16 PHYSICAL PROPERTIES AND COMPOSITION 



It is different as soon as the gas departs from the ideal 

 state of dilution. Take e. g. the values of the product PV 

 for ethylene at 20 and high pressure : 



P 31-58 atm. 84.16 atm. 398-71 atm. 



PF= 0-914 0-399 1-248 



The above fundamental equation for perfect gases has to 

 he transformed into the so-called characteristic equations 

 . in order to account for such deviations. None of them is 

 strictly rationally based, and in satisfactory agreement 

 with the facts, else it would be possible to obtain a reliable 

 insight into the molecular weights of liquids also. Still 

 colligative relations may be shown, on the strength of these 

 characteristic equations, which give a point of departure 

 for molecular weight determinations, and must therefore 

 be considered here. 



Budde 1 pointed out the necessity for a correction on 

 account of the volumes of the gas molecules, and put instead 

 of the total volume, V, a quantity smaller by the constant b, 



Van der Waals 2 pointed out the equally necessary cor- 

 rection for the molecular attraction, by which the pressure 

 directed outwards, P, is reduced. Assuming this attrac- 

 tion as a first approximation to be inversely proportional 

 to the square of the volume, he obtained 



Clausius 3 showed the assumption that the attraction 

 depends only on the volume to be inadmissible and pre- 

 ferred : 



whilst it appeared later that a more complicated formula 4 is 



1 Journ.f. Prakt. Chem. 9. 30. 



3 Continuity of the Gaseous and Liquid States. 



3 Wied. Ann. 9. 337. * 1. c. 14. 279. 



