Degree Of Freedom Class 11 Notes | EduRev

Chemistry Class 11

Class 11 : Degree Of Freedom Class 11 Notes | EduRev

The document Degree Of Freedom Class 11 Notes | EduRev is a part of the Class 11 Course Chemistry Class 11.
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The number of independent variables or coordinates needed to describe the motion of a particle is called the degree of freedom.

  • Total number of DOF = 3N (where N = atomicity)
  • No. of translational DOF (ft) = 3 (for all gases)
  • No. of rotational DOF (fr) = 0 (for monoatomic gas)
    No. of rotational DOF (fr) = 2 (for diatomic gas)
    No. of rotational DOF (fr) = 2 (for polyatomic linear molecules)
    No. of rotational DOF (fr) = 3 (for polyatomic nonlinear molecule)
  • No. of vibrational dof (fv) = 3N - f- fr

In a monoatomic species, rotational and vibrational modes of motion are absent. Hence three degrees of freedom corresponds to three translational motion along three different axes.
For a diatomic molecule, total degree of freedom = 3 × 2 = 6

Break up of the Degree of Freedom:
(i) 3 translation degrees of freedom representing translation motion of center of mass in three independent directions.
Degree Of Freedom Class 11 Notes | EduRev(ii) Two possible axes of rotation, hence two rotational degrees of freedom.
Degree Of Freedom Class 11 Notes | EduRev(iii) One vibration degree of freedom.
Degree Of Freedom Class 11 Notes | EduRev

Vibrational DOF is active only at high temperatures.

Q. Find the total degree of freedom and break up as translational, rotational, or vibrational DOFs in following cases.
(i) O = C = O
(ii)Degree Of Freedom Class 11 Notes | EduRev
(iii) He
(iv) NH3
Solution.
(i) CO2: Total dof = 3 x 3 = 9
Translational = 3
Rotational = 2 (∵ linear molecule)
Vibrational = 4

(ii) SO2: Total dof = 3 x 3 = 9
Translational = 3
Rotational = 3 (∵ Bent molecule)
Vibrational = 3

(iii) He: Total dof = 3 (∵ Monoatomic molecule)
Translational = 3 

(iv) NH3: Total dof = 3 x 4 = 12
Translational = 3
Rotational = 3 (∵ non linear molecule)
Vibrational = 6

Law of Equipartition of Energy

Energy equal to  ½ kT is associated with each translational and rotational degree of freedom per ideal gas molecule.
Energy equal to kT is associated with each vibrational degree of freedom per ideal gas molecule.
Where k = R/NA Boltzmann constant

Degree Of Freedom Class 11 Notes | EduRev
∴ For n moles,

Degree Of Freedom Class 11 Notes | EduRev
On ignoring vibrational degree of freedom

Degree Of Freedom Class 11 Notes | EduRev

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