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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 · 2020 · Paper I

Q6(c). Excess pressure inside a soap bubble

  • 10 marks
  • Answered
Question

A spherical soap bubble of volume (π)/(6) cm³ stands suspended in air. If the interfacial tension for soap solution-air interface is 27 dyn cm⁻¹, calculate the excess pressure inside the bubble.

Answer in brief

r=0.50 cm. A soap film has two surfaces, so Δ p=4γ/r=4(27)/0.50=216 dyn cm⁻² = 21.6 Pa.

Key points

  • Radius: 43π r³=(π)/(6) ⇒ r³=18, r=0.50 cm
  • the pressure on the concave side exceeds that on the convex side by Δ p=2γ/r. (Expanding the sphere by dr needs work Δ p 4π r²dr to create area 8π r dr: Δ p=2γ/r.)
  • the film has an outer and an inner surface, each with tension γ and nearly the same radius; the two pressure jumps add: Δ p=2×(2γ)/(r)=(4γ)/(r)
  • Δ p=(4×27)/(0.50), Δ p=216 dyn cm⁻²=21.6 Pa (2.13×10⁻⁴ atm)

The full model answer

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

Given: V=π/6 cm³, γ=27 dyn cm⁻¹.

  1. Radius: 43π r³=(π)/(6) ⇒ r³=18, r=0.50 cm
  2. Laplace equation for one curved surface: the pressure on the concave side exceeds that on the convex side by Δ p=2γ/r. (Expanding the sphere by dr needs work Δ p 4π r²dr to create area 8π r dr: Δ p=2γ/r.)
  3. Soap bubble: the film has an outer and an inner surface, each with tension γ and nearly the same radius; the two pressure jumps add: Δ p=2×(2γ)/(r)=(4γ)/(r)
  4. Substitution: Δ p=(4×27)/(0.50), Δ p=216 dyn cm⁻²=21.6 Pa (2.13×10⁻⁴ atm)
  5. If only one surface is counted (a gas bubble inside a liquid), Δ p=2γ/r=108 dyn cm⁻². A soap bubble standing alone in air always has two surfaces, so 216 dyn cm⁻² is the answer.

Application. Δ p∝1/r: of two connected bubbles the smaller empties into the larger. The same Laplace pressure fixes the size of foam cells and the pressure in alveoli of the lung, where surfactants lower γ so that small alveoli do not collapse into large ones; it is also the basis of the maximum-bubble-pressure method for measuring surface tension.

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Model answer to Q6(c), 2020 Paper I: solution page 31
Solution page 31 of 45
Read the whole 2020 solution2020 question paper

All parts of Question 6