Reaction before Complete Equilibrium, < S< .J 



Integrated, this equation gives 



K"t= - log^%+ const. 



At the beginning of the reaction, when t = 0, T = T,„., we 

 have 



— —oo + constant ; 



«'. e. constant = x , and 



i. e. the temperature can at no value of T rise in a finite time, 

 and this is an evident impossibility. It is true, we could avoid 

 this difficulty by making the assumption thai the equation 



d ±=K" («.-<) (<-/„) 



is to hold good only for heterogeneous systems; i. e. thai T 

 cannot be put =T OT , since in this case the solid pari of the 

 gygtem =0, and the system becomes homogeneous. This, 

 however, would scarcely be quite satisfactory and justifiable 

 in view of the fad that overcooled or supersaturated solutions 

 always crystallize out by themselves after a certain limit of 

 overcooling or of supersaturation ha- been reached, though 

 no solid is present in the system. On the contrary,the insta- 

 bility constant K shows that there is always an internal force 

 present in an overcooled ora supersaturated solution (generally 

 in all heterogeneous systems which are removed from the 

 point of equilibrium) which i- striving to drive the system 

 from a state of instability into a state of reaction, which is 

 ultimately to bring it to a state of equilibrium. Tin- force is 

 the greater the further the system is removed from the point 

 of equilibrium. In the above equation K i- taken a- directly 

 proportional to the remoteness of the system Erom the point 

 of equilibrium T„ — T. Since, however, the value of K is 

 small, it cannot be decided with certainty whether the real 

 form of variation of K with the amount of overcooling is uot 

 another one It is the passive forces in the system which 

 hinder the force represented by K from setting the same into 

 a state of reaction; a-, however, K increases with the 

 amount of overcooling or supersaturation, &c, K ultimately 

 arrives at a value greater than those counteracting j » ; i — i \ * - 

 force-, so thai after a certain limit the system must crystallize 



out by itself. 



