Effective Atomic Number (EAN) Calculation

The Effective Atomic Number (EAN) rule helps predict the stability of coordination complexes. It is calculated as the total number of electrons around the central metal ion in the complex. The formula used for calculating EAN is:

EAN = Atomic number of metal - Oxidation state of metal + Number of electrons donated by ligands

Let's apply this formula to the complex ion $[\text{Fe(CN)}_6]^{4-}$.

Identifying the Central Metal and its Atomic Number

The central metal atom in the complex $[\text{Fe(CN)}_6]^{4-}$ is Iron (Fe). The atomic number of Iron (Fe) is 26.

Determining the Oxidation State of $\text{Fe}^{2+}$

We need to find the oxidation state of Iron in the complex ion $[\text{Fe(CN)}_6]^{4-}$. Let the oxidation state of Fe be $x$. The cyanide ligand ($\text{CN}^-$) has a charge of -1. There are 6 cyanide ligands. The overall charge of the complex ion is -4.

We can set up the equation:

$\text{Oxidation state of Fe} + (\text{Number of ligands} \times \text{Charge of ligand}) = \text{Overall charge of complex}$

$x + (6 \times -1) = -4$
$x - 6 = -4$
$x = -4 + 6$
$x = +2$

So, the oxidation state of Iron in $[\text{Fe(CN)}_6]^{4-}$ is +2. This means the central metal ion is $\text{Fe}^{2+}$.

Calculating Electrons Donated by Ligands

The ligand is cyanide ($\text{CN}^-$). It is a monodentate ligand, meaning each $\text{CN}^-$ ligand donates one pair of electrons (2 electrons) to the central metal ion. There are 6 such ligands.

Total electrons donated by ligands = Number of ligands $\times$ Electrons donated per ligand
Total electrons donated by ligands = $6 \times 2 = 12$ electrons.

Calculating the Effective Atomic Number (EAN)

Now, we can use the EAN formula:

EAN = Atomic number of Fe - Oxidation state of Fe + Electrons donated by ligands
EAN = $26 - (+2) + 12$
EAN = $24 + 12$
EAN = $36$

The Effective Atomic Number (EAN) of $\text{Fe}^{2+}$ in the complex $[\text{Fe(CN)}_6]^{4-}$ is 36.

Significance of EAN 36

An EAN value of 36 corresponds to the atomic number of the noble gas Krypton (Kr). Complexes that achieve an EAN equal to the atomic number of a noble gas are often stable, following the EAN rule (also known as the 18-electron rule in many cases for transition metals).