How many degrees of freedom does nitrogen gas (N2) have? How many translations, rotations, and vibrations does it have?
The correct answer and explanation is:
Nitrogen gas (N₂) is a diatomic molecule, meaning it consists of two atoms bonded together. The degrees of freedom of a molecule refer to the different ways in which it can store energy via motion, including translation, rotation, and vibration.
Degrees of Freedom for N₂
A nonlinear molecule has 3N3N degrees of freedom (where NN is the number of atoms), but since N₂ is a linear molecule, its degrees of freedom are given by: Total Degrees of Freedom=3N=3(2)=6\text{Total Degrees of Freedom} = 3N = 3(2) = 6
Types of Motion
- Translational Motion (3 degrees of freedom)
- The molecule can move along the x, y, and z axes in space.
- These motions contribute to kinetic energy but do not affect the internal energy distribution.
- Rotational Motion (2 degrees of freedom)
- A linear molecule like N₂ can rotate about two axes perpendicular to its bond.
- It does not rotate around its bond axis because such rotation has negligible energy.
- Vibrational Motion (1 degree of freedom at low temperatures, 2 at high temperatures)
- For a diatomic molecule, the number of vibrational degrees of freedom is given by: 3N−(3+2)=6−5=13N – (3 + 2) = 6 – 5 = 1
- This represents the stretching and compressing of the N–N bond.
- At higher temperatures, quantum effects allow an additional vibrational mode to be excited, making it effectively 2.
Summary
- Total Degrees of Freedom: 6
- Translation: 3
- Rotation: 2
- Vibration: 1 (or 2 at high temperatures)
Now, I’ll generate an image representing the motion of an N₂ molecule.
Here is an image illustrating the degrees of freedom of a nitrogen (N₂) molecule, including its translational, rotational, and vibrational motions. Let me know if you need any modifications or further explanations!
