Dissociation of Compounds in Water. 493 



The Constant for Water. 



If all substances were completely undissociated, molecular 

 solutions for any given solvent should give very nearly the 

 same lowering of the freezing-point of that solvent. Gram- 

 molecular normal solutions in water would give a certain 

 lowering of the freezing-point, and this would be the constant 

 for water. As we have seen, certain compounds like urea 

 and alcohol behave thus, except for very dilute solutions, and 

 enable one to determine this value experimentally. 



The same value has been calculated by van't Hoff* from 

 the latent heat of fusion of the solvent. The calculation has 

 been developed rather more fully by Ostwaldf thus : — 



Let us take a solution consisting of n molecules of the 

 dissolved substance and N molecules of the solvent (molecule 

 = gr.-mol. wt.), Let T = temperature of solidification of the 

 solvent, and A= the lowering of the freezing-point. Here 

 as much of the solvent is allowed to solidify as would serve 



N 

 for the solution of one molecule of the substance, = — molecules. 



; n 



Let X = the molecular heat of fusion of the solvent ; the 



amount of heat liberated would be — X. If now the ice be 



n 



separated from the solution, warmed to temperature T and 

 melted, and finally allowed to mix with the solution bypassing 

 through a semipermeable membrane, it will exert an osmotic 

 pressure p. If v = volume of solvent which had solidified, the 



N 

 work=£W, the heat= — X ; from which 



pvn 



A 



NX T' 

 h\\tpv = ~RT and R = 2 cal. Substituting, we have 



A n 2T 2 



A= NT' 



Let M=mol. wt. of the solvent, and substituting N= -«- 

 we have 



A= TooX W 



* van't Hoff, Zeits. phijs. Chem. i. p. 490. 

 f Ostwald, Lehrb. i. p. 759. 



