Question

Pick out the complex in which the central metal atom obeys the EAN rule strictly:
(A.) $K_{ 4 }[Fe(CN)_{ 6 }]$
(B.) $K_{ 3 }[Fe(CN)_{ 6 }]$
(C.) $[Cr(H_{ 2 }O)_{ 6 }]Cl_{ 3 }$
(D.) $[Cu(NH_{ 3 })_{ 4 }]SO_{ 4 }$

Answer 1

Hint: We should know that EAN is the acronym for an effective atomic number. It is the sum total of electrons around the central metal ion present in any complex compound.

Complete step by step solution:
First, let’s know about the EAN rule -
This rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals (1 s orbitals, 3 p orbitals, and 5 d orbitals). These nine valence orbitals can collectively accommodate 18 electrons as either bonding or nonbonding electron pairs. It is the attainment of noble gas configuration.
The total number of electrons linked with the central metal atom or ion in a complex plus the electrons donated by the ligand is known as Effective Atomic Number, i.e., EAN.

The formula for EAN is,
EAN = Z - X + Y
Z is the atomic number of the metal.
X is the number of electrons lost from metal during the formation of the metal ion
Y is the number of electrons donated by ligands

Now, let's calculate the EAN value of the given complexes.

A) $K_{ 4 }[Fe(CN)_{ 6 }]$ = (26−2)+(6×2) = 36 = follows EAN rule.
B) $K_{ 3 }[Fe(CN)_{ 6 }]$ = (26−3)+(6×2) = 35 = does not follow the EAN rule.
C) $[Cr(H_{ 2 }O)_{ 6 }]Cl_{ 3 }$ = (24-3)+(6x2) = 33 = does not follow the EAN rule.
D) $[Cu(NH_{ 3 })_{ 4 }]SO_{ 4 }$= (29−2)+(4×2) = 35 = does not follow EAN rule.

Here, only (A) $K_{ 4 }[Fe(CN)_{ 6 }]$ follows the correct EAN rule.

Therefore, we can conclude that the correct answer to this question is option A.

Note: You should know that Sidgwick suggested that the metal ion will continue accepting electron pairs till the total number of electrons in the metal ion and those donated by ligands is equal to that of the next higher noble gas.
This total number of electrons is called the effective atomic number (EAN) of the metal.