Q8(a)(ii). Crystal field theory; [CoF₆]³- versus [Co(NH₃)₆]³+

Oₕt_(2g) -0.4Δₒ, e_g +0.6ΔₒSPIN STATEΔₒ vs pairing energy Pμₛ4.90 μ_B vs 0

Crystal field theory

1. Model: the metal–ligand bond is purely electrostatic; ligands are point charges (or point dipoles). In the isolated ion the five d orbitals are degenerate.
2. Octahedral field: d_(x²-y²) and d_(z²) point at the ligands and are raised (e_g, +0.6Δₒ); d_(xy), d_(xz), d_(yz) point between them and are lowered (t_(2g), -0.4Δₒ). The barycentre is unchanged. Tetrahedral: the order is reversed and Δₜ≈49Δₒ.
3. Filling for d⁴–d⁷: if Δₒ<P (pairing energy) electrons go to e_g unpaired (high spin); if Δₒ>P they pair in t_(2g) (low spin). Δₒ follows the spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < H₂O < NH₃ < en < CN⁻ < CO.
4. CFSE =(-0.4n_t_(2g)+0.6n_(e_g))Δₒ (+ pairing energies) explains colour (d–d transitions of energy Δₒ), magnetism, hydration-enthalpy trends and Jahn–Teller distortions.

How CFT differs from VBT

1. VBT: covalent bonds from ligand pairs into empty hybrid orbitals of the metal (d²sp³ inner orbital, sp³d² outer orbital). CFT: no hybridisation, no covalency; only the splitting of d levels by the ligand field.
2. VBT cannot explain colour or spectra, does not give the magnitude of magnetic moments or their temperature dependence, and cannot predict which complexes are high spin; CFT explains these through Δₒ and P (and gives numbers such as CFSE). Neither model includes π bonding; ligand field (MO) theory does.

[CoF₆]³- and [Co(NH₃)₆]³+

1. Both contain Co(III), d⁶, octahedral.
2. F⁻ is a weak-field ligand: Δₒ<P. Configuration t_(2g)⁴e_g², 4 unpaired electrons: μₛ=√(4(4+2))= 4.90 μ_B, paramagnetic (measured close to 5 μ_B). CFSE =-0.4Δₒ.
3. NH₃ gives a much larger Δₒ (higher in the spectrochemical series, and Co(III) is highly charged): Δₒ>P. Configuration t_(2g)⁶e_g⁰, no unpaired electron: diamagnetic. CFSE =-2.4Δₒ+2P.
4. The same metal ion and geometry give different magnetism only because of the size of Δₒ relative to P; in VBT language [CoF₆]³- is an outer-orbital (sp³d²) and [Co(NH₃)₆]³+ an inner-orbital (d²sp³) complex, a label CFT explains.

Application. nearly all Co(III) complexes are low spin and therefore kinetically inert (t_(2g)⁶); [CoF₆]³- and [Co(H₂O)₃F₃] are the exceptions. The inertness is why Werner could isolate and count the isomers of cobalt(III) ammines.