381 



14. In conclusion a remark ma}' be added about the dilute 

 gaseous condition. It follows from equation (11) that: 



Representing by c„ the molecular concentration of the n-fold 



molecules, namely the number of gram-mols for unit of volume, 



1 ,v„ 



we have c,, = r, , and the above equation may be written as 



V nM 



follows : 



c 1 



~=z-{Mve^Y-^ (28) 



Cj" n 



For very large volumes this becomes 



— = -(iifg9)«-i = ir, (28') 



Cj" n 



in other words, to a first approximation this ratio is independent of 



the volume; this ,is the well-known law of Guldberg-Waage, as 



applied to the transformation of ri-fold molecules into single ones. 



It further follows that 



d log K dX E 



— ^7— =(n-l) — — _(n-l) , . . . (29) 



dT ^ ' dT ^ ' RT' ^ ^ 



the expression — (n — 1) E giving the heat effect of the transfor- 

 mation (VAN 't Hoff's law). 



Finally representing the total molecular concentration by Cm, so 



1 .^'„ 1 1 



that c,n =~ 2 — =r - . — , we find from (12) : 

 V nM V aM 



Mc,r,= \log{\+eX) (30) 



For V very large and also e^ (strong association), we may write 

 by approximation 



M.c,n = -log{i + /■()) ')...... (30') 



r 



where r represents the density and q ^ e^ a coefficient depending 



upon the temperature, that is: decreasing with rising temperature'^). 



') This relation (but in that case for the dissolved condition, o being the 

 ordinary concentration by weight of the dissolved substance) was several years 

 ago derived by me empirically for water from determinations of the molecular 

 weight (cf. Acad. Roy. de Bruxelles, loc. cit., p. 20, 23 and 37). 



2) This is also confirmed by the experimental data (cf. Acad. Roy. de Bruxelles, 

 loc. cit. p. 47). From the change of this coefficient with the temperature : 



^=-— - = — — —- I calculated doc. cit., p. 61) the heat of dissociation E of 



dt dT Rl" 



2 M grms ol double molecules of water. 



