226 PHENOMENA, ATOMS, AND MOLECULES 



that a field of about 2.4 X 10'^ volts per centimeter is needed for the orien- 

 tation. The work done when the orientated molecule is brought into the 

 field is of the same order of magnitude, so that a field sufficient to cause 

 nearly complete orientation of dipole molecules will also cause marked 

 segregation. A field of 2.4 X 10'^ will exist at a distance r = 8 X io"V(f )^'^" 

 cm. from a univalent ion, or at a distance r = 3 X lO^VC^)^'^^ cm. along the 

 axis of a dipole molecule having a moment \i = 10"^^. In other directions 

 than along the dipole axis the force will be less and therefore the distance 

 at which effective orientation or segregation occurs will be less than that 

 just given. 



From these calculations we conclude that the interaction between di- 

 pole molecules of moment io~^^ can cause mutual orientation only when 

 they are practically in contact. If they were separated by one additional 

 molecule, so that the distance between centers is 6 X io~^ cm., even if they 

 were still orientated, the force would be only one-sixteenth as great, since 

 it varies inversely as the fourth power of the distance. However, at this 

 greater distance, the orientation would be far from complete, so that the 

 force would actually vary inversely as the sixth power of r, and would thus 

 be only one sixty-fourth as great as if the molecules were in contact. 



The electric force necessary to deform a molecule sufficiently to give it 

 a dipole moment j.i = io~^^ (viz., 3 X 10'^ volts per centimeter) is prac- 

 tically the same as that needed to produce orientation of a dipole molecule 

 having this same moment. Thus when two dipole moment molecules are in 

 contact, the dipole moment which each possesses is practically doubled 

 liecause of their mutual deformation. 



Taking the electric field near a dipole to be proportional to r~^, and 

 remembering that the distance between the center of one molecule and the 

 surface of its neighbor is only one-third the distance to the surface of the 

 far neighbor, we realize that the electric field intensity at one side of tlie 

 dipole molecule is twenty-seven times as great as at the opposite side. 



The latent heat of evaporation of a liquid expressed per molecule gives 

 the energy which must be expended to separate the molecules of liquid 

 from one another. Pentane, a non-polar liquid, which boils in the neigh- 

 borhood of room temperature (^6°C.), has a heat of evaporation of about 

 40 X 10"^^ erg per molecule, which is roughly equal to 10 kT. According 

 to the rough empirical rule of Trouton, the absolute boiling points of 

 liquids are proportional to their latent heats of evaporation, so that in 

 general, to the same degree of approximation, the heats of evaporation per 

 molecule for all liquids will be about jo kT, where T is the temperature at 

 the boiling point. This can be looked upon as a consequence of the Boltz- 

 mann law. The coefificient A in this case, however, is quite different from 

 unity. 



