in order to consider the distribution of energies for different modes of motion, one should have the idea of the vibrational degrees of freedom.
degree of freedom is the number of independent co-ordinates required to locate all the atoms in a molecule.
the location of an atom can be specified by three coordinates.
the total degrees of freedom of a molecule = 3N
where N is the number of atoms in that molecule. translational degrees of freedom are always three. rotational degrees of freedom depends upon the fact that whether the molecule is linear or non-linear.
for a linear molecule, rotational degrees of freedom =2
for a non-linear molecule, rotational degrees of freedom = 3
after the completion of rotational and translational degrees of freedom, we should calculate the vibrational degrees of freedom.
total degrees of freedom = 3×1 = 3
Translational degrees of freedom = 3
Rotational degrees of freedom = 0
Vibrational degrees of freedom = 0
so, the atoms of He, Ne, Ar, Kr, Hg and Na vapors spend their energies only for translational motions along x, y, and z-axis, but not for rotational and vibrational motions.
total degrees of freedom = 3×2= 6
Translational degrees of freedom = 3
rotational degrees of freedom= 3 ( diatomic molecule are always linear)
vibrational degrees of freedom= 6-3-32= 1
Energy expended for one translational degree of freedom = 1/2RT
Energy expended for one rotational degree of freedom = 1/2RT
Energy expended for one vibrational degree of freedom = 1/2RT + 1/2RT
(1/2RT is kinetic energy and 1/2RT is potential energy)
now, let us do the calculations for total energy being expended by the diatomic linear molecule.
it means that a diatomic molecule like H2, F2, Cl2, O2, N2, HCl, etc. needs the energy of 3.5 RT to maintain all their motions for six degrees of freedom. this energy is more than double than those of monoatomic molecules.
total degrees of freedom = 33= 9
translational degrees of freedom = 3
rotational degrees of freedom(linear) = 2
vibrational degrees of freedom ( for linear) = 9-3-2= 4
A triatomic linear molecule like Co2, CS2, COS, etc. has four vibrational degrees of freedom. the total energy can be calculated as follows.
for triatomic non-linear molecules like H2O, H2S, H2Se, SO2, etc. then translational degrees of freedom are three, rotational are three and vibrational are also three. so total energy of such a molecule is,
it means that the total energy being expended by water is a little bit less than that ofCO2.
Total degree of freedom = 3 x 4 = 12
Translational degrees of freedom = 2
Rotational degrees of freedom = 3
Vibrational degrees of freedom = 12-3-3= 6
it means that energy possession goes an increase for molecules having higher atomicities. the whole process is called the derivation of the law of equipartition of energies theorem.
Read Also: Heat capacities of Gases : ( at Constant Volume and Temperature)
When it comes to creativity, you might ask yourself whether or not you can feel…
In the dynamic landscape of India, where tradition and technology frequently intersect, the domain of…
In this article, we will provide a comprehensive explanation of IMDb's basic information, simple usage…
Boostcraft.net is your one-stop destination for all your WoW retail boost needs. Our team of…
California's logistics and warehousing industry has experienced tremendous growth over the years. With the increasing…
In recent years, the food and beverage industry has witnessed a significant shift towards digitization,…