In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $$\Delta_o$$ be the highest?

For an octahedral complex, the magnitude of crystal-field splitting $$\Delta_o$$ depends mainly on two factors:
  • the oxidation state of the metal ion (higher charge → larger $$\Delta_o$$)
  • the position of the ligands in the spectrochemical series (strong-field ligands → larger $$\Delta_o$$).

All four complexes contain cobalt in the +3 oxidation state (Co$$^{3+}$$), so the metal-ion charge is the same for every case. Hence the deciding factor is the field strength of the ligand set.

Spectrochemical series (selected part, strongest on the left):
$$CN^- \gt NO_2^- \gt en \gt NH_3 \gt H_2O \gt ox^{2-} \gt F^- \gt Cl^- \gt Br^-$$

Comparing the given ligands:

Case 1: $$[Co(CN)_6]^{3-}$$   — ligand = $$CN^-$$ (very strong-field)

Case 2: $$[Co(C_2O_4)_3]^{3-}$$   — ligand = $$C_2O_4^{2-}$$ (oxalate, weak-to-moderate field)

Case 3: $$[Co(H_2O)_6]^{3+}$$   — ligand = $$H_2O$$ (moderate-field, weaker than $$NH_3$$)

Case 4: $$[Co(NH_3)_6]^{3+}$$   — ligand = $$NH_3$$ (moderate-field, stronger than $$H_2O$$ but much weaker than $$CN^-$$)

Since $$CN^-$$ is the strongest field ligand among those listed, it produces the largest splitting of the d-orbitals in an octahedral environment. Therefore $$\Delta_o$$ is maximum for $$[Co(CN)_6]^{3-}$$.

Option A which is: $$[Co(CN)_6]^{3-}$$