On the basis of crystal field theory explain why Co(III) forms paramagnetic octahedral complex with weak field ligands whereas it forms diamagnetic octahedral complex with strong field ligands.

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> [!TLDR]
> Crystal field theory explains that the **splitting of $d$-orbitals** in an octahedral field ($\Delta_o$) relative to the pairing energy ($P$) determines the electron configuration. For Co(III), weak field ligands give a **high-spin, paramagnetic** $t_{2g}^4 e_g^2$ configuration, while strong field ligands give a **low-spin, diamagnetic** $t_{2g}^6 e_g^0$ configuration.

## The Core Idea: Crystal Field Splitting and Electron Configuration

Crystal field theory (CFT) is a model that explains the electronic structure of transition metal complexes. In an octahedral complex, the five $d$-orbitals are no longer degenerate. The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals (the $e_g$ set) point directly at the ligands and experience strong repulsion, raising their energy. The $d_{xy}$, $d_{xz}$, and $d_{yz}$ orbitals (the $t_{2g}$ set) point between the ligands and experience less repulsion, lowering their energy. The energy gap between these two sets is called the **crystal field splitting energy**, denoted by $\Delta_o$ (or $10 Dq$).

The key to understanding the magnetic behaviour of a $d^6$ ion like Co(III) lies in a simple competition: **the energy cost of pairing electrons ($P$) versus the energy gain from occupying the lower-energy $t_{2g}$ orbitals ($\Delta_o$)**.

1.  **Identify the metal ion and its $d$-electron count.** Cobalt in the +3 oxidation state, Co(III), has an electronic configuration of $[Ar] 3d^6$. This means we have six electrons to place in the $d$-orbitals of the octahedral complex.

2.  **Understand the two competing factors.** When placing electrons into the split $d$-orbitals, two rules apply:
    *   **Hund's rule:** Electrons prefer to occupy different orbitals with parallel spins to minimise electron-electron repulsion.
    *   **Aufbau principle:** Electrons will first fill the lower-energy $t_{2g}$ orbitals.
    The conflict arises because placing an electron in a higher-energy $e_g$ orbital (following Hund's rule) costs energy $\Delta_o

Q.On the basis of crystal field theory explain why Co(III) forms paramagnetic octahedral complex with weak field ligands whereas it forms diamagnetic octahedral complex with strong field ligands.

The Core Idea: Crystal Field Splitting and Electron Configuration

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