MCAT General Chemistry Practice Test 2: Bonding and Intermolecular Forces

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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

MoleculeBond Energy (kJ/mol)
H2436
N2946
O2497
F2155

1. Which of the following molecules has nine normal modes of vibration?

  • A. NI3
  • B. CH4
  • C. PF5
  • D. SCl6

2. A change in which of the following combinations of molecular movement can never produce a peak in an IR spectrum?

  • A. Translation and rotation
  • B. Stretching and bending
  • C. Vibration and translation
  • D. Rotation and bending

3. Assuming their reduced masses are the same, which molecule will have the highest energy of vibration in the v = 0 state?

  • A. N2
  • B. O2
  • C. F2
  • D. Cannot be determined from the information given.

4. All of the following molecules will display absorption peaks in an IR spectrum EXCEPT

  • A. HClO4
  • B. SO3
  • C. CO
  • D. O2

5. In VSEPR theory, T-shaped is a sub-class of the trigonal bipyramidal geometric family in which the central atom has exactly three atoms bound to it and two lone pairs of electrons. Which of the following molecules is T-shaped?

  • A. SF4
  • B. NH3
  • C. BrCl3
  • D. FO3-

6. For a diatomic molecule, the reduced mass is given by u = (m1 × m2) / (m1 + m2) where m1 and m2 are the atomic weights of the two bonded atoms. What will be the ratio of the ground state vibration energies of D2 to H2 assuming the force constant k is the same for both?

  • A. 0.5
  • B. 0.7
  • C. 1.4
  • D. 2.0

7. Nitrate is best described by a resonance average of three structures:

What best describes the peaks in an IR spectrum that result from the three N—O bond stretches?

  • A. One peak at the double bond N=O stretch frequency and two peaks at the single bond N—O stretch frequency
  • B. One peak at the double bond N=O stretch frequency and one peak at the single bond N—O stretch frequency
  • C. One peak at the double bond N=O stretch frequency and one peak between the single N—O and double bond N=O stretch frequencies
  • D. One peak between the single N—O and double bond N=O stretch frequencies