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  4. 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 per N2 molecule is

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Q. 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 per $N_{2}$ molecule is

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Solution:

Average kinetic energy per molecule per degree of freedom $=\frac{1}{2}kT$ . Since, both the gases are diatomic and at the same temperature $\left(300 \, K\right)$ , both will have the same number of rotational degree of freedom i.e., two. Therefore, both the gases will have the same average rotational kinetic energy per molecule $=2\times \frac{1}{2}kT=kT$ . Thus, ratio will be $1:1$ .