Assuming that the forces between atoms that form molecules can be approximated b
ID: 2304717 • Letter: A
Question
Assuming that the forces between atoms that form molecules can be approximated by elastic restoring forces, count the number of energy degrees of transla- tions and rotations, for (a) O2 molecules, (b) H2O molecules, (c) a hypothetical triangular molecule consisting of three identical atoms with identical bonds between each pair, and (d) the ammonia molecule NH3. Note that, in addition to the bonds shown, there are additional effective "springs." For example, the H2O molecule has one additional vibrational mode in which the H-O-H bond angle oscillates. Ammonia has even more. freedom, including those for b)Explanation / Answer
Molecules have 3N degrees of freedom, where N is the number of atoms in it.
An O2 molecule has 6 degrees of freedom: 3 translational (of the center of mass), 2 rotational (about the center of mass)(only 2 because out of 3 rotations possible on a 3D object, 2 are identical in O2) and 1 vibrational (around the center of mass) degrees of freedom.
H2O has 9 degrees of freedom: 3 translational (of the center of mass), 3 rotational (about the center of mass) and 3 vibrational (symmetric vibration of H atoms on the plane of H-O-H bond, symmetric bend vibrations of H atoms perpendicular to the plane of H-O-H and asymmetric stretch on the plane of H-O-H ) degrees of freedom.
A triangular triatomic molecule has 9 degrees of freedom: 3 translational (of the center of mass), 3 rotational (about the center of mass) and 3 vibrational (vibration of each atom from the center of mass at the center of the triangle ) degrees of freedom.
NH3 has 12 degrees of freedom: 3 translational (of the center of mass), 2 rotational (about the center of mass) and 6 vibrational (4 vibrations of each atom from the COM, 1 symmetric bending of H atoms crossing the plane that contains N and 1 asymmetric bending of H atoms crossing the plane that contains N) degrees of freedom.