The complex that has highest crystal field splitting energy (Δ), is:

🧠 Compare Δ Across the Four

| Complex | Metal/OS | Ligand | Geometry | Δ | |---|---|---|---|---| | $\mathrm{K_3[Co(CN)_6]}$ | Co(III) | 6 CN⁻ (strong) | Oct | largest ✓ | | $[\mathrm{Co(NH_3)_5Cl}]\mathrm{Cl_2}$ | Co(III) | 5 NH₃ + Cl⁻ | Oct | medium-high | | $[\mathrm{Co(NH_3)_5(H_2O)}]\mathrm{Cl_3}$ | Co(III) | 5 NH₃ + H₂O | Oct | medium-high (slightly more than the Cl⁻ one) | | $\mathrm{K_2[CoCl_4]}$ | Co(II) | 4 Cl⁻ | Td | smallest ($\Delta_t$) |

$\mathrm{K_3[Co(CN)_6]}$ wins: highest OS (+3), strongest ligand (CN⁻), full octahedral coordination.

🗺️ Three Multiplicative Effects

For maximum Δ, look for the product of three large factors:

1. High oxidation state: +3 > +2 (more positive metal pulls ligands closer, stronger field).
2. Strong-field ligand: CN⁻ at the top of the spectrochemical series.
3. Octahedral geometry: $\Delta_o > \Delta_t$ for the same metal/ligand.

$\mathrm{K_3[Co(CN)_6]}$ scores the highest on all three.

⚡ The Co(III)–CN⁻ Reference

$[\mathrm{Co(CN)_6}]^{3-}$ with $\Delta_o \approx 33{,}500$ cm⁻¹ is one of the largest measured Δ values for a 3d metal. The complex absorbs in the UV → appears nearly colourless or pale yellow.

⚠️ Td Δ_t Is Always Smaller

$\mathrm{K_2[CoCl_4]}$ — even with Co(II) and Cl⁻ (both weak field) — sits at the bottom not just because of the ligand but also because $\Delta_t \approx \frac{4}{9}\Delta_o$. Td vs oct alone is ~50% reduction in Δ.

$\boxed{\text{Answer: (1) } \mathrm{K_3[Co(CN)_6]}}$