JEE Main 2023 · 15 April · morning · Single correct · +4 / −1

A flask contains Hydrogen and Argon in the ratio 2: 1 by mass. The temperature of the mixture is 30° C. The ratio of average kinetic energy per molecule of the two gases ( K argon/K hydrogen) is :
(Given: Atomic Weight of Ar=39.9 )

  1. (a) 39.9/2
  2. (b) 2
  3. (c) 39.9
  4. (d) 1
Answer and solution

Answer (d) 1

Solution

Physics sir · 4 steps

Kinetic theory's average KE per molecule is 3/2kT: same temperature, same energy, whatever the gas.

  1. What sets the energy. In kinetic theory, the average translational kinetic energy of a molecule depends only on the absolute temperature. It does not depend on the molecule's mass or on how much of each gas is in the flask.

    K̄ = 3/2kT

  2. Same flask. Hydrogen and argon are mixed in one flask, so both are at T = 303 K. Each gets the same 3/2kT. The 2 : 1 mass ratio and the atomic weight 39.9 are distractors.
  3. Why translational. Hydrogen also has 2 rotational degrees of freedom, which would make its total 5/2kT and the ratio 3/5. That is not an option, so the question means the standard translational average, 3/2kT for every gas.
  4. So. K_(argon)/K_(hydrogen) = (3/2kT)/(3/2kT) = 1, option (d).

The idea to keep. Equal temperature means equal average translational KE per molecule, 3/2kT. Heavier molecules do not get more energy, they just move slower: vᵣₘₛ ∝ 1/√M.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Kinetic Theory of Gases

Asked about 130 times in JEE Main since 2020. This question is from 2023.