VKC ScienceChemistry for written exams Telegram

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

Q3(d). Capillary action of water and mercury in tubes of two radii

  • 10 marks
  • Answered
Question

Draw diagrams showing the capillary action of (i) water and (ii) mercury in two glass tubes of different radii. Explain their behavior also.

Answer in brief

Water wets glass (contact angle near 0°): concave meniscus, rises; mercury does not wet glass (about 140°): convex meniscus, is depressed. In both cases h=2γθ/ρ gr: the narrower the tube, the larger the rise or the depression.

Key points

  • The attraction between water and glass (adhesion, hydrogen bonds to Si–OH groups) is stronger than between water molecules (cohesion). Water spreads on glass: contact angle θ≈0°.
  • a concave meniscus. The pressure just under a concave surface is lower than outside by 2γ/r (Laplace), so liquid is pushed up the tube until the hydrostatic pressure ρ gh balances it: ρ gh=(2γθ)/(r).
  • halving the radius doubles the rise. For water at 293 K (γ=72.75 mN m⁻¹, θ=0): r=0.2 mm gives h=7.4 cm; r=0.1 mm gives h=14.9 cm.
  • Cohesion in mercury (metallic bonding) is much stronger than its adhesion to glass. Mercury does not wet glass: θ≈140°, θ<0.

The full model answer

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

(i) Water

  1. The attraction between water and glass (adhesion, hydrogen bonds to Si–OH groups) is stronger than between water molecules (cohesion). Water spreads on glass: contact angle θ≈0°.
  2. The surface curves upward at the wall: a concave meniscus. The pressure just under a concave surface is lower than outside by 2γ/r (Laplace), so liquid is pushed up the tube until the hydrostatic pressure ρ gh balances it: ρ gh=(2γθ)/(r).
  3. h∝1/r: halving the radius doubles the rise. For water at 293 K (γ=72.75 mN m⁻¹, θ=0): r=0.2 mm gives h=7.4 cm; r=0.1 mm gives h=14.9 cm.

(ii) Mercury

  1. Cohesion in mercury (metallic bonding) is much stronger than its adhesion to glass. Mercury does not wet glass: θ≈140°, θ<0.
  2. The surface curves downward at the wall: a convex meniscus. The pressure under it is higher by 2γ/r, so the level in the tube is depressed below the outside level; h comes out negative.
  3. Again |h|∝1/r: with γ=472 mN m⁻¹, r=0.2 mm gives a depression of 2.7 cm and r=0.1 mm gives 5.4 cm.
  1. Comparison: the sign of θ decides rise or fall; the radius decides how much. Mercury's large γ is offset by its large density, so its depression is smaller than water's rise in the same tube.

Application. capillary rise is used to measure surface tension (γ=ρ grh/2 for a wetting liquid); capillarity also lifts water through soil and wicks, and explains why mercury barometers and thermometers need wide bores and a correction for the convex meniscus.

Practising this answer? Write it in a Mains test and get it checked by VKC. Civil Services Mains test series · Telegram

Model answer to Q3(d), 2018 Paper I: solution page 21
Solution page 21 of 55
Read the whole 2018 solution2018 question paper

All parts of Question 3