The degree of freedom of an oxygen gas molecule at normal temperature is 5.
Understanding Degrees of Freedom
In the context of thermodynamics and statistical mechanics, degrees of freedom (DoF) refer to the number of independent coordinates required to completely describe the position and orientation of a molecule in space, as well as its internal motions. Essentially, they represent the number of independent ways a molecule can store energy.
For a molecule in a gas phase, these degrees of freedom typically include:
- Translational Motion: The movement of the molecule's center of mass through three-dimensional space.
- Rotational Motion: The rotation of the molecule around its center of mass.
- Vibrational Motion: The oscillation of atoms within the molecule relative to each other.
The number of active degrees of freedom depends on the molecule's structure and the ambient temperature, as higher temperatures can excite additional modes of motion.
Degrees of Freedom of an Oxygen (O₂) Molecule
Oxygen (O₂) is a diatomic molecule, meaning it is composed of two oxygen atoms bonded together. At typical or normal temperatures, the energy distribution within an oxygen gas molecule predominantly involves translational and rotational movements.
An oxygen gas molecule possesses:
- 3 translational degrees of freedom: These allow the molecule to move independently along the three perpendicular axes (X, Y, and Z) in space.
- 2 rotational degrees of freedom: As a linear molecule, it can rotate independently about two axes that are perpendicular to the bond connecting the two oxygen atoms. Rotation around the internuclear axis (the axis running through the two atoms) is generally considered negligible because the moment of inertia about this axis is very small.
Therefore, the total number of degrees of freedom for an oxygen gas molecule at normal temperatures is the sum of its translational and rotational components.
| Type of Motion | Degrees of Freedom |
|---|---|
| Translational | 3 |
| Rotational | 2 |
| Total (Normal Temp) | 5 |
Temperature Dependence and Vibrational Modes
While oxygen molecules do have vibrational degrees of freedom, these are typically not active or excited at normal (room) temperatures. This is because the energy quanta required to excite these vibrational modes are significantly higher than the average thermal energy available at such temperatures.
At sufficiently high temperatures, however, these vibrational modes become active. For a diatomic molecule like oxygen, there would be an additional 2 degrees of freedom from vibration (one for kinetic energy and one for potential energy associated with the vibration). This would bring the total degrees of freedom to 7 (3 translational + 2 rotational + 2 vibrational) at very high temperatures.
Significance
The concept of degrees of freedom is fundamental to understanding the specific heat capacity of gases. According to the Equipartition Theorem, each active degree of freedom contributes $\frac{1}{2}kT$ to the average energy of a molecule (where $k$ is Boltzmann's constant and $T$ is the absolute temperature). This direct relationship helps explain why diatomic gases like oxygen have a specific heat ratio ($\gamma = \frac{C_P}{C_V}$) of approximately 1.4 at normal temperatures, which is consistent with 5 active degrees of freedom.
