PROTEINS AND THEIR CLASSIFICATION. 1029 



molecules of H in it as a liter of solution containing 342 p-ms. of sugar has 

 of sugar molecules. On the assiunption that a molecule in solution exerts 

 an osmotic pressure that is exactly equal to the gas-pressure exerted by a 

 gas molecule moving in the same space and at the same temperature, we 

 are justified in saying that the osmotic pressure of a gram-molecular solu- 

 tion of cane-sugar, or of any other substance that is not an electrolyte, is 

 equal to the gas-pressure of 2 gms. of H when compressed to the volume 

 of 1 liter. This fact gives a, means of calculating the osmotic pressure of 

 solutions in certain cases according to the following method: 



Calculation of the Osmotic Pressure of Solutions. — To illustrate this 

 method we may take a simple problem such as the determination of the 

 osmotic pressure of a 1 per cent, solution of cane-sugar. One gm. of IT at 

 atmospheric pressure occupies a volume of 11.16 liters; 2 gms. of H, there- 

 fore, under the same conditions will occupy a volume of 22.32 liters. A 

 gram-molecule of H — that is, 2 gms. of H — when brought to the volume 

 of 1 liter will exert a gas-pressure equal to that of 22.32 liters compressed 

 to 1 liter — that is, a pressure of 22.32 atmospheres. A gram-molecular solu- 

 tion of cane-sugar, since it contains the same number of molecules in a liter, 

 must therefore exert an osmotic pressure equal to 22.32 atmospheres. A 

 1 per cent, solution of cane-sugar contains, however, only 10 gms. of sugar 

 to a liter; hence the osmotic pressure of the sugar in such a solution will 

 be .^^2 of 22.32 atmospheres, or 0.65 of an atmosphere, which in terms of 

 a column of mercury gives 760 X 0.65 = 494 nuns. This figure expresses 

 tlie osmotic pressure of a 1 per cent, solution of cane-sugar when dialyzed 

 against pure water through a membrane impermeable to the sugar molecules. 

 In such an experiment water would pass to the sugar side until the hydro- 

 static pressure on this side was increased by an amount equal to the pres- 

 sure of a colunm of mercury 494 mms. high. Certain additional calculations 

 that it is necessary to make for the temperature of the solution need not be 

 specified in this connection. If, however, we Avish to apply this method 

 to the calculation of the osmotic pressure of a given solution of an electro- 

 lyte, it is necessary first to ascertain the degree of dissociation of the electro- 

 lyte into its ions, since, as was said above, dissociation increases the num- 

 ber of parts in solution and to the same extent increases osmotic pressure. 

 In the body the liquids that concern us contain a variety of substances in 

 solution, electrolytes as well as non-electrolytes. In order, therefore, to 

 calculate the osmotic pressure of such complex solutions it is necessary to 

 ascertain the amount of each substance present, and, in the case of electro- 

 l3i,es, the degree of dissociation. Under experimental conditions such a 

 calculation is practically impossible, and recourse nmst be had to other 

 methods. One of the simplest and most easily applied of these methods 

 is the determination of the freezing point of the solution. 



Determination of Osmotic Pressure by Means of the Freezing Point. 

 — This method depends upon the fact that the freezing point of water is low- 

 ered by substances in solution, and it has been discovered that the amount 

 of lowering is proportional to the nimiber of parts (molecules and ions) 

 jiresent in the solution. Since the osmotic pressure is also proportional to 

 the number of parts in solution, it is convenient to take the lowering of the 

 freezing point of a solution as an index or measiu-e of its osmotic pressure. 

 In practice a simple apparatus (Beckmann's apparatus) is used, consisting 

 essentially of a very delicate and adjustable differential themiometer. By 

 means of this instrument the freezing point of pure water is first ascertained 

 upon the empirical scale of the thermometer. The freezing point of the 

 solution under examination is then detemiinetl, and the number of degrees 

 or fractions of a degree by which its freezing point is lower than that of pure 

 Tvater is noted. The lowering of the freezing point in degrees centigrade 

 is expressed usually by the symbol A- For example, mammalian blood- 

 serum gives A = 0.56° C. A 6.95 per cent, solution of NaCl gives the same 

 A ; hence the two solutions exert the same osmotic pressure, or, to put it in 

 another way, a 0.95 per cent, solution of NaCl is isotonic or isosmotic with 

 mammalian serum. The A of any given solution may be expressed in terms 

 of a gram-molecular solution by dividing it by the" con.stant 1.87. since a 



