ABSORPTION 361 



same as the pressure that would be exerted by a gas, say hydrogen, 

 if all the water were removed, and a molecule of hydrogen substituted 

 for each molecule of the substance, or as would be exerted by the 

 substance itself if, after removal of the solvent, it could be left as a 

 gas filling the same volume. And the osmotic pressure of a solution 

 of one substance is the same as that of a solution of any other 

 substance which contains in a given volume the same number of 

 molecules of the dissolved substance. In other words, the osmotic 

 pressure is not dependent on the nature, but on the molecular con- 

 centration, of the substance. The analogy of the laws of osmotic to 

 those of gaseous pressure becomes still more obvious when it is 

 added that the osmotic pressure of a substance with any given 

 molecular concentration is proportional to the absolute temperature ; 

 and that when a solution contains more than one dissolved substance, 

 the total osmotic pressure is the sum of the partial osmotic pressures 

 which each substance would exert if it were present alone in the 

 same volume of the solution. 



The osmotic pressure of a solution may reach an enormous amount. 

 Thus, a i per cent, solution of cane-sugar has a pressure at o C. of 

 493 mm. of mercury. A 10 per cent, solution of cane-sugar would have 

 an osmotic pressure of more than six atmospheres, and a 17 per cent. 

 solution of ammonia a pressure of no less than 224 atmospheres. 

 The osmotic pressure must be due to the kinetic energy of the 

 moving molecules. Where the molecules are hindered from passing 

 a bounding membrane, the pressure exerted by their impacts on the 

 boundary is greater than where the membrane is easily permeable, 

 because in the latter case many of the molecules pass through, 

 carrying with them their kinetic energy. The pressure must be still 

 less when a dissolved substance diffuses freely into water ; but how- 

 ever small it may become, it is in the osmotic pressure of the 

 molecules of the dissolved substance that the force which causes 

 diffusion must be sought. 



In practice it is inconvenient, and in many cases impossible, to 

 directly measure the osmotic pressure by means of a semi-permeable 

 membrane like ferrocyanide of copper. Recourse is therefore 

 had to indirect methods. Of these, one of the most generally 

 used depends on the fact that the freezing-point of a solution 

 is lower than that of the solvent ; for example, salt water freezes 

 at a lower temperature than fresh water. The amount by which 

 the freezing-point is lowered depends on the molecular concen- 

 tration of the dissolved substance, to which, as we have seen, the 

 osmotic pressure is also proportional. When a gramme-molecule of 

 a substance is dissolved in water, and the volume made up to a litre, 

 the freezing-point is lowered by i'8 C.; the osmotic pressure is 22-35 

 atmospheres (16,986 mm. of mercury). It is therefore easy to calculate 

 the osmotic pressure of any solution if we know the amount by which 

 its freezing-point is lowered. A i per cent, solution of cane-sugar, 

 for example, would freeze at about - 0-052 C. Its osmotic pressure 



-= ' 2 x 16,986 = 490 mm. of mercury. 



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