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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2018 · Paper I

Q2(b)(i). Significance of the Kelvin equation

  • 5 marks
  • Answered
Question

Explain the significance of Kelvin equation.

Answer in brief

ln(p/p*)=2γ Vₘ/rRT: the vapour pressure of a liquid depends on the curvature of its surface. It is higher over a small convex droplet and lower over a concave surface, which explains supersaturation, nucleation, Ostwald ripening and capillary condensation.

Key points

  • The pressure inside a droplet is raised by the Laplace pressure 2γ/r. This raises the chemical potential of the liquid, and with it the vapour pressure: p=p*exp(2γ Vₘ/rRT), where p* is the vapour pressure over a flat surface.
  • The effect matters only for small r. For water at 293 K (γ=72.75 mN m⁻¹): p/p*=1.011 at r=100 nm, 1.11 at 10 nm and 2.94 at 1 nm.
  • a tiny droplet evaporates faster than vapour condenses on it, so vapour can be cooled below its condensation point without forming droplets. Condensation starts on nuclei (dust, ions); this is the basis of cloud seeding and of…
  • large drops (and large crystals, which are more stable for the same reason) grow at the expense of small ones.

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

  1. The pressure inside a droplet is raised by the Laplace pressure 2γ/r. This raises the chemical potential of the liquid, and with it the vapour pressure: p=p*exp(2γ Vₘ/rRT), where p* is the vapour pressure over a flat surface.
  2. The effect matters only for small r. For water at 293 K (γ=72.75 mN m⁻¹): p/p*=1.011 at r=100 nm, 1.11 at 10 nm and 2.94 at 1 nm.
  3. Supersaturation and nucleation: a tiny droplet evaporates faster than vapour condenses on it, so vapour can be cooled below its condensation point without forming droplets. Condensation starts on nuclei (dust, ions); this is the basis of cloud seeding and of the Wilson cloud chamber.
  4. Ostwald ripening: large drops (and large crystals, which are more stable for the same reason) grow at the expense of small ones.
  5. Concave surfaces (r<0): the vapour pressure is lowered. Vapour condenses in fine pores below p* (capillary condensation), and a bubble needs superheating before it can grow (bumping of liquids).

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Model answer to Q2(b)(i), 2018 Paper I: solution page 11
Solution page 11 of 55
Read the whole 2018 solution2018 question paper

All parts of Question 2