194 GUGGENHEIM art. b 



But 



Nxd log iVi + Nd \0gN2 ... + Nnd log iV„ 



= dNi + dNi . . . + rfiVn = (50) 



according to (25). It follows from (49) and (50) that 



Nid log /i + N^d log /2 . . . + Nnd log /„ = 0. (51) 



From (51) we can conclude in particular that, if throughout a 

 range of concentrations extending down to pure solvent the 

 activity coefficients of all the solute species are unity, then this 

 must also be the case for the solvent species. This is equivalent 

 to the following theorem : If at given temperature and pressure 

 but varying composition every solute species has a partial 

 vapor pressure proportional to its mol fraction (Henry's law), 

 then so has the solvent (Raoult's law). 



11. Osmotic Coefficients. Owing to the relation (51), if the 

 mol fraction of the solvent species is almost unity and the 

 mol fractions of all the solute species are very small compared 

 with unity, the value of log/o for the solvent species will generally 

 be of a considerably smaller order of magnitude than that of 

 log /, for any of the solute species Sg. Thus it is quite usual in a 

 centimolar aqueous solution of a uni-univalent strong electrolyte 

 for the activity coefficient of the solute to be less than unity by 

 about 0.1, while the activity coefficient of the solvent in the same 

 solution will be approximately 1.00006. Thus for purely 

 numerical reasons the activity coefficient of the solvent species, 

 in contrast to the activity coefficient of the solute species, may 

 be an inconvenient function to work with. For this reason it is 

 often convenient to define another function called the "osmotic 

 coefficient" of the solvent, and denoted by g, by the relation 



or 



g log No = logNofo. (53) 



