Question

Determine the number of translational, rotational and vibrational degrees of freedom of HCl, CO2, H2O, NH3, and CH4.

Answer 1

Answer-1)

Formula to Determine the number of translational, rotational and vibrational degrees of freedom for molecules or atoms various geometry are tabulated below.

Note N = Number of atoms in a molecule.

Type of Freedom	Translational	Rotational	Vibrational
Atom	3	0	0
Linear molecule	3	2	3N-5
Non-linear molecule	3	3	3N-6

Based on these formula let us calculate or assign Number of various degrees of freedom as,

1) HCl

HCl is a linear molecule with N = 2 hence,

a) # of translational Degrees of fredom = 3

b) # of rotational Degrees of fredom = 2

c) # of vibrational Degrees of fredom = 3N - 5 = 3x2 - 5 = 1

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2) CO2 i.e. O=C=O

CO2 is a linear molecule with N = 3 hence,

a) # of translational Degrees of fredom = 3

b) # of rotational Degrees of fredom = 2

c) # of vibrational Degrees of fredom = 3N - 5 = 3x3 - 5 = 4

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3) H2O

H2O is an Angular (non-linear molecule) with N = 3 hence,

a) # of translational Degrees of fredom = 3

b) # of rotational Degrees of fredom = 3

c) # of vibrational Degrees of fredom = 3N - 6 = 3x3 - 6 = 3

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4) NH3

NH3 is an pyramidal (non-linear molecule) with N = 4 hence,

a) # of translational Degrees of fredom = 3

b) # of rotational Degrees of fredom = 3

c) # of vibrational Degrees of fredom = 3N - 6 = 3x4 - 6 = 6

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5) CH4

CH4 is an Tetrahedral (non-linear molecule) with N = 5 hence,

a) # of translational Degrees of fredom = 3

b) # of rotational Degrees of fredom = 3

c) # of vibrational Degrees of fredom = 3N - 6 = 3x5 - 6 = 9

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