Practice Passage Test - 2 | Practice Passages for MCAT PDF Download

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Molecules are not rigid, unchanging structures. Their atoms are in constant motion even relative to each other, ceaselessly oscillating around their average bond lengths and bond angles. For instance, in non-linear triatomic molecules there are three possible modes of vibration. There is the symmetric stretch in which both bonds in the molecule lengthen and contract in unison. In the asymmetric stretch, one bond lengthens while the other contracts. Finally, there is the bend in which the bond angle alternately widens and narrows.

Figure 1 Vibrations of a Triatomic Molecule 

More generally, each atom in a molecule is capable of moving in three distinct directions, often represented by x, y and z. In a molecule with N atoms, there will be 3N possible atomic movements. However, if all the atoms in a molecule move in the same direction, translational movement and not vibration will result. Likewise, there are some combinations of atomic motions that result in rotation of the molecule and not vibration. Taking this into account, in a molecule containing N atoms there will be 3N - 6 normal modes of vibration in non-linear molecules and 3N - 5 normal modes of vibration in linear molecules.

If we make the rough approximation that atoms in a molecule are harmonic oscillators, then the energy of their vibration is given by:

where v is the quantum vibrational number, h is Planck's constant, k is the force constant of the bond which increases with bond strength, and u is the reduced mass of the molecule. Changes in the vibrational quantum state are associated with energies similar to infrared photons. Thus, IR spectroscopy is the study of the energetics of a molecule's vibrational quantum states. However, only those normal modes of vibration that induce a change in the dipole moment of a molecule can be excited with IR light.

Table 1 Bond Energies of Select Diatomic Elements