Stability Hybridization and Isomerism of Transition Metal Coordination Complexes

To determine the correct statements, let us evaluate each statement individually:

1. Statement A: $[\text{Fe}(\text{C}_2\text{O}_4)_3]^{3-}$ is the most stable complex among $[\text{Fe}(\text{OH})_6]^{3-}$, $[\text{Fe}(\text{C}_2\text{O}_4)_3]^{3-}$, and $[\text{Fe}(\text{SCN})_6]^{3-}$.

   • The oxalate ion ($\text{C}_2\text{O}_4^{2-}$) is a bidentate chelating ligand. Chelation leads to an increase in entropy upon complex formation, conferring extra thermodynamic stability (known as the chelate effect) compared to complexes with unidentate ligands such as $\text{OH}^-$ and $\text{SCN}^-$.
   • Hence, $[\text{Fe}(\text{C}_2\text{O}_4)_3]^{3-}$ is indeed the most stable complex.
   • Statement A is correct.

2. Statement B: The stability of $[\text{Cu}(\text{NH}_3)_4]^{2+}$ is greater than that of $[\text{Cu}(\text{en})_2]^{2+}$.

   • Ethylenediamine ($\text{en}$) is a bidentate ligand that forms stable five-membered chelate rings with $\text{Cu}^{2+}$, whereas $\text{NH}_3$ is a monodentate ligand.
   • Due to the chelate effect, $[\text{Cu}(\text{en})_2]^{2+}$ is significantly more stable than $[\text{Cu}(\text{NH}_3)_4]^{2+}$.
   • Statement B is incorrect.

3. Statement C: The hybridization of $\text{Fe}$ in $\text{K}_4[\text{Fe}(\text{CN})_6]$ is $d^2sp^3$.

   • In $\text{K}_4[\text{Fe}(\text{CN})_6]$, the oxidation state of iron is $+2$, which corresponds to the electronic configuration $\text{Fe}^{2+}: [\text{Ar}]\,3d^6$.
   • Since cyanide ($\text{CN}^-$) is a strong field ligand, it causes pairing of the $3d$ electrons: $\text{Fe}^{2+} \text{ in } [\text{Fe}(\text{CN})_6]^{4-}: 3d^6 \rightarrow (t_{2g})^6 (e_g)^0$
   • This leaves two empty $3d$ orbitals available for hybridization along with one $4s$ and three $4p$ orbitals, resulting in $d^2sp^3$ hybridization (inner orbital complex).
   • Statement C is correct.

4. Statement D: $[\text{Fe}(\text{NO}_2)_3\text{Cl}_3]^{3-}$ exhibits linkage isomerism.

   • The nitrite ion ($\text{NO}_2^-$) is an ambidentate ligand capable of coordinating to the metal center through either the nitrogen atom ($-\text{NO}_2$) or an oxygen atom ($-\text{ONO}$).
   • Consequently, the complex exhibits linkage isomerism.
   • Statement D is correct.

5. Statement E: $\text{NO}_2^-$ and $\text{SCN}^-$ ligands are NOT ambidentate ligands.

   • Ambidentate ligands possess two different donor atoms through which they can bind to a metal ion. Both $\text{NO}_2^-$ (donor atoms: $\text{N}$ or $\text{O}$) and $\text{SCN}^-$ (donor atoms: $\text{S}$ or $\text{N}$) are standard examples of ambidentate ligands.
   • Statement E is incorrect.

Thus, the correct statements are A, C and D only.

Correct Option: C