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Question: The non-existent metal carbonyl among the following is? A. \(Cr{(CO)_6}\) B. \(Mn{(CO)_5}\) C....

The non-existent metal carbonyl among the following is?
A. Cr(CO)6Cr{(CO)_6}
B. Mn(CO)5Mn{(CO)_5}
C. Ni(CO)4Ni{(CO)_4}
D. Fe(CO)5Fe{(CO)_5}

Explanation

Solution

To test the existence of metal carbonyls, we can make use of the EANEAN rule, where EANEAN 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=EAN = atomic number of central atom + number of electrons contributed by ligands
Where EANEAN stands for Effective Atomic Number.

Complete step by step answer:
-The EANEAN 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 EANEAN 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 EANEAN numbers for each compound given.
EAN=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 EANEAN numbers of each compound should be equal to 36 for them to exist. Also, in the ligand here, COCO, is a unidentate ligand (attached to the central atom through only one bond), and therefore each COCO ligand will donate a pair of electrons, that is, 2 electrons.
-Therefore, for Cr(CO)6Cr{(CO)_6} atomic number of the central atom, CrCr is 24 and the number of electrons contributed by the ligands are (6×2)=12(6 \times 2) = 12, as there are six COCO ligands, each contributing a pair of electrons. Substituting these values, we get:
EAN=24+12=36EAN = 24 + 12 = 36
Therefore, this carbonyl can exist.
-For Mn(CO)5Mn{(CO)_5}, atomic number of central atom is 25 and the number of electrons contributed by the ligands are (5×2)=10(5 \times 2) = 10, as there are five COCO ligands, each contributing a pair of electrons. Substituting these values, we get:
EAN=25+10=35EAN = 25 + 10 = 35
Therefore, this carbonyl cannot exist.

-For Ni(CO)4Ni{(CO)_4} atomic number of the central atom, NiNi is 28 and the number of electrons contributed by the ligands are (4×2)=8(4 \times 2) = 8, as there are four COCO ligands, each contributing a pair of electrons. Substituting these values, we get:
EAN=28+8=36EAN = 28 + 8 = 36
Therefore, this carbonyl can exist.
-For Fe(CO)5Fe{(CO)_5} atomic number of the central atom, FeFe is 26 and the number of electrons contributed by the ligands are (5×2)=10(5 \times 2) = 10, as there are five COCO ligands, each contributing a pair of electrons. Substituting these values, we get:
EAN=26+10=36EAN = 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, EANEAN 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.