PHYSICAL CHEMISTRY IN BRIEF

CHAP. 12: BASIC TERMS OF CHEMICAL PHYSICS [CONTENTS] 417

Example

The relative permittivity of chlorobenzene at 20◦C isε 1 = 5. 71. At 25◦C it drops toε 2 = 5. 62.

Calculate the polarizability and the dipole moment of chlorobenzene. Its density in the given

temperature interval is approximately constant,ρ= 1. 11 g cm−^3 andM= 112. 5 g mol−^1.

Solution

By substituting into equations (12.3) and (12.9) for both temperatures while using the constants

kB= 1. 381 × 10 −^23 J K−^1 andε 0 = 8. 854 × 10 −^12 C^2 J−^1 m−^2 we obtain a set of two equations

with two unknowns (in SI units)

112. 5 × 10 −^3

1. 11 × 103

5. 71 − 1

5 .71 + 2

=

6. 022 × 1023

3 × 8. 854 × 10 −^12

(

α+

μ^2

3 × 1. 381 × 10 −^23 × 293. 15

)

and

112. 5 × 10 −^3

1. 11 × 103

5. 62 − 1

5 .62 + 2

=

6. 022 × 1023

3 × 8. 854 × 10 −^12

(

α+

μ^2

3 × 1. 381 × 10 −^23 × 298. 15

)

.

By solving this set of equations we obtainα= 1. 5 × 10 −^39 C^2 m^2 J−^1 (α′= 1. 35 × 10 −^29 m^3 ) and

μ= 3. 86 × 10 −^30 C m= 1. 16 D.

12.1.6 Permeability and susceptibility

The magnetic field^3 B~ produced by a short segment of wire described by vector~carrying electric currentIin the direction of~is given by theBiot-Savart law,

B~= μ

4 π

I~`×~r

r^3

, (12.10)

where~ris the vector determining the point at which the magnetic field is measured and×
indicates the vector product^4. The proportionality constant μis thepermeabilityof the

(^3) More preciselyinduction of the magnetic fieldormagnetic flux density.
(^4) Vector~c=~a×~bis perpendicular to both~aand~b, the magnitude of~cis|~c|=c=absinγ, whereγis the
angle between vectors~aand~b, and vectors~a,~b, and~cform a right-handed system.