1078 



The value of h^ is h , {;\ ~—.t) -\- h .,x ; or as h^ = V),, we find ilie 

 value l\ ^l+-^') for bx- And the value of üx consists of 3 terms, 

 viz. 1. «1 (1 — ocy, the contribution yielded by the single molecules 

 present. 2. 2 X '^cii^ (1 — ■'^')> ^h® attraction of the single molecules 

 present exerted on the present double molecules and vice versa, and 

 3. the term. {^a^xy. Joining these we find : 



a^{\—x-\-2xy=a,{\-\-x)\ 



We can then reduce the equation of state to the following form : 



RT 



p = 



When we compare this shape of the equation of state of the 



associating substance with that of the substance, when it would 



contain only single molecules, we see, that with given pressure and 



T 

 temperature = T^ , a volume Vx of the associating substance 



corresponds to a volume V^ of the single molecules, which volume 

 Vx is ('i+.t') times larger, and that over the entire region. Only the 

 value of .V is variable. And as I may suppose known, another 



equation, viz. ( — ) ^ is required for the determination of ,v. But 



'Ai the moment we do not require the knowledge of the course of .t'. 



A (piantity J/j of a substance, consisting only of single molecules, 



is in a volume ï\, and a quantity M^{l-\-x) of an associating 



substance is in a volume 2\ {l-\--i;). The density is therefore the same 



for given p and in these cases. I had expected this result, 



and even pronounced it, though I may only consider this thesis as 

 proved by the foregoing. 



Before proceeding further in the investigation of the value of s 

 for the associating substance, I will point out some particularities 

 about the critical circumstances. We find for {RTk)x by approximation : 



8 a^il+XkY 8 a 



^^'^•^^- 27(^^(1^^) = 27 (^).('^-'^-^^' 

 and for {i)k)x- 



__ 1 a.il^xkY _ 1 a, 



^^^^' " 27 {b,)k {l+.'VkY " 27 {b,%^ ' 

 CTfT \ 



and for — — ^ the value 8 (/vj)/,. (l-|-'a-\ ^I'l^ '^« (''^J/c is smaller than 



{Pk)x 



{h,)g, about: 



