Question

Calculate the contribution of each normal mode to the molar vibrational heat capacity of H₂O(g) at 600K. For a water molecule, the frequencies of the three normal modes are hν/k_B=2290 K, 5160 K, and 5360 K

Answer 1

Solution:-

For a polyatomic molecule, the vibrational energy is the sum of the contributions from each normal mode

So,

Here Normal modes mean just the result of a change in the variables we use to describe the internal degrees of freedom.(Other than translations and rotations)

Therefore, there are as many normal modes as vibrational degrees of freedom.

So,, for water we have: 9 total - 3 translational - 3 rotation = 3 vibrational.

So in this given problem, we are given three values for Θvibr, one for each normal mode.

Thus, for water in the above equation has three terms:-

Molar vibrational heat capacity of H₂O(g) at 600K=

So

So  Molar vibrational heat capacity of H₂O(g) at 600K = 0.35925