OSMOTIC PRESSURE. 29 



Solutions have a lower freezing-point than the pure solvent, and as 

 in dilute solutions the solvent can be frozen out from the dissolved body, 

 then isosmotic solutions have the same freezing-point. The depres- 

 sion of the freezing-point is also proportional to the concentration. 



The determination of the elevation of the boiling-point for the esti- 

 mation of the osmotic pressure of animal fluids is applicable only in 

 exceptional cases, because on heating, precipitates often form. The 

 determination of the depression of the freezing-point has been found of 

 much greater use. This can be accomplished in a easy manner by aid of 

 the apparatus suggested by BECKMANN. In regard to the use of this 

 method we must refer to more complete works. 1 



The above rule that equimolecular solutions of different bodies have 

 the same osmotic pressure is only applicable to non-electrolytes. The 

 electrolytes (bases, acids, salts) show in aqueous solution a much greater 

 pressure (i.e., a much lower depression of the freezing-point) than equi- 

 molecular solutions of non-electrolytes. As is known, ARRHENIUS has 

 explained this lack of correspondence by the assumption that the mole- 

 cule of the electrolyte is divided or dissociated into so-called ions hav- 

 ing an opposed electric charge. An ion exerts upon the osmotic pressure 

 the same influence as the non-dissociated molecule. The larger the 

 number of dissociated molecules the more does the osmotic pressure 

 of the solution rise above the pressure of an equimolecular solution of a 

 non -dissociated body. The osmotic action of a dissociated body is equal to 

 that of a non-dissociated body which in a given volume contains as many 

 molecules as the dissociated body contains ions plus non-dissociated mole- 

 cules. If we assume that a is the degree of dissociation, i.e., the number of 

 the molecules that are dissociated, then 1 a is the number that is not 

 dissociated. If in the dissociation of a molecule n ions are formed, 

 then the relation of the molecules present before the dissociation to the 

 ions + molecules present after the dissociation is 1:(1 a+na) or 

 = 1 : (1 + [n l]a) . The expression (1 -f [n l]a) is generally denoted by 

 the letter i, and can be directly determined b}^ estimating the freezing- 

 point of a solution of known molecular concentration. 



A gram-molecule aqueous solution (one that contains as many grams per 

 liter as the molecular weight of the substance) of any non-electrolyte freezes 

 at about 1 .86, or, the depression of the freezing-point J is = 1 .86. For example, 

 if we find that ^ for a gram molecular solution of NaCl is 3.40 then we have 

 according to the above 1 : (1 + [n l]a) = 1.86 : 3.40. In the dissociation of 

 NaCl two ions are formed, therefore n = 2, and from the above equation the degree 

 of dissociation can be calculated, a = 0.83. The degree of dissociation can also 

 be calculated from the electrical conductivity. Only the ions take part in the con- 



1 Fuchs, Aiileitung zu Molekulargewichtsbestimmungen. Leipzig, 1895; Ostwald- 

 Luther, Hand- und Hilfsbuch zur Ausfiihrung physik.-chemischer Messung, 2. Aufl., 

 1902. 



