Question

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is : (Give : Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/ mol )

• A. 1 : 10
• B. 10 : 1
• C. \( 1 : \sqrt{10} \)
• D. 1 : 1

Hint:

The average kinetic energy per molecule of an ideal gas depends only on the temperature, not on the mass or type of the gas, as long as they are at the same temperature. This is a direct consequence of the equipartition theorem.

Answer 1

The Correct Option is D

To determine the ratio of average kinetic energies per molecule for helium and argon at the same temperature, we use the formula for the average kinetic energy per molecule of an ideal gas:

K.E. = \frac{3}{2} k T

where:

• K.E. represents the average kinetic energy per molecule,
• k is the Boltzmann constant, and
• T is the absolute temperature in Kelvin.

Crucially, this formula for kinetic energy is independent of the mass or type of gas, depending solely on the temperature. This holds true for all ideal gases.

Given that both helium and argon are at the identical temperature of 300 K, their average kinetic energy per molecule will be equivalent.

Consequently, the ratio of the average kinetic energies per molecule for helium and argon is:

1 : 1

This equality arises because kinetic energy is exclusively contingent upon temperature, which is uniform for both gases in this scenario.

Conclusion: The correct answer is 1 : 1. This signifies that every gas molecule, irrespective of its composition, possesses the same average kinetic energy at a specified temperature.