﻿Theory of Super saturation. 39 



be obtained from the results of Ostwald *, according to 

 which a quantity of solid solute less than 10 ~ 9 gram was no 

 longer capable of bringing about the crystallization of a 

 supersaturated solution of sodium chlorate prepared from 

 107 parts of salt and 100 parts of water. This corresponds 

 with a radius of about 10 fi, and this must therefore be less 

 than the equilibrium size in equation (3). At lower tempe- 

 ratures very much smaller particles would, however, be 

 active; and it is conceivable that molecular groups having 

 radii from 0'Olyu, to O'l /uu could be formed by multiple 

 molecular collisions in the solution. 



A diminution of active radius would result in solutions of 

 the second type from a rise of temperature. Such solutions 

 should therefore crystallize spontaneously when heated above 

 a certain temperature, which would be higher the less 

 the supersaturation. There appear to be no quantitative 

 experiments in this field. 



In the case of ordinary supersaturated solutions, the 

 active size of particle will be formed from a smaller number 

 of molecules the lower the temperature. The favourable 

 collisions will therefore change with falling temperature 

 from higher to lower orders, and the probabilities of such 

 collisions will then increase enormously. De Coppet seems 

 to have regarded the diminished molecular velocity resulting 

 from the lowering of temperature as the chief cause of the 

 spontaneous crystallization of supersaturated solutions. In 

 the sense of the theory now proposed, the main cause of that 

 phenomenon is rather the variation of the equilibrium size 

 with temperature, i.e. the shift of the probability of the 

 formation of particles of active size from smaller to larger 

 values with fall of temperature. 



A rougn calculation shows that the equation (14) gives 

 results of at least the right order of magnitude, which is all 

 that can at present be expected. If we consider a solution 

 of Glauber's salt normally saturated at 27° C, then 



^=0 = 273 + 27 = 300. 



Also 2M = 284 = 300 approx. In the cases which have been 

 quantitatively examined f, a- is of the order 10 3 erg. We can 

 further assume that p = o, and A = 500 cal. = 25 x 10° erg. 

 Then 



k = 3f =25xl0 4 cm.- 1 . 

 2Mo- 



* Lehrb. allgem. Chem. 2 Aufl., ii. p. Tot. 

 f Of. Jones, loc. cit. 



