Coordination Compounds: Application Problems (7)

Question

For the complex $[\text{Co(NH}_3)_6]^{3+}$: (a) Find the oxidation state of Co. (b) Determine its coordination number. (c) Predict its geometry, hybridisation, and magnetic behaviour. ($\text{NH}_3$ is a strong-field ligand.)

Solution — Step by Step

Why This Works

In an octahedral field, the five $d$-orbitals split into three lower ($t_{2g}$) and two upper ($e_g$) sets. Strong-field ligands cause large splitting, forcing electron pairing in $t_{2g}$ before any $e_g$ population — this gives a low-spin complex.

The freed inner $d$-orbitals then hybridise with the $4s$ and $4p$ orbitals to form the $d^2 sp^3$ set used for ligand bonding.

Alternative Method

Use crystal field theory directly: count $t_{2g}$ vs $e_g$ electrons. For low-spin $d^6$: $t_{2g}^6 e_g^0$. All paired, so diamagnetic. Same result via a different framework — JEE Main accepts either.

Common Mistake