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At a certain temperature, molecules of methane gas. CH4 have an average velocity of 0.098 m/s. What is the average velocity of carbon dioxide molecules at this same temperature? Detailed explanation please!

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superman1987

Answer: Average velocity of CO₂ = 0.059 m/s.

Explanation:

  • Average velocity of a molecule = √(3KbT / molar mass)
  • Kb: Boltzmann constant and T: the temperature (K)
  • At constant temperature; the average velocity of a molecule is inversely proportional to square root of its molar mass (velocity ∝ 1 / √molar mass).

For two molecules (CH₄ & CO₂):

  • Velocity of CH₄ / Velocity of CO₂ = √(molar mass CO₂ / molar mass CH₄)
  • molar mass of CH₄ = 16.0 g/mol & molar mass of CO₂ = 44.0 g/mol and the average velocity of CH₄ = 0.098 m/s.
  • (0.098 / average velocity of CO₂) = √(44.0 / 16.0)
  • Average velocity of CO₂ = 0.098 / √(44.0 / 16.0) = 0.059 m/s.

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