Degree Of Freedom Notes | EduRev

Chemistry Class 11

Class 11 : Degree Of Freedom Notes | EduRev

The document Degree Of Freedom Notes | EduRev is a part of the Class 11 Course Chemistry Class 11.
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DEGREE OF FREEDOM
Number of independent variables or coordinates needed to describe motion of a particle is called 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)
    = 2 (for diatomic gas)
    = 2 (for polyatomic linear molecules)
    = 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 degree of freedom correspond to three translational motion along three different axes.
For a diatomic molecule, total degree of freedom = 3 × 2 = 6

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

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

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

(iii) He: Total dof = 3
Translational = 3

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

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 Notes | EduRev
∴ For n moles,

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

Degree Of Freedom Notes | EduRev

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