598 



Physics. — "Some remarks on t/ie values of the critical quantities 

 in case of association'' By Dr. J. J. van Laar. (Comnmni- 

 cated b}' Prof. H. A. Ijorentz). 



(Communicated in the meeting of May 30, 1914). 



1. Though this subject was treated already very fully bv me iu a 

 paper in the Arch. Teyler^) iul908; and use was made afterwards 

 (in 1909) of the contents of this paper in niy Treatises on the Solid 

 State ^) — I wish to make a few remarks induced by a paper by 

 Prof. VAN DEH Waals in These Proceedings of April 1914 (p. 1076 et seq.) 

 which may contribute to tiie removal of the pretty large difference 

 found by him (p. 1081) for the volume value of CH^ for methyl- 

 alcohol (2,12) and for ethylalcohol (2,76). 



V'^an der Waals makes namely use of ^•alues of Vk, HTu and ^;^, 

 of which he states (on p. 1078) that they would be exact by approxi- 

 mation. But it has appeared from the investigation made by me iu 

 1908 that the "linear" dependence of the quantities BTk and s of 

 the association factor 2 : (1 + /j) cannot be assumed even by approxi- 

 mation. 



Not only does this hold when fas v. d. W. assumes) the volume 

 of the molecules does not undergo any change on association ; wdien 

 in other words Lh = — Vs ^^i 4" ^^i = — but the deviation in question 

 presents itself to a much greater degree, when A/y is not = 0, as is 

 certainly the case for water ') and the alcohols. 



In the cited Teyler article I started from the eqiuition 



1+|3 RT a 



P = -^ 7 ^' (1) 



2 V — v^ 



in which ^ represents the degree of dissociation of the double mole- 

 cules, so that to the original \l^ double molecule are found Vz (1 — ^, 

 double molecules and 72 • 2,i =1 /? single molecules, together Vs (1 + ?) 

 molecules. 



^) Arch. Teyler (2) T. XI, Troi-sième partie (1908) : Theorie générale de I'asso- 

 ciation de molecules semblables et de la combinaison de molecules différentes. 

 (p. 1—96). 



' 2) These Proc. of April 22, June 25, Aug. 31 1909; Nov. 24, 1910; Jan. 2G 

 and June 23, 1911; resp. p. 765, 26, 120, 183, 454, 636 and 84. (See especially 

 the third paper, p. 127—130). 



'■') Already in 1899 1 think I showed that the phenomenon of maximum 

 density at 4° C. can be explained in a very simple way by the assumption of a 

 negative value of [yh, so that a double molecule would have a larger volume 

 than two single molecules. [Zeitsolir. f. physik. Cli. 31 (Jubelband fur van 't Hoff)], 



