Physics. — ''On Heats of Mixing of Normal and Associating 

 Liquids." By Dr. J. J. van Laar. (Communicated by Prof. 



H. A. LORENTZ). 



(Communicated at the meeting of November 25, J 922). 



5. Some Remarks. Before proceeding to the case of anomalous 

 coiiiponeiits we will make a few remarks. 



a). So far we have always written n^ and n^ for the molecule 

 values. But often n^=^l — x and n^=zx is put, so that n^-\-n^=::\. 

 The differential quotients of lu with respect lo ?z, and n^ can then 

 also be calculated by the differential quotient with respect to x by 

 means of the equations 



öto dfo ö(o dü) 



on^ Ox 011^ Ox 



This immediatdly follows from w = n^tv^ -\- n^io^ and 



dtu b(o dn^ do) dn^ dcj du) 



dx dn, dx dn, dx dn^ dn^ ^ "' 



The same thing, of course, holds not only for iv, but for every 

 homogeneous function of the 1^* degree with respect to the mole- 

 culai' values n^ and n, (e.g. v). 



For a homogeneous function of the 0''' degree with respect to 

 /Zj and n, (e.g. w^,Vi, etc.; the degree of dissociation of the double 

 molecules /? (see further), etc.) we have : 



On^ Ox On^ Ox 



which fol lo ws fro m : 



n,^ h n, ^— ^ and — = — \- -— (see above). 



On^ Oti^ ox drïj on, 



b). We have seen that when v^*\/'a, — v^''\/a^=:0 (i.e. when the 

 critical pressures of the two components are the same) At; becomes 

 = according to (3) (hence also Li\ and AvJ. But according to 

 (1) then also w = (and this holds also for iv^ and iv,). 



Now 



26 

 Proceedings Royal Acad. Amsterdam. Vol. XXV. 



