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Question: The effective atomic number of iron in complex \[\left[ {\left( {{\eta ^5} - {C_5}{H_5}} \right]Fe\l...

The effective atomic number of iron in complex [(η5−C5H5]Fe(II)(CO)2Cl]  \left[ {\left( {{\eta ^5} - {C_5}{H_5}} \right]Fe\left( {II} \right){{\left( {CO} \right)}_2}Cl} \right]\; is:
a.) 36
b.) 46
c.) 39
d.) 40

Explanation

Solution

To get the desired solution of the above problem, firstly we should know the meaning of the effective atomic number. The sum of the number of electrons, donated by all ligands and those present on the central metal ion or atom in the complex is called the effective atomic number (EAN).

Complete step by step answer:
Generally, EAN of central metal ions will be equal to the number of electrons in the nearest noble gas. If the EAN of the central metal is equal to the number of electrons in the nearest noble gas then the complex possesses greater stability.
Hence, we can write a formula for the effective atomic number of a central metal ion in a given complex as follows,
EAN = [(atomic number of central metal) – (the oxidation state of the metal) + (the number of electrons gained by the metal from the ligands through coordination)]
EAN= [Zmetal{Z_{metal}} – (oxidation state of the metal) + 2(coordination number of the metal)].
Here we see that the central atom is iron itself.
So, the atomic number of irons= Zmetal=26{Z_{metal}} = 26,

oxidation state of the iron metal in the complex [(η5−C5H5]Fe(II)(CO)2Cl]  \left[ {\left( {{\eta ^5} - {C_5}{H_5}} \right]Fe\left( {II} \right){{\left( {CO} \right)}_2}Cl} \right]\;= +2, (it is also the same as the number of the electrons lost for the formation of the ion)
Also, the number of the electrons gained by the metal from the ligands is the same as that of the twice the coordination number of the metal.
Here, the number of the electrons gained by the metal iron (II) from the ligands = 12
Hence putting the values in the formula,
EAN=[26−2=12]=36EAN = \left[ {26 - 2 = 12} \right] = 36

Hence The effective atomic number of irons in complex [(η5−C5H5]Fe(II)(CO)2Cl]  \left[ {\left( {{\eta ^5} - {C_5}{H_5}} \right]Fe\left( {II} \right){{\left( {CO} \right)}_2}Cl} \right]\; is 36.
So, the correct answer is “Option A”.

Note: Scientist Sidgwick suggested that the central atom or ion will accept electron pairs from ligands till the EAN of the metal equalizes itself with the atomic number of the nearest noble gas. There is a rule known as EAN rule. EAN rule, that in a number of metal complexes the metal atom tends to surround itself with sufficient ligands that the resulting effective atomic number is numerically equal to the atomic number of the noble-gas element found in the same period in which the metal is situated.