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:

1 : 1

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1 : 2

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2 : 1

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Depends on the moments of inertia of the two molecules

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Solution

The correct option is B $1 : 1$
A diatomic gas has 2 degrees of freedom associated with rotational motion. Law of equipartition of energy states that the rotational kinetic energy per degree of freedom is $\frac{1}{2} K T$
Since two gases are at same temperature their rotational kinetic energies will be equal.
Hence Option A is correct answer.

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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 O2 molecule to that per N2 molecule is:

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: