310 



be more greatly accentuated, and the negative term with (p -f~ "■jv^^'v 

 will predominate still more. 



Already Hakeiuis Roozkboom — now about twenty years ago — 

 drew my attention to the iusufticiency of the a|)proximative expres- 

 sion, but at the time we attributed this to other causes ^), thinking 

 that — especially in quasi-ideal mixtures — the possible volume- 

 contraction would probably be quite negligible. Not until J 912, when 

 in a letter my friend Prof. Kremann at Graz put a question to me 

 on this subject, was I led to carry out the perfectly accurate 

 calculation of the quantity Av '), 



In what follows I may be allowed to give the exact theory, ürst 

 of all of mixtures of normal components. Here too the perfectly 

 accurate derivation appears to be by no means more difficult or 

 longer than the approximated derivation, and the result is almost 

 equally simple. The same thing is found here as before with the 

 exact derivation of the equations of the spinodal and the plaitpoint 

 line *). There the perfectly accurate results are even simpler than 

 the earlier approximated expressions. 



2. Heat of mixing ot normal components. 



From the well-known expression for the total energy 



a 



V 



in which the energy constant e' is =in^e\ -f" ^^«^'i' ^"^ t^^® ^^^^ capacity 

 at constant (infinitely great) volume k=in^k^-\-n^k,, we find for the 

 pure components : 



e: = e\^k,T 4-fpi;/ 



V = ^', + ^,T--l- + p./ 



For the integral heat of mixing of n^ gr. mol. of one component 

 and n, gr. mol. of the other component the expression 



^) Inaccuracy of Van der Waals' equation of state; non-validity of Berthelot's 

 assumption ajo = l/ttittg, etc. But since then I have got more than ever convinced 

 of the absolute validity (in liquids) of the said equation and B's assumption. Of 

 course a and h then have other values than in the gaseous slate, but this need, 

 of course, not be considered here. 



») Later inserted summarized in his valuable — unfortunately too little known 

 — book: 'Die Eigenschaften der binaren Flüssigkeitsgemische etc." (Sammlung 

 (Herz) chemischer Vortriige Bd. 23, Stuttgart, Enke, 1916) ; see p. 170—171. 



») These Proc. Vol. VU, p. 646; Vol. Vill, p 33. 



