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Shyam Dubey • 3.70K Points
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Q. In an ideal gas, which of the following is true at the same temperature?

  • (A) All gases have the same density.
  • (B) All gases have the same average kinetic energy per molecule.
  • (C) All gases have the same molar mass.
  • (D) All gases have the same number of molecules in any given volume.
  • Correct Answer - Option(B)
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Explanation by: Shyam Dubey
At a given temperature, the average translational kinetic energy per molecule depends only on temperature: (1/2)mv^2_avg ∝ kT. Different gases have different molar masses and densities, so options 1 and 3 are false. Option 4 is false because number of molecules in a given volume depends on pressure and temperature; at the same T and P equal volumes contain same number of moles (Avogadro's law) but the statement lacked pressure and is ambiguous — moreover molar masses differ so mass density changes.

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