OSMOTIC PRESSURE 25 



pressure were different, work would be performed by the re- 

 transfer of the same quantity of solvent through the mem- 

 branous wall; this would mean a continuous process in an 

 isolated system, attended by gain or loss of energy. As this 

 is impossible, equal vapor tension means equal osmotic pres- 

 sure, and vice versa. Consequently the same number of 

 molecules always produce the same depression of vapor 

 tension in a solvent. Exactly the same sort of reasoning 

 would show that solutions having the same freezing-point 

 have like osmotic pressures. Both of these laws are identical 

 with those found empirically by Raoult. Thermodynamic 

 reasoning further shows that the molecular depression of 

 vapor tension is indeed one hundredth of the molecular weight 

 of the solvent, while the depression of the freezing-point 



depends more directly upon the nature of the solvent, being 



TZ 

 a function of its latent heat of liquefaction: =0.02 where 



T is the absolute temperature of congelation of the pure sol- 

 vent, W is the latent heat per kilogram, and t is the molec- 

 ular depression. 



These are the main results of van 't Hoff 's deductions, as 

 far as molecular weight determinations are concerned. They 

 enable us to employ for this purpose, with perfect confidence, 

 observations upon the phenomena of evaporation, freezing, 

 and osmose. 



The direct measurement of osmotic pressure, as was done 

 by Pfeffer, is difficult and not universally feasible. On the 

 other hand, de Vries has shown how to compare such pres- 

 sures by means of plant cells. 1 It is found that the living pro- 



1 Pringsheim's Jahrbucher fur Wissenschaftl. Botanik, 14, 4. See also Z. physik. 

 Chem. 2,414 (1888). Bonders and Hamburger have shown that the same phenom- 

 ena can be studied in the behavior of blood-corpuscles; Archiv. fiir Anatomic und 

 Physiologic, Physiolog. Abth. 1886, 476, also Hamburger, Maanbl. Nat. Wetensch. 

 1889, 63. 



