Identify the complex ion in potassium ferrocyanide

Potassium ferrocyanide is: $K_4[Fe(CN)_6]$

So the coordination entity is: $[Fe(CN)_6]^{4-}$

Find oxidation state of iron

Let oxidation state of Fe be $x$.

Each $CN^-$ ligand has charge $-1$, so total ligand charge is $-6$. Overall charge on the complex is $-4$.

Therefore, $x-6=-4$ $x=+2$

So iron is: $Fe^{2+}$

Find the d-electron configuration of $Fe^{2+}$

Atomic number of Fe is $26$.

Neutral Fe: $[Ar]3d^64s^2$

For $Fe^{2+}$, remove two electrons from $4s$ first: $Fe^{2+}=[Ar]3d^6$

So it is a $d^6$ system.

Determine strong field or weak field

The ligand $CN^-$ is a strong field ligand. Therefore, $[Fe(CN)_6]^{4-}$ is a low-spin octahedral complex.

Fill electrons in octahedral crystal field

In an octahedral field, the $d$ orbitals split into:

• lower energy $t_{2g}$
• higher energy $e_g$

For low-spin $d^6$: $t_{2g}^6 e_g^0$

Count pairs of electrons in $t_{2g}$

The $t_{2g}$ set has 3 orbitals, and $6$ electrons occupy them as: $\uparrow\downarrow\; \uparrow\downarrow\; \uparrow\downarrow$

Hence, number of electron pairs in the $t_{2g}$ set is: $3$

Comparison with stored answer

Derived answer = $3$

Stored correct answer = $3$

Hence, both agree.