UPSC Combined Geo-Scientist, Mains · 2023 · Mains Paper II
Q1(b). Exceptional behaviour of hydrogen and helium
Question
Why do hydrogen and helium show exceptional behaviour while discussing with van der Waals equation?
Answer in brief
Their attraction constant a is very small, so b > a/RT at ordinary temperatures: Z > 1 at every pressure with no dip, and they warm on throttled expansion.
Key points
- Only two electrons, low polarisability ⇒ weak dispersion forces ⇒ very small a (He 0.0346, H₂ 0.248 bar L² mol⁻²).
- At 298 K, b > a/RT: initial slope positive ⇒ Z > 1 from P = 0, no minimum; N₂ and CO₂ first dip below Z = 1.
- Room temperature is far above their Boyle temperature (a/Rb: He 18 K, H₂ 112 K).
- Their Joule–Thomson inversion temperatures are low, so at room temperature they warm on throttled expansion.
- Below TB they too show the dip: the behaviour is “exceptional” only at ordinary temperatures.
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.
Covershydrogen and heliumcompressibility factorvan der Waals equationBoyle temperatureJoule–Thomson inversion temperature
All parts of Question 1
- 1(a) van der Waals equation: meaning of a and b5 marks
- 1(b) Exceptional behaviour of hydrogen and helium5 marks
- 1(c) Unit cell of solid C₆₀ and its carbon atoms5 marks
- 1(d) Planes that diffract: simple cubic, a = 5 Å5 marks
- 1(e) Chemical potential and its link with Gibbs energy5 marks
- 1(f) Debye–Hückel limiting law for γ±5 marks
- 1(g) Activation energy of 2HI → H₂ + I₂5 marks
- 1(h) Best coagulant for the Sb₂S₃ sol5 marks
- 1(i) E° of Na⁺/Na from ΔrH° and ΔrS°5 marks
- 1(j) pH from a calomel–quinhydrone cell5 marks
- 1(k) Degeneracy of the level 6h²/8mL² in a cubic box5 marks
- 1(l) Is Peⁱᵏˣ + Qe⁻ⁱᵏˣ an eigenfunction?5 marks
- 1(m) Zero-point energy in joule and in cm⁻¹5 marks
- 1(n) Microwave activity of SF₆, CO, H₂, H₂O and CO₂5 marks
- 1(o) Stark–Einstein law and the quantum yield5 marks
- 1(p) Decay routes of a photoexcited molecule5 marks