PHYSICAL

PROPERTIES

5.135

5.6.1

Refractive Index

The refractive index

n is the ratio of the velocity of light in a particular substance to the velocity of

light in vacuum. Values reported refer to the ratio of the velocity in air to that in the substance

saturated with air. Usually the yellow sodium doublet lines are used; they have a weighted mean of

589.26 nm and are symbolized by

D

. When only a single refractive index is available, approximate

values over a small temperature range may be calculated using a mean value of 0.000 45 per degree

for dn

/dt, and

remembering that

decreasesn Dwith an

increase in

temperature. If a transition point

lies within the temperature range, extrapolation is not reliable.

The

specific refraction

r D

is given by the Lorentz and Lorenz equation,

n

D2

1

1

R D

·

n

D2

2

where is the density at the same temperature as the refractive index, and is independent of tem-

perature and pressure. The molar refraction is equal to the specific refraction multiplied by the

molecular weight. It is a more or less additive property of the groups or elements comprising the

compound. A set of atomic refractions is given in Table 5.19; an extensive discussion will be found

in Bauer, Fajans, and Lewin, in

Physical Methods

of

Organic Chemistry,

3d ed., A. Weissberger

(ed.), vol. 1, part II, chap. 28, Wiley-Interscience, New York, 1960.

The empirical Eykman equation

n

D2

1

1

·

constant

n D

0.4

offers a more accurate means for checking the accuracy of experimental densities and refractive

indices, and for calculating one from the other, than does the Lorentz and Lorenz equation.

The refractive index of moist air

can be calculated from

the

expression

103.49

177.4

86.26

5748

(n 1) 10 6

p 1

p 2

1 T

p 3

T

T

T

where p 1 is the partial pressure of dry air (in mmHg),

p 2

is the partial pressure of carbon dioxide (in

mmHg),

p 3 is the partial pressure of water vapor (in mmHg), and

T is the temperature (in kelvins).

Example:

1-Propynyl acetate

has

n D

1and.4187

density

at0.209982

C; the molecular

weight is 98.102. From the Lorentz and Lorenz equation,

r D

(1.4187) 2

1

·

1

0.2528

(1.4187)

2

2

0.9982

The molar

refraction is

Mr D

(98.102)(0.2528)

24.80

From the atomic and group refractions in Table 5.19, the molar refraction is computed as follows:

6 H

6.600

5 C

12.090

1 C

#C

2.398

1 O(ether)

1.643

1 O(carbonyl)

2.211

Mr

D

24.942