II. OSMOTIC PRESSURE MEASUREMENTS 49 



AT = -{RT,T/Lf)\nN, (7) 



where Tq and T are the freezing points in degrees absohite of tlie i)ure 

 solvent and of the solvent in the solution, respectively, Lf is the molar 

 latent heat of fusion in calories, and R is given in calories per degree 

 per mole and has a numerical value of 1.9864. One calorie is equal 

 to 41.3 milliliter atmospheres and, when Lf is expressed in milliliter 

 atmospheres, R has the same value as in the preceding equations, 

 i.e., 82.07. 



From equations (7) and (4) we find : 



TT = LfAT/ToV^ 



When water is the solvent, and Lf is expressed in milliliter atmos- 

 pheres — L/(H20) = 59,200 milliliter atmospheres^ — Vi is 18 ml. and 

 To is 273 °K. Then: 



59,200 X AT 



T — 



273 X 18 



= 12.06 AT 



The molar freezing point depression for water solutions is 1.857 °C. = 

 AT. Then: 



TT = 12.06 X 1.857 = 22.4 atmospheres 



2. In Actual Solutions 



Many solutions, when sufficiently dilute, obey the van't Hoff law 

 (equation 6) but deviate from this relationship to an increasing de- 

 gree as the concentration of solute increases. Agreement is com- 

 monly found to maintain through a wider change in concentration if 

 C2 is measured in grams per unit weight of solvent rather than in 

 grams per unit volume of solution. 



Deviations from van't Hoff's law in actual solutions may be traced 

 to failure of either of two fimdamental assumptions made in the 

 derivation of this relationship. In the first instance, van't Hoff's law- 

 may fail, even in "ideal" solutions (where equation 3 holds), because 

 the higher terms in A^2 (equation 5) become increasingly important 

 as concentration of the solute increases. It is repeatedly observed, 

 particularly in studies of the osmotic behavior of high molecular sub- 

 stances in solution, that the rate of increase of osmotic pressure with 

 concentration increases more or less markedly with concentration. 

 Often the excessive increase in the osmotic pressure with increase in 

 concentration is greater than can be accounted for on the basis of 



