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 · 2017 · Paper I

Q2(b). Two mercury drops merge: change of area and energy

  • 10 marks
  • Answered
Question

Find the change in surface area and energy when two identical mercury droplets of diameter 2 mm merged isothermally to one drop. Given that surface tension of mercury is 490 dyne cm⁻¹ at experimental temperature.

Answer in brief

The area falls by 5.18 mm² (5.18×10⁻⁶ m², 20.6 %); the surface energy falls by 2.54×10⁻⁶ J (25.4 erg), released as heat.

Key points

  • Radius of the new drop. Volume is conserved: 43π R³=2×43π r³, so R=2^(1/3)r=1.260 mm.
  • Initial area: A₁=2×4π r²=8(3.14)(1.0)²=25.12 mm²
  • Final area: A₂=4π R²=4(3.14)(1.260)²=19.94 mm²
  • Δ A=A₂-A₁=-5.18mm²=-5.18×10⁻⁶m² (-0.0518cm²) a fall of 20.6 %.

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: r=1 mm =1.0×10⁻³ m (diameter 2 mm); γ=490 dyn cm⁻¹=0.490 N m⁻¹; π=3.14 (as printed).

  1. Radius of the new drop. Volume is conserved: 43π R³=2×43π r³, so R=2^(1/3)r=1.260 mm.
  2. Initial area: A₁=2×4π r²=8(3.14)(1.0)²=25.12 mm²
  3. Final area: A₂=4π R²=4(3.14)(1.260)²=19.94 mm²
  4. Change in area: Δ A=A₂-A₁=-5.18mm²=-5.18×10⁻⁶m² (-0.0518cm²) a fall of 20.6 %.
  5. Change in surface energy. γ is the work to create unit area isothermally, so Δ E=γ Δ A=(0.490N m⁻¹)(-5.18×10⁻⁶m²) Δ E=-2.54×10⁻⁶ J=-25.4 erg
  6. The surface energy decreases: 2.54×10⁻⁶ J is released (as heat, to keep the process isothermal). This is why small drops coalesce spontaneously: merging lowers the area and the surface Gibbs energy.

Application. the same loss of surface energy drives the coalescence of droplets in emulsions and the growth of large crystals at the cost of small ones (Ostwald ripening); emulsifiers lower γ to slow coalescence.

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

Model answer to Q2(b), 2017 Paper I: solution page 9
Solution page 9 of 38
Read the whole 2017 solution2017 question paper

All parts of Question 2