Answer:
The ethanol has 21 vibrational modes.
Explanation:
A molecule can show 3 types of motions: one external called translational and two internal called rotational and vibrational.
In order to calculate the vibrational modes of a molecule we need to know the degrees of freedom of this molecule, it means the number of variables that are involved in the movement of this particle.
If we know that atoms are three dimensional we will know that they have 3 coordinates expressed as 3N. But the atoms are bonded together so they can move not only in translational but also rotational and vibrational. So, the rotational move can be described in 3 axes and the other vibrational move can be described as
3N-5 for linear molecules
3N-6 For nonlinear molecules like ethanol
So using the formula for nonlinear molecules where N is the amount of atoms in the chemical formula, so ethanol has 9 atoms
3(9)-6= 21
Thus, ethanol has 21 vibrational modes.
