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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 · 2026 · Mains Paper II

Q1(f). Kₚ and K_c for A+B⇌ C

  • 5 marks
  • Topic: Chemical equilibrium
  • Answered
Question

Write down the relation between Kₚ and K_c of the reaction: A(g)+B(g)⇌ C(g). (Assuming all gases in the reaction mixture behave ideally) Under what conditions Kₚ will be equal to the K_c?

Answer in brief

Kₚ=K_c(RT)^(Δ n)=(K_c)/(RT) (Δ n=-1). Kₚ=K_c only if Δ n=0 (not so here) or if RT=1 in the units used, i.e., T=12.0 K for P in bar and c in mol L⁻¹.

Key points

  • Kₚ=K_c when Δ n=0 (RT drops out); for this reaction Kₚ=K_c would need RT=1: with R=0.08314 L bar K⁻¹ mol⁻¹, T=1/R=12.03 K, a purely formal value.
  • In terms of dimensionless thermodynamic constants, Kₚ=K_c (c^° RT/P^°)^(Δ n); the two coincide when c^° RT=P^°.

The full model answer

Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.

Pᵢ=cᵢRT: Kₚ=(P_C)/(P_AP_B)=(c_C)/(c_Ac_B)·1/RT=K_c(RT)⁻¹, with Δ n=1-2=-1.

  • Kₚ=K_c when Δ n=0 (RT drops out); for this reaction Kₚ=K_c would need RT=1: with R=0.08314 L bar K⁻¹ mol⁻¹, T=1/R=12.03 K, a purely formal value.
  • In terms of dimensionless thermodynamic constants, Kₚ=K_c (c^° RT/P^°)^(Δ n); the two coincide when c^° RT=P^°.
Model answer to Q1(f), 2026 Mains Paper II: solution page 5
Solution page 5 of 22
Read the whole 2026 solution2026 question paper

CoversKₚ and K_cKₚ and K_c for A+B⇌ C

All parts of Question 1