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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2019 · Paper I

Q5(b). d-orbital splitting in square-pyramidal and trigonal-bipyramidal fields

  • 10 marks
  • Answered
Question

Draw, giving reasons, the d-orbital splitting in the 5 coordinate square pyramidal and trigonal bipyramidal arrangements.

Answer in brief

Square pyramid: d_(x²-y²) highest, then d_(z²), then d_(xy), with d_(xz),d_(yz) lowest. Trigonal bipyramid: d_(z²) highest, then the pair d_(x²-y²),d_(xy), then the pair d_(xz),d_(yz).

Key points

  • d_(x²-y²) points straight at the four basal ligands: strongest repulsion, highest (b₁, 3e_σ).
  • d_(z²) points at the one apical ligand and has its small torus near the basal four: second (a₁, 2e_σ). It is far below d_(x²-y²) because the sixth (trans) ligand is missing.
  • d_(xy) lies in the basal plane between the ligands: no σ interaction (b₂); π donors raise it slightly above d_(xz),d_(yz).
  • d_(xz),d_(yz) point between ligands in vertical planes: lowest, degenerate (e).

The full model answer

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

Axes: the four-fold axis of the square pyramid is z, with the metal in the basal plane and four ligands on ± x, ± y; the trigonal bipyramid has two axial ligands on ± z and three in the xy plane.

Square pyramid (C₄ᵥ)

  1. d_(x²-y²) points straight at the four basal ligands: strongest repulsion, highest (b₁, 3e_σ).
  2. d_(z²) points at the one apical ligand and has its small torus near the basal four: second (a₁, 2e_σ). It is far below d_(x²-y²) because the sixth (trans) ligand is missing.
  3. d_(xy) lies in the basal plane between the ligands: no σ interaction (b₂); π donors raise it slightly above d_(xz),d_(yz).
  4. d_(xz),d_(yz) point between ligands in vertical planes: lowest, degenerate (e).

Trigonal bipyramid (D₃ₕ)

  1. d_(z²) points at the two axial ligands and its torus meets the three equatorial ones: highest (a₁', 2+3×14=2.75 e_σ).
  2. d_(x²-y²) and d_(xy) lie in the equatorial plane with the three ligands: a degenerate pair (e', 3×342=1.125 e_σ each).
  3. d_(xz),d_(yz) point between the ligands, above and below the plane: lowest (e”, 0 for σ-only).
  4. Check: each ligand contributes 1 e_σ in all, so the totals are 3+2=5 e_σ (SP) and 2.75+2(1.125)=5 e_σ (TBP).

Application. the two arrangements lie close in energy: low-spin d⁸ [Ni(CN)₅]³- crystallises with both square-pyramidal and trigonal-bipyramidal anions, and Fe(CO)₅ (TBP) shows axial–equatorial exchange through a square-pyramidal intermediate (Berry pseudorotation).

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Model answer to Q5(b), 2019 Paper I: solution page 23
Solution page 23 of 40
Read the whole 2019 solution2019 question paper

All parts of Question 5