Chemical Potential to the Theory of Solutions. 041 



of pressure p—p r , we obtain the equation 



| VO, 6)&x 



M r.h n->„, e) + y-no { ffigff,? - 1 } -(n'-n). (io) 



If we make s' = 0, the osmotic difference of pressure 

 becomes the so-called osmotic pressure of the solution and 

 the equation becomes 



V(.r, 6)dx 



f 



This equation may be put into a form suitable for practical 

 calculation by substitution of the values of F (s, II-»/>, 0) 

 and r(0, IT ^ , 6) given by equations (2) and (3). In this 

 way we obtain the equation 



*y r 



VO, 6)dx 



(p ln f '«W,fl)(l-fl,e, ( ) ^ (n m ,,„ 



I 



where 



e=i(jp + n) — w and e =Kpo + I[ )— OT . 



If we neglect the second and third terms and also the com- 

 pressibility factor in the first term, we obtain an approximate 

 value fl a given by the equation 



n 



YO, 6)dx 



- J JL 



« P {s, <v, 6) ' 



In general it will be sufficiently accurate to calculate this 

 value first, and then apply two corrections (1) a compressi- 

 bility correction, equal to ^ a MiCp + ^« + ^) — *r}, (2) a 

 pure solvent pressure correction equal to the second term of 

 the above expression with the compressibility factors omitted. 

 Since the ratio of II — II to O is of the same order of mag- 

 nitude as the ratio of the specific volume of the liquid to 

 that of the vapour, the third term is negligible in all ordinary 

 cases. 



