1080 



molecules present, the possibility of the existence of which chemistry 

 must be able to show by means of the construction of the molecule ; 

 in case of quasi-association, however, there are local accumulations 

 of molecules, which may lead to the question if the cause why they 

 occur in a greater degree for one substance than for another, may 

 perhaps be found in the form of the molecules. But this question 

 cannot be answered with any certainty yet. Nor can the question 

 be answered as yet for real association why for acetic acid and for 

 aldehydes and perhaps some other substances as nitriles, this asso- 

 ciation exists 



The degree of aggregation for the quasi-association will probably 

 not be the same for each of these aggregations, but to simplify the 

 calculation we may assume on an average the value n for it, which 

 I estimated already before at 8 or 9. It is, however, to be expected 

 that also the mean \'alue n will vary with pressure and temperature. 

 But since we have only to examine the influence of the quasi 

 association on the critical circumstances here, we may confine 

 ourselves to an invariable value of n. Proceeding here as we did 

 above, we find for 1 — x non aggregated molecules, and x aggregations 

 the molecular weight equal to M^ (1 — x -f nx). For hk w^e find 

 ^^ (1 — x-\-nx) and for ni, the value n^\V —x-\-nx\„. 



And we may write the equation of state: 



RT 



\-\-{n — \)x ttj 



, p = 



1 -i-(n — l).r 



-h. 



l-\-(n — \)x 



Hence with given pressure and temperature - — ; — — - = 2\ is 



'^-- = 1',, if w^e should call i\ the volume which the substance 



l+(n-l).r 



would occupy at the same pressure and corresponding temperature, 



when it were not in quasi-association. The value of z;=rri {l-{-{n — l)^')- 



In the tirsl case the density is equal to — in the second to 



''1 



^—^ — ^, so of the same value. Thus we shall also find: 



V 



U,U01293 ,, „ , , ,. , 0«)i 



and 



{pk)r={pk), 



{\kh = {vk)^ li+('*-1)''^-aJ 



