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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 · 2026 · Paper I

Q1(a). Attraction and repulsion parameters of the van der Waals equation

  • 5 marks
  • Answered
Question

One real gas equation is van der Waals equation
[(P+n²aV²)(V-nb)=nRT]
Which parameter in the above equation reflects the intermolecular force of attraction and which one reflects the intermolecular force of repulsion? Give their units in SI system.

Answer in brief

a reflects attraction, unit Pa m⁶ mol⁻². b reflects repulsion, unit m³ mol⁻¹.

Key points

  • a molecule about to strike the wall is pulled back by its neighbours. Both the number of collisions and their force fall in proportion to n/V, so the pressure falls by a(n/V)². The term n²a/V² (the internal pressure) puts this…
  • molecules are impenetrable spheres. Two molecules of diameter d exclude a sphere of volume 4/3π d³=8V_(molecule), so per mole b≈4V_(molecule)N_A. The volume open to motion is V-nb, not V.
  • n²a/V² is a pressure, so a=PV²/n²: a: Pa m⁶ mol⁻² (=N m⁴ mol⁻²=kg m⁵ s⁻² mol⁻²)
  • Units of b: nb is a volume, so b: m³ mol⁻¹

The full model answer

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

  1. a, attraction: a molecule about to strike the wall is pulled back by its neighbours. Both the number of collisions and their force fall in proportion to n/V, so the pressure falls by a(n/V)². The term n²a/V² (the internal pressure) puts this back.
  2. b, repulsion: molecules are impenetrable spheres. Two molecules of diameter d exclude a sphere of volume 4/3π d³=8V_(molecule), so per mole b≈4V_(molecule)N_A. The volume open to motion is V-nb, not V.
  3. Units of a: n²a/V² is a pressure, so a=PV²/n²: a: Pa m⁶ mol⁻² (=N m⁴ mol⁻²=kg m⁵ s⁻² mol⁻²)
  4. Units of b: nb is a volume, so b: m³ mol⁻¹
  5. CO₂: a=3.610 atm dm⁶ mol⁻²=0.366 Pa m⁶ mol⁻². A large a gives Z<1 at moderate pressure; at high pressure b wins and Z>1.

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Model answer to Q1(a), 2026 Paper I: solution page 2
Solution page 2 of 55
Read the whole 2026 solution2026 question paper

All parts of Question 1