1076 



Physics. — ''On the critical density for associating substances.''* 

 By Prof. J. D. van der Waals. 



(Communicated in the meeting of March 28, 1914). 



For non-associating' substances the critical density is determined 

 by the relation : 



D), — 0,001293 ^^ s. 



28,84 RTu 



We then understand by density the number of grams that 1 cni^ 

 weighs, by M the molecular weight, and by .v the factor introduced 

 by Sydney Young, which denotes how many times the critical volume 

 is smaller than would be the case if the substance should have 

 followed the laws of Boyle and Gay-Lussac. So that s corresponds 

 to the relation: 



Vh Vk PoVo 

 s 



or as />„ = 1 and R2\:=zl, io: 



PkVk _ 



If we imagine a quantity of substance present equal to M, then 



28,84 « . ' 



v,, = = 22305, and the üiven eiiuatioji lor Dl- becomes 



0,001293 Ö 1 



duly : 



Dk = -. 



vk 



The determifiation of Vk is therefore sufficient for the determination 

 of Dk) and also, when Tk and pk are laken into account, for the 

 determination of the quantitj' .s\ We owe it chiefly to vSydney Young 

 that the value of Dk and the corresponding value of s is known 

 for a great number of substances. If the observations do not allow 

 the direct determination of Vk, one may avail oneself of other methods 

 to determine Dk for the calculation of s, but not with the same 

 certainty, and determine the quantity s by the aid of this value and 

 the knowledge of M, pk, and Tk according to the above given 

 formula. Now it is remarkable to how high a degree this quantity 

 is found the same for alle non-associating substances, and how little 

 it appears to differ from 3,77. Whether it really has this value for 

 all normal substances, whether a smaller value will exist particularly 

 for substances with small molecules, I will not discuss again at 



