342 KEYES 



ART. J 



the Gibbs-Dalton law (Gibbs, I, 155, beginning line 7), the 

 implications of which can only be fully developed by using an 

 equation connecting p, v, t and the mass, which is valid at 

 sensible pressures (one atm. for example). Such an equation 

 may be readily obtained by the use of equation [92] of Gibbs' 

 Statistical Mechanics^'^, viz., 



V = ^7^7^' B = -2x71 I (e-'^'' - 1) rW. (VII) 



Employing the van der Waals' model," for example, there 

 is obtained the following simple equation for B at low pressures 



^ = ^-^ 



/ aiA atA" \ 



It is true that the van der Waals model is often inadequate 

 (case of helium, neon) but it gives results sufficiently in 

 accord with fact for the purposes of this section to make it 

 unnecessary to deal with the considerably more involved expres- 

 sion following from a model more in accord with contemporary 

 ideas of atomic and molecular structure '- i3. i4, 15, le, 17. is 'pjjg 

 quantity B of (Vila) is a pure temperature function in which 

 /?, -A, ai and ai are constants. 



Gases, it is apropos to state, may be sorted into two classes, 

 those which have a permanent electric moment in the sense of 

 the dielectric constant theory and those which have not. In 

 the former class^^ are found water, ammonia, the hydro- 

 halogen acids, sulphur dioxide, the alcohols, etc., while the 

 noble gases, nitrogen, hydrogen, oxygen, methane have no 

 moments. The simpler more symmetrical structure of the 

 latter substances is reflected in their physical and quasi-chemical 

 behavior (adsorption for example). Thus the departure from 

 relation (II) for the latter gases is less, and it is not necessary 

 to retain many terms of the bracketed part of (Vila). Mole- 

 cules having permanent moments exhibit on the contrary great 

 departure from relation (II).* 



* At zero degrees and one atmosphere nitrogen has a pressure less than 

 that calculable from (II) by about one twentieth of one percent. Am- 



