UPSC Civil Services (Mains), Chemistry optional · 2023 · Paper I
Q1(d). Root-mean-square speed of water molecules
Question
(i) Find the temperature at which water molecules can have a root-mean-square speed of 719 m s⁻¹. (ii) What is the root-mean-square velocity of water molecules at 473 K?
Answer in brief
(i) T = Mc²ᵣₘₛ/3R = 373 K (100 °C); (ii) cᵣₘₛ = 810 m s⁻¹.
Key points
- Kinetic theory gives pV = ⅓Nmc̄²; with pV = RT for one mole, cᵣₘₛ = √(3RT/M) with M in kg mol⁻¹.
- T = 0.018 × (719)²/(3 × 8.314) = 373 K, the normal boiling point of water.
- At 473 K, cᵣₘₛ = √(3 × 8.314 × 473/0.018) = 810 m s⁻¹.
- Cross-check: cᵣₘₛ ∝ √T, so 719 × √(473/373) = 810 m s⁻¹; a rise of 100 K raises the speed by only 13 %.
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.
Coversroot-mean-square speedkinetic theory of gasesMaxwell distributionmolecular speedwater vapour
All parts of Question 1
- 1(a) Light emitted by a particle in a box; the uncertainty principle10 marks
- 1(b) Lewis structures of [Br₃]⁻ and thiourea; the most polar bond10 marks
- 1(c) Bragg equation and the layer spacing10 marks
- 1(d) Root-mean-square speed of water molecules10 marks
- 1(e)(i) E° of Cr³⁺/Cr from two couples5 marks
- 1(e)(ii) Surface tension, contact angle and loss of gravity5 marks