Chap21 solutions

Physical Chemistry

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21 Molecular interactions Solutions to exercises Discussion questions E21.1(b) When the applied field changes direction slowly, the permanent dipole moment has time to reorientate—the whole molecule rotates into a new direction—and follow the field. However, when the frequency of the field is high, a molecule cannot change direction fast enough to follow the change in direction of the applied field and the dipole moment then makes no contribution to the polarization of the sample. Because a molecule takes about 1 ps to turn through about 1 radian in a fluid, the loss of this contribution to the polarization occurs when measurements are made at frequencies greater than about 10 11 Hz (in the microwave region). We say that the orientation polarization, the polarization arising from the permanent dipole moments, is lost at such high frequencies. The next contribution to the polarization to be lost as the frequency is raised is the distortion polar- ization, the polarization that arises from the distortion of the positions of the nuclei by the applied field. The molecule is bent and stretched by the applied field, and the molecular dipole moment changes accordingly. The time taken for a molecule to bend is approximately the inverse of the molecular vibrational frequency, so the distortion polarization disappears when the frequency of the radiation is increased through the infrared. The disappearance of polarization occurs in stages: as shown in Justification 21.3, each successive stage occurs as the incident frequency rises above the frequency of a particular mode of vibration. At even higher frequencies, in the visible region, only the electrons are mobile enough to respond to the rapidly changing direction of the applied field. The polarization that remains is now due entirely to the distortion of the electron distribution, and the surviving contribution to the molecular polarizability is called the electronic polarizability. E21.2(b) There are three van der Waals type interactions that depend upon distance as 1 /r 6 ; they are the Keesom interaction between rotating permanent dipoles, the permanent-dipole–induced dipole-interaction, and the induced-dipole–induced-dipole, or London dispersion, interaction. In each case, we can visualize the distance dependence of the potential energy as arising from the 1 /r 3 dependence of the field (and hence the magnitude of the induced dipole) and the 1 /r 3 dependence of the potential energy of interaction of the dipoles (either permanent or induced). E21.3(b) The goal is to construct the radial distribution function, g(r) , which gives the relative locations of the particles in the liquid (eqn 21.35). Once g(r) is known it can be used to calculate the thermodynamic properties of the liquid. This expression is nothing more than the Boltzmann distribution of statistical thermodynamics for two molecules in a field generated by all the other molecules in the system.
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