50 DAVID R. BRIGGS 



equation (5). In many cases it is not possible to attain a dilution 

 sufficient such that the 7r/c2 relationship becomes constant, but as has 

 been shown by Ostwald (6) it is usually possible to obtain osmotic 

 pressure measurements at concentrations sufficiently dilute so that 

 when t/c2 is plotted against C2 a straight line (constant slope) is ob- 

 tainable that can be extrapolated to C2 = 0. It has become common 

 practice to assume that the value of t/c2 at C2 = obtainable by this 

 procedure can be inserted in the van't Hoff equation to yield a de- 

 pendable value of M2, i.e.: 



limit (Tr/ca) = RT/M2 (8) 



This treatment of the experimental results is based upon the assump- 

 tion that in all such cases the systems are acting as "ideal" as a limit- 

 ing law, i.e., that In ai = In Ni at infinite dilution. 



While in many instances this may approximate the truth, there 

 is also the probability that in others this assumption will be unten- 

 able. Certainly there are many systems in which In ai (= AFi) is 

 not definable entirely in terms of an ideal entropy of mixing. Other 

 entropy factors may arise from failure of the molecules when in a 

 solution and surrounded by unlike molecules to retain properties, 

 such as volume and heat capacity, identical to those exhibited when 

 they are surrounded by like molecules. Also the partial molar heat 

 content term in equation (1) will not be zero in solutions where dilu- 

 tion is accompanied by evolution or absorption of heat, or by devia- 

 tion of volume from additivity. Such changes constitute evidences 

 of differences in the play of intermolecular forces between similar 

 and dissimilar molecules. Of great importance is the likelihood that, 

 when molecules of very great difference in size and shape are mixed 

 in solution, the entropy of mixing will not be described by the rela- 

 tionship, — aS/R = In tti = In A^i, but by some more complex rela- 

 tionship. For example, Flory (7) and Huggins (8) have derived equa- 

 tions in which, on the basis of statistical considerations wherein flex- 

 ible long chain polymers are pictured as acting kinetically as seg- 

 ments rather than as single units per molecule, they describe the ac- 

 tivity of solvent in a solution in the following terms : 



In a, - In Ki + fl - y) V2 + M1-2 (9) 



where Vi and V2 are the volume fractions of solvent and solute, re- 

 spectively, in solution, Vi and V2 are the partial molar volumes of the 



