Concise Physical Chemistry

c18 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

DIPOLE MOMENTS 295

Thedielectric constantof substancexis defined as the ratio

εx=

Cx

C 0

which is always greater than one. Dielectric constants are very different for different

molecules; for example, the dielectric constants are 1.000272 for H 2 (g), 2.283 for

benzene, and 78.0 for water at 298 K. We describe benzene as anonpolarsolvent

and we describe water as apolarsolvent.

The molar polarization of a substancePis related to the dielectric constant by

P=

ε− 1

ε+ 2

M

ρ

where M is the molar mass. This is sometimes called thetotal molar polarization

because it is made up of two parts: thedistortion polarizationand theorientation

polarization,PT=Pd+Po.

Distortion polarization exists for all substances, which is the reason thatεis never

less than one. Consider a collection of atoms of a monatomic gas such as neon or

argon. The electronic charge distribution within each atom is spherically symmetrical

in the absence of a field; but in the presence of a field, the atomic charge distribution

is distorted into something like the ellipses shown in Fig. 18.7, and a dipolar nature

isinducedin it.

Orientation polarization results from the permanent dipole brought about by an

unsymmetrical charge distribution in the unperturbed molecule. A familiar example

is HCl, which has a negative end (Cl) and a positive end (H).

The mathematical form of these two distinct types of polarization enables us to

determine both. Distortion polarization is not a function of temperature,

Pd=

4

3

πNAα

but orientation polarization is inversely dependent uponT:

Po=

4 πNA

9 kBT

μ^2

whereNAis the Avogadro number andkB is the Boltzmann constant. One can

rearrange the equation for the total polarization as a function of 1/Tto emphasize its

linear nature:

PT=

4 πNAμ^2

9 kB

1

T

+

4

3

πNAα=

4 πNA

3

[(

μ^2

3 kB

)

1

T

+α

]