154 



i-('(liu't' it to .1 one has lo cryslalli/c llic ollici- H, dc. In 

 llu'st' suc'c'i'ssix'c operations the (juaiit it ics ol' watci- s('))a- 

 ratrd l)y crystallization I'roiii the original (iuantity ])rt'seiil 

 would he 1 - !>, then 1 - ',, tiien 1-1, etc. Assnming that 

 the lieat pi-odncod by the crystallization of these (piantities 

 of solvent is dissipated pro|)<)rtionally to the time one lias 

 the following values for the frei'zing temperatures in tei-ms 

 ot" time (the original concentration of the solution is sup- 

 posed to be 0.01 weight-molar, its freezing point, therefore 

 - 0.0186°, and the unit of time is the time that it would take 

 to freeze all the water of the solution) : 



Freezing rr- Freezing rr- 



n ■ t lime r> :, i lime 



Point Point 



-0.0186° XI 1-1 = - 0.0186° X 4 l-i = 0.75 



- 0.0186° X 2 1-Jy = 0.5 - 0.0186° X 5 1-1=0.80 



- 0.0186° X 3 1-i = 0-666 



The freezing point F decreases as an arithmetic progres- 

 sion; the time t increases as a harmonic sequence; it is 

 known that the relation between two such quantities is 

 hyperbolic. The formula of this relation is 



F = ^ (E) 



where k is the freezing point depression of a weight-molar 

 solution. 



In the establishment of this formula many factors have 

 l)een left behind, which should be taken into consideration 

 in most of the quantitative studies on freezing curves: 1. 

 The law of the freezing point depression holds only in dilute 

 solutions of non-electrolytes ; 2. The heat produced is not 

 withdrawn proportionally to the time, its withdrawal de- 

 pends on the difference between the temperature of the 

 bath and that of the material, a difference which is con- 

 tinuously decreasing; 3. By the gradual formation of ice, 

 the specific heat and the heat conductivity of the system 

 are changing and this also affects the rate of heat with- 

 drawal ; 4. There is some heat of solution involved in the 

 ])hase sepai-ation. The hyperbolic relation, therefore, 

 should be considered only as a first approximation law. 



