Question

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per $O_{2}$ molecule to that per $N_{2}$ molecule is

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. Depends on the moments of inertia of the two molecules

Answer 1

Answer: (A)

1 : 1

Answer 2

Kinetic energy per degree of freedom$= \frac{1}{2}kT$

As diatomic gas possess two degree of freedom for rotational motion therefore rotational K.E.$= 2\left( \frac{1}{2}kT \right) = kT$

In the problem both gases (oxygen and nitrogen) are diatomic and have same temperature (300 K) therefore ratio of average rotational kinetic energy will be equal to one.