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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 · 2022 · Mains Paper II

Q1(b). Boyle temperature of oxygen as a van der Waals gas

Question

What is Boyle temperature (TB)? Assuming oxygen as a van der Waals gas, calculate the Boyle temperature of it. The values of van der Waals constants a and b for oxygen respectively are a = 1.36 dm⁶ atm mol⁻² and b = 0.0318 dm³ mol⁻¹. Given: R = 0.08206 dm³ atm K⁻¹ mol⁻¹.

Answer in brief

TB is the temperature at which a real gas obeys Boyle’s law over a range of low pressures; for O₂, TB = a/Rb = 521 K (248 °C).

Key points

  • Boyle temperature: PVm stays constant (Z = 1) as P → 0, i.e. (∂Z/∂P)T = 0; the second virial coefficient B(T) = 0.
  • For a van der Waals gas at low P, Z = 1 + (b − a/RT)P/RT; setting the coefficient of P to zero gives TB = a/Rb.
  • TB = 1.36/(0.08206 × 0.0318) = 1.36/0.0026095 = 521 K (248 °C).
  • Below TB, Z first dips below 1 (attraction wins); above TB, Z > 1 at all P (size wins); TB = (27/8)Tc.
  • Measured B(T) of O₂ is zero near 406 K: the van der Waals model overestimates TB by about 28%.

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(b), 2022 Mains Paper II: solution pages 3 and 4
Solution pages 3 and 4 of 37
Read the whole 2022 solution2022 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 →

CoversBoyle temperaturevan der Waals constantssecond virial coefficientcompressibility factoroxygen

All parts of Question 1