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A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :
- a)1:1
- b)1:2
- c)2:1
- d)depends on the moment of inertia of the two molecules
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A vessel contains a mixture of one mole of oxygen and two moles of nit...
Average kinetic energy per molecule per degree of freedom = 1/2 KT. Since both the gases are diatomic and at the same temperature (300K). 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
So Ratio will be 1 :1
So Ratio will be 1 :1
Most Upvoted Answer
A vessel contains a mixture of one mole of oxygen and two moles of nit...
Ratio of average rotational kinetic energy per O2 molecule to per N2 molecule
Given:
Number of moles of oxygen (O2) = 1
Number of moles of nitrogen (N2) = 2
Temperature (T) = 300 K
To find the ratio of average rotational kinetic energy per O2 molecule to per N2 molecule, we need to compare the rotational kinetic energies of the two molecules.
The rotational kinetic energy (K_rot) of a molecule can be calculated using the formula:
K_rot = (1/2) * I * ω^2
Where:
I is the moment of inertia of the molecule
ω is the angular velocity of rotation
1. Calculate the moment of inertia for O2 and N2 molecules.
The moment of inertia (I) depends on the molecular structure and mass distribution. For a diatomic molecule like O2 and N2, the moment of inertia can be approximated using the formula:
I = μ * r^2
Where:
μ is the reduced mass of the molecule
r is the internuclear distance between the atoms in the molecule
The reduced mass (μ) for a diatomic molecule can be calculated using the formula:
μ = (m1 * m2) / (m1 + m2)
Where:
m1 and m2 are the masses of the atoms in the molecule
The internuclear distance (r) for O2 and N2 molecules can be assumed to be approximately equal.
2. Calculate the angular velocity of rotation for O2 and N2 molecules.
The angular velocity of rotation (ω) depends on the moment of inertia and the rotational kinetic energy. Since we want to compare the ratios of rotational kinetic energies, we can assume that the angular velocity is the same for both molecules.
3. Calculate the rotational kinetic energy for O2 and N2 molecules.
Using the calculated moment of inertia and assuming the same angular velocity, we can calculate the rotational kinetic energy for both O2 and N2 molecules using the formula mentioned earlier.
4. Compare the rotational kinetic energies.
Since the angular velocity is assumed to be the same for both molecules, the ratio of the rotational kinetic energies is equal to the ratio of the moment of inertia.
5. Conclusion
The ratio of the average rotational kinetic energy per O2 molecule to per N2 molecule is 1:1, as it depends on the moment of inertia of the two molecules.
Given:
Number of moles of oxygen (O2) = 1
Number of moles of nitrogen (N2) = 2
Temperature (T) = 300 K
To find the ratio of average rotational kinetic energy per O2 molecule to per N2 molecule, we need to compare the rotational kinetic energies of the two molecules.
The rotational kinetic energy (K_rot) of a molecule can be calculated using the formula:
K_rot = (1/2) * I * ω^2
Where:
I is the moment of inertia of the molecule
ω is the angular velocity of rotation
1. Calculate the moment of inertia for O2 and N2 molecules.
The moment of inertia (I) depends on the molecular structure and mass distribution. For a diatomic molecule like O2 and N2, the moment of inertia can be approximated using the formula:
I = μ * r^2
Where:
μ is the reduced mass of the molecule
r is the internuclear distance between the atoms in the molecule
The reduced mass (μ) for a diatomic molecule can be calculated using the formula:
μ = (m1 * m2) / (m1 + m2)
Where:
m1 and m2 are the masses of the atoms in the molecule
The internuclear distance (r) for O2 and N2 molecules can be assumed to be approximately equal.
2. Calculate the angular velocity of rotation for O2 and N2 molecules.
The angular velocity of rotation (ω) depends on the moment of inertia and the rotational kinetic energy. Since we want to compare the ratios of rotational kinetic energies, we can assume that the angular velocity is the same for both molecules.
3. Calculate the rotational kinetic energy for O2 and N2 molecules.
Using the calculated moment of inertia and assuming the same angular velocity, we can calculate the rotational kinetic energy for both O2 and N2 molecules using the formula mentioned earlier.
4. Compare the rotational kinetic energies.
Since the angular velocity is assumed to be the same for both molecules, the ratio of the rotational kinetic energies is equal to the ratio of the moment of inertia.
5. Conclusion
The ratio of the average rotational kinetic energy per O2 molecule to per N2 molecule is 1:1, as it depends on the moment of inertia of the two molecules.
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A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :a)1:1b)1:2c)2:1d)depends on the moment of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer?
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A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :a)1:1b)1:2c)2:1d)depends on the moment of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :a)1:1b)1:2c)2:1d)depends on the moment of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :a)1:1b)1:2c)2:1d)depends on the moment of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer?.
A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :a)1:1b)1:2c)2:1d)depends on the moment of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :a)1:1b)1:2c)2:1d)depends on the moment of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to Per N2 molecule is :a)1:1b)1:2c)2:1d)depends on the moment of inertia of the two moleculesCorrect answer is option 'A'. Can you explain this answer?.
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