II. OSMOTIC PRESSURE MEASUREMENTS 51 



components, mi is a constant characteristic of a given solute-solvent 

 system at a given temi)era.ture, and aj is the thermodynamic activity 

 of the solvent. The factor, ni, which may be considered constant 

 at low pol>'Tner concentrations (25 g. per liter or less), appears to de- 

 pend strongly upon forces acting between solvent and solute mole- 

 cules, i.e., solvation forces. It is dependent in part upon the heat 

 of mixing (A^^ term) and in part on the departure from perfect ran- 

 domness of mixing of molecules in the solution ( AS term other than 

 that of ideal mixing). AVhen /ii = and F1/F2 = 1, Fi is equal to 

 A^i, and equation (9) reduces to equation (3). With flexible long 

 chain molecules as the solute, however, Huggins concludes that equa- 

 tion (9) will better define In Ui, and by a procedure analogous to that 

 used above in the derivation of the van't Hoff law, he arrives at the 

 following equation as describing the osmotic relationships in solutions 

 containing such molecular species as solute : 



TT RT , RTd, ^^. ^ , RTd, 2 . 



~ ^ IvT '^ lyTfi (/2 - Mi)c2 + i C2 + ... 



C2 M2 Midi 3 Midi 



where di and d^ refer to the densities of solvent and solute, respec- 

 tively, Ml to the molecular weight of solvent, and the remaining 

 terms have the same connotation as above. From a plot of the term : 



T _ RTdi 2 

 C2 3 Midi ^' 



versus C2, the intercept would yield a value of RT/M^ (and hence ikfa) 

 and Ml could be calculated from the slope. Thus: 



limit (^ _ RTdicl \ _ RT 

 ""^^ \c, 3 Midi) M2 ^ ^ 



It is obvious that values of M2 obtained with equations (8) and (10) 

 from a given set of osmotic pressure data will differ to a degree that 

 will be a function of the extent to which the values of Vi/ V2 differ 

 from unity and the extent to which /xi differs from zero. 



This short discussion of the osmotic pressure relationships in ac- 

 tual solutions, while necessarily fragmentary, will serve to empha- 

 size some of the limitations of interpretation imposed upon such 

 studies. Thus, while it is possible to calculate the values for the 

 various colligative properties for a given solution from the determined 

 value of any one colligative property {i.e., the value of ai determined 



