260 THE .PROPERTIES OF PROTOPLASM 



below the freezing-point of pure water. Hence, the Freezing-point 

 of water is lowered by 'dissolved substances, and that in proportion 

 to their molecular concentration. 



The osmotic pressure of a solution of a diffusible substance may 

 therefore be measured either directly, employing a semipermeable 

 membrane, or indirectly, by measuring the elevation of the boiling- 

 point or the lowering of the freezing-point. Conversely the molecular 

 concentration of a dissolved substance may be estimated in the same 

 ways. The osmotic pressure exerted by a molecular solution, that is, 

 by one gram-molecule of substance dissolved in a liter of water is 

 22.4 atmospheres. The elevation of the boiling-point in the same 

 solution is 0.54, while the depression of the freezing-point is 1.86. 

 If, however, the dissolved substance undergoes Electrolytic Dissociation 

 then each of the ions which it yields exerts osmotic pressure and 

 affects the boiling- and freezing-points in the same way as a molecule, 

 so that for a substance completely dissociated into two ions, such as 

 sodium chloride in dilute solution, the osmotic pressure per gram- 

 molecule of dissolved substance is double the above-mentioned figure, 

 and the molecular elevation of the boiling-point and lowering of the 

 freezing-point are similarly enhanced. If different solvents are 

 employed the osmotic pressures obtained are the same as those obtained 

 when water is used as a solvent, provided the molecular condition of 

 the dissolved substance is the same in both solvents, but if it be 

 ionized in one and not in the other, or forms double molecules in one 

 and not in the other solvent, the pressures observed will, of course, 

 differ from one another in a corresponding manner and degree. The 

 magnitude of the effect upon the boiling- and freezing-points, although 

 always proportionate in any one solvent to the molecular plus ionic 

 concentration of the dissolved substance, differs with different solvents. 



The osmotic pressures of tissue-fluids and of fluids expressed from 

 cells are usually estimated by the Cryoscopic Method or measurement 

 of the lowering of the freezing-point of the solvent, in this case water. 

 This measurement is much less tedious and less subject to interference 

 by colloidal admixtures, etc., than the direct measurement of pressure 

 in an osmometer. The elevation of the boiling-point is usually not 

 applicable because of the extensive changes induced in these solutions 

 by elevated temperatures, for example the coagulation of proteins 

 and the transformation of bicarbonates into carbonates with the 

 evolution of carbon dioxide. The former of these changes can be 

 obviated, of course, by measuring the elevation of the boiling-point 

 under reduced pressures when ebullition occurs at a correspondingly 

 lower temperature, but the difficulty created by the evolution of 

 carbon dioxide still remains. 



The following are illustrative measurements, obtained by Hamburger 

 and others, of the lowering of the freezing-point in blood-sera* of various 

 species of Mammalia: 



