Question

A vessel contains a mixture of 1 mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O₂ molecule to that per N₂ molecule is ______.

Options

• 1 : 1

• 1 : 2

• 2 : 1

• depends on the moment of inertia of the two molecules

Answer 1

A vessel contains a mixture of 1 mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O₂ molecule to that per N₂ molecule is 1 : 1.

Explanation:

Kinetic energy per degree of freedom = `1/2 kT`

As diatomic gases possess two degrees of freedom for rotational motion, therefore rotational.

K.E. = `2(1/2kT)` = kT

In the problem, both gases (oxygen and nitrogen) are diatomic and have the same temperature (300 K); hence, the ratio of their average rotational kinetic energies is 1.