Chemistry - Coordination Chemistry Question with Solution | TestHub

The Effective Atomic Number (EAN) rule states that a metal atom in a complex tends to achieve the electron configuration of the nearest noble gas. This means the sum of the metal's electrons and the electrons donated by the ligands should equal the atomic number of a noble gas (e.g., Kr=36, Xe=54, Rn=86).

Let's calculate EAN for each option:

A. ${\mathrm{K}}_3\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$

Iron (Fe) atomic number = 26. Oxidation state of Fe is +3 (since K is +1, CN is -1).

Electrons from Fe³⁺ = $26-3=23$.

Electrons from 6 CN⁻ ligands (each donates 2 electrons) = $6\times 2=12$.

EAN = $23+12=35$. This does not follow the EAN rule (Kr=36).

B. $\left[\mathrm{Fe}{\left({\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5\right)}_2\right]$ (Ferrocene)

Iron (Fe) atomic number = 26. Oxidation state of Fe is +2 (since each ${\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5$ is a 6-electron donor, but in ferrocene, it's considered a 5-electron donor, making the overall charge neutral for Fe(II)).

Electrons from Fe²⁺ = $26-2=24$.

Electrons from two ${\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5$ ligands (each donates 5 electrons in this context) = $2\times 5=10$.

EAN = $24+10=34$.

Alternatively, considering ${\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5$ as a 6-electron donor (aromatic cyclopentadienyl anion, C₅H₅⁻), then Fe is in 2+ oxidation state.

Electrons from Fe²⁺ = $26-2=24$.

Electrons from two C₅H₅⁻ ligands = $2\times 6=12$.

EAN = $24+12=36$. This follows the EAN rule (Kr=36).

C. $\mathrm{Na}\left[\mathrm{Ag}(\mathrm{CN}{)}_2\right]$

Silver (Ag) atomic number = 47. Oxidation state of Ag is +1.

Electrons from Ag⁺ = $47-1=46$.

Electrons from 2 CN⁻ ligands = $2\times 2=4$.

EAN = $46+4=50$. This does not follow the EAN rule (Xe=54).

D. $\left[\mathrm{Ni}(\mathrm{en}{)}_3\right]{\mathrm{Cl}}_2$

Nickel (Ni) atomic number = 28. Oxidation state of Ni is +2.

Electrons from Ni²⁺ = $28-2=26$.

Electrons from 3 'en' (ethylenediamine) ligands (each is a bidentate ligand, donating 2 electrons per donor atom, so 4 electrons per 'en' molecule) = $3\times 4=12$.

EAN = $26+12=38$. This does not follow the EAN rule (Kr=36).

Therefore, only option B, $\left[\mathrm{Fe}{\left({\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5\right)}_2\right]$, follows the Sidgwick EAN rule.

The final answer is $\boxed{B}$