192 GUGGENHEIM art. e 



Hence 



, „ At N,"U" ,^„, 



where [vh] is defined by 



M = ^A* I 1 - KA ^ 1 



(41) 



and is the partial molar volume of the species Sh in an infinitely 

 dilute solution at the given temperature and at a pressure 

 equal to the mean of the pressures p' and p" on either side of 

 the membrane. Formula (40) is exact for membrane equihb- 

 rium as regards the species Sh between two non-ideal solutions 

 of the most general type in the same solvent, whether Sh denote 

 the solvent or one of the solute species. It is important to 

 observe that the values of the activity coefficients to be inserted 

 in the formula are those at the actual pressures at membrane 

 equilibrium, that is fh at the pressure p' smdfh" at the pressure 



8. Osmotic Equilibrium. If in particular the membrane is 

 permeable to the solvent only, but impermeable to aU the solute 

 species, the membrane equilibrium is called "osmotic equilib- 

 rium." If the phase denoted by a double accent is the pure 

 solvent the difference p' — p" is called the "osmotic pressure" 

 of the solution represented by the single accent. In this case, 

 using the suffix to denote the solvent, we have 



N," = 1, (42) 



and so the osmotic pressure P in ideal solutions is given by 



At 1 

 P = p'-p" = j^log^,. (43) 



while in non-ideal solutions it is given by 



At 1 



