Courses

# Degree Of Freedom Notes | EduRev

## 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.
All you need of Class 11 at this link: Class 11

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. (ii) Two possible axes of rotation, hence two rotational degree of freedom. (iii) One vibration degree of freedom. 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) (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 ∴ For n moles, On ignoring vibrational degree of freedom Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;