368 



that the volume of the molecules is not modified bj the grouping 

 of the molecules, which agrees with van der Waals's manner of 

 considering associated (or quasi-associated) molecules as "mere com- 

 plexes of the simple molecules, which can be formed without further 

 radical modifications in the structure of the molecules themselves").^) 



3. As to the quantity üx van der Waals had originally ^) made 

 some simplifying assumptions which resulted in this factor also 

 becoming independent of the degree of association ; later on') he 

 made his theorj' independent of these special suppositions on the 

 ground, that when molecular complexes are formed only a part of 

 the cohesion can make itself felt as internal pressure. In order to 

 conform to this view it is natural in our case to replace the form 

 flfj. = rï [(1 — x) -\- kvY chosen by van der Waals in the case of only 

 one kind of complex molecules by the more general form ^) 



(h- = « (-2" k»a;„y ( 3) 



where a is independent of the degree of association. In this nianner 

 we obtain an equation of the following form : 



RT ^^ Xf, a 



P = 1^ -i^SfCnXnY , (4) 



b 



V 



which is a generalisation of the one assumed by van der Waals 

 (I.e. p. 92)').. 



The coefficients kn may no doubt be assumed to have definite 

 numerical values, only depending on the ordinal number n (/(:, = 1). 



1) These Proceedings, V (1902), p. 304. Van Laar on the other hand (Arch. 

 Teyler, (2), XI, 1908) assumes, that the molecular volume does change 

 (increases or diminishes) by association. This assumption is an essential one in 

 his theory, as he derives from it the possibility of a coexistence of the vapour 

 and liquid with a third (solid) phase (These Proceedings 1909 — 1911). 



~} Conlinuilat II, p. 28. See also van Rij and van Laar (loc. cit.). 



3) These Proceedings, XIII (1), p. 119. 



•*) This form is arrived at by assuming in general a = San a;,i2 -f 2^.2" a«v a;,(/ Xv, 

 and making the additional simplifying assumption aV^ = ay. av (cf. v. d. Waals, 

 loc. cit., p. 120). 



5) We might have retained the equation used by van der Waals, assuming 

 that in it x represents that fraction of the substance which is present as complex, 

 w-fold molecules, n being the mean complexity of all not-single molecules; the 

 possibiUty of such a generalisation was pointed out by van der Waals himself, 

 loc. cit., p. 494 ; n would then have to be considered as a function of v and T, 

 connected with a by the relation : 



1 ■ .V n — 1 



-= 1 — x + ~= 1 X. 



li n n 



