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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)
    1 : 1
  • b)
    1 : 2
  • c)
    2 : 1
  • d)
    Depends on the moments of inertia of the two molecules
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A vessel contains a mixture of one mole of oxygen and two moles of nit...
Explanation:

Given:
- 1 mole of oxygen (O2) and 2 moles of nitrogen (N2) at 300 K.
- We need to find the ratio of the average rotational kinetic energy per O molecule to that per N molecule.

Rotational Kinetic Energy:
- The rotational kinetic energy of a molecule is given by the formula: \( KE_{rot} = \frac{1}{2} I \omega^2 \), where I is the moment of inertia and ω is the angular velocity.

Analysis:
- For diatomic molecules like O2 and N2, the moment of inertia is given by \( I = μr^2 \), where μ is reduced mass and r is the bond length.
- Since both O2 and N2 are diatomic molecules, they have similar bond lengths and reduced masses.

Ratio Calculation:
- The rotational kinetic energy only depends on the moment of inertia and angular velocity.
- Since both O2 and N2 have similar reduced masses and bond lengths, their moments of inertia will be similar.
- Therefore, the ratio of the average rotational kinetic energy per O molecule to that per N molecule will be 1:1.

Conclusion:
- The ratio of the average rotational kinetic energy per O molecule to that per N molecule is 1:1.
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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 O molecule to that per N molecule isa)1 : 1b)1 : 2c)2 : 1d)Depends on the moments of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer?
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