of Mixed Solutions. 287 



membrane is permeable have nearly the same mutual proportion 

 on both sides of the membrane. On this supposition, neglecting 

 quantities of second order 



where // = F (ci , Ca . . . c,._i , 0, pr)- 



We multiply the equations (28) with 1, Ci, Ca ... c,._i in succes- 

 sion and add them together, and inserting the value for ff 



r-X s=r—l i=r-l^f. 



(29) l>{fi-f/)Ci= X (c;-c,,)2 ^c, 



where we have to remember that Cq = 1. From equation (7a) we 

 get 



From a well-known property of thermodynamic potential 

 -^ = qi where qi is the volume occupied by unit mass of the com- 

 ponent (i) in a solution of the same substances as the secondary 

 solution, but with concentrations equal to those of the primary one 

 Ci, Ca ... Cr-i. Then 



Fi (ci, c.2... Cr-i, 0, P) -Fi{ci,Co... Cr-i , 0,pr) = I q/ dp. 



J Pr 



Fi (Ci, C,... Cr-i, Cr, P) -Fi{c^,C,... Cr-i, 0, P) = \'' p dCr- 



Jo OCr 



Adding these two equations together 



fi -fi = j ^ dcr +\ qldp. 

 Inserting into (29) 



(^«> rci'a^"')''^"=-/i(tc'''--'"')*' 



but T |£'c; = _c,|i:, 



r- 1 ^ y 



■i qi Ci'= J r7> , 



{mo) 



where V is the volume of a solution with concentrations 

 Ci , C2 . . . Cr-i and (77io)" the amount of mass of the component (0) 

 contained in the same solution. 



19—5 



