Crafts et al. 



94 



Water in Plants 



The value so obtained is not the true freezing point, because of (a) supercooling 

 of the solution, and (b) absorption of heat by the apparatus. Harris and Gortner 

 (1914) proposed a correction for the supercooling. Since crystallization usually be- 

 gins at a temperature lower than the true freezing point, the liquid phase at the ob- 

 served freezing point, in equilibrium with the ice crystals, is more concentrated than 

 it would be at the true freezing point. Since one eightieth of the weight of water 

 solidifies per degree of undercooling, 



(^-^) 



or 



V 



Al — 0.0125 u Al 



ai) 



(12) 



where A^ and A = observed and true freezing point depressions, V = volume of 

 solution, and u = number of degrees of undercooling. This correction has been 

 widely used in cryoscopy. If undercooling can be avoided by salting with ice crystals, 

 jarring, etc., the correction is unnecessary. 



O-Z 



0.^ o.c o.a 



Mots 6ucro6e per IQOOg water 



1.0 



Fig. 30. — Calibration curve for the apparatus shown in figure 29. The 

 lower curve was constructed from data from the International Critical Tables 

 (1933) ; the upper curve presents the observed values. 



An approximate correction for heat capacity eflfects may also be calculated if the 

 following values are known : 1 ) the weight and heat capacity of glass sample tube, 

 thermometer, and stirrer in contact with the solution; 2) volume of solution; J) tem- 

 perature at which freezing begins; 4) temperature of bath; and 5) observed freezing 

 point. The heat capacity effect is small and the correction unnecessary where the 

 volume of solution is large in comparison with the volume of the thermometer and 

 glass. For small amounts the error may be serious. 



By use of a modified procedure (Currier, 19446), it has been found possible to 

 eliminate these two corrections. The semimicro apparatus (Figure 29) was standard- 

 ized by recording the observed freezing points of carefully prepared molal sucrose 

 solutions, ranging in concentration from 0.1 M to 1.0 M in steps of 0.1 M, and com- 

 paring them with the accurately known theoretical values (Int. Crit. Tables, 1933). 

 The results of this comparison are shown in Figure 30. By referring an observed 

 value to this graph, the corrected value may be obtained at once. The increasing dis- 

 crepancy between A obs. and A corr., as the solutions become more concentrated, is not 

 due to supercooling effects as the correction for supercooling, when calculated accord- 

 ing to Harris and Gortner's formula, remains at about 0.01° C. for all concentrations. 

 The probable explanation is that with increasingly concentrated solutions a greater 

 amount of heat is lost to the system because crystallization is slower, and the time re- 

 quired to reach the apparent freezing point is longer. Walter (1931o) recommended 

 that in the cryoscopic determination the amount of supercooling be constant and ap- 



