UPSC Combined Geo-Scientist, Mains · 2018 · Mains Paper II
Q1(a). Equal molecular speeds
Question
At what temperature is the average speed of oxygen molecules equal to that of hydrogen molecules at 20 K?
Answer in brief
T_(O₂)=320 K, using molar masses 32 and 2 g mol⁻¹.
Key points
- For an ideal gas, c̄=√(8RT/(π M)). Equal mean speeds require equal T/M.
- Thus T_(O₂)/32=20/2, giving T_(O₂)=320 K.
- Use molecular, not atomic, masses and absolute temperatures. Oxygen needs the higher temperature because its molecules are heavier.
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.
CoversEqual molecular speedsKinetic theory
All parts of Question 1
- 1(a) Equal molecular speeds5 marks
- 1(b) Fugacity under repulsion5 marks
- 1(c) Wetting of glass5 marks
- 1(d) FCC particle count5 marks
- 1(e) Joule–Thomson cooling5 marks
- 1(f) Gibbs and Helmholtz changes5 marks
- 1(g) Equilibrium-constant conventions5 marks
- 1(h) Very dilute hydrochloric acid5 marks
- 1(i) Pressure controlling boiling5 marks
- 1(j) Primary kinetic salt effect5 marks
- 1(k) Heat of spontaneous adsorption5 marks
- 1(l) Conductivity as an intensive property5 marks
- 1(m) Anthracene photodimerization5 marks
- 1(n) Particle-in-a-box eigenvalue5 marks
- 1(o) Second Balmer line5 marks
- 1(p) Normal-mode counts5 marks