98 J. van't Hoff on the Function of Osmotic Pressure 



Now (1) and (5) refer to operations opposite in sign on the 

 same substances, with the same mass, at the same temperature; 

 hence (1) + (5) = 0. And for similar reasons, (2) + (4) = 0; 

 whence (3) + (6)=0. 



This conclusion leads directly to Guldberg's and Waage's 

 law. 



The work expressed by (3) is from that law 22a„T -^, and 



d? *" 



(6) is 22a,T ^ ; hence it follows that 



S (2a„Tf'-2 a ,Tf)=0 ) or2( a „f'-a,f)=0. 

 By integrating, 



^( a u l°g P//"~ a / l°g Pi) = constant ; 



and here P is proportional to the concentration, or to the 

 active mass C ; so that C may be substituted without altering 

 the equation : — 



2(a„ log C tl — a t log C y ) = constant. 



This is the logarithmic form of Guldberg's and Waage's 

 formula. 



X. Deviation from Avogadro's Law in Solutions. — Variations 

 in Guldberg and Waage's Law. 



We have attempted to show the connexion between Guld- 

 berg and Waage's law and the laws of Boyle, Henry, Gay- 

 Lussac, and Avogadro, as applied to liquids ; as applied to 

 gases, the truth of Guldberg and Waage's law has been long 

 proved from thermodynamical considerations. 



It remains to develop further the laws of chemical equili- 

 brium, and, first, to investigate more closely the limits of 

 applicability of the three fundamental principles from which 

 Guldberg and Waage's law has been deduced. 



So long as " ideal solutions " are under consideration, there 

 exists strict analogy between gases and solutions ; and just 

 as there are deviations from Avogadro's law in the case of 

 gases, so we may expect to find them with solutions. As, 

 for example, the pressure of the vapour of ammonium chloride 

 was found to be too great to be accounted for by Avogadro's 

 law, so the osmotic pressure is in many cases abnormal ; and as 

 the high pressure in the first case is due to dissociation into 

 ammonia and hydrogen chloride, it may be conceived that 

 similar dissociation occurs in solutions. It must, indeed, be 

 acknowledged that deviations are much more frequent with 

 solutions than with gases, and occur often with bodies the 



