SURFACES OF MOLECULES 225 



In estimating quantitatively the magnitude of the segregation and 

 orientation that result from molecular fields, we may apply the Boltzmann 

 equation ; 



- = Ail/'-'' 



112. 



where n^ ''^nd n^ represent the relative numbers of molecules in two given 

 positions, or orientations, and X is the work done in transferring a mole- 

 cule from one of these states to another. The constant A involves the 

 ratio of the a priori probabilities of the molecules in the two regions or 

 states under consideration. These probabilities are frequently dependent 

 upon geometrical factors, but often involve a knowledge of the quantum 

 phenomena accompanying the change in state. The quantity £ in this equa- 

 tion is the base of the natural system of logarithms, 2.718; k is the Boltz- 

 mann constant, 1.37 X 10"^^ erg per degree ; T is the absolute temperature. 



We see from the Boltzmann equation, that when the constant A is not 

 too far removed from unity, the effects of segregation and orientation 

 usually begin to be important only when the energy X becomes of the same 

 order of magnitude as kT. At room temperature the value of kT is 4.1 X 

 10"^* erg, which is the energy that an electron would acquire in falling 

 through a potential of 0.025 volt. 



In Debye's theory for the contribution of dipole molecules to the 

 dielectric constant of liquids, it is shown that the efifective dipole moment 

 m. of the dipole molecules (of moment \i) is ^^jj. when the field is of such 

 intensity that the work done by the field in orientating the molecule is 

 equal to 2kT. 



The segregation of ions of one sign around an ion of the opposite sign 

 will be marked at distances r less than that at which the potential is 0.025 

 volt ; that is when r is less than 57 X io"Ye cm. If 8 has a low value, of a 

 few units only, then even in very dilute solutions, where the distances 

 between the ions are more than ten times greater than the molecular diam- 

 eters, the ions will tend to be swept out of the solution and brought into 

 contact with each other. This is in accord with the fact that such salt-like 

 substances as NaCl, whose crystals are held together by forces of the 

 Coulomb type, are practically insoluble in organic liciuids of low dielectric 

 constant. On the other hand, in water and other liquids of high dielectric 

 constant, in solutions of even moderate concentration, the ions are far 

 enough apart so that their potentials with respect to one another are less 

 than kT, which agrees with the fact that these salts are soluble in these 

 liquids, and that their solutions behave as electrolytes. 



We have seen that to orientate the larger portion of dipole molecules in 

 liquids requires a field F which makes |iF greater than 2 kT. This means 



