A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27°C. The ratio of their average kinetic energy per molecule respectively will be :

Solution

Physics sir · 4 steps

Same flask, same temperature, so each molecule carries the same average translational kinetic energy.

1. What kinetic theory says. In kinetic theory, the average kinetic energy per molecule means the translational part. Each molecule has 3 translational degrees of freedom, and each one gets 1/2kT.

   Ēₜᵣₐₙₛ = 3/2kT

2. Only temperature matters. This expression has no mass and no molar mass in it. The 3 : 2 mass ratio only changes how many molecules of each gas there are, not the energy of each molecule. Both gases are at 27°C = 300 K.
3. A note on rotation. O₂ also has 2 rotational degrees of freedom, so its total energy per molecule is 5/2kT, against 3/2kT for monatomic Ar. That would give 3 : 5, which is not an option, so the question means translational kinetic energy.
4. So. Both gases have 3/2kT per molecule at 300 K, so the ratio is 1 : 1, option (d).

The idea to keep. Average translational KE per molecule is 3/2kT for every ideal gas. Mass, molar mass and amount do not enter it. Equal temperature means equal energy per molecule.

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