THE MEASUREMENT OF OSMOTIC PRESSURES 103 



Hence one inol of sucrose will bind six tiioIs of water. One thousand 

 grams of water is equivalent to 55.5 mols of water (1000/18). Since the 

 water of hydration is not free to act as a solvent, in effect the solution con- 

 sists of I mol of sucrose dissolved in 49.5 mols of water. A simple calcula- 

 tion (22.4 X 55.5/49.5) yields the value 25.12 atmos. as the theoretical 

 osmotic pressure of a weight molar sucrose solution if hydration of the sucrose 

 molecules is taken into account. This value is in close agreement with those 

 which have been obtained experimentally. 



Van't Hoff's demonstration of the analogy between osmotic pressure and 

 gas pressure led many subsequent investigators to consider that osmotic pres- 

 sure results from the impacts of the solute molecules against the interior wall 

 of the membrane, an assumption which van't Hoff himself was careful to 

 avoid. One reason for the persistence of this hypothesis of osmotic pressure 

 has been the difficulty in understanding why — if the osmotic pressure is due 

 to the solvent molecules — it should be approximately equal to the pressure 

 which would be developed if the solute molecules were present in the same 

 volume in the form of a gas. 



The solvent pressure hypothesis holds that the osmotic pressure which 

 develops in an osmometer or similar closed system is due to the excess of 

 the inwardly directed diffusion pressure of the solvent over the outwardly 

 directed diffusion pressure of the solvent. Haldane (1918) has shown that 

 this excess inwardly directed diffusion pressure of the solvent is ?nathematically 

 equal to the pressure which the solute molecules inside the osmometer would 

 exert if present as a gas in the same volume as the solution. Thus it has 

 become possible to reconcile the concept that osmotic pressure is due to the 

 solvent molecules with van't Hoff's classical discoveries regarding the analogy 

 between osmotic and gas pressures. 



The Measurement of Osmotic Pressures. — The osmotic pressure of a 

 solution, as such, can be measured only by the direct manometric method as 

 employed by Pfeffer, Morse, and others. Precise results can be obtained 

 by this method only at the cost of an elaborate technique and infinite precau- 

 tions. Hence the actual number of measurements of osmotic pressures which 

 have been made by this direct method are very limited. As is well known 

 there is a direct proportionality between the osmotic pressure, lowering of 

 the vapor pressure, elevation of the boiling point, and depression of the freez- 

 ing point of solutions. Hence osmotic pressures of solutions can be calculated 

 from the determined results of one of these three physical quantities. Most 

 frequently determinations are made of the depression of the freezing point 

 of a solution, and its osmotic pressure calculated from this. Since the the- 

 oretical freezing point depression of a weight-molar solution of an un-ionized 



