Passage
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
Question for Practice Passage Test - 2
Try yourself:Which of the following molecules has nine normal modes of vibration?
Explanation
None of these molecules are linear. The passage states that the number of normal modes of vibration is 3N – 6 for non-linear molecules. If there are nine normal modes of vibration, 3N – 6 = 9, and N = 5. Only methane, choice B, has 5 atoms.
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Question for Practice Passage Test - 2
Try yourself:A change in which of the following combinations of molecular movement can never produce a peak in an IR spectrum?
Explanation
From the passage, stretching and bending are types of vibration, while translation and rotation are not. All vibrations can potentially produce peaks in IR spectra, so choices B, C, and D are eliminated. Changes in translational and rotational movements alone do not show up in IR.
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Question for Practice Passage Test - 2
Try yourself:Assuming their reduced masses are the same, which molecule will have the highest energy of vibration in the v = 0 state?
Explanation
If v = 0 and h and u are constant, the equation for vibration energy reduces as follows:
The energy of the ground state is proportional to the square root of the force constant k. The passage states that k is larger for stronger bonds, and the bond in N2 is strongest since it has the highest bond energy (see Table 1). N2 must have the highest vibrational energy in the ground state.
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Question for Practice Passage Test - 2
Try yourself:All of the following molecules will display absorption peaks in an IR spectrum EXCEPT
Explanation
The passage states that only those normal modes of vibration that produce a change in the dipole moment of a molecule will absorb IR light. Since O2 has no dipole, it will not have any peaks in an IR spectrum. Note that while the molecule SO3 as a whole has no dipole, its individual bonds do have detectable dipoles.
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Question for Practice Passage Test - 2
Try yourself:Nitrate is best described by a resonance average of three structures:
Explanation
A molecule essentially exists as an average of its resonance structures. No individual resonance structure exists in isolation. In nitrate there are three bonds of equal strength, containing about 33% N=O double bond character and about 67% N—O single bond character. Therefore, there will be only one stretch peak in the IR spectrum intermediate to the N—O and N=O stretches that accounts for all three of these bonds in nitrate.
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