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Using the Lippmann equation, calculate the surface tension of a mercury electrode when the potential changes from 0 V to –0.5 V. The capacitance per unit area is 0.20 mF cm⁻² and the surface tension at 0 V is 485 mN m⁻¹.

hard 5 marks Class 12 · Chemistry · Electrochemistry
Answer
235 mN m⁻¹

The correct answer is 235 mN m⁻¹ — Convert back to mN m⁻¹: 0.235 N m⁻¹ = 235 mN m⁻¹.

Step-by-step solution

  1. Convert capacitance to SI units: 0.20 mF cm⁻² = 0.20×10⁻³ F / (10⁻⁴ m²) = 2.0 F m⁻².
  2. Write the Lippmann equation: γ = γ₀ – ½ C V².
  3. Insert the values: γ₀ = 485 mN m⁻¹ = 0.485 N m⁻¹, C = 2.0 F m⁻², V = –0.5 V.
  4. Compute the change: ½ C V² = 0.5 × 2.0 × (0.5)² = 0.5 N m⁻¹.
  5. Subtract from γ₀: γ = 0.485 N m⁻¹ – 0.5 N m⁻¹ = 0.235 N m⁻¹.
  6. Convert back to mN m⁻¹: 0.235 N m⁻¹ = 235 mN m⁻¹.
Common mistake: Using V² without the ½ factor or mixing units

Concept tested: Surface tension variation with potential (Lippmann equation)

Published · How this solution was prepared and checked

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