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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 · 2024 · Mains Paper II

Q1(a). Volume and critical temperature of two van der Waals gases

Question

Gases A and B are van der Waals gases. Their van der Waals constants (in SI units) are: a = 21.764 (A) and 3.457 (B); 10³b = 0.024 (A) and 0.024 (B). (i) Which of these would occupy greater volume under identical conditions? (ii) Which gas has the highest critical temperature? [table of a and b values given in the paper]

Answer in brief

(i) B occupies the greater volume (smaller a, weaker attraction); (ii) A has the higher critical temperature: Tc ∝ a at equal b, ratio 6.30.

Key points

  • Same b ⇒ same excluded volume (same molecular size); the gases differ only in a, the intermolecular attraction.
  • aB < aA ⇒ smaller internal pressure a/Vm²; the molecules are pulled together less ⇒ B occupies the greater volume.
  • Tc = 8a/27Rb; at equal b, Tc ∝ a: Tc(A)/Tc(B) = 21.764/3.457 = 6.30 ⇒ A has the higher Tc.
  • Stronger attraction lets A be liquefied at a higher temperature.

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(a), 2024 Mains Paper II: solution pages 3 and 4
Solution pages 3 and 4 of 37
Read the whole 2024 solution2024 question paper

Topic notes: real gases, the van der Waals equation, critical constants and Boyle temperature, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coversvan der Waals constantscritical temperatureTc = 8a/27Rbcompressibility factorreal gas volume

All parts of Question 1