Molecular degrees of freedom refer to the ways a gas molecule can move, rotate, or vibrate. A molecule's degrees of freedom depend on the number of atoms it contains. A monatomic gas molecule has 3 translational degrees of freedom. A diatomic gas molecule has 3 translational and 2 rotational degrees of freedom at high temperatures, and 3 translational and 5 total degrees of freedom at room temperature. A triatomic nonlinear gas molecule has 3 translational and 3 rotational degrees of freedom at high temperatures, and 3 translational and 6 total degrees of freedom at room temperature.

3.  DEGREE OF FREEDOM OF GAS MOLECULES
 TYPES OF MOTION
 DOF OF MONOATOMIC GAS
 DOF FOR DIATOMIC GAS
 DOF OF TRIATOMIC GAS
 TABLE
 LAW OF EQUIPARTITION OF ENERGY

4. Molecular degrees of freedom refer to the number of ways a molecule in the gas phase
may move, rotate, or vibrate in space. It is defined as the number of coordinates required
to specify the position of all the atoms in a molecule.
Three coordinates x, y and z are required to specify the position of one atom in space.
DEGREE OF FREEDOMOF GAS MOLECULES
The molecule containing ‘n’ atoms will have 3n degrees of freedom which are
distributed among the different kinds of motion.
a. The translational motion
b. The rotational motion
c. The vibrational motion

5. • Mechanical phenomenon whereby oscillations occur about an equilibrium point.
• The motion by which a molecule shifts from one point in space to another.
• The movement of a molecule around an axis.
A. The translational motion
B. The rotational motion
C. The vibrational motion

6. A monatomic molecule consists of only a single atom of point
mass hence it has three degrees of freedom of translatory motion
along the three coordinate axes x, y and z.
Degree of freedom of monoatomic gas
Examples : Molecules of Inert gases like helium(He), Neon(Ne),
Argon(Ar), etc.

7. •The diatomic molecule can rotate about any axis at right angles to its own axis.
Hence it has two rotational degrees of freedom ,in addition it
has three translational degrees of freedom along the three axes. A diatomic
molecule shows one vibrational degree of freedom. So, a diatomic molecule has a
total of six degrees of freedom at high temperature.
•At room temperature the total degree of freedom of a diatomic molecule
is Five because vibrational motion is not contributed.
Degree of freedom of
diatomic gas
Examples: molecules of O2, N2, CO, Cl2, etc.

8. Degree of freedom of
triatomic gas
Examples : molecules of H2O, SO2, etc.
•In triatomic molecule the center of mass lies at the central atom.
• It have three degrees of freedom of translation and two degrees of freedom of rotation
and five degrees of freedom at room temp.
•At high temperatures, It shows four vibrational degrees of freedom. Hence, it shows a total
of nine degrees of freedom.
•At room temperature a triatomic nonlinear molecule possesses three degrees of freedom of
rotation in addition to three degrees of freedom of translation. Hence it has six degrees of
freedom.
•At high temperatures, it shows a total of nine degrees of freedom.

10. For a system in equilibrium, there is an average energy of ½ kT or ½ RT per molecule associated with each
degree of freedom. (where k = Boltzmann constant and T is the temperature of the system). This energy
associated with each degree of freedom is in the form of kinetic energy and potential energy.
•One translational degree of freedom = ½ kT or ½ RT
•One rotational degree of freedom= ½ kT or ½ RT
•One vibrational degree of freedom= kT or RT
Note: As regard the vibrational motion the two atoms oscillate against each other therefore both potential
and kinetic energy the energy of vibration involve two degree of freedom, so that vibrational motion in a
molecule is associated with energy= 2 x ½ kT = kT
Total energy E= Etr + Erot + Evib + Eelc

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