Question

The non-existent metal carbonyl among the following is?
A. $Cr{(CO)_6}$
B. $Mn{(CO)_5}$
C. $Ni{(CO)_4}$
D. $Fe{(CO)_5}$

Answer 1

Hint:To test the existence of metal carbonyls, we can make use of the $EAN$ rule, where $EAN$ stands for effective atomic number. It is defined as the sum of the atomic number of the central atom and the number of electrons donated by the ligands attached to it.
Formula used:
$EAN = $ atomic number of central atom + number of electrons contributed by ligands
Where $EAN$ stands for Effective Atomic Number.

Complete step by step answer:
-The $EAN$ rule states that for a metal carbonyl to be stable and for it to exist naturally, the sum of the atomic number of the central atom and the number of electrons contributed in the coordination compound by the ligands attached to it should be equal to the atomic number of the noble gas present in the period to which the central atom belongs to. Or in other words, the $EAN$ number should be equal to the atomic number of the first noble atom coming after the central atom in the periodic table.
-Let us now calculate the $EAN$ numbers for each compound given.
$EAN = $ atomic number of central atom + number of electrons contributed by ligands
-Central atoms of all the compounds given are members of period 4 in the periodic table, in which the noble gas is Krypton, having an atomic number of 36. So, the $EAN$ numbers of each compound should be equal to 36 for them to exist. Also, in the ligand here, $CO$, is a unidentate ligand (attached to the central atom through only one bond), and therefore each $CO$ ligand will donate a pair of electrons, that is, 2 electrons.
-Therefore, for $Cr{(CO)_6}$ atomic number of the central atom, $Cr$ is 24 and the number of electrons contributed by the ligands are $(6 \times 2) = 12$, as there are six $CO$ ligands, each contributing a pair of electrons. Substituting these values, we get:
$EAN = 24 + 12 = 36$
Therefore, this carbonyl can exist.
-For $Mn{(CO)_5}$, atomic number of central atom is 25 and the number of electrons contributed by the ligands are $(5 \times 2) = 10$, as there are five $CO$ ligands, each contributing a pair of electrons. Substituting these values, we get:
$EAN = 25 + 10 = 35$
Therefore, this carbonyl cannot exist.

-For $Ni{(CO)_4}$ atomic number of the central atom, $Ni$ is 28 and the number of electrons contributed by the ligands are $(4 \times 2) = 8$, as there are four $CO$ ligands, each contributing a pair of electrons. Substituting these values, we get:
$EAN = 28 + 8 = 36$
Therefore, this carbonyl can exist.
-For $Fe{(CO)_5}$ atomic number of the central atom, $Fe$ is 26 and the number of electrons contributed by the ligands are $(5 \times 2) = 10$, as there are five $CO$ ligands, each contributing a pair of electrons. Substituting these values, we get:
$EAN = 26 + 10 = 36$
Therefore, this carbonyl can exist.
Hence, the only carbonyl which cannot exist is option B.


Note:
While calculating the number of electrons make a note to always check the denticity (number of bonds through which the ligand is attached to the central atom) of the ligand. Bidentate ligands like ethylenediamine donate four pairs of electrons. Also, $EAN$ can have an additional definition, where it is defined as the sum of the number of electrons of the central atom and the number of electrons contributed by the ligands. Both yield the same result.