Chemistry I / Gases, Kinetic Theory and Intermolecular Forces
Practice question · Estimate

Helium has molar mass 4 g/mol and oxygen 32 g/mol. At the same temperature, set how many times faster the root-mean-square speed of helium is than that of oxygen.

Estimate on a scale from Equal speeds (1x) (1) to Five times faster (5).

Hints
  1. Root-mean-square speed goes as the inverse square root of molar mass.
  2. Compute the square root of 32/4.
Show the answer

2.83 (answers within ±0.25 count)

Why

Both gases share the same average kinetic energy, so u1/Mu \propto 1/\sqrt{M} and the ratio is 32/4=8=2.83\sqrt{32/4} = \sqrt{8} = 2.83. Helium is not eight times faster, the square root matters, and getting it wrong is the standard error here.

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