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UPSC Combined Geo-Scientist

Chemist

  • 3 descriptive papers
  • 200 marks each
  • 3 h per paper

Mains Paper II covers physical chemistry.

UPSC Combined Geo-Scientist, Mains · 2018 · Mains Paper II

Q1(p). Normal-mode counts

Question

Find the number of normal vibrational modes of (i) N₂; (ii) CO₂; (iii) H₂O; (iv) acetylene; (v) ethylene.

Answer in brief

The respective numbers are 1, 4, 3, 7 and 12.

Key points

  • A linear N-atom molecule has 3N-5 vibrational modes. Thus N₂ has 1, CO₂ has 4 and linear C₂H₂ has 7.
  • A nonlinear molecule has 3N-6 modes: bent water has 3 and planar but nonlinear C₂H₄ has 12.
  • Degenerate bending coordinates count separately; the number of distinct observed frequencies may therefore be smaller than the number of normal modes.

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

Model answer to Q1(p), 2018 Mains Paper II: solution pages 5 and 6
Solution pages 5 and 6 of 17
Read the whole 2018 solution2018 question paper

CoversNormal-mode countsVibrational spectroscopy

All parts of Question 1