PHYSICAL CHEMISTRY IN BRIEF

CHAP. 12: BASIC TERMS OF CHEMICAL PHYSICS [CONTENTS] 416

U Main unit:C^2 m J−^1.

Note:Polarizabilityαis usually converted to the so calledpolarizability volumeα′,

α′=

α

4 πε 0

,

traditionally called also “polarizability”. It has dimensions of volume and equals very

roughly 1/10 of the volume of a molecule.

Polarization also occurs in polar molecules. In this case the total dipole moment is the

vector sum of the permanent and induced dipole moments.

12.1.5 Clausius-Mossotti and Debye equations

For nonpolar substances, the molar polarizationPM is related to the polarizability of the

molecules by the approximate relation called theClausius-Mossottiequation,

PM=

NAα

3 ε 0

, (12.8)

whereNAis the Avogadro constant.

For polar substances, the molar polarization is also influenced by the magnitude of the

dipole moment. For not too large dipole moments relation(12.8) becomes

PM=

NA

3 ε 0

(

α+

μ^2

3 kBT

)

, (12.9)

wherekB is the Boltzmann constant (kB=R/NA= 1. 381 × 10 −^23 J K−^1 ). This more general

relations is called theDebye equation, and it expresses the fact that polar molecules tend to

further increase the permittivity of their environment by orienting themselves prevailingly in

the direction of the electric field. With increasing temperature, however, the thermal motion

of the molecules disturbs this orientation, and the effect of the molecular dipole moments

gradually decreases. By measuring the thermal dependence of molar polarization it is possible

to determine both the polarizability of molecules and their dipole moment.