363 



Chemistry. — ''Tlie Apixiretit Contradiction hatioccn Thronj and 

 Practice in the Cryatallisation, of AUotropic Substances from 

 Different Solvents". By Prof. A. Smits. (Communicated by 

 Prof. J. D. VAN DER Waals). 



1. Derivation of the eqiiation for the connection, hetn^'.en tin' satU' 

 ration concentrations and those of the internal equilihriunt. 



In this communication I will give in the first place the thermo- 

 dynamic derivation of the equations derived in the first communi- 

 cation on this subject in simpler but less rigorous way. 



We shall suppose for this purpose that in a homogeneous phase, 

 a gas phase or a solution, at a definite temperature and pressure 

 between two kinds of molecules of the same substance the following 

 equilibrium |)revails : 



v,A:^v,B (1) 



We further suppose tluit in two separate spaces at the same 

 temperature the solid substances A and B are in equiiil)rinm witli 

 their saturate vapour resp. solution, hence: 



As-^Ag (2) 



Bs-^Bq (a) 



Now we sliall assume that i\ mol. of solid A by the aid of the 

 homogeneous phase, which is a gas resp. a liquid phase, is converted 

 into 1', mol. of solid B 



In the first process, which we shall consider now, the homogeneous 

 phase is thought to be a gas phase, in which internal equilil)rium 

 prevails, and in the second process the homogeneous phase is thought 

 to be a solution, in which the kinds of molecules A and B are 

 likewise in internal equilibrium. In these two cases the increase of 

 the molecular potential 2£v[i must, of course, be the same. 



Before proceeding to the fii'st process, I will first observe, that 

 for the increase of the molecular potential or : 



2(vii), = i\^sj^ — v^li,^. (4) 



may be written : 



^(j7i)s=:i',fis^,— r,f),^=pjt,^— r,ftG^-fv,fiG^— VifiG^ + v.fxc^— i»,fts^(5) 



in which hq ^ and hq represent the molecular potentials of A and 

 B in the saturate vapour. 



For the heterogeneous equilibrium between solid ^4 and its vapour 

 and solid B and its vapour hold the following relations : 



