PHYSICAL PROPERTIES

5.137

where the summation extends over all charges (electrons and nuclei) in the molecule. The numerical

values of the dipole moment, expressed in the c.g.s. system of units, are in debye units, D, where

1 D 10 18 esu of charge			centimeters.	The conversion factor to SI units is
			1 D 3.335 64	10 30	C · m	[coulomb-meter]
Tables 5.17 and 5.18 contain a selected group of compounds for which the dipole moment is
given. An extensive	collection	of	dipole moments (approximately 7000		entries)	is contained in
A. L. McClellan,	Tables	of Experimental Dipole Moments,				W. H. Freeman, San Francisco, 1963. A

critical survey of 500 compounds in the gas phase is given by Nelson, Lide, and Maryott, NSRDSNBS 10, Washington, D.C., 1967.

5.6.4 Dielectric Constants

If two oppositely charged plates exist in a vacuum, there is a certain force of attraction between them, as stated by Coulomb’s law:

1

q1 q2

F

· r 2

4 0

where

F is the force, in newtons, acting on each of the charges

q1

and q2 ,r is the distance between

the charges, is the dielectric constant of the medium between the plates, and

0

is the permittivity

of free

space.

q1 ,q2

are expressed in coulombs

and

r in meters. If

another substance,

such as a

solvent, is in the space separating these charges (or ions in a solution), their attraction for each other

is less. The dielectric constant is a measure of the relative effect a solvent has on the force with

which two oppositely charged plates attract each other. The dielectric constant is a unitless number.

Dielectric constants for a selected group of inorganic and organic compounds are included in

Tables 5.17 and 5.18. An extensive list has been compiled by Maryott and Smith,

National Bureau

Standards

Circular 514,

Washington, D.C., 1951.

For gases the values of the dielectric constant can be adjusted to somewhat different conditions

of temperature and pressure by means of the equation

( 1)t,p

p

( 1)20 ,1 atm

760[1 0.003 411(

t 20)]

where

p is the pressure (in mmHg) and

t is the temperature (in

C). The errors associated with this

equation probably do not exceed 0.02% for gases between 10 and 30

C and for pressures between

700 and 800 mm. The dielectric constants of selected gases will be found in Table. 5.18.

5.6.5Viscosity

The	dynamic viscosity,				or coefficient of viscosity,	of a Newtonian fluid is defined as the force per
unit area necessary to maintain a unit velocity gradient at right angles to the direction of flow between
two parallel planes			a unit distance apart. The SI unit is pascal-second or newton-second per meter
squared			2	The].c.g.s. unit of viscosity is the poise [P];			1 cP	2
		[N · s · m						1 mN ·Thesdynamic· .
viscosity		decreases	with	the	temperature approximately according	to the	equation: log
A B /T . Values of				A	and B for a large number of liquids are given by Barrer,			Trans. Faraday Soc.
39:	48 (1943).

5.138		SECTION	5
TABLE 5.21	Aqueous Glycerol Solutions
		Relative			Viscosity, mN · s · m		2
% Weight	Grams	density
glycerol	per liter	25 /25C		20 C		25 C		30 C
100	1261	1.262 01		1 495		942		622
99	1246	1.259 45		1 194		772		509
98	1231	1.256 85		971		627		423
97	1216	1.254 25		802		521		353
96	1201	1.251 65		659		434		296
95	1186	1.249 10		543.5		365		248
80	966.8	1.209 25		61.8		45.72		34.81
50	563.2	1.127 20		6.032		5.024		4.233
25	265.0	1.061 15		2.089		1.805		1.586
10	102.2	1.023 70		1.307		1.149		1.021

		Kinematic viscosity v				is the ratio				of the			dynamic	viscosity to			the density of a fluid. The					SI	unit
is meter squared per second							2					1			are called stokes								[cm	2			1]; poises
							[mThe·c.sg.]s. units																		· s
stokes			density.
		Fluidity		is the reciprocal of the dynamic viscosity.
		The primary reference liquid for viscosity measurements is water. The absolute viscosity of water
at 20 C			is	1.0019 (		0.0003)	mN · s · m						2	(or centipoise), as determined by Swindells, Coe, and
Godfrey, J. Research Natl. Bur. Standards														48:	1 (1952). The relative viscosity of water,												is / 20 ,
0.8885 at 25 C, 0.7960 at 30							C, and 0.6518 at 40									C. Values at temperatures between 15 and 60											C
are best represented by Cragoe’s equation:
						log					1.2348(20				t) 0.001 467(					t 20)		2
							20									t	96
		The	Reynolds number			for flow in a tube is defined by													/ ,		d	is the diameter of the tube,
																	wheredv
																is the density of the fluid, and									is its dynamic
	vis the average velocity of the fluid along the tube,
viscosity. At flow velocities corresponding with values of the Reynolds number of greater than 2000,
turbulence is encountered.
TABLE 5.22 Aqueous Sucrose Solutions
											Relative									Viscosity, mN · s · m					2
% Weight						Grams						density
																	15 C					20	C				25 C
		sucrose				per liter						20 /4 C
75						1034				1.379 0						4 039					2 328					1 405
70						943.0				1.347 2							746.9					481.6					321.6
65						855.6					1.316 3						211.3					147.2					105.4
60						771.9					1.286 5						79.49						58.49				40.03
50						614.8					1.299 6						19.53						15.43				12.40
40						470.6				1.176 4							7.463					6.167					5.164
30						338.1				1.127 0							3.757					3.187					2.735