OSMOSIS 191 



small particle weighs 0.05 gram and a large particle weighs 0.25 

 gram, 5 grams of the former and 25 grams of the latter will give 

 to each lot the same number of particles, viz., 100. In the same 

 way, 44 (the molecular weight) grams of carbon dioxide, CO2, 

 and 342 (the molecular weight) grams of sugar, C12H22O11, will 

 each have the same number of molecules. A mole of carbon 

 dioxide (44 grams) and a mole of sugar (342 grams) having been 

 obtained, it may then be observed whether or not the pressure of 

 the gas is equal to that of the sugar solution, temperature and 

 volume being alike in both instances. The pressure of 1 mole of 

 a gas is 1 atmosphere when it occupies 22.4 1. at 0°C. If the 

 volume (22.4 1.) is reduced to 1 1., then the pressure will be 22.4 

 atmospheres. If all our hypotheses are correct, then the same 

 number of molecules of sugar in solution, i.e., 1 mole of sugar, 

 should give 22.4 atmospheres of osmotic pressure when dissolved 

 in 1 1. of water. So much for theory. 



Pfeffer found that a 4 per cent solution of cane sugar at 15°C. 

 has an osmotic pressure of 208.2 cm. of mercury. This would be 

 197.4 cm. of mercury at 0°C. A 4 per cent solution (4 grams in 

 100 cc.) is the equivalent of 40 grams in a liter. A molar solu- 

 tion of sugar is ^^/<40j or 8.55 times as concentrated; therefore, 

 10% 5 5 of the theoretical value of 22.4 atmospheres (22.4 atmos- 

 pheres = 1,702.4 cm. of mercury) should equal Pfeffer's experi- 

 mental value of 197.4 cm. of mercury for a 4 per cent solution. 

 The theoretical value thus calculated is 199.1 cm. of mercury, 

 a very close agreement to the experimental value of 197.4. 

 (Since Pfeffer's day, results in still better agreement have been 

 obtained.) The first law of gases, therefore, holds for solutions. 



The analogy (first made by van't Hoff) is not a perfect one 

 and does not hold accurately. It holds more perfectly for dilute 

 solutions. Because of this, it is sometimes objected to, but the 

 reply can be made that it is a striking and fundamental fact that 

 a calculation such as that of Pfeffer, based on the theory of van't 

 Hoff, should hold so very closely when tested experimentally. 

 That the analogy is not perfect must be recognized. This is, 

 however, everywhere true where the laws of one type of system 

 are applied to another type. Gas pressure, solution pressure, 

 and imbibition pressure take place in three distinct types of 

 systems, yet they have certain properties in common. It has 

 been shown that the imbibition pressure of a gel is closely com- 



