244 MOREY ART. G 



cryohydrate point the weight fraction KNO3 is 0.021; since the 

 vapor is pure water, its weight fraction of KNO3 is zero, and that 

 of the soHd phase is unity. Substituting these values, we get 



The coefficient of the second term in both numerator and 

 denominator is a fractional coefficient. Without an actual 

 determination of the entropy of any phase, certain definite 

 conclusions can be drawn. In the numerator, we have the 

 entropy differences: (vapor — liquid), a positive quantity, and 

 (solid — liquid), a negative quantity. The former is always 

 several times the latter; in the case of this dilute solution their 

 ratio is probably not very different from the ratio of the entropy 

 of vaporization of water to the entropy of fusion of KNO3, which 

 is of the order of magnitude of 20 to 1. The first term predomi- 

 nates, and the numerator is a positive quantity of the order of 

 magnitude of the entropy of vaporization of water at zero degrees, 

 or a little less than 2.18. In the denominator the term affected 

 by the fractional coefficient, the difference in specific volume of 

 liquid and solid, is negative and is itself very small. The first 

 term, the volume difference (vapor-liquid), is comparatively 

 enormous; at the cryohydrate temperature and pressure it is 

 even larger than the volume difference in pure water at its 

 freezing point, 206 liters per gram. The slope of the pressure- 

 temperature curve is at the beginning close to that of pure 

 water; that of pure water is concave upward, owing to the 

 denominator decreasing in value more rapidly than the numer- 

 ator, and the same is true in this case. The pressure-tempera- 

 ture curve of all systems containing a volatile component at low 

 pressure will show a similar initial upward concavity, owing to 

 the rapid decrease in the specific volume of the vapor phase with 

 increasing pressure. 



As the temperature is raised, the fraction of KNO3 in the liquid 

 increases, while the composition of the other phases remains 

 the same. The specific entropy of the vapor continually 



