number of the central atom ...

Question

What is ‘effective atomic number’(EAN)?
Calculate the effective atomic number of the central atom in the following compounds:
(a) $K_4 Fe(CN)_6$ Fe(Z = 26) (b) $Cr(CO)_6$ Cr(Z = 24)

Answer 1

Solution

Try to figure out what exactly the effective atomic number means. EAN is the total number of electrons of the atom which are involving or not involving in the bond formation. We have to subtract the charge of the central atom while calculating the EAN of the atom.

Complete step by step answer:
We know that coordination compounds are formed by donation of electron pairs by ligands. In coordination compounds, central atom electrons do not involve bonding.
EAN of the central atom of coordination compound = Total number of electrons in the uncharged central atom – charge of the central atom in the compound + number of electrons that are involved in forming a complex.
Let us calculate EAN of given atoms:
(a) Complex is $K_4 Fe(CN)_6$
The central atom is Fe.
The total number of electrons in the uncharged central atom is the atomic number of the central atom which is equal to 26.
Potassium atom valency is +1 and cyanide ion valency is -1. Total charge on the complex is 0. Let x be in charge of the Fe atom. Then
$4\quad ×\quad (+1)\quad +\quad x\quad +\quad 6\quad ×\quad (-1)\quad =\quad 0$
$4\quad +\quad x\quad -\quad 6\quad =\quad 0$
$x\quad =\quad 2$
The charge of the Fe atom is +2.
EAN of Fe atom = $26\quad -\quad (+2)\quad +\quad 12\quad =\quad 38\quad -\quad 2\quad =\quad 36$
Therefore EAN of the central atom of complex $K_4 Fe(CN)_6$ is 36.
(b) The complex is $Cr(CO)_6$
The central atom is Cr.
The total number of electrons in the uncharged central atom is the atomic number of the central atom which is equal to 24.
The charge of carbonyl ligand is 0 so the charge of the central atom will be 0.
EAN of Cr atom = $24\quad +\quad 12\quad =\quad 36$

Therefore EAN of Cr atoms in $Cr(CO)_6$ is 36.

Note: Complexes with EAN equal to the atomic number of noble gas nearest to the central metal atom are stable. We need to check the sign of charge while calculating the EAN of the central atom.