348 BULLETIN OP THE UNIVERSITY OF WISCONSIN. 



for ideal gases, and that the solutions with which Dieterici 

 worked varied between 0.1 and 1.0 normal, and that those 

 used in experiments detailed above frequently were much 

 stronger than normal. That a normal solution is nevertheless 

 for many of the practical purposes of life a rather dilute solu- 

 tion will hardly be disputed. ~No one expects the gas equation 

 to hold strictly for a normal solution or even for one consider- 

 ably more dilute ; but what one has a right to expect from the 

 modern theory of solutions is, that with increasing concentration 

 a solution should behave at least qualitatively as a gas does with 

 increase of pressure. And this requirement is clearly not met, 

 since while all gases behave alike under increase of pressure (so 

 that van der Waals has been able to express their behavior by 

 means of his well known equation) solutions, as has been shown, 

 often behave in a manner opposite to that of gases, and this, 

 too, frequently in solutions that can not be termed concentrated. 

 This demonstrates, then, that the van't Hoif law is at best only 

 approximate and must be applied with great care. As Dieterici 

 well says : 



"Raoult hat seine Gesetze der Damfspannungs- und Gefrierpunkts- 

 depression durchaus nicht als absolut streng giiltige Naturgesetze 

 aufgestelit, sondern als nahezu zutreffende Erfahrungssatze, welche fur 

 die Zwecke der Molekulargewichtsbestimmung genau genug sind." 



We have seen above (and the literature is replete with records 

 of facts illustrating the same point) that substances of similar 

 chemical composition, when dissolved in the same solvent, be- 

 have similarly, as far as the change of the boiling- or freezing- 

 points are concerned ; this clearly shows that the influence of the 

 chemical nature of the dissolved substance enters into the de- 

 termination of the molecular rise of the boiling-point and the 

 molecular lowering of the freezing-point. 



In pressing the analogy between gases and solutions (which 

 undoubtedly exists and from which at times valuable sugges- 

 tions may be derived) it has often been forgotten that this is 

 after all simply an analogy; and like other analogies it fails 

 when carried too far. It is so easy to compare the process of 

 dissolving a lump of sugar in a beaker of water with the expan- 



