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# exp3 - Experiment 3 page 1 Version of September 4 2009...

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Experiment 3, page 1 Version of September 4, 2009 Experiment 446.3 DIPOLE MOMENTS Theory A molecule has an electric dipole moment if it has a net separation of centers of positive and negative charge. If the separation of charge is characteristic of the molecule without the application of an electric field, it is said to have a permanent electric dipole moment . Molecules with no net separation of charge outside a field may also have, through interaction with the field, an induced electric dipole moment that exists only when the molecule is in the field. Permanent dipole moments are fixed relative to molecular axes. A permanent electric dipole may be modeled as two charges, -Q and +Q, of equal magnitude and opposite sign, separated by a distance given by the vector r . If the vector r points from the negative to the positive charge, the electric dipole is r d Q . (3.1) In real molecules, charges are distributed (as shown for electrons by a plot of the square of the electronic wave function.), and the dipole moment results from the fact that the distributions of positive and negative charge are not commensurate. The dipole moment of such a molecule is determined by integration over the charge distributions. In the SI system of units, the appropriate unit of dipole moment is the coulomb-m. This is much too large a unit to be useful, so one typically finds molecular dipole moments reported in debyes . 1 [1 D = 1 10 -18 statcoulomb-cm] 2 In SI units, the debye is 3.33564 x 10 -30 coulomb- meter. In what follows, I shall use the centimeter-gram-second (cgs) set of units, where the unit of charge is the statcoulomb. When an electric field is applied, a dipole has an energy of interaction, U , with the electric field, E , that depends on the orientation, , of the dipole relative to the electric field. cos E d E d U . (3.2) For N molecules, each of which has a permanent dipole, d , exposed to an electric field, at equilibrium there is a tendency for the dipoles, on average, to be oriented along the field. This situation is described by the molar electric polarization , P , the total electric dipole moment per mole. If L is Avogadro’s number, the total equilibrium polarization is d P L (3.3) where d is the average molecular dipole moment. 1 The naming of this unit honors the great Dutch scientist, Peter J. W. Debye, who did pioneering work on the electrical properties of solutions, among his many contributions to science. 2 The statcoulomb is the unit of charge in the cgs system of units. 1 statcoulomb = 3.3356 x 10 -10 coulomb.

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Experiment 3, page 2 Version of September 4, 2009 The molar electric polarization contains two contributions, one due to permanent electric dipoles, P p , and a second, P i , due to induced electric dipoles caused by distortion of the electric cloud and of the nuclear framework: i p P P P (3.4) To determine any one of these quantities, the other two must be measured or estimated. The molar polarization can be determined from the dielectric constant,
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exp3 - Experiment 3 page 1 Version of September 4 2009...

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