UPSC Civil Services (Mains), Chemistry optional · 2016 · Paper I

Q5(a)(ii). CFSE and spin-only moment of [Co(NH₃)₆]Cl₂

Question

Calculate the crystal-field-stabilization energy and spin-only magnetic moment of [Co(NH₃)₆]Cl₂.

Co(II), d⁷, high spin t_(2g)⁵e_g²: CFSE =-0.8 Δₒ (-8 Dq); three unpaired electrons, μₛ=√(15)=3.87 BM.

Oxidation state: x+6(0)=+2, so Co²+, d⁷.
NH₃ is a medium-field ligand, and Δₒ for a dipositive ion is small (aqua Co²+: Δₒ=8400 cm⁻¹ against a pairing energy P=22 500 cm⁻¹). With Δₒ<P the complex is high spin: t_(2g)⁵e_g².
CFSE =5(-0.4 Δₒ)+2(+0.6 Δₒ), CFSE=-0.8 Δₒ=-8 Dq (two pairs, as in the gaseous ion, so no pairing term).
Unpaired electrons n=3: μₛ=√(3(3+2))=√(15), μₛ=3.87 BM

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

Oxidation state: x+6(0)=+2, so Co²+, d⁷.
NH₃ is a medium-field ligand, and Δₒ for a dipositive ion is small (aqua Co²+: Δₒ=8400 cm⁻¹ against a pairing energy P=22 500 cm⁻¹). With Δₒ<P the complex is high spin: t_(2g)⁵e_g².
CFSE =5(-0.4 Δₒ)+2(+0.6 Δₒ), CFSE=-0.8 Δₒ=-8 Dq (two pairs, as in the gaseous ion, so no pairing term).
Unpaired electrons n=3: μₛ=√(3(3+2))=√(15), μₛ=3.87 BM
Low spin (t_(2g)⁶e_g¹) would give one unpaired electron and only 1.73 BM; magnetic measurement distinguishes the two.

Practising this answer? Write it in a Mains test and get it checked by VKC. Civil Services Mains test series · Telegram